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Mental Arithmetic and Evaluative Pressure: The Role of Distributed Cognition
by
Anna-Stiina Wallinheimo
Submitted for the Degree of Doctor of Philosophy
School of PsychologyFaculty of Health and Medical Sciences
University of Surrey
Supervisors: Dr Harriet Tenenbaum and Dr Adrian Banks
©Anna-Stiina Wallinheimo 2019
Declaration
This thesis and the work to which it refers are the results of my own efforts. Any
ideas, data, images or text resulting from the work of others (whether published or
unpublished) are fully identified as such within the work and attributed to their originator in
the text, bibliography or in footnotes. This thesis has not been submitted in whole or in part
for any other academic degree or professional qualification. I agree that the University has
the right to submit my work to the plagiarism detection service TurnitinUK for originality
checks. Whether or not drafts have been so-assessed, the University reserves the right to
require an electronic version of the final document (as submitted) for assessment as above.
Signature: Anna-Stiina Wallinheimo
Date: July 2nd, 2019
Abstract
The purpose of this thesis was to further our understanding of the role of distributed
cognition (with the use of pen and paper) in defusing the impact of evaluative pressure
caused by priming gender-related stereotypes about girls’ maths performance and
performance-approach goals on mental arithmetic performance. Interactivity is the
transferring of internal cognitive process (e.g., computing simple maths tasks) to the outside
world by using different tools (e.g., pen and paper). Some members of social groups (e.g.,
women) may not perform well in mathematics after negative stereotypes about their academic
performance in the mathematical domain, which is known as stereotype threat. Stereotype
threat is the risk of confirming a negative stereotype expectation about one’s group. Another
decrement to performance may be caused by achievement goals, such as performance-
approach goals. Performance-approach goals are linked to normative behaviour where the
individual is motivated by outperforming others in academic performance. Negative
stereotyping and performance-approach goals can generate anxiety that deplete existing
working memory resources. However, some of these working memory limitations can be
compensated by off-loading the internal cognitive process to the external environment. We
tested whether off-loading could buffer the effects of stereotype threat and performance-
approach goals in four experiments.
In Studies 1 (16-year-old girls) and 2 (female university students), participants carried
out mental arithmetic tasks in the stereotype threat condition or control, crossed with
interactivity or no interactivity. There was increased maths performance (accuracies) with
interactivity, confirming existing literature. Additionally, the solution latencies were
improved when the mental arithmetic tasks were in a known format. However, when the
maths tasks were in a novel format, the participants of the second study became slower
because of speed-accuracy trade-off. The first two studies found no statistically significant
i
effects of stereotype threat on maths performance. Nevertheless, working memory in
participants in Study 1 was depleted in the stereotype threat condition, but it did not affect
mental arithmetic performance. Finally, the participants in the interactive conditions in Study
2 had a reduction of their state maths anxiety levels measured at the end of the experiment.
Studies 3 (Pilot Study) and 4 focused on achievement goals and their differing effects on
working memory. Female university students carried out modular arithmetic tasks in a
performance-approach goal or mastery-approach goal condition crossed with interactivity or
no interactivity. Performance-approach goal endorsement hampered cognitive performance,
as measured by maths accuracy in Study 3, but not in Study 4. These findings were extended
in Study 4 where these negative effects were reduced with the help of interactivity. Across
both studies, individuals in the mastery-approach goal condition had a performance drop in
the interactive condition (Study 3 and 4). Thus, interactivity did not benefit the cognitive
performance of these participants. Finally, Study 4 reported higher maths anxiety levels for
the individuals in the performance-approach condition. However, the increased maths anxiety
levels were not reduced with the help of distributed cognition. Reasons for the findings and
future implications will be discussed.
ii
Publications
Conference Presentations:
Wallinheimo, A., Tenenbaum, H., & Banks, A. (2019, July). Achievement goals and mental
arithmetic: The role of distributed cognition. A 6-page submission has been accepted to be
presented at the 41st Annual Conference of the Cognitive Science Society. Montreal, Canada.
Wallinheimo, A., Banks, A., & Tenenbaum, H. (2018, August). Modular arithmetic tasks
and phonological loop: The role of distributed cognition. Paper presented at the British
Psychological Society Cognitive Section Annual Conference, Liverpool, UK.
Wallinheimo, A., Tenenbaum, H., & Banks, A. (2017, September). Interactivity reduces the
effects of stereotype threat on maths performance, and maths anxiety. Poster presented at the
European Society of Cognitive Psychology, Potsdam, Germany.
Wallinheimo, A., Tenenbaum, H., & Banks, A. (2017, July). Interactivity, stereotype threat,
and working memory. Poster presented at the 39th Annual Conference of the Cognitive
Science Society. London, England, UK.
Wallinheimo, A. (2016, April). Interactivity, maths anxiety, and mental arithmetic. Poster
session presented at the Annual Conference of British Psychological Society, Nottingham,
UK.
iii
Acknowledgements
I would like to express my sincere gratitude to my supervisors, Dr Harriet Tenenbaum
and Dr Adrian Banks, for their continuous support of my PhD study and related research, for
their patience, motivation, and immense knowledge. Their guidance helped me in all the time
of research and writing of this thesis. I could not have imagined having better supervisors and
mentors for my PhD study.
I would also like to thank my family, my husband and my children, without whom I
would not have been able to complete the PhD journey.
iv
Table of Contents
Abstract.......................................................................................................................................i
Publications...............................................................................................................................iii
Acknowledgements...................................................................................................................iv
Table of Contents.......................................................................................................................v
List of Tables..........................................................................................................................xiii
List of Figures..........................................................................................................................xv
Preface........................................................................................................................................1
A Summary of the Thesis.......................................................................................................1
Chapter 1: Introduction..............................................................................................................6
1.1 The Extended Mind and the History of Distributed Cognition............................................7
1.2 Complementary Strategies...................................................................................................9
1.2.1 Primary Areas of Distributed Cognition.....................................................................10
1.2.2 The Concept of Interactivity.......................................................................................11
1.2.3 Interactivity and Problem Solving..............................................................................12
1.2.4 Critical Evaluation of Kirsh's Work…………………………………………………14
1.3 Stereotype Threat...............................................................................................................16
1.3.1 Women and Maths Performance.................................................................................20
1.3.2 Non-Academic Domains of Stereotype Threat...........................................................21
1.3.3 An Integrated Process Model of Stereotype Threat Effects on Performance.............23
1.3.4 Stereotype Threat and Working Memory...................................................................29
1.4 Introduction to Achievement Goals...................................................................................31
1.4.1 Academic Consequences of Performance-Approach Goals.......................................33
1.4.2 Maladaptive Behaviours of Performance-Approach Goals........................................34
v
1.4.3 Components of Performance-Approach Goals...........................................................35
1.4.4 Performance-Approach Goals and Distraction...........................................................37
1.4.5 Negative Affect...........................................................................................................38
1.4.6 Achievement Goals and Theories about Intelligence..................................................38
1.4.7 Motivation and Task Values.......................................................................................39
1.4.8 Choking under Pressure..............................................................................................40
1.4.9 Evaluative Pressure.....................................................................................................42
1.4.10 The Effects of Performance-Approach Goals on Working Memory Capacity.........44
1.4.11 Achievement Goals and Cognition...........................................................................45
1.5 Working Memory...............................................................................................................46
1.5.1 Working Memory and Intrusive Thoughts..................................................................48
1.5.2 Working Memory and Mental Arithmetic..................................................................49
1.6 Maths Anxiety....................................................................................................................50
1.6.1 Onset of Maths Anxiety..............................................................................................51
1.6.2 Maths Anxiety and Mathematical Problem Solving...................................................52
1.6.3 Mathematics Anxiety and Working Memory.............................................................53
1.6.4 Emotional Processing and Maths Anxiety..................................................................54
1.6.5 Maths Anxiety and Individuals with High Working Memory....................................55
1.6.6 Physiological Factors Linked to Maths Anxiety.........................................................56
1.6.7 Maths Anxiety and Stereotype Threat.........................................................................57
1.7 Conclusion..........................................................................................................................57
vi
Chapter 2: The Effects of Stereotype threat on Girls’ Mathematics Performance: The Role of
Distributed Cognition...............................................................................................................57
2.1.1 Stereotype Threat and Working Memory...................................................................58
2.1.2 Maths Anxiety.............................................................................................................59
2.1.3 Mental Arithmetic and Working Memory..................................................................60
2.1.4 External Representations.............................................................................................61
2.1.5 Mental Arithmetic and Interactivity............................................................................64
2.2 The Present Experiment.....................................................................................................65
2.3 Method...............................................................................................................................67
2.3.1 Participants..................................................................................................................67
2.3.2 Materials......................................................................................................................67
2.3.3 Procedure.....................................................................................................................69
2.4 Results................................................................................................................................70
2.4.1 Data Analysis Plan......................................................................................................70
2.4.2 Percentage Correct (Solution Accuracy).....................................................................71
2.4.3 Latency to Solution.....................................................................................................73
2.4.4 Working Memory........................................................................................................73
2.4.5 Mathematics Anxiety (State).......................................................................................74
2.4.6 Correlational Analysis.................................................................................................74
2.5 Discussion..........................................................................................................................77
2.6 Limitations.........................................................................................................................80
2.7 Future Studies.....................................................................................................................80
Chapter 3: The Effects of Stereotype threat on Female University Students’ Maths
Performance: The Role of Distributed Cognition....................................................................81
vii
3.1.1 Maths Anxiety and Interactivity..................................................................................83
3.2 Pilot Study..........................................................................................................................84
3.3 Method...............................................................................................................................84
3.3.1 Participants..................................................................................................................84
3.3.2 Material and Measures................................................................................................85
3.3.3 Procedure.....................................................................................................................87
3.4 Pilot Study Findings...........................................................................................................87
3.5 The Current Study..............................................................................................................89
3.6 Method...............................................................................................................................90
3.6.1 Participants..................................................................................................................90
3.6.2 Material and Measures................................................................................................90
3.6.3 Procedure.....................................................................................................................92
3.7 Results................................................................................................................................94
3.7.1 Data Analysis Plan......................................................................................................94
3.7.2 Group Differences.......................................................................................................95
3.7.3 Percentage Correct (Mental Arithmetic Tasks)...........................................................95
3.7.4 Percentage Correct (Modular Arithmetic Tasks, Low WM Load).............................98
3.7.5 Percentage Correct (Modular Arithmetic Tasks, High WM Load).............................98
3.7.6 Latencies (Mental Arithmetic Tasks)..........................................................................99
3.7.7 Latencies (Modular Arithmetic Tasks, Low WM Load)............................................99
3.7.8 Latencies (Modular Arithmetic Tasks, High WM Load)..........................................100
3.7.9 Working Memory......................................................................................................101
3.7.10 Maths Anxiety (State).............................................................................................101
viii
3.7.11 Individual Differences.............................................................................................102
3.8 Discussion........................................................................................................................103
3.9 Limitations.......................................................................................................................106
3.10 Future Studies.................................................................................................................107
Chapter 4: Achievement Goals and Mental Arithmetic: The Role of Interactivity...............107
4.1.1 Achievement Goals...................................................................................................108
4.1.2 Mastery-Approach Goals and Performance-Approach Goals...................................109
4.1.3 Achievement Goals and Modular Arithmetic Tasks.................................................110
4.1.4 Achievement Goals and Working Memory..............................................................110
4.1.5 The Benefits of Interactivity.....................................................................................111
4.2 Present Study (Pilot Study to Study 4).............................................................................113
4.2.1 Hypotheses of the Study............................................................................................113
4.3 Method.............................................................................................................................115
4.3.1 Participants................................................................................................................115
4.3.2 Material and Measures..............................................................................................115
4.3.3 Procedure...................................................................................................................118
4.4 Results..............................................................................................................................119
4.4.1 Data Analysis Plan....................................................................................................119
4.4.2 Group Differences.....................................................................................................119
4.4.3 Accuracy...................................................................................................................122
4.4.4 Latencies...................................................................................................................124
4.5 Discussion........................................................................................................................125
4.6 Limitations of the Study...................................................................................................128
ix
4.7 Future Studies...................................................................................................................129
Chapter 5: Achievement Goals, Maths Performance, and Interactivity.................................130
5.1.1 Maths Anxiety...........................................................................................................130
5.1.2 Maths Anxiety and Working memory.......................................................................131
5.1.3 Achievement Goals and Maths Anxiety...................................................................132
5.1.4 Positive Affect and Working Memory......................................................................133
5.1.5 The Current Study.....................................................................................................133
5.2 Method.............................................................................................................................135
5.2.1 Participants................................................................................................................135
5.2.2 Material and Measures..............................................................................................136
5.2.3 Procedure...................................................................................................................140
5.3 Results..............................................................................................................................141
5.3.1 Data Analysis Plan....................................................................................................141
5.3.2 Group Differences.....................................................................................................141
5.3.3 Accuracy...................................................................................................................143
5.3.4 PANAS......................................................................................................................145
5.3.5 Maths Anxiety (State)...............................................................................................146
5.3.6 Mediation..................................................................................................................147
5.3.7 Correlations...............................................................................................................148
6 Discussion...........................................................................................................................149
7 Limitations..........................................................................................................................155
8 Future Studies......................................................................................................................155
Chapter 6: Discussion............................................................................................................156
x
1.1 Summary of the Findings.............................................................................................156
1.2 The Effects of Interactivity on Maths Performance.....................................................159
1.3 The Impact of Stereotype Threat on Mental Arithmetic Performance........................160
1.4 Stereotype Threat and State Maths Anxiety.................................................................163
1.5 Stereotype Threat and Working Memory....................................................................166
1.6 Achievement Goals......................................................................................................170
1.7 The Impact of Interactivity on Maths Performance.....................................................171
1.8 Interactivity and the Impaired Maths Performance of the Participants in the Mastery-
Approach Goal Condition..................................................................................................172
1.9 The Maths Performance of the Performance-Approach Goal Participants..................174
1.10 The Endorsement of Performance-approach Goals and Interactivity........................178
1.11 State Maths Anxiety...................................................................................................179
1.12 State Maths Anxiety and Distributed Cognition........................................................180
2 Limitations and Future Studies...........................................................................................182
3 Contributions of the Findings..............................................................................................182
References..............................................................................................................................186
Appendix A: Ethical Approval for Study 1.......................................................................203
Appendix B: SAFE for Study 2...........................................................................................205
Appendix C: SAFE for Study 3...........................................................................................208
Appendix D: SAFE for Study 4...........................................................................................211
Appendix E: Basic Arithmetic Skills Test (BAS), Study 1, 2, and 4................................215
Appendix F: Mathematics Self-Efficacy and Anxiety Questionnaire, Study 1 and 2....216
Appendix G: Maths Anxiety Scale (Trait), Study 2 and 4................................................217
Appendix H: Computation Span (Working Memory), Study 1, 2, and 4.......................219
xi
Appendix I: Mental Arithmetic Tasks (Known Format), Study 1 and 2........................234
Appendix J: Modular Arithmetic Tasks, Study 2.............................................................235
Appendix K: Modular Arithmetic Tasks, Study 3 and 4.................................................237
Appendix L: Positive and Negative Affect Scale (PANAS), Study 4...............................240
Appendix M: Maths Anxiety Scale (State), Study 1, 2, and 4..........................................241
xii
List of Tables
Table 1: Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data) 71
Table 2: Descriptive Statistics: Means and Standard Errors (Post-Testing Data) 72
Table 3: Correlation Matrix for the Performance Measures (Percentage Correct, Latencies,
Working Memory, and Mathematics Anxiety) in the Stereotype Threat, Interactive Condition
75
Table 4: Correlation Matrix for the Performance Measures (Percentage Correct, Latencies,
Working Memory, and Mathematics Anxiety) in the Stereotype Threat, Non-Interactive
Condition 76
Table 5: Correlation Matrix for the Performance Measures (Percentage Correct, Latencies,
Working Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Interactive
Condition 76
Table 6: Correlation Matrix for the Performance Measures (Percentage Correct, Latencies,
Working Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Non-Interactive
Condition 77
Table 7: Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data) 97
Table 8: Descriptive Statistics: Means and Standard Errors (Post-Testing Data) 97
Table 9: Descriptive Statistics: Means and Standard Errors of Modular Arithmetic
Performance (Accuracy and Latency to Solution) in Block 1 120
Table 10: Descriptive Statistics: Means and Standard Errors of Modular Arithmetic
Performance (Accuracy and Latency to Solution) in Block 2 (Interactive Condition) 120
Table 11: Descriptive Statistics and Standard Errors of Modular Arithmetic Performance
(Accuracies and Latencies to Solution) in Block 2 121
Table 12: Descriptive Statistics and Standard Errors of Modular Arithmetic Performance
Difference (B2 - B1) across the Experimental Conditions 123
Table 13: Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data) 142
Table 14: Descriptive Statistics and Standard Errors of Modular Arithmetic Performance
(Accuracy and Latencies to Solution) in Block 1 142
xiii
Table 15: Descriptive Statistics and Standard Errors of Modular Arithmetic Performance
(Accuracy and Latencies to Solution) in Block 2 143
Table 16: Descriptive Statistics and Standard Errors of the Primary Dependent Variables
(Based on a Performance Difference Score, B2 – B1) 145
Table 17: Summary of Correlations in the Performance-approach Goal and Non-Interactive
Condition only 149
Table 18: Summary of Correlations in the Performance-approach Goal and Interactive
Condition only 149
xiv
List of Figures
Figure 1: Examples of low-load and high-load modular arithmetic tasks 116
Figure 2: Examples of vertical and horizontal modular arithmetic tasks 117
Figure 3: Mean difference in modular arithmetic performance (%) as a function of
experimental condition (performance-approach goal or mastery-approach goal crossed with
interactivity or control) 123
Figure 4: Mean difference in modular arithmetic performance (%) as a function of
experimental condition (performance-approach goal or mastery approach goal) 124
Figure 5: Examples of low-load and high-load modular arithmetic tasks 138
Figure 6: Examples of vertical and horizontal modular arithmetic problems 138
Figure 7: Mean difference in modular arithmetic performance (%) as a function of
experimental condition (performance-approach goal or mastery-approach goal crossed with
interactivity or control) 144
Figure 8: Mean difference in state maths anxiety levels as a function of experimental
condition (performance-approach goal or mastery-approach goal) 147
xv
Preface
A Summary of the Thesis
The aim of this thesis is to further the understanding of the role of distributed cognition in
mental arithmetic performance, in evaluative pressure situations. When people are in a high-
stakes testing situation (e.g., caused by a standardised maths test), the stressful situation can
adversely affect people’s ability to solve maths problems. Individuals might be fully
motivated to perform well in these stress-laden situations, but the circumstances can have
detrimental consequences and cause people to perform at their worst (i.e., choke under
pressure), (Beilock, 2008). The additional pressure (caused by for example stereotype threat
or performance-approach goal) can fill working memory with thoughts about the stressful
situation (Eysenck & Calvo, 1992). This thesis focuses on whether interactivity can overcome
negative consequences of distraction in situations activated by stereotype threat and goal
theory. The first focus, stereotype threat, occurs when awareness of a negative stereotype
about how one’s social group is expected to perform (e.g., girls are not good at maths tasks)
can produce less than optimal academic performance (Steele, 1997). Past research has
suggested that this might be due to additional taxation of the working memory (due to
additional worries) and therefore the individual has less capacity available to deal with the
task (Schmader & Johns, 2003). The second focus is on achievement goals, which can be
associated with increased worry of succeeding in achieving optimal performance. The
achievement goals construct refers to the way individuals represent and pursue competence in
challenging settings (Elliot & Dweck, 2005). Due to the nature of the performance-approach
goals (dominated by normative structure and social comparison to peers), there can be
worries about succeeding, similar to stereotype threat, consequently leading to reduced
working memory resources (Crouzevialle & Butera, 2013)
1
The negative thoughts caused by these stress-laden situations compete with the resources
that are normally allocated to the execution of the required task. This additional pressure
serves to create a dual-task environment where the additional pressure and the task in hand
compete for the same limited working memory resources (Beilock, Holt, Kulp, & Carr,
2004). Explicit monitoring (self-focus) theories, on the other hand, claim that when there is
increased performance pressure (e.g., caused by a normative performance-approach goal
where a social comparison is made), this can elevate anxiety levels and self-consciousness
about performing correctly and to a high standard. The individual is conscious about the
required steps to the solution and therefore is being careful of every step and hoping that by
being careful, the overall performance is improved. However, attention to performance at
such a component specific level is thought to disrupt the proceduralized processes that are not
normally completed with the help of working memory (Beilock & Carr, 2001). When an
individual is concerned of not reaching academic standards or goals (e.g., when faced with a
stereotype threat), there are ruminative thoughts that can consume attentional resources of the
working memory. This concern about not reaching the goals, is called self-evaluation threat
and it can induce attentional focusing leading to reduced working memory capacity (Koole &
Dijksterhuis, 1999).
The overall structure of this thesis takes the form of six chapters, including this
introductory chapter (Summary of the Thesis). In Chapter 1, we begin by introducing the
literature on distributed cognition and its associations with working memory off-loading and
enhanced problem solving and mental arithmetic performance in particular (Guthrie &
Vallée-Tourangeau, 2015; Kirsh, 2010; Maglio, Matlock, Raphaely, Chernicky, & Kirsh,
1999). The focus is then moved to the stereotype threat literature followed by a review of the
literature on achievement goals.
2
The first experiment is presented in Chapter 2. The purpose of the first study was to
investigate the role of interactivity in defusing the impact of gender stereotype threat on
difficult mental arithmetic tasks, having 16-year-old girls as participants. The effects of
negative stereotyping on working memory and maths anxiety were also investigated as part
of the study. The study found statistically significant effects of stereotype threat on working
memory capacity but failed to find a causal effect of working memory on mental arithmetic
performance. One inference was that the maths tasks were in an easily recognisable format
and therefore the participants used well-rehearsed patterns, almost automatic processes that
were less working memory resource demanding.
Chapter 3 summarises the background and findings of Experiment 2. Similar to the
first study, the purpose of the second study was to look at the negative effects of stereotype
threat on female university students’ maths performance and working memory. Two different
types of maths tasks (with varying levels of working memory taxation) were utilised: mental
arithmetic tasks (known format) and modular arithmetic tasks that were in a novel format
(low WM load and high WM load). As before, we further explored whether distributed
cognition could be employed to mitigate the negative effects of stereotype threat on the maths
performance. Additionally, the study investigated whether there were any carry-over effects
of stereotype threat and interactivity on state maths anxiety that was measured at the
completion of the experiment. Finally, there were no statistically significant effects of
stereotype threat on the mental arithmetic performance, modular arithmetic performance, and
on working memory. However, the participants in the interactive condition were less maths
anxious after the experiment.
We then move to Chapter 4 where the third experiment is presented. The aim of the
Study 3 was to further examine the influence of achievement goal states on working memory.
As before, we also investigated whether interactivity could be used to mitigate any of the
3
possible negative effects of achievement goals on maths performance. It was argued that if
working memory is loaded due to outcome related worry then there is additional taxation on
the working memory (Crouzevialle & Butera, 2013). Together with the horizontally
presented maths problems (modular arithmetic tasks) there can be maths performance
decrements when in the performance-approach goal condition (Beilock, 2008). We reasoned
that, if worries of outperforming others lead to poor maths performance, then giving students
the opportunity to externalize the internal cognitive process would reduce the internal
working memory demands and enhance the maths performance. As expected, it was reported
that the maths performance of the individuals in the performance-approach goal condition
was lower than the participants in the mastery-approach goal when there was no interaction
with external artefacts. In addition, mastery-focused individuals’ maths performance
deteriorated from the use of interactivity confirming existing findings. If the agent has the
internal cognitive abilities to complete the task, then there is limited need to make use of
external artefacts. The coupling of internal and external resources is an exercise relative the
degree of tasks difficulty and the cognitive resources of the agent (Kirsh, 2010; Vallée-
Tourangeau & Wrightman, 2010; Webb & Vallée-Tourangeau, 2009). These findings lend
their support to the theory by Crouzevialle and Butera (2013) who stated that mastery-
focused individuals are not as distracted as their performance-approach goal counterparts, and
therefore their internal cognitive resources (working memory in particular) are not affected.
Chapter 5 presents the findings for the Study 4. This study expands on the findings of
the earlier study (Study 3). Additionally, we argued that it would be the performance-focused
individuals who would show higher levels of maths anxiety (due to outcome related concerns,
in a mathematical domain). Experiment 4 therefore measured maths anxiety of the
participants both before the experiment (trait maths anxiety) and after (state maths anxiety).
Additionally, it was argued that if there is increased state maths anxiety when performance-
4
approach goal is made salient, then clearly there should be more benefits of externalizing the
internal cognitive process to the outside world for the performance-focused individual. As
predicted, the performance-focused participants benefited from coupling the internal and
external resources and their maths performance was enhanced. As before, the benefits of
distributed cognition were not experienced by the mastery-focused participants; their maths
performance was depleted when interactivity was employed. These results match those
observed in previous studies (Kirsh, 2010; Vallée-Tourangeau & Wrightman, 2010; Webb &
Vallée-Tourangeau, 2009). Finally, the study confirmed that it was the performance-approach
goal individuals who experienced increased maths anxiety levels after the experiment.
However, these increased maths anxiety levels were not reduced with the help of
interactivity.
The final chapter (Chapter 6) draws upon the entire thesis, tying up the various
theoretical and empirical strands in order to conclude on the empirical findings of the entire
thesis. Additionally, a discussion of the implication of the findings to future research into this
area is included.
5
Chapter 1: Introduction
According to the classical view of cognitive psychology to solve a problem, internal
representations of a problem’s structure are created (the problem space) to complete a
required task. The traditional cognitive view suggests that there are core set of processes for a
variety of different problems. Additionally, if two agents have different capacities (i.e.,
expertise and intellectual ability) they face different task environments (Newell & Simon,
1972). However, the classical view has been heavily criticized by the school of situated
cognition (also called embodied and interactive cognition) where problems are not believed
to follow a formal structure that maybe the same across different activities. The situated view
claims that each problem is directly linked to a concrete setting and is only resolved by
reasoning in situation-specific ways. The agent makes use of the material and cultural
resources locally available in order to solve the required problem (Kirsh, 2009). Clearly,
problem-solving is a form of reasoning that is connected with the activities and context in
which it takes place. However, according to the traditionalists, putting a finger on an object,
utilising pen and paper, and talking to one-self are not part of the actual problem-solving
activity. This is in complete contrast with the situationalist view where these actions are
regularly observed and further linked to the successful performance of the agent (Kirsh,
2009).
Kirsh (1995a) claimed that individuals use the external world to support their thinking
and problem solving. Complementary strategies (external representations) are any organizing
activities which recruit external elements to reduce cognitive loads (e.g., pointing, arranging
the position and orientation of objects, writing things down, and manipulating artefacts that
can encode the state of a process or simplify perception), (Kirsh, 1995a). Hutchins (1995)
stated that cognition was a socially distributed phenomenon. Based on his observations on the
navigation bridge of a US navy ship, Hutchins (1995) defined navigation as it was performed
6
by a team on the bridge as the unit of cognitive analysis. It was concluded that human
cognition (naturally situated cognition) was not just influenced by culture and society, it was
a cultural and social process in itself. Clearly, as human cognition is situated in a relatively
complex sociocultural world, it cannot be unaffected by its surroundings (Hutchins, 1995).
The purpose of this programme of research is to investigate ways of reducing the
additional taxation of working memory caused by evaluative pressure. There are various
situations that are linked to evaluative pressure but the research reported here concentrates on
stereotype threat about females’ maths performance and achievement goals (performance-
approach goals and mastery-approach goals, in particular). These two situation-inducing
stress situations have been chosen due to their similar taxing effects of existing working
memory resources. It has been suggested that one creative way of off-loading the increased
working memory load caused by stereotype threat or achievement goals (and performance-
approach goals in particular) is interactivity (i.e., the use of pen and paper).
1.1 The Extended Mind and the History of Distributed Cognition
Research in cognitive science and philosophy of mind called for rethinking of the
historical concepts of cognition because of evidence that cognition is distributed across brain,
body, and the world (Clark & Chalmers, 1998). According to Clark and Chalmers (1998), the
objects within the environment around us function as part of the mind and therefore it would
be arbitrary to say that the mind is contained only within the head alone (traditional cognitive
view). As external objects have an important role in assisting with the cognitive processes,
there is a coupled system between the mind and the environment which functions as a
complete cognitive system of its own (Clark & Chalmers, 1998). However, the notion of
utilising tools to navigate through the world is not new. People have always utilised external
7
artefacts and objects in assisting with tasks that require internal cognitive resources. For
example, small children use their fingers to help with a simple maths task.
As mentioned earlier, there is a close coupling in how navy crew members use external
artefacts to bring a ship into a port. This distributed cognitive system comprises of sailors,
procedures, and instruments. These cognitive systems are composed of multiple agents and
external artefacts (Hutchins, 1995). Distributed cognition accentuates the ways that cognition
is off-loaded into the environment through both technological and social means. It is a way
for studying and understanding cognition rather than a type of cognition. The distributed
cognition framework involves the co-ordination between individuals, artefacts, and the
environment. Additionally, distributed cognition is a framework that aims to understand how
the cognitive properties emerge from the interactions of the different component parts (across
the members of the social group, between people and environment, and over time),
(Hutchins, 2001).
Additionally, the theory of distributed cognition is focused on comprehending the
organisation of cognitive systems. It does this by extending beyond the individual to
encompass interactions between people, resources, and materials in the environment. Firstly,
it differs with the traditional views of cognition in the way that it looks for cognitive
processes wherever they might take place. This is based on the functional relationships of
elements that are part of the process. Secondly, distributed cognition looks for a broader class
of cognitive events and it does not expect these events to take place internally in people’s
heads. Cognitive processes can be distributed across the members of a group. There can be
coordination between internal and external structure and cognitive processes can be
distributed through time so that the earlier events can change the nature of the later events
(Hollan, Hutchins, & Kirsh, 2000).
8
Finally, there is no single definition of interactivity. Interactivity has links to Human-
Computer Interaction (HCI). It can be viewed as dialogue, transmission, optimal behaviour,
embodiment, and tool use (Hornbaek & Oulasvirta, 2017). According to Cowley and Vallée-
Tourangeau (2017), human-computer interaction (HCI), language, problem solving, and other
cognitive skills are based in sense-saturated coordination or interactivity (Cowley & Vallée-
Tourangeau, 2017). Additionally, cognitive interactivity is defined as “the meshed network of
reciprocal causations between an agent’s mental processing and the transformative actions
she applies to her immediate environment to achieve a cognitive result” (Vallée-Tourangeau
& Vallée-Tourangeau, 2017, p. 133). The research reported here uses the term interactivity
when pen and paper are used to come to the solution of the mathematical tasks. Distributed
cognition refers to the actual framework of externalising the internal cognitive process to the
outside world. Distributed cognition as a descriptive framework explains human work
systems in informational and computational terms. Distributed cognition is particularly useful
for analysing situations that require problem solving (e.g., mathematical problem solving)
and as such it was chosen as the framework for this thesis.
1.2 Complementary Strategies
One of the most common complementary strategies is the use of pen and paper to assist
the individual in adding multi-digit numbers. This programme of research has employed pen
and paper as a form of complementary strategy. By doing this, individuals off-load the
portion of working memory that is needed to store intermediate results. These actions
complement the internal cognitive processes while adding up the numbers. There are several
factors involved in the choice of a complementary strategy: speed, reduction of probable error
rate, to cope with larger problems, and to deal with interference more successfully (measures
9
of performance). Complementary strategies allow agents to compensate for processing power
and working memory resource limitations.
There are several reasons to enhance cognitive power, thinking, and comprehension.
External representations are used to save internal memory but this is not the only reason.
Interactivity changes the cost structure of the cognitive process. People go where ever it is
easier to perform the required task. If it is simpler to draw a picture of a process rather than
only thinking internally, then people externalize the process and draw a picture (Kirsh, 2010).
Additionally, interaction allows the agent to process more efficiently and more effectively
than by working inside the head alone. Interactive cognition can enhance efficiency due to
fewer errors and greater speed. Finally, effectiveness allows individuals to deal with harder
problems and it can assist people to compute more deeply and more precisely (Kirsh, 2010).
1.2.1 Primary Areas of Distributed Cognition
It has been reported that there are four primary areas of distributed cognition. The first
one relates to the use of tools that can change the way we think and perceive. The second idea
is that people generally think with their bodies and not just with the brains. Thirdly, people
know more about doing than by seeing. And finally, there can be situations when people do
their thinking with things. Kirsh (2013) explored these ideas in an experiment that tested the
effectiveness of three diverse ways of practicing a new dance phrase. Partially modelling a
dance phrase by marking the phrase (a form of practicing a dance phrase aspect-by-aspect in
a less than complete manner) was a better method of practising than working on the complete
phrase. It was also concluded that marking and full-out practice were better than repeated
mental stimulation. In other words, it is better to practise physically rather than in one’s head
only. In conclusion, by externalizing one’s thought process, the inner processes can be
improved and reshaped (Kirsh, 2013).
10
When the cognitive process is externalized, the entire cognitive process becomes more
visible to the outside world and people around the agent. This process of sharing the internal
thought makes the thoughts more identifiable and clearer to everybody. The thoughts can
now be manipulated and probed by the environment too. Additionally, the act of
materializing can function as a stepping-stone for the next set of thoughts. The power of
physical re-arrangement is that it gives one the opportunity to visually compare items. This
re-arrangement makes it possible to examine relations that can feel distant or visually
complex (a good example of this is a when completing a puzzle). One would not complete a
puzzle without trying whether the pieces fit together both physically and visually. With the
help of interaction, the world can be converted from a place where only internal computation
is required to solve a problem to one where the relevant property can be physically
discovered. Unlike the internal representations, external representations offer physical
persistence and stability over time and the external representations allow us to reinstate our
thoughts. We cannot be sure that the mental image that we have today is the same as next
week. Additionally, there is normally a better idea of the effect of for example, rotation,
translation, and lighting when interacting with external representations than with the internal,
mental representations (Kirsh, 2010).
1.2.2 The Concept of Interactivity
Kirsh (1997) has explored the concept of interactivity by critiquing the decision cycle
model by Norman (1986). In this model, interaction is seen to be corresponding to a model
driven feedback system; the user would have a mental model of the environment and then
formulate a plan internally. There would then be a direct instruction to the environment and at
the end, feedback would be observed. What this model ignores is the fact that goals are not
fully formed in an agent’s head only. People use the possibilities of the surrounding
environment to help shape the thoughts and goals to see that what is possible (e.g., when
11
writing an essay). Additionally, the decision cycle model fails to recognize the dynamics that
emerge due to long term contact with the process and with the environment. Agents do
somewhat shape their environments by action as they go along. An example of this would be
when an agent writes an essay and has papers on the desk, marks books, and makes lists that
are used later on to assist with the writing process. These activities might be considered
trivial but would make it easier to write the essay next time by assisting with the writing
process (Kirsh, 1997).
1.2.3 Interactivity and Problem Solving
There are various ways that people interact with environments when they try to make
decisions and solve problems. Interactivity has been linked to better performance in problem
solving due to better allocation of attentional resources (attention available to perform
cognitive tasks) and better distribution of the cognitive load, caused by the task in hand. Most
importantly the performance increments have been achieved by allowing the agent to shape
and reshape the physical problem presentation by gestures, pointing and the use of external
artefacts (e.g., use of pen and paper or use of tokens). In one study, four levels of interactivity
(no interactivity, pointing, use of pen and paper, and use of wooden tokens) were used to
complete mental arithmetic tasks. Participants completed 5 sums that consisted of 11 single-
digit numbers in all 4 conditions. Mental arithmetic performance was enhanced with
increasing levels of interactivity. Additionally, the participants felt happier and more engaged
with the task when they were allowed to reconfigure the problem through interactivity
(Guthrie & Vallée-Tourangeau, 2015). Furthermore, interactivity can be used to mitigate the
impact of depleted working memory resources (e.g., caused by articulatory suppression) and
mathematics anxiety on maths performance (Vallée-Tourangeau, Sirota, & Vallée-
Tourangeau, 2016). Finally, in a simple coin counting experiment (seen as a simple mental
12
arithmetic task), the participants in the no hands condition were slower and less accurate than
the participants who were allowed to point and count the coins (Kirsh, 1995b).
Additionally, interactivity defuses the impact of maths anxiety in primary school
children’s maths performance. Allen and Vallée-Tourangeau (2016) explored whether
interactivity could be used to reduce the impact of primary school children’s maths anxiety
on simple addition problems. There were two independent variables: the length of the sums
(either 7 or 11 number tokens) and the level of interactivity (low or high). As expected,
longer sums led to poorer performance. The performance was increased in the high
interactivity condition (accuracy, absolute calculation error, and efficiency). In the low
interactivity condition, maths anxiety levels predicted the children’s maths performance but
not in the high interactivity condition. Finally, these results suggested that elevated
interactivity can be used to defuse the impact of maths anxiety on maths performance and
working memory resources can be augmented (Allen & Vallée-Tourangeau, 2016). However,
the study failed to show a reduction of state maths anxiety levels. Only the trait maths anxiety
of the participants was measured in the beginning of the experiment. Based on the level of
maths anxiety, the participants were either high or low in maths anxiety. The study concluded
that there were more benefits of interactivity for the more maths anxious individual.
Another innovative way to lighten the cognitive load is gesturing while a person talks.
Children and adults were asked to remember a list of words or letters while explaining how
they had solved a maths problem. Gesturing improved the performance of both groups; both
of the groups remembered more words and letters when they were allowed to gesture. It was
found that gesturing saved the speakers’ cognitive resources on the explanation task allowing
the participants to allocate more resources on the memory task (Goldin-Meadow et al., 2001).
Gesturing can take different forms; when a gesture is produced on its own and it is the main
form of communication, it takes on a language like form. However, when gesture is produced
13
in conjunction with speech and it takes an imagistic form and can convey information not
normally found in a speech. Additionally, gesture sheds light on how people think and it can
change those thoughts. In other words, gesture can be part of language or it can itself be the
language, by changing its form to fit the function (Goldin-Meadow, 2006).
1.2.4 Critical Evaluation of Kirsh’s Work
Whilst there is ample evidence of the benefits of applying complementary strategies to
complete problem solving tasks and to support people with reduction of their cognitive load
to complete tasks (Kirsh, 1995a; Kirsh 1995b; Kirsh, 2009; Kirsh, 2010), there are a number
of methodological and theoretical problems with the work of Kirsh. First, in the simple coin
counting experiment (Kirsh, 1995a) where complementary strategies were utilised to enhance
cognitive performance, participants were shown images, each depicting a different
arrangement of quarters, dimes, and nickels (functioning as a simple counting exercise based
on an everyday activity). The participants needed to determine the dollar value of represented
images. The speed of completing the task was improved by allowing the participants to point
or count when using fingers or hands compared to when the participants were not allowed to
touch the images. Additionally, there were fewer mistakes made in the hands condition
compared to the no-hands condition. However, these findings were based on a very small
sample size (n = 5) and as such they lack statistical power. Another limitation of Kirsh
(1995a) was the use of images rather than actual coins when computing the task. The
experiment utilised an everyday activity (coin counting) to illustrate the concept of
complementary strategies but did not allow the participants to actually physically interact
with coins not making the task representative of real life and as such, the actual effects of
complementary strategies on the dollar counting performance cannot be measured.
Kirsh (1995b) explains that people intelligently use space around them by
investigating and observing workplace for particular everyday tasks and how this workplace
14
was managed throughout the activity. The study found that spatial arrangements were mainly
made to simplify choice for the participants (e.g., by organising a kitchen in a way that only
certain subtasks were performed in a certain area and therefore reducing the range of possible
actions that could be done in that station) and that internal computation was assisted by
utilising different spatial activities. Finally, spatial adjustments allowed for simplified human
perception (e.g., an obvious way of making perception simpler is to arrange objects in a way
that they form classes that reflect properties that are useful to notice). The data for the study
were drawn from various videos of cooking and everyday observations in supermarkets,
workshops, and playrooms and is heavily influenced by the author’s own views rather than
experimental manipulations. Although Kirsh argues that environments are arranged in a
logical fashion, there are many arguments to the contrary. Moreover, Kirsh did not test
whether arranging environments differently would have had a negative impact on
performance. Clearly, the findings of the Kirsh 1995b study have highlighted the importance
of managing the spatial arrangement of items and how there are clear benefits of utilising
spatial adjustments. Clearly, there is a gap in the research to experimentally investigate the
effects in of interactivity on maths performance by using experimental manipulations.
Kirsh (2010) claimed that interactivity allows enhanced efficiency because it leads to
fewer errors and greater speed. Effectiveness, on the other hand, translates to deeper and
more accurate performance. However, the examples that have been used to demonstrate this
behaviour are simplistic and as before, not based on experimental manipulations. Kirsh
(2010) talks about drawing a diagram to further our understanding of complex information. It
is clearly easier to draw a right angle triangle and median when faced with the claim ‘in a
right-angled triangle, the median of the hypotenuse is equal in length to half the hypotenuse’.
Whilst it is evident that it is easier to understand the properties of the right angle diagram
with the help of drawing, there are no measurements taken to measure possible errors or
15
speed when completing the task. Another limitation of the findings is that the concept of
speed-accuracy trade-off is ignored. According to the speed-accuracy trade-off, decisions can
be made slowly with high accuracy or fast with reduced performance (Chittka, Skorupski, &
Raine, 2009). Kirsh (2010) claims that efficiency is enhanced with interactivity but ignores
the fact that there can be a speed-accuracy trade-off. By responding quicker to the task, there
might be a decline in accuracy or by responding slower, there might be improved accuracy.
This is clearly something that would require further attention.
1.3 Stereotype Threat
As mentioned in the introduction, the research reported here is focused on two different
types of situation-induced stress caused by stereotype threat or achievement goals. This
section focuses on the literature of stereotype threat. Stereotype threat is one of the most
widely researched areas of Social Psychology. In the classic Steele and Aronson (1995)
paper, stereotype threat is defined as being at risk of confirming a negative stereotype about
one’s group (Steele & Aronson, 1995). The stereotype threat concept has been widely used to
explain differences of academic performance mainly between African-Americans and
European-Americans and between men and women. However, there are multitude of factors
that shape academic performance and not just stereotype threat and therefore it could be
argued that the stereotype threat predicament is an elementary way of explaining academic
performance differences. A large meta-analysis of stereotype threat effects was conducted
and an overall mean effect size of .26 was found (Nguyen, 2008). The analysis confirmed that
a number of studies have been able to replicate the original findings of Steele and Aronson
(1995) but it was also found that some researchers were unable to replicate these findings.
The finding of the stereotype threat effect suggests that there are a number of moderating
effects for stereotype threat (stereotype threat relevance, domain identification, and test
difficulty), (Nguyen, 2008). However, the effects of stereotype threat on performance have
16
been tested in various circumstances and therefore it is possible that the tasks may have
varied in relation to the degree difficulty and challenge that the participants have
encountered. Hence, it can be difficult to draw comparable conclusions of the stereotype
threat effects. Consequently, it is important to focus on understanding the underlying
mechanisms of stereotype threat instead. Hence, the research reported here is focusing on
these mechanisms, and particularly on the effects of stereotype threat on working memory.
There are certain preconditions for the stereotype threat phenomenon to occur. Stereotype
threat happens in situations that bring to mind negative stereotypes about one’s group identity
(e.g., women are not good at mathematics). The occurrence of these effects requires
knowledge of these negative stereotypes, desire to be successful in the domain (e.g.,
mathematics), and a test (e.g., maths test) that tests the upper boundaries of the person’s skill
level (Steele, 1997). Stereotype threat is closely linked to the domain identification that
assumes that in order to succeed in an educational setting, the individual has to identify with
school and its subdomains (Osborne & Jones, 2011). However, there are certain groups (e.g.,
women in the mathematics domain and African-Americans in an educational setting) that
face achievement barriers. In other words, there are pressures on these groups that can disrupt
this identification (e.g., economic disadvantage, segregation, and gender roles). There can be
further achievement barriers due to stereotype threat. This can cause dis-identification with
school in general, and academic performance (Steele, 1997).
Steele and Aronson (1995) gave African-American and European-American university
students a test that comprised of difficult items from the verbal Graduate Record Examination
(GRE). The participants in the stereotype threat condition were told that the test was
diagnostic of their intellectual ability. The participants in the non-stereotype threat condition
were advised that the test was a laboratory problem-solving task (i.e., non-diagnostic test).
African-Americans performed worse than European-Americans when in the ability-
17
diagnostic condition but not in the non-diagnostic condition compared to their previous
performance (Studies 1 and 2). In Study 3, participants in the stereotype threat condition felt
more self-doubt and wanted to distance themselves from African-American stereotypes. The
participants were requested to complete word fragments that included words that were
symbolic of African-American stereotypes. African-American participants showed more
stereotype and self-doubt related words and they had fewer preferences for things that were
related to African-American culture (e.g., basketball and hip-hop music). Additionally, in
Study 4, African-American students’ performance was impaired when stereotype threat was
made salient by asking the participants to record their race (an example of priming racial
identity). This performance impairment happened even when the test was not described as
diagnostic of intellectual ability (Steele & Aronson, 1995). However, whilst the study made
strong findings about the effects of stereotype threat on academic performance, this study
utilised standardised verbal tests (the verbal Graduate Record Examination, GRE) and as
such it can be difficult to generalise these findings to other domains. Additionally, the study
concluded that stereotype threat caused an inefficiency of processing which is similar to the
effects of evaluative pressure. Consequently, the stereotype-threatened participants seemed to
spend more time doing fewer items more inaccurately. However, the inefficiency of
processing was not measured as part of the investigation, no working memory processing
measure was taken as part of the study. The conclusions were solely based on the task
performance, number of items that the participants answered, and on the fact that the African-
American participants reread the items more than the European-American participants. It was
concluded that the African-American participants were alternating attention between
answering the required questions and assessing the self-significance of their frustration of the
task, causing the inefficiency of processing. Finally, the study also failed to confirm that
whether the stereotype-threatened participants were more anxious than the control
18
participants which could have explained the behaviour of the participants in the stereotype
threat condition. Increased anxiety can reduce the working memory capacity available to
compute the task (Eysenck & Calvo, 1992). In another study, African-American participants
performed better on an IQ test when it was introduced as a test of eye-hand co-ordination
rather than a diagnostic test of their academic ability (manipulation of stereotype threat),
(Katz, Roberts, & Robinson, 1965).
Schmader and Johns (2003) hold the view that stereotype threat can affect any
individual’s academic performance (assuming that the situation evokes a stereotype-based
expectation of poor performance). When a working memory test (Operation Span Test) was
described as a measure of general intelligence, the working memory capacity of Latinx
participants was negatively affected and they remembered fewer words than Latinx
participants in the control condition and the European-American participants. The Latinx
individuals also reported feeling more anxious than their European-American counterparts
(Schmader & Johns, 2003). However, when the actual maths tasks (used to trigger a level of
brain processing) were further analysed, it was concluded that priming of stereotype threat
did not reduce the maths performance of the African-American participants. It was only the
recall of words (as part of the Operations Span Task) that was affected by stereotype threat.
Additionally, it has been confirmed that students from poorer backgrounds perform worse on
intellectual tasks. One of the explanations for this performance difference is stereotype threat.
When participants from low socioeconomic statuses were told that a test was diagnostic of
their intellectual ability, they performed worse than participants from high economic statuses.
However, when the test was presented to participants as non-diagnostic of intellectual ability,
the performance of the low socioeconomic participants did not deplete (Croizet & Claire,
1998).
19
It should be noted here that stereotype threat does not always require history of
stigmatization or feelings of inferiority; it can arise as a result of situational pressures alone.
Two experiments were conducted to test this notion. The participants were European-
American math-proficient men from Stanford University who were chosen for their high
ability in the domain (mathematics). In Study 1, stereotype threat was induced by a
comparison with a minority group, stereotyped to excel in mathematics (Asians). It was
confirmed that the European-American men in the stereotype threat group performed worse
in the difficult maths (at the upper limit of the student’s abilities) tasks than the control group.
The second study confirmed the results of the first study. However, it also concluded that
stereotype threat is partly mediated by domain identification and therefore it is most likely to
affect the participants who are highly identified with the domain being tested (Aronson,
Quinn, & Spencer, 1998).
1.3.1 Women and Maths Performance
Women risk being judged by the negative stereotype that females perform worse in
mathematics than males do. There is evidence to suggest that this form of stereotype threat
can disrupt women’s maths performance. Previous research has shown that women
underperform on the difficult maths tests but not on the easy ones when stereotype threat has
been made salient. There were equal numbers of women and men in this study and the
participants had strong maths background. The second study concluded that if stereotype
threat was lowered (by telling the participants that the test does not produce gender
differences) the performance issues could be eliminated. However, when the stereotype threat
was high and the female participants were made aware of the gender differences, the maths
performance of the females was worse than the males (Spencer, Steele, & Quinn, 1999).
Whilst this study was conducted in a laboratory setting it has strong external validity as the
20
participants were tested in mixed male and female groups of 3 to 6 attempting to create a
more realistic educational setting.
Recent research has suggested that negative stereotypes can also carry a strong message
that a certain group (e.g., women in mathematics) is less valued than men in the domain.
When a negative stereotype about women in mathematics is made salient, women might feel
less accepted in the maths community as a whole. Thus, women would have lower sense of
belonging to maths. Students who believe that maths skills can be acquired rather than
something that you are born with, can maintain a high sense of belonging to the maths
domain which in turn can reduce the power of stereotype threat (Good, Rattan, & Dweck,
2012). Investigation on women who majored in maths-related fields found that the women
who believe that there are gender differences in maths performance, are more likely to
endorse gender stereotypes about women’s maths abilities. This predicted more negative self-
perceptions of maths competence and also reduced interest in continuing to study maths at a
higher level. Additionally, these women were also found to be more susceptible to negative
stereotypes which in turn affected their maths performance (Schmader, Johns, & Barquissau,
2004).
1.3.2 Non-Academic Domains of Stereotype Threat
Since the Steele and Aronson classic experiment (1995), stereotype threat research has
broadened its scope to other areas; stereotype threat extends beyond underachievement on
academic performance. There are a number of non-academic domains where stigmatized
individuals’ performance is affected by negative stereotypes. The literature reported here as
part of the thesis is not an exhaustive literature review but rather a summary of the main non-
academic domains of stereotype threat. There are various findings made in this field but as
with the stereotype threat literature, various domains and different methods have been used
and therefore the findings are not easily generalizable. When European-American
21
participants were told that a laboratory golf task was about natural athletic ability, they felt
threatened about confirming the negative stereotype about poor white athleticism. Poor
natural athletic ability, can been seen as a widely held negative stereotype about European-
American athletes. When the participants were made aware of this negative stereotype, the
participants felt worried about confirming this stereotype. This resulted in European-
American athletes avoiding sports practice, using a behavioural self-handicapping strategy.
This kind of strategy is used to explain poor performance. The poor performance is explained
by lack of effort and that more practice would have achieved better results (Stone, 2002). As
the golf task was completed in a laboratory setting, it is possible that these findings are not
transferable to the real world. It is possible that the White-American participants felt
threatened about the negative stereotype about white athleticism only when a laboratory golf
task was used.
Similar findings have been made about racial stereotypes about African-American or
European-American athletes and how these stereotypes affect performance in sports. When a
golf task was framed as diagnostic of sports intelligence, the African-American participants
performed significantly worse than their European-American counterparts. When the task
was framed as diagnostic of natural athletic ability the European-American participants
performed worse than the control participants (Stone, Lynch, Sjomeling, & Darley, 1999). In
another experiment, women were told that females are poor drivers to see if this particular
stereotype disrupts control of an automobile. These women were twice more likely to collide
with jaywalking pedestrians than the control group who were not told about the negative
stereotype (Chi, Yeung, & Von Hippel, 2008).
Additionally, when gay men were reminded of their stigmatized identity (before
interacting with young children in a nursery school) their childcare abilities were poorer than
the participants in the control group. This effect was driven by the men’s non-verbal anxiety,
22
in the presence of children. Non-verbal anxiety was defined as any behaviours that
communicate discomfort, anxiety, awkwardness or a similar emotion (e.g., fidgeting,
chewing on lip, playing with hair, nervous smiling, biting nails, stiff posture, and averting
eyes), (Bosson, Haymovitz, & Pinel, 2004). In another study, when stereotypically feminine
traits were linked to successful negotiating skills, women performed better in a mixed-gender
negotiation scenario. However, this was not the case when gender-neutral traits were
associated with negotiation success. Women outperformed men in a mixed-gender
negotiation scenario when masculine traits were linked to poor negotiating performance.
However, men outperformed women when poor negotiation skills were linked to feminine
traits (Kray, Galinsky, & Thompson, 2002).
1.3.3 An Integrated Process Model of Stereotype Threat Effects on Performance
There are three distinct mechanisms that can disrupt performance (performance on
both cognitive and social interaction tasks) under stereotype threat (Schmader, Johns, &
Forbes, 2008): physiological stress, monitoring of performance, and suppression. The
integrated process model of stereotype threat contributes to the stereotype threat literature in
a way that it allows further our understanding of the biological and behavioural aspects of
stereotype threat, to build a complete view of the effects of stereotype threat on performance
of cognitive and interaction tasks. To start with, there is a physiological stress that directly
impairs prefrontal processing. Working memory is situated in the prefrontal cortex which is
responsible for deploying inhibitory processes, and controlling attention (Kane & Engle,
2002). There are vast amounts of empirical studies that have investigated physiological stress
response of stereotype threat. The physiological stress response studies give strong evidence
of the existence of stereotype threat. To start with, greater sympathetic nervous system (SNS)
activation (the area responsible for the fight and flight response) was measured when female
participants were watching a group of students (a group of unbalanced ratio of men to women
23
or a balanced group) conversing about a math, science, and engineering conference.
Furthermore, the women who watched the gender-imbalanced video reported a lower sense
of belonging and less desire to participate in the conference, compared with the women who
saw a gender-balanced video (Murphy, Steele, & Gross, 2007).
In another study, the effect of stereotype threat on blood pressure reactivity was
investigated. African-Americans under stereotype threat (compared with European-
Americans, and African-Americans under little or no stereotype threat) exhibited larger
increases in mean arterial blood pressure during an academic test that was described as
diagnostic of intellectual ability than one that was not (Blascovich, Spencer, Quinn, & Steele,
2001). The extent to which ethnic minority group members or a devalued group caused threat
reactions from interaction partners was measured in a study. When European-Americans
were interacting with African-Americans or disadvantaged confederates, participants
exhibited cardiovascular threat responses, whereas participants collaborating with European-
American or advantaged confederates primarily showed cardiovascular challenge responses.
In line with cardiovascular responses, participants who were paired with European-
Americans performed better (during a cooperative task) than participants who were paired
with African-American participants (Mendes, Blascovich, Lickel, & Hunter, 2002). Another
study supporting this relationship was conducted by Klein and Boals (2001). Participants
with more life event stress performed more poorly on Turner and Engle's (1989) operation
word span task (working memory task), and particularly on the longer operations of the task.
The participants tried to remember sequentially presented words in the correct order while
simultaneously solving simple maths equations. The maths equations consist of between 2
and 6 successively presented equation–word pairs (e.g., 8 ÷ 4 + 3 = ? moon). The stressful
life events competed with the task demands for attentional resources of the working memory
(Klein & Boals, 2001).
24
Various empirical studies have looked at the relationship between elevated cortisol
levels caused by stress and cognitive performance. In one study, the association between
cortisol levels and memory performance in healthy adults was investigated. In the first study,
the participants were exposed to a brief psychosocial laboratory stress with the help of Trier
Social Stress Test (TSST). Induced stress was created with the help of socially evaluative
situations (divided into 5-minute components). During the first 5 minutes, the participants
were asked to plan a presentation, this presentation was then given to the judges during the
next 5 minutes. The test was concluded with a mental arithmetic task where participants were
asked to count backwards from 1022 in steps of 13. The TSST was followed by a test of
declarative memory performance. The first study concluded that there was a significant
negative relationship between stress-induced cortisol levels and performance in the
declarative memory task. The participants (with high cortisol response to the stressor)
showed poorer memory performance. In the second study, the authors investigated that if
cortisol alone (without any psychological stress) would impair performance of the
participants. The participants received either 10 mg of cortisol or placebo (orally). They were
then tested one hour later for procedural memory, declarative memory and spatial thinking.
The participants who received cortisol showed impaired performance in the declarative
memory and spatial thinking tasks but not in the procedural memory task. Thus, elevated
cortisol levels were associated with impaired memory function of healthy adults
(Kirschbaum, Wolf, May, Wippich, & Hellhammer, 1996).
Another study was conducted to investigate whether the effects of cortisol on working
memory depended on the level of adrenergic activity (as measured by sympathetic activation)
during memory performance. Participants were (after exposure to a psychosocial stress task),
divided into cortisol responders and cortisol non-responders. There were working memory
impairments for the cortisol responders during the psychosocial stress phase, when cortisol
25
and adrenergic activity were enhanced. This same pattern could not be found for the cortisol
non-responders. Working memory of cortisol responders did not differ from that of non-
responders during recovery when cortisol levels were elevated but adrenergic activity was
normalized. There were several stress measures but cortisol was the only significant predictor
for working memory performance during stress. Thus, adrenergic activation is essential for
the impairing effects of stress-induced cortisol on working memory (Elzinga & Roelofs,
2005).
In regards to the second mechanism that is associated with disrupted performance,
there is a tendency for individuals to actively monitor the self-relevance of performance.
Individuals become more conscious of the self and one’s performance. Schmader et al.,
(2008) stated that when individuals try to avoid failure when stereotype threat has been made
salient, they switch from a more automated state of functioning into a more controlled state of
monitoring the self within the situation. The more conscious approach is employed to assist
in managing the new situation caused by the primed conditions (Schmader et al., 2008). This
paradigm was investigated further in another study by looking at the effects of high-pressure
performance situations (caused by offering performance-contingent rewards) on golf putting
performance. The authors investigated whether choking under pressure was caused by
distraction (cognitive load) where the high-pressure performance situation distracts the
attention away from the task in hand or self-focus, whereby the individual completing the
task shifts the attention to oneself which in turn interferes with the putting performance.
Cognitive load was elevated by asking the male participants to count backwards from 100.
Furthermore, self-awareness was manipulated by videotaping half of the participants (during
the practice trials). As expected, golf putting performance dropped dramatically in the high-
pressure performance condition. Additionally, in the high-pressure condition (without
distraction treatment), there was increased performance for the self-awareness adopted
26
participants. This pattern could not be found in the low-pressure condition. In other words,
self-awareness adaptation treatment allowed the participants in the high-performance
condition to elevate the effects of high pressure on putting performance. These results
confirmed the self-focus account of the choking under pressure phenomenon (Lewis &
Linder, 1997). In line with the previous study, Seibt and Forster (2004) found that the
individuals who had been primed to stereotype threat became more conscious of avoiding
failure on the task in hand. This is in turn, helped the participants to have a more careful and
systematic performance as opposed to a more creative and eager performance that the
positively stereotyped individuals endorsed (Seibt & Förster, 2004). There can also be
increased vigilance to threat- and failure-related cues. This vigilance occurs when individuals
become more vigilant to external feedback that might confirm that one is not performing well
enough and up to the required academic standard and therefore there is a risk of confirming
the stereotype (e.g., the negative stereotype of girls and maths). This was investigated further
in another study by looking at the effects of stereotype threat effects on minority students’
(African-American and Latinx participants, in particular) tendency to be more vigilant to task
errors in an academic setting. The two groups of ability-stigmatized participants completed a
basic response-conflict task (a flanker task). The task was described either as a measure of
intellectual ability (stereotype threat condition) or a neutral pattern task (control). Event-
related potential (ERP) methodology was employed while the participants completed the
response-conflict task. ERPs were recorded from scalp regions that were located above the
dorsal anterior cingulate cortex. This is the region of the brain that is involved in monitoring
behaviour that conflicts with goals. The authors confirmed that the (academic) minority
students showed larger ERP amplitudes when the task was completed in the intellectually
threatening condition compared with the neutral condition. It was concluded that this elevated
27
neural activity was caused by the increased vigilance to the errors on the response-conflict
task (Forbes, Schmader, & Allen, 2008).
And finally, according to Schmader et al., (2008) the third mechanism that can
contribute to cognitive inefficiency is linked to individuals’ efforts to suppress negative
thoughts and emotions while in the stereotype threat condition. The individuals who bear the
burden of negative stereotypes might experience self-doubt in relation to their performance
on the task. For example, Steele and Aronson (1995) Study 4 showed that African-American
students’ performance could be impaired by the mere salience of the stereotype threat even
when informed that the test was not diagnostic of ability (Steele & Aronson, 1995).
Negative stereotypes can also make the stigmatized individuals feel that there is
generally a negative expectancy in relation to their academic performance. When the
participants were told that they had high ability on a task this predicted future performance on
similar tasks compared with the other group where they were given ambiguous feedback
about their academic abilities to complete the task. However, when the negative stereotype
was made salient, the positive performance expectations of the performance deteriorated
(Stangor, Carr, & Kiang, 1998).
The role of negative thinking was investigated and whether it was a possible mediator
of maths performance decrements when stereotype threat had been made salient. Sixty female
participants were asked to complete a difficult maths task after being assigned to a stereotype
threat condition or control. The women who were primed into the stereotype threat condition,
reported a larger number of negative thoughts compared with the women in the control
condition. The increased negative thoughts were particularly related to the task in hand and to
mathematics in general. Additionally, there was a large performance drop for the women in
the stereotype threat condition, particularly during the second half of the test which was
28
mediated by the elevated negative thoughts of completing the task (Cadinu, Maass,
Rosabianca, & Kiesner, 2005).
The suppression process regulating negative thoughts consumes the internal cognitive
resources, and working memory in particular. Muravan and Baumeister (2000) reported that
self-control that is part of the inhibitory control (the ability to regulate one’s emotions,
thoughts, and behaviour in the face of temptations) is a limited resource. Self-control efforts
are required when coping with a stressful situation, resisting temptations, and regulating
negative affect. Unfortunately, after multitude of self-control efforts, subsequent attempts of
self-control might fail, confirming the fact that self-control can been seen as a limited
resource. The authors concluded that these self-control decrements were not caused by
negative moods or learned helplessness. These decrements were specific to behaviours that
involved self-control (Muraven & Baumeister, 2000). To sum up, it is evident that all of the
three mechanisms consume the existing working memory resources, and as a consequence
negatively affect task performance.
1.3.4 Stereotype Threat and Working Memory
Stereotype threat can increase the levels of situation-induced feelings of pressure and this
in turn can create anxiety about the situation. These increased worries can compete for
working memory resources that would normally be available for maths performance. The
maths performance of individuals who rely heavily on working memory resources (higher-
WM individuals) can deplete when there is pressure caused by the stress-laden environment.
This type of situation causes the individual to complete the maths tasks in a dual-task setting.
The maths task execution and the worries of the stressful situation tax working memory
capacity simultaneously (Beilock, 2008). It has been suggested that verbal processes (e.g.,
thinking) are more compromised in a stressful situation. In the Beilock (2008) study,
participants who completed horizontal modular arithmetic tasks (these tasks rely heavily on
29
phonological aspects of working memory) under stereotype threat, performed worse than the
participants who completed vertical modular arithmetic tasks. The vertical MA tasks use the
column subtraction format and therefore the participant does not need to rely on the working
memory resources as much as with the horizontal MA tasks. When the vertical format is
used, the participant can use the layout of the maths task to their own benefit. Unlike with the
horizontal tasks, all the required steps need to be stored in the working memory. The Beilock
(2008) study utilised high WM load and low WM load tasks but the difficulty level of the low
WM load tasks was too low to see any taxation of the working memory resources. The tasks
were single-digit numbers up to 10 and as such they might not have taxed the working
memory in a way that was anticipated.
There are a large number of empirical studies on the effects of stereotype threat on task
performance but far less is known that how these effects are realized. Beilock, Rydell, &
McConnell (2007) used mathematical problems (modular arithmetic tasks) that relied heavily
on working memory as a test bed to see any performance decrements in simple maths tasks
when stereotype threat was made salient. The authors examined the types of modular
arithmetic tasks that were most susceptible to stereotype threat (vertical or horizontal
problems). The purpose of these type of modular arithmetic tasks is to judge the validity of
maths problems like 61 ≡ 18 (mod 4). The middle number is subtracted from the first number
(i.e., 61-18) and then the difference is divided by 4. If the answer is a whole number, the
maths problem is true. The horizontally presented maths problems were more reliant on
phonological resources. Therefore, it was concluded that stereotype threat taxed the verbal
working memory resources and consequently harmed women’s maths performance. The
worries of stereotype threat put extra burden on the working memory (phonological loop, in
particular), and together with the horizontally presented maths problems there were maths
performance decrements under stereotype threat (Beilock, Rydell, & McConnell, 2007).
30
In similar vein, Schmader and Johns (2003) confirmed that negative stereotypes reduced
working memory capacity by putting extra burden on cognitive resources, and working
memory in particular. The authors tested this hypothesis with three experiments. Women
completed the working memory assessment as a test that was related to their mathematical
ability (stereotype threat condition), (Study 1). In the second study, Latinx participants in the
stereotype threat condition were advised that the working memory test was a measurement of
general intelligence. Working memory capacity of both women and Latinx participants was
reduced by priming these self-relevant negative stereotypes. Finally, the Study 3 found that
working memory capacity mediates the negative effects of stereotype threat (Schmader &
Johns, 2003). However, when these findings were further analysed it was found that the
performance of the actual maths tasks of the working memory task (Operation Span Task)
that was a dual-task (comprising of simple mental arithmetic tasks and recall of words) did
not deteriorate. It was only the word recall of the task that was affected in the stereotype
threat condition.
1.4 Introduction to Achievement Goals
Another area in which interactivity may support people in situations of evaluative
pressure is when they endorse performance-approach goals. This programme of research
focused on two different situations linked to evaluative pressure (stereotype threat and
achievement goals). The purpose of the following section is to focus on the latter. There are
a multitude of empirical studies on achievement goals and their effects on academic
outcomes. Over the past 25 years, achievement goals have inspired over 1000 published
papers. Nevertheless, much less is known about the effects on working memory and whether
interactivity supports elevated mental arithmetic performance for participant with normative
strivings (performance-approach goal participants). The achievement goals construct refers to
the way individuals represent and pursue competence in challenging settings (Elliot &
31
Dweck, 2005). According to Poortvliet and Darnon (2010) achievement goals are said to
reflect the aim of an individual’s achievement pursuits. Additionally, achievement goals
function as frameworks that can help to understand how individuals react to various
achievement situations (e.g., in academic setting), (Poortvliet & Darnon, 2010).
Achievement goal theory (Harackiewicz & Barron, 2002) distinguishes between
mastery-approach goals (i.e., task mastery and knowledge acquisition), mastery-avoidance
goals (i.e., avoiding the failures of not learning the required task), performance-approach
goals (i.e., aiming for outperforming others and demonstrating competence in the subject
field), and performance avoidance goals (i.e., avoiding to do worse than others). However,
this theory assumes that there are 4 distinct achievement goals and that they function in
isolation. The theory ignores the fact that there can be situations where a mixture of goals can
be experienced. Current educational practices strongly promote the endorsement of
performance-approach goals (the notion of normative success and dominance over others).
For example, students’ knowledge acquisition is measured via exams and tests that allow the
examiners to give grades based on the students’ academic performance. Striving for academic
success over others can cause elevated feelings of pressure. Hence, the programme of
research reported here focuses on performance-approach goals only (with mastery approach-
goals functioning as a comparison group), (Crouzevialle & Butera, 2013).
Individuals pursuing performance-approach goals are good at knowing the material
that is essential for the task in hand (Elliott, Shell, Henry, & Maier, 2005). They listen to the
cues about the future assignments and tests and then adjust their individual learning based on
these cues. Students perform better when they focus on topics that the teacher deems
important and that are tested as part of the curriculum (Broekkamp, Hout-Wolters, & Van
Hout-Wolters, 2007). Students with performance-approach goals concentrate on memorising
rather than elaboration and knowledge construction (Entwistle, 1988). This approach can lead
32
to surface learning and rote learning (Harackiewicz & Linnenbrink, 2005). Performance-
focused students tend not to not earn the same high marks in the more advanced classes that
require deeper understanding because of the surface learning strategies of performance-
approach goals (Senko, Hulleman, & Harackiewicz, 2011). On the contrary, students with
mastery-focused goals are freer to pursue their own agenda which is guided by their own
personal interests and their curiosity of the current topic. Hence, mastery-approach goals
predict the use of adaptive cognitive strategies that lead to deeper processing. This kind of
approach might benefit the students in the long run because it promotes deeper learning but
might not help in gaining the highest grades because it is based on personal interests rather
than the areas that might be tested. When people endorse performance-approach goals, their
focus is on the outcome of the task and therefore the individuals might not be fully engaged
with the process and the activity to complete the task. Mastery-approach goals allow the
individual to focus on the learning process rather than the activity of outperforming others.
Mastery-focused individuals focus on learning and their personal improvement, and therefore
have a focus on the task that allows them to explore both intrinsic and utility value. Finally, it
is this task focus that allows the individual to experience both intrinsic and utility value
(Hulleman, Durik, Schweigert, & Harackiewicz, 2008).
1.4.1 Academic Consequences of Performance-Approach Goals
There are mixed empirical findings regarding the academic consequences of
performance-approach goal pursuits. On the one hand, performance-approach goal adaption
has been seen as a positive predictor of exam performance and academic achievement in a
multitude of studies (Church, Elliot, & Gable, 2001; Elliot & Church, 1997; Harackiewicz,
Barron, Tauer, Carter, & Elliot, 2000; Skaalvik, 1997; Wolters, Yu, & Pintrich, 1996).
However, most of these investigations have been longitudinal studies based on self-reported
questionnaires rather than studies that measure the current academic performance.
33
Additionally, some of the current academic exam performance is assessed using multiple
choice questionnaires (MCQs) which generally only measure surface level understanding of
the material. These types of exams do not allow the student to exhibit deeper understanding
of the material and therefore allows the student to be efficient and only to learn that what is
required for the exam. The superficial way to prepare for an exam is a successful way of
preparing for a multiple-choice type of assessment but this same approach would not work
for an assessment that requires deeper understanding of the topic (Harackiewicz, Barron,
Carter, Lehto, & Elliot, 1997). The link between performance goals (both approach and
avoidance goals) and academic performance is mediated by the perceived difficulty of the
academic task. Achievement goal endorsement leads to perceiving the task either as
something within reach (in the case of performance-approach goals) or as too difficult and
impossible to complete for the avoidance goal participants. As a consequence, the perceptions
of difficulty then influence the task performance and in the case of performance-approach
goals, provides a buffer against the harmful effects of fear of failure (Darnon, Butera, Mugny,
Quiamzade, & Hulleman, 2009).
1.4.2 Maladaptive Behaviours of Performance-Approach Goals
Additionally, performance-approach goal pursuits can be linked to various
maladaptive behaviours and outcomes in an educational setting. Performance-focused
students are generally less inclined to cooperate and share information with their peers
(Poortvliet, Janssen, Van Yperen, & Van De Vliert, 2007). Additionally, when there is a
disagreement, individuals with performance-goal reject other people’s opinion and, just
impose their own views and ideas (Darnon, Muller, Schrager, Pannuzzo, & Butera, 2006).
This kind of behaviour can have detrimental consequences for the performance-driven
students and it can hinder learning. Finally, performance-approach goals have also been
associated with cheating. It was reported that individuals who intended to cheat in the areas
34
of education, sport and work, did it as a function of their achievement goals in that particular
environment. Additionally, by imposing achievement goals on participants affects their actual
cheating behaviour during the required task performance. The normative goal endorsement
encourages individuals to achieve their performance-approach goal for any price. The
performance-focused individuals do not seem to care how this goal is attained. Hence,
cheating might help them to achieve their normative goal (Van Yperen, Hamstra, & Van Der
Klauw, 2011).
1.4.3 Components of Performance-Approach Goals
Grant and Dweck (2003) hold the view that there are four different components of
performance-approach goals that help individuals to perform and reach their academic goals.
To begin with, validation of ability is where the individual concentrates on appearance and
wanting to look good in front of peers. Normative comparisons allow the individual to
compete with peers. Normative ability is where the individual aims to outperform others
doing similar tasks (combined ability validation and normative comparisons) and finally,
outcome goals that are focused on attaining a positive outcome in the form of good grades
(Grant & Dweck, 2003). However, the general study of achievement goals (including
performance-approach goals) has clearly found basic motivational processes but there still
remains controversy surrounding their nature and impact on performance. First, the effects of
achievement goals on academic performance and on motivation have been tested on a
number of circumstances by using e.g., puzzles, concept-formation tasks, and solving
difficult maths problems (Elliott & Harackiewicz, 1998; Elliott & Dweck, 1998; Barron &
Harackiewicz, 2001) and it is possible that the tasks have varied in relation to the actual
degree of difficulty and the challenge that the participants have faced. The different ways of
operationalising achievement goals might explain some of the inconsistent findings by
various researchers of the achievement goal effects on academic performance. Grant and
35
Dweck (2003) attempted to investigate some of these issues further with the help of five
studies and found that the impact of the various achievement goals depended on how they
were operationalised. Active learning predicted active coping, sustained motivation, and
higher achievement (in the face of a challenge). Ability goals predicted withdrawal and lower
performance (when challenged). However, there was a performance boost when students
were met with success. Additionally, there were no performance or motivation decrements
with normative goals.
However, the achievement goal inventory items that were utilised as part of the
investigation, comprised of three items only for each achievement goal (outcome goal, ability
goal, normative outcome goal, normative ability goal, learning goal, and challenge-mastery
goal), which therefore reduced the validity and reliability of the inventory. Originally, there
were 10 items for each goal. These were clearly tested and the most reliable items were kept.
Whilst it has been shown that the remaining achievement goal items employed have high
Cronbach alpha values, it is possible that the 3-item scale might not have accurately reflected
the behaviour of the participants and therefore reducing the validity and reliability of the
scale and its findings. The authors justified the use of three items to make it simpler for the
participants to respond to a multitude of achievement goal items and to avoid any form of
confusion by using a multitude of similarly worded items. Additionally, the Confirmatory
Factor Analysis (CFA) that was used as part of the Study 1 found that there were two models
that provided a good fit to the data. Although Model B (a 6-factor model, based on all of the
achievement goals that were measured) was a slightly better fit, Model A with only 4 primary
factors (an ability goal factor, an outcome goal factor, a normative factor comprising of
normative ability and normative outcome factors, and a learning factor that included learning
and challenge-mastery factors) was used as the basis of analysis as it was consistent with the
earlier results of the Exploratory Factor Analysis (EFA). In the 4-factor model, there is no
36
further specification of the normative goal items (i.e., outcome and ability) and of the
learning goal items (i.e., learning and challenge-mastery). The 6-factor model included these
specifications. It can therefore be argued that the additional information provided by the 6-
factor model was not taken into consideration as part of the Grant and Dweck (2003)
investigation and therefore not allowing the authors to develop these thoughts further.
Additionally, this theory assumes that the different achievement goals function in isolation. It
could be argued that people have more than one goal and as such the use of categorical
measurements (as part of the achievement goal inventory) can mask these effects.
1.4.4 Performance-Approach Goals and Distraction
Performance-approach goals are also linked to distraction and diminished task focus.
Distraction theory suggests that the additional pressure creates an environment that draws
attention away from the primary task. In other words, the execution-irrelevant activity in
working memory caused by the pressure situation causing skill failure (Beilock et al., 2004).
Concerns of outperforming peers distract students from the task (Brophy, 2005).
Additionally, individuals are less likely to become fully immersed and absorbed in the
academic task when they are mainly concerned with their self-worth in comparison to others.
On the other hand, mastery-approach goals are linked to various positive processes (e.g.,
challenge appraisals and absorption during preparation), (McGregor & Elliot, 2002).
According to the processing efficiency theory, anxiety can reduce the storage (mainly
phonological loop) and processing capacity (central executive) of the working memory
system available for the task in hand. Additionally, anxiety can make individuals increase
task effort and activities to improve performance (e.g., maths performance), (Eysenck &
Calvo, 1992).
37
1.4.5 Negative Affect
Performance-approach goals are related to increased negative affect. On the contrary,
mastery-approach goals are associated with reduced negative affect, which in turn is related
to increased working memory functioning. These results indicated a clear difference between
the two achievement goal endorsements, and their relation with negative affect. Performance-
approach goal endorsement together with a challenging task may not allow the individual to
meet their goal of outperforming peers and as a consequence levels of negative affect might
become elevated. Mastery-approach goal adoption, on the other hand, allows the individual to
experience the difficult task as a challenge and therefore the individual is not worried about
failure, and as a consequence the levels of negative affect are reduced (Linnenbrink, Ryan, &
Pintrich, 1999). Negative affect leads to increased task-irrelevant thoughts which in turn taxes
working memory and as a consequence, the overall cognitive capacity is depleted. As a
result, the phonological loop is filled with task-irrelevant thoughts and central executive
processing is affected by additional processing of this information that is not related to the
task (Elliman, Green, Rogers, & Finch, 1997). Achievement goals are directly linked to task-
irrelevant thoughts. As mentioned earlier, performance-focused students focus on their
academic performance and how it relates to others (normative behaviour). Mastery-oriented
students, in contrast, stay focused on the task in hand. Thus, these two approaches have
different effects on the thoughts that do not support the task in hand (Elliott & Dweck, 1988).
1.4.6 Achievement Goals and Theories about Intelligence
Previous developmental research has shown that children’s theories about intelligence
may guide them towards different achievement goals (Dweck, 1986). When children believe
that intelligence is a fixed trait, they tend to orient towards performance-approach goals to
gain favourable judgements about their competence from their peers. The goal is to gain
positive judgements, and to avoid negative judgements of competence. When the child’s
38
confidence in ability is high, the child seeks challenge, and is persistent in achieving the goal.
But when the confidence is low, the child feels helpless and avoids the challenge, and is low
in persisting in the goal. On the contrary, the children who believe that intelligence is a
malleable quality tend to orient towards developing competence. And in both high and low
confidence, the child seeks challenge that fosters learning and remains persistent with this
approach (Dweck, 1986).
Mastery-achievement goals involve the aim for improving one’s own performance. In
contrast, performance-approach goals reflect the pursuit of outperforming others. People who
strive for mastery-approach goal, mainly compare their present performance with their own
previous performance. By doing this, they develop a self-referenced focus in different
achievement situations. Individuals who pursue performance-approach goals tend to compare
their performance to others and they therefore develop an other-referenced focus (Dweck,
1986).
1.4.7 Motivation and Task Values
Interest in the activity is one of the most important components of motivation, and
motivated behaviour (Schiefele, 1991). One way to develop this interest is to find value (task
values that individuals perceive when engaging in tasks), and meaning in the activities that
people do. Achievement goals help individuals to find value in the tasks that they do
(Pintrich, 2003). Two of these values are intrinsic and utility value. When it comes to tasks
with utility value, they are seen important by the individual because they are relevant beyond
the immediate situation. These are tasks that are also useful for other future tasks, and other
aspects of an individual’s life. Tasks of intrinsic value are important to the individual because
they are seen as enjoyable and fun. There are studies that show a clear relationship between
how the utility of a task is perceived and how the subsequent performance is. For example,
persistence and performance in a physical education class was elevated by informing the
39
participants of the usefulness of the activity (Simons, Dewitte, & Lens, 2003). In another
study, it was concluded that students’ classroom performance was predicted by the relevance
of school work to students’ future goals. There are experimental studies that have
documented a correlation between mastery-approach goals and both utility and intrinsic value
(Linnenbrink, 2005; Shim & Ryan, 2005).
1.4.8 Choking under Pressure
Pressure of high-level performance from either stereotype threat or performance-
approach goals can create mental distractions that compete for working memory resources
that would normally be used for executing the task in hand (Beilock & Carr, 2005). To
understand this process, Beilock et al., (2004) talk about the term choking under pressure
which is defined as performing more poorly (across diverse task domains) than expected in a
high-stake situation, given one’s skill level (Beilock et al., 2004). This happens particularly
when the desire for high-level performance is maximal. Choking under pressure has been
mostly explained by explicit monitoring theories rather than distraction theories. Beilock and
Carr (2001) investigated golf playing performance under pressure with the help of a golf
putting task to further understand whether practice at explicit attention or distraction would
reduce pressure-induced failure of the task. It was concluded that choking occurred for those
individuals who were trained on the putting task in the single-task condition (used as a
baseline) and also for the individuals trained in the dual-task environment that caused
distraction for the participants. Nonetheless, choking did not occur for those trained in the
self-conscious condition. In other words, the self-consciousness training allowed the
participants to inoculate against the negative consequences of over-attending to a well-
learned performance process. According to explicit monitoring theories these are the
mechanisms that are responsible for performance decrements in high-pressure situations.
40
Attending to skills that are proceduralized (e.g., putting) can hurt the overall performance
(Beilock & Carr, 2001).
Most of the explicit attention studies have used sensorimotor skills as a test bed which
might not be the right environment for investigating the distraction theory and its effect on
complex cognitive processes (e.g., mental arithmetic). Beilock (2001) investigated choking
under pressure by examining mental arithmetic performance under pressure in the
mathematical problem-solving domain (with the help of modular arithmetic tasks).
Experiment 1 concluded that there were performance decrements in the difficult and
unpractised modular arithmetic tasks when in the high-pressure condition. Additionally, it
was demonstrated that these pressure-induced failures only occurred when the most difficult
(unpractised) and capacity demanding equations were used (Experiment 2). These findings
lend their support to the distraction theories of choking in the domain of mathematical
problem solving.
In another study, Beilock et al., (2004) tested the idea that increased pressure caused
by a high-stakes situation can constrain individuals to allocate their limited working memory
resources both to the task at hand, and to the management of the outcome concerns. In their
study, the participants were asked to solve a series of arithmetic tasks under either low or
high evaluative pressure situation. There were three different ways of creating the high-stakes
environment (high evaluative pressure): monetary rewards (e.g., scholarships and research
opportunities), peer pressure, and social evaluation (e.g., mentors, teachers, and peers). All
the three sources of pressure were at play in an academic setting. The high-pressure situation
compared to the non-pressure condition taxed the available working memory resources which
resulted in a decrement of mental arithmetic performance, and particularly for the high-load
working memory tasks (Beilock et al., 2004).
41
1.4.9 Evaluative Pressure
There are various empirical studies that have looked at the cognitive consequences of
evaluative pressure on academic performance. However, little is known about the feelings of
evaluative pressure that might be caused by achievement goals and normative goal pursuit in
particular. Current literature suggests that there are two main ways of explaining why
performance might fall in stressful situations. Explicit monitoring (self-focus) theories
suggest that performance pressure about performing well on the task increases the
individual’s self-consciousness and anxiety. This focus in turn, increases the attention to skill
processes and their step-by-step control. However, attention to performance at such
component specific level is thought to disrupt the automated processes of high-level skills
that are normally run outside the scope of working memory system. This is in contrast to
distraction theory that suggests that the additional pressure fills working memory with
thoughts about the stressful situation and its importance that compete with the attention that is
normally allocated to the execution of the task. This additional pressure serves to create a
dual-task environment where the additional pressure and the task in hand compete for the
same limited working memory resources (Beilock et al., 2004). Whilst working memory is a
short-term memory system that maintains a limited amount of information required to
complete the demanding cognitive task at hand (e.g., mental arithmetic task), it
simultaneously aims to prevent distractions from the environment (including irrelevant
thoughts), (Kane & Engle, 2000). It has been argued that the impact of distracting thoughts
and anxiety about mental arithmetic performance derives from the disruption of the central
executive component of working memory which has the function of controlling and applying
of the sequence of arithmetic operations during problem solving (e.g., carrying during
addition and borrowing during subtraction), (Ashcraft & Kirk, 2001). Finally, Beilock and
Carr (2005) reported that performance pressure harmed individuals most qualified to succeed
42
by consuming the working memory capacity that they relied on for their superior maths
performance (Beilock & Carr, 2005).
Additionally, Beilock and DeCaro (2007) demonstrated that individual differences in
working memory capacity can impact the strategies used to solve complex math problems
and the type of testing situations (low or high pressure) can alter the strategy that has been
used to come to the solution. Experiment 1 found that under low-pressure conditions, the
higher the individual’s working memory capacity the more likely they were to use
computationally demanding algorithms (vs. the simpler shortcuts) to solve the required maths
problems and the more accurate their math performance. Higher WM individuals used
simpler problem-solving strategies (under high-pressure conditions) and their accuracy
suffered. Experiment 2 used a math task where a simpler strategy was optimal; accurate
maths performance was achieved with a few problem steps. When in the low-pressure
conditions, the lower individuals' WM, the better their maths performance as they relied on a
simple, but accurate problem strategy. When in the high- pressure condition, higher WM
individuals performed optimally by using the simpler strategies (the same ones the lower
WM individuals had employed). In sum, the level of working memory capacity influences
how individuals approach maths problems. Additionally, the nature of the task (simple
strategy or difficult strategy) and the performance environment (high or low pressure) make a
clear difference on the maths performance (Beilock & DeCaro, 2007).
Activation of performance-approach goals creates an evaluative context as the
individual is focused on outperforming others. The determination and focus of winning and
being the best can create distractive thoughts and worries. This can be problematic when the
performance-approach goals have been activated under immediate and demanding testing
situations. Performance-approach goal pursuits can have different cognitive outcomes
depending on the timing of the testing. There are differences whether one focuses on an
43
immediate testing situation or on a period of an academic semester. There can be a divided-
attention situation that can generate goal attainment concerns in short-term setting. However,
for the long-term setting, there are benefits with the long-term setting as it allows for tactical
planning for course-specific demands (Crouzevialle & Butera, 2013).
1.4.10 The Effects of Performance-Approach Goals on Working Memory Capacity
There is a wealth of research on achievement goals and their effects on academic
performance, but much less is known about the cognitive processes of these goals, and
particularly the effects on the working memory. Crouzevialle and Butera (2013) concluded
that the pressure to outperform others (performance-approach goal) can generate anxiety that
depletes available working memory resources. In their first experiment, the induction of the
performance-approach goal during a demanding task reduced task performance. Their second
experiment confirmed this as there were distractive concerns that drew on the verbal
resources of the working memory (phonological loop). The final study concluded that the
performance drop was due to performance-approach goal related thoughts (Crouzevialle &
Butera, 2013). The same authors also looked at the high working memory students (the high
achievers) and tested whether this group of individuals would experience the high working
memory capacity as a burden because of high level of disruptive outcome concerns that
would have a causal effect on the maths performance. It was proposed that anxiety might be
higher for students who are used to succeeding in an academic setting. Study 1 concluded that
the higher the individual’s working memory capacity the lower the maths performance during
performance-approach goal. Study 2 confirmed that this pattern was caused by uncertainty to
outperform others (Crouzevialle, Smeding, & Butera, 2015).
In another study, the influence of achievement goal pursuits on working memory
capacity was investigated when varying levels of executive load were used. When high
executive load (3-back) was used, there were achievement goal effects on working memory
44
but this same pattern could not be found under the less demanding loads (1-back, 2-back).
Under the high executive load, there was poorer working memory processing during the
performance-approach goal than when mastery-approach goal or no-goal control were used
(Avery & Smillie, 2013).
Interestingly, Avery et al., (2013) reported that the largest performance decrement
occurs in a mastery-approach goal condition suggesting that mastery-approach goal is more
strongly influenced by working memory load than performance-approach goal. This was in
line with previous research that indicated that mastery-approach goals are linked with higher
working memory engagement (Harackiewicz & Linnenbrink, 2005). Participants in the Avery
et al., (2013) study were presented with a 4 x 4 letter matrix and required to make as many
words as possible. This task was used because working memory has been suggested to play a
role in word formation games, allowing the retrieval of verbal information from long-term
memory (Halpern & Wai, 2007). This primary word game was then interleaved with a
secondary task (digit order: high load or low load). Study 2 examined the role of working
memory further (in relation to achievement goal) using a primary task known to vary in
working memory intensity (modular arithmetic tasks: high/low working memory load). As in
Study 1, the primary task (modular arithmetic tasks) was interleaved with a secondary task
(letter order). But this time, self-reported strategy use was also used as a means of
understanding the link between achievement goals and working memory capacity. Those
pursuing a mastery-approach goal experienced the largest performance decline under high
secondary load on those parts of task that placed high demands on working memory
resources (Avery, Smillie, & De Fockert, 2013).
1.4.11 Achievement Goals and Cognition
Graham and Golan (1991) investigated the underlying processes linking motivation
(achievement goals, in particular) and cognition. The authors concluded that when deep
45
processing on a memory task was required, participants in the mastery-approach goal
condition showed better recall than participants in the performance-approach goal condition.
Children (5th and 6th grade) were assigned to either task-focused motivational condition
(mastery goal), an ego-focused condition (performance goal), or a control group. They were
then given a list of 60 words manipulated to be encoded at either shallow (Phonemic: Does
the word rhyme with make?) or deep levels of processing (Category: Is the word a kind of
animal? and Sentence: Does the word fit in the sentence?), followed by an unexpected recall
test (Graham & Golan, 1991). Additionally, DiCintio and Parkes (1997) investigated how
achievement goals are linked to working memory. The authors reported that the mastery-
focused individuals had larger working memory spans compared with performance-focused
participants (Dicantio & Parkes, 1997). In another study, it was found that mastery-approach
goals were positively related to working memory and that working memory mediated the
overall maths performance. However, it was reported that children (year 4 and 6) who were
pursuing performance-approach goals had a negative relationship with working memory and
maths performance. These findings suggest that reduced working memory resources could
explain the reduced maths performance for the children with more normative goal
endorsement (Lee, Ning, & Goh, 2014).
1.5 Working Memory
According to Baddeley and Hitch (1974, updated in 2000), working memory is a
multicomponent system for temporarily storing and managing information that is required to
carry out cognitive tasks (e.g., learning, reasoning and comprehension), (Baddeley & Hitch,
1974). This limited capacity system is mainly involved in processing and short-term storing
of information either in verbal or visual format. The phonological loop of the working
memory is involved in the short-term storage of verbal information (phonological
information). The visuo-spatial sketchpad on the other hand, is for short-term storage of
46
visual or spatial information. The central executive is involved in the planning and allocation
of resources (e.g., in a multi-step maths task, deciding where to go next to complete the
computation). According Kane and Engle (2002), working memory represents executive
attention. Working memory has limited ability to keep task relevant information and goal
representations accessible in case of interference form task-irrelevant information (e.g., worry
caused by stereotype threat or distractive thoughts caused by performance-approach goals). In
other words, working memory is an executive process that also coordinates cognition and
controls behaviour to achieve performance goals of the individual (Kane & Engle, 2002).
Furthermore, high working memory capacity allows the ability to control attention and
simultaneously minimize the influence of intrusive thoughts while completing a resource-
demanding cognitive task. Thus, working memory is critical for efficient thought regulation
in situations that place heavy demands on attention (e.g., stereotype threat, performance-
approach goal endorsement), (Kane & Engle, 2002).
Dual-process theory differentiates two distinctive processes (associative process and
rule-based process) that support performance in decision-making and reasoning. To begin
with, associative processes comprise of similarity-based associations that have been built up
over repeated exposure to existing events. These processes operate relatively spontaneously
and therefore make few demands on working memory resources (Rydell, McConnell,
Mackie, & Strain, 2006). Rule-based processes on the other hand, rely on explicit knowledge
as conventions to guide processing (e.g., multistep mental arithmetic tasks with carrying or
borrowing). Hence, the use of the explicit rules, puts heavy demand on working memory
resources (Stevenson & Carlson, 2003).
In the Beilock and DeCaro (2007) study, modular arithmetic tasks were used to
investigate mathematical problem solving in evaluative pressure situations (Beilock &
DeCaro, 2007). These tasks are useful as not only are they in a format that is normally
47
unrecognisable by the participant [32 ≡ 8 (mod 4)] but also, they can be solved in two
different ways, depending on whether rule-based or associative process is utilised. In order to
go through the required computation multitude of steps have to be taken and interim totals
stored in the working memory. First, 8 is subtracted from 32 (32 – 8 = 24). The answer is
then divided by 4 (24/4 = 6). Additionally, the participant needs to state whether the answer is
a whole number or not (true or false). This type of computation is based on rule-based
processes, and evidently in order to compute the task, working memory is heavily relied on
(for short-term storage and processing or computational information). On the other hand, the
computation can be completed without any calculations (use of associative processes). If the
numbers are even then the response is true. This type of reasoning is based on prior exposure
to the numbers used as part of the computation. Beilock and Carr (2005) concluded that in the
low-pressure condition, the high WM individuals outperformed the low WM individuals.
However, situation induced pressure impaired the maths performance of the high working
memory individuals. However, the performance of the low working memory individuals was
not affected under the pressure condition. These results were explained by higher WM
individuals relying more on rule-based computations that tax the existing working memory
resources heavily (Beilock & Carr, 2005). Together with the added pressure, the working
memory resources of the high WM were compromised, and as a consequence maths
performance suffered.
1.5.1 Working Memory and Intrusive Thoughts
According to Engle (2002), working memory capacity (executive attention) is of
particular importance when there are conditions (situations) that can lead to retrieval of
response tendencies that conflict with the task in hand. Additionally, working memory system
enables one to deal with the relevant task at hand while inhibiting irrelevant information
(Miyake & Shah, 1999). Individuals who have low working memory spans are less able than
48
people with high working memory spans of completing the mental work required to block
distracting information (Engle, 2002). Rosen and Engle (1998) conducted two experiments to
explore whether there was a relationship between an individual’s working memory capacity
and the ability to suppress intrusive thoughts and behaviours. Participants learned three lists
in a modified paired-associates task that contained pairs of cue-response items. During the
first experiment when speed was stressed, individuals with high working memory produced
fewer first-list intrusions during the second list learning. During the second experiment,
accuracy was stressed and the high working memory individuals were slower than the control
group to retrieve first-list responses on the list 3. The participants had already suppressed the
first-list responses during the second-list learning. The low working memory individuals were
faster than the individuals in the control condition. There was a relationship between an
individual’s working memory capacity and their ability to suppress intrusive thoughts. In
other words, people who have high working memory capacity are good at suppressing task-
irrelevant information. Finally, there is a domain free limitation in ability to control attention
in working memory (Rosen & Engle, 1998).
1.5.2 Working Memory and Mental Arithmetic
Working memory plays a vital role in mental arithmetic. When a double-digit sum
(e.g., 24 + 66) is performed, all three areas of the multicomponent working memory model
(central executive, phonological loop, and visuospatial sketchpad) are used to complete the
sum. Central executive keeps a track of the overall process and that which part of the
calculation has already been completed. Additionally, it also directs the actions of
phonological loop (speech-based information) and visuospatial sketchpad (visual
information). The role of the phonological loop is to maintain the intermediate results of the
calculation. The visuospatial sketchpad functions as a space where the actual problem and the
solution to it could be visually represented (DeStefano & LeFevre, 2004).
49
1.6 Maths Anxiety
Evaluative pressure (e.g., stereotype threat or achievement goals) can make individuals
feel more anxious about the task in hand. Hence, maths anxiety was measured as part of this
investigation. Maths anxiety is defined as ‘a feeling of tension, apprehension, or fear that
interferes with maths performance’ (Richardson & Suinn, 1972, p. 551). The first systematic
instrument to measure maths anxiety was the Mathematics Anxiety Rating Scale (MARS)
published by Richardson and Suinn in 1972. This test was created to test the participants’
maths anxiety levels in everyday situations with a mathematics component (e.g., calculating a
restaurant bill or taking a mathematics test), (Richardson & Suinn, 1972). Ashcraft claimed
that individuals who are high in maths anxiety have less practice than individuals with low
levels of maths anxiety due to negative thoughts and the avoidance of the subject and any
maths related situations. Due to this avoidance tendency, high maths anxious individuals get
less practice, and exposure in mathematics. General achievement tests show no competence
differences between the high maths anxious individuals and the low maths anxious
individuals. However, when the tests are timed the maths anxiety effects on whole-number
arithmetic problems can be seen (e.g., 46 + 27), (Ashcraft, 2002). The individuals with high
maths anxiety have negative attitudes towards mathematics and they have negative self-
perceptions about their skills in mathematics. However, there is only a weak link between
maths anxiety and overall intelligence (a small correlation of -.17). Individuals who are high
in maths anxiety score high on other anxiety tests too. The strongest link is between test
anxiety and maths anxiety (.52 correlation). When it comes to gender differences, women
report more feelings of maths anxiety but this might be due to the fact that women are more
honest about their feelings (Ashcraft, 2002).
Arithmetic problems with larger numbers (e.g., multiplication problems and two-column
additions) have shown two important maths anxiety effects. The individuals who are high in
50
maths anxiety respond quickly to the maths tasks which is typical of avoidance behaviour.
However, by being as quick as possible can lead to a sharp increase in errors. Addition
problems that have a carrying element are difficult for the high maths anxious individuals due
to the extra burden on the working memory (Ashcraft, 2002). Additionally, individuals who
are high in maths anxiety, demonstrate smaller working memory spans. This is particularly
evident with a computation-based span task. There is an increase of reaction times and errors
when the mental additions are performed concurrently with a memory load task. Maths
anxiety causes a transitory disruption of working memory. The lower working memory
capacity of high maths anxious individuals is partially responsible for the maths performance
decrements. This reduced working memory capacity is on on-line effect that disrupts
information processing in maths tasks (Ashcraft & Kirk, 2001).
In support of this idea, a meta-analysis reported an average correlation of -.31 between
mathematics anxiety and maths achievement for college students and an average correlation
of -.34 for school students (Hembree, 1990). Ma (1999) included 26 studies in her meta-
analysis to investigate the relationship between maths anxiety and achievement in
mathematics (elementary and secondary school children). It was confirmed that the common
population correlation for this relationship is significant (-.27), (Ma, 1999). Additionally,
there is a strong link between maths anxiety and mathematics self-efficacy. People who think
that they are not particularly good at mathematics are also more likely to be maths anxious
(Hembree, 1990).
1.6.1 Onset of Maths Anxiety
Whenever a maths anxious individual is asked to perform mathematics in a high-stakes
and timed setting, the individual’s maths anxiety is aroused and causes an affective drop, a
decline in performance. It is also likely that a student’s maths anxiety is aroused in the maths
classroom itself and particularly when a student is asked to answer or solve a mathematical
51
problem. Finally, maths anxiety is certainly aroused when a student takes a maths test
(Ashcraft & Moore, 2009). Finally, there are no gender differences in standardized maths
tests through elementary and middle school. These differences start from the high school and
go through college and adulthood (Hyde, Fennema, & Lamon, 1990).
1.6.2 Maths Anxiety and Mathematical Problem Solving
Ashcraft and Faust (1994) have shown that people who are high in maths anxiety can find
two column additions (e.g., 34 + 28) difficult due to the element of carrying. Carrying puts
extra pressure on the working memory resources. The individuals with high maths anxiety
took 3 times more time (when the problems were answered correctly) than the low maths
anxious participants on the maths problems that required carrying. When the participants
were faced with relatively difficult arithmetic tasks, there were higher error rates on these
problems for the high maths anxious individual. And often showing classic speed-accuracy
trade-offs; participants wanting to be as quick as possible and ignoring the level of accuracy.
The participants wanted to avoid these types of calculations and be as quick as possible.
Faust, Ashcraft, and Fleck (1996) reported that maths anxiety and maths competence are not
fully confounded. In their study, there was equal maths performance across the different
maths anxiety groups when simple one- and two-column additions and multiplication
problems were completed in a pencil and paper format and when the tasks were not timed
(Faust, Ashcraft, & Fleck, 1996). However, Lyons and Beilock (2012) concluded that it is not
the actual maths that causes the anxiety, but the anticipation of doing the maths task that
causes the anxiety. The higher an individual’s maths anxiety levels were the more increased
brain activity was detected in the areas associated with visceral threat detection and there can
also be the actual feel of pain itself (bilateral dorso-posterior insula). This relationship was
not seen during the actual maths activity (Lyons & Beilock, 2012a).
52
1.6.3 Mathematics Anxiety and Working Memory
Working memory is involved in mathematical problem solving and particularly when the
operands get bigger (problem-size effect). When the size of the operands increases, the errors
and response latencies also increase. This increase can be explained by the larger arithmetic
problems occurring less frequently and therefore these types of problems are stored in
memory at lower levels of strength. Another explanation is that the larger mathematical
problems are solved via a non-retrieval processes (strategy-based trials). These kinds of
processes are slower and there is more room for errors. Strategy based solutions are more
demanding on working memory. Retrieval is fast and relatively fast process, with little
demand on working memory. High maths anxiety works like a dual-task setting. The anxious
thoughts about maths performance function as a resource demanding secondary task
(Ashcraft & Krause, 2007).
Mathematics anxiety affects performance by overloading working memory (Hopko,
Ashcraft, Gute, Ruggiero, & Lewis, 1998). According to the processing efficiency theory,
when a person is anxious about something, these worrying thoughts may distract attention
from the task and therefore overload working memory. General anxiety is associated with
working memory deficits. The intrusive thoughts compete with the ongoing cognitive task for
the limited working memory resources. This can cause slowing of performance or reduced
accuracy (lower cognitive efficiency), (Eysenck & Calvo, 1992). Similarly, maths anxious
individual might be preoccupied with the dislike of mathematics and the previous bad
experiences of this area and as a consequence the working memory gets taxed. These
intrusive thoughts act like a secondary task, reducing the attention from the actual task in
hand (Ashcraft, 2002).
Maths anxiety may tax working memory. Indeed, Ashcraft and Kirk (2001) Study 1
concluded that participants who were high in maths anxiety had significantly lower working
53
memory capacity scores than the participants who were low in maths anxiety. In the second
study, a dual-task was used to measure working memory capacity. A demanding secondary
task (memory task) was combined with a primary task of completing a mental addition task.
These two tasks were competing for the working memory resources for a successful
performance. When the mental addition tasks increased in difficulty, the working memory
was overloaded and this in in turn caused an increase in reaction times or errors. The
manipulation of the difficulty of the mental additions was whether it included a carrying or
not. It was concluded that the more difficult addition problems with carrying relied strongly
on working memory capacity and maths performance was compromised when the working
memory system was also taxed with the memory load task (secondary task). The third study
confirmed that maths anxiety affected performance in maths-related tasks and that this effect
was a transitory disruption of working memory. It was suggested that this effect took place in
the central executive of working memory. This is also the location where intrusive thoughts
and worry are initially registered (Ashcraft & Kirk, 2001). Finally, individuals who are higher
in maths anxiety, also score lower on a measure of working memory capacity (Ashcraft,
2002).
1.6.4 Emotional Processing and Maths Anxiety
In another study, it was confirmed that the preoccupation of the emotional content of
the maths stimuli can consume the existing working memory resources which can cause
decreased deactivation of areas that are associated with the default mode network (DMN)
which are activated during emotional processing. Eighteen individuals with high maths
anxiety were matched with 18 low maths anxious individuals and their BOLD-response
(Blood Oxygenation Level Dependent Signal) was matched for mathematical performance to
number comparison and number bisection tasks. There was stronger deactivation within the
DMN in low maths anxious individuals but only restricted to the mathematical tasks. This
54
effect was more pronounced when the stimuli required inhibitory functions. DMN
deactivation is an indication of processing efficiency and these results indicate that the HMAs
have reduced processing efficiency during mathematical cognition. However, there were no
differences in BOLD-response in task-related activation areas between HMAs and LMAs
(Pletzer, Kronbichler, Nuerk, & Kerschbaum, 2015).
1.6.5 Maths Anxiety and Individuals with High Working Memory
There are studies to suggest that the negative link between maths anxiety and maths
performance is the strongest with individuals who have high working memory capacity.
Maths anxiety affects the individual’s with high working memory capacity use of working
memory intensive strategies (Ramirez, Gunderson, Levine, & Beilock, 2013). In another
study, 154 first year and second year children were tested on maths achievement and working
memory capacity. There was a negative relation between maths anxiety and maths
achievement for children high in working memory. Children with high working memory
capacity rely more on working memory as they use working memory intensive strategies to
complete mathematical problems and these strategies can be disrupted by maths anxiety
(Ramirez et al., 2013). However, further studies have shown that this only relates to
individuals with high working memory who have low attentional control (measured with a
flanker task). Finally, higher attentional control prevent pressure-induced worries from co-
opting working memory resources (Sattizahn, Moser, & Beilock, 2016).
Impaired attentional mechanisms could also affect mathematical problem solving due to
attentional bias towards maths-related stimuli. High maths anxious individuals are slower at
identifying the colours of maths related words in an emotional Stroop task, compared with
neutral words. It was concluded that maths anxious individuals find maths related stimuli
threatening and therefore it impairs their ability to allocate their attention to relevant aspects
of the current task (Suárez-Pellicioni, Núñez-Peña, & Colomé, 2015).
55
1.6.6 Physiological Factors Linked to Maths Anxiety
There are some physiological factors that might explain some of the math
performance gap between low maths anxious individuals and high maths anxious individuals.
Individuals with high working memory have increased salivary cortisol concentration which
predicts poor maths performance (Mattarella-Micke, Mateo, Kozak, Foster, & Beilock,
2011). There is increased activation in brain regions that are normally associated with pain
perception in dorso-posterior insula (Lyons & Beilock, 2012a) and negative emotional
processing that can be indexed as hyperactivity in right amygdala. There is also reduced
activity in the brain regions that are associated with working memory and numerical
processing, dorsolateral prefrontal cortex and posterior parietal lobe (Young, Wu, & Menon,
2012).
To investigate how a person’s physiological arousal relates to their maths
performance as a function of individual differences in working memory (WM) capacity,
participants completed difficult maths problems and salivary cortisol levels were measured
before and after the maths tasks. Salivary cortisol levels were measured because these
hormone levels are associated with stressors in humans and these hormones can also have
effects on working memory. The performance of the lower working memory individuals was
not dependant on cortisol concentration or maths anxiety level. However, the higher the
concentration of salivary cortisol for the high working memory individuals with high maths
anxiety levels, (after the demanding maths task) the worse their performance. For the higher
working memory individuals (lower in maths anxiety), the higher their salivary cortisol
concentration, the better their performance. In other words, the relation between
physiological response (cortisol concentration) and maths performance, depended on a
participant’s maths anxiety and working memory capacity. For the participants who were low
in maths anxiety, stress boosted their performance (Mattarella-Micke et al., 2011). Ashcraft
56
and Kirk (2001) investigated maths competence and maths anxiety further. It was concluded
that simple whole number arithmetic problems (e.g., 5 + 6, 8 x 5) showed no maths anxiety
effects. However, for the high math anxiety individual there was a decline in performance
with more difficult arithmetic tasks (e.g., mixed fractions), (Ashcraft & Kirk, 2001).
1.6.7 Maths Anxiety and Stereotype Threat
Girls may experience more maths anxiety because of stereotype threat about girls and
mathematics. This can happen when girls are told that they are not as good at mathematics as
are boys. Girls would therefore feel that they are at risk of confirming a negative stereotype
about a group that they belong to (Steele, 1997). However, it is also possible that stereotype
threat does not increase maths anxiety levels and that the reason the girls’ maths performance
suffers is because girls decide to conform to social expectations (Dowker, Sarkar, & Looi,
2016). There are, of course, also environmental and social factors that are equally important
in trying to explain that how maths anxiety relates to maths performance (e.g., parents’ maths
anxiety, parents’ support, teacher’s maths anxiety, and the classroom environment), (Chang
& Beilock, 2016).
1.7 Conclusion
The section above has given summary of the current literature on distributed cognition
and how it can be used for off-loading working memory and improving mathematical
problem-solving performance. Additionally, we presented existing findings of negative
stereotyping about female maths performance and about the role of achievement goals on
working memory. The next section (chapter two) will now move on to presenting the
empirical findings of the thesis.
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Chapter 2: The Effects of Stereotype threat on Girls’ Mathematics Performance: The
Role of Distributed Cognition
Numeracy skills are an important part of the primary and secondary school
curriculum. Therefore, there is a strong emphasis on achievement in mathematics.
Unfortunately, however, some groups may not perform well in mathematics because of
stereotypes, or more specifically, stereotype threat. Stereotype threat is the risk of confirming
a negative stereotype expectation about one’s group. Females and African-Americans are
more likely to underperform in various test-taking situations (e.g., mathematics tests) if a
negative stereotype has been evoked than when it has not (Steele, 1997). The purpose of the
research reported here was to investigate the role of interactivity (distributed cognition) in
defusing the impact of gender stereotype threat on difficult mental arithmetic tasks.
Additionally, the effects of negative stereotyping on working memory and maths anxiety
were also investigated as part of the study.
2.1.1 Stereotype Threat and Working Memory
Women risk being judged based on the negative stereotype of not performing well in
mathematics tests. Stereotype threat can induce task-related thoughts and worries related to it.
Additionally, under stereotype threat there is an expectation for poor maths performance
(Spencer, Steele, & Quinn, 1999). Women underperform on difficult maths tests when told
that there have been gender differences in the past (Spencer et al., 1999). Stereotype threat
may influence maths performance by reducing working memory capacity. Schmader and
Johns (2003) found a lower working memory performance for women and Latinx participants
after receiving a stereotype threat manipulation when compared to the candidates in a control
group who did not receive a stereotype threat manipulation. The authors also conducted a
follow-up test that confirmed that stereotype threat led to poorer maths performance in the
stereotype condition which was mediated by working memory capacity.
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Stereotype threat may also harm maths performance, particularly maths problems that
rely heavily on phonological areas of working memory (modular arithmetic problems, in
horizontal format). In a study conducted by Beilock, Rydell, and McConnell (2007),
participants completed a mixture of horizontal and vertical modular arithmetic tasks at the
same time as a phonological secondary task. The modular arithmetic tasks and the
phonological task used the same pool of working memory resources. When stereotype threat
was made salient, there were performance decrements when the modular arithmetic tasks
were high in working memory demands (e.g., requiring borrowing) and when they were
presented in a horizontal fashion (Beilock et al., 2007).
2.1.2 Maths Anxiety
Maths anxiety is closely related to stereotype threat in that it also has a negative effect
on the overall performance of relatively simple mental arithmetic tasks (DeStefano &
LeFevre, 2004). Maths anxiety and stereotype threat are distinct constructs but they share the
same underlying mechanisms; stereotype threat and maths anxiety compromise the working
memory capacity that people have available for mathematics performance (Maloney,
Schaeffer, & Beilock, 2013).
There has been a great deal of research around the area of maths anxiety since the
publication of the Mathematics Anxiety Rating Scale (MARS) by Richardson and Suinn
(1972). Individuals who are maths anxious are preoccupied with maths fears and bad
experiences in the past and the overall capacity of working memory gets affected. This
preoccupation functions as a secondary task and is particularly resource demanding (Ashcraft
& Krause, 2007). There is poorer performance in mathematics for maths anxious individuals
when the maths problems are more complex, for example when a carry or borrow operation is
used as part of the calculation (Faust et al., 1996). Furthermore, processing efficiency theory
states that cognitive performance is affected by anxiety and worry because working memory
59
resources are concentrated on rehearsing negative thoughts about past failures (Eysenck &
Calvo, 1992).
Maths anxiety is a multidimensional construct and a full list of the causes is still
undetermined (Ashcraft, 2002). This type of anxiety can be defined as a feeling of
apprehension and tension in a mathematical setting (e.g., ordinary arithmetic problems in a
timed task). It is a fear that can also affect overall maths performance. Females normally
score higher than males in maths anxiety tests (Hembree, 1990). One possible reason for the
gender differences in maths anxiety is stereotype threat. It is possible that negative
stereotyping about girls’ mathematics performance can increase maths anxiety and therefore
reduce maths performance. Unfortunately, however, empirical studies do not normally
include a state maths anxiety measure to test this. Another explanation is that maths
performance is reduced when the participants decide to conform to social expectations rather
than because of increased levels of maths anxiety (Dowker et al., 2016).
Individuals who are high in maths anxiety avoid maths as a topic; they choose fewer
elective maths courses in secondary school and university. This avoidance causes individual
with maths anxiety to perform lower than people with less maths anxiety because the former
have had less practice with mathematics. Maths anxious individuals hold negative attitudes
toward maths and have negative self-perceptions about their maths skills and abilities
(Ashcraft, 2002). Another explanation is that it is the thought of solving maths that causes
maths anxiety and not the maths itself. Brain scans have revealed that the area of the brain
that is triggered when someone is highly maths anxious overlaps with the same area of the
brain where bodily harm is registered (bilateral dorso-posterior insula), (Lyons & Beilock,
2012b).
2.1.3 Mental Arithmetic and Working Memory
Working memory has an important role in mental arithmetic and in mathematical
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cognition. When the size of the mathematical operands become larger, the latencies and
errors increase (the problem-size effect), (Zbrodoff & Logan, 2005). It is easier to calculate 2
+ 3 and 4 x 5 than 6 + 7 and 9 x 6. One explanation for this is that people see the larger
mathematical problems less frequently than smaller mathematical problems and therefore
they are not stored in long-term memory as strongly. Furthermore, larger problems are not
simply solved through memory retrieval but based on computational processes that are slower
and rely on working memory resources. Memory retrieval, in contrast, is a quick and almost
an automatic process, making very little demand on working memory resources (Tronsky,
2005).
Problems requiring carrying have much higher error rates and take longer than
problems that do not require carrying (Ashcraft & Kirk, 2001). Addition problems that
require carrying cause additional working memory processing because there is additional
cognitive processing involved. When there are multiple number additions, working memory
must be used to obtain the correct answer and such calculations require interim totals and
executive functioning skills to plan and sequence activities (Ashcraft, 1995). These
calculations require interim totals but also executive function skills to direct the individual’s
attention to decide what to do next. The opportunity to manipulate the external environment
to facilitate more effective thinking encourages different arithmetic strategies. However, any
possible working memory limitations can be compensated by off-loading the process to the
external environment (e.g., by using pen and paper), (Neth & Payne, 2011).
2.1.4 External Representations
External representations are created to assist people to make sense of different
situations and problems. These representations can save internal memory and therefore
enhance a person’s cognitive resources. It might be easier to understand a particular sentence
by drawing a picture of it rather than just thinking internally. And therefore, with the help of
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the drawing the overall cognitive cost of sense making is also reduced. This is closely linked
to computing mental arithmetic tasks. These tasks are completed without the help of pen and
paper, but the cognitive process required can benefit from using these external artefacts
(Kirsh, 2010). These are extra actions that facilitate comprehension. They are complementary
strategies that function as an organizing activity that use the external environment to reduce
the overall cognitive load (e.g., pointing, arranging of the nearby objects, writing things
down, and manipulation of artefacts). In one study, the complementary strategies were
particularly used when people were trying to make sense of origami instructions. The
candidates pointed on the instruction sheet on the different elements. But additionally, the
participants also moved the paper, gestured, and muttered (Kirsh, 2010). The same pattern
was found with people who were not experienced cooks who tried to follow cooking
instructions. The participants kept place with their finger to arrange the ingredients in the
right order, they read the recipe aloud, they asked themselves questions, and they muttered.
Rather than just reading instructions, people used these various types of superfluous actions
to facilitate comprehension. These actions are vital in understanding the instructions and it is
not incidental that they take place (Kirsh, 1995a).
In another study, a simple coin-counting experiment was conducted where it was
observed whether complementary strategies could enhance simple maths performance. The
participants were asked to sum a set of coins as quickly and as accurately as possible. There
were two testing conditions: 1) a no-hands condition where the candidates were not allowed
to do any pointing or moving of their hands or fingers, and 2) a hands condition where they
could point and move their hands. Performance was enhanced with the increased
interactivity. The error rate in the no-hands condition was 68% which decreased to 42% in
the hands condition. Additionally, there was a reduction of the time to complete the task as
well (i.e., an average of 22.50 seconds in the no-hands condition compared to 18.70 seconds
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in the hands condition), (Kirsh, 1995a). People use the space around them (intelligent use of
space) to enhance performance (e.g., enhanced reliability of execution and the number of
different jobs that a human agent can manage to do at the same time). People might not be
aware of this informational and structural structuring at their workplace, but it is something
that happens all the time. This structuring is an important part of the way that humans think,
plan, and behave and is not just something that happens without a purpose (Kirsh, 1995b)
Another study was conducted to test if physical manipulation of letters would help
produce more words in a Scrabble task (Maglio et al., 1999). The key to beneficial interactive
skill was that the benefits of taking physical actions outweigh the costs of doing it. The main
aim of the word game was to create as many words as possible from seven Scrabble letters.
There were two testing conditions: in the first one the participants could manipulate the
letters but in the second one, they could not. More words were produced in the hands
condition that allowed physical manipulation of the letters than in the no-hands condition.
Additionally, there was a significant interaction between the physical manipulation condition
(use of hands) and specific letters chosen. By physically re-arranging the letters, there was
enhanced performance only with one of the two sets of letters; this was the letter string with
which less frequent words could be produced and therefore harder for the participants to
generate. Thus, the word generation process with these letters was augmented by
interactivity, more so than when the Scrabble task involved a set of letters that could produce
more familiar higher frequency words. The participants did not have enough skill in
generating these words because they were less frequent and therefore it was more beneficial
for the subjects to manipulate physically the words in this condition to improve performance
(Maglio et al., 1999).
The manipulation of the external environment increased performance and reduced the
pressure of the internal resources (e.g., working memory) in a word production task. The
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study examined the effects of manipulating the order of different letter tiles in a word
production task in children with developmental dyslexia (Webb & Vallée-Tourangeau, 2009).
As in Maglio et al., (1999), the participants were expected to create words from sequences of
letter tiles in a hands condition and no hands condition. The manipulation of the word tiles
significantly increased the word production of children with dyslexia with an easy set of
letters but not with the hard set. Hence, it was concluded that the manipulation of the external
environment is relative to the task difficulty together with the cognitive abilities of the
candidate (Webb & Vallée-Tourangeau, 2009).
2.1.5 Mental Arithmetic and Interactivity
Studies have examined the different forms of interactivity and how they help the
participants think and create smart solutions in a mathematical context. In one study, Neth
and Payne (2011) asked participants to add coins on a computer screen in two different
conditions (move versus look). The coins could not be physically touched in the move
condition as they were on a computer screen but a drag and drop condition was used instead.
The evidence suggested that the participants moved the coins because they wanted to sort
them by value to put them into clusters rather than just marking them by location and this
clustering then helped them to create smart solutions. Accuracy increased with interactivity
but not speed which contrasts with Kirsh (1995a) who found that elevated interactivity
increased both accuracy and speed. Neth and Payne (2011) reported a non-significant result
regarding latencies which failed to confirm that there might have been a trade-off between
accuracy and speed. In other words, when a participant tries to increase the accuracy of the
calculations, there might be a cost in time (Neth & Payne, 2011).
Both accuracy and speed were increased with the help of using hands (in the pointing
condition) when counting arrays of items ( acting as a simple arithmetic task) (Carlson,
Avraamides, Cary, & Strasberg, 2007). When pointing was not allowed, the candidates used
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nodding instead. Nodding was equally associated with increased accuracy (Carlson et al.,
2007). Thus, gestures do not just have communicative functions, but they might help with
cognitive functions as well. Efficiencies in accuracy and speed can be achieved with the help
of gestures (Goldin-Meadow & Wagner, 2005). There is evidence to suggest that interactivity
can enhance performance and in particular, accuracy and efficiency when it comes to longer
sums involving 11 single-digit numbers (Vallée-Tourangeau, 2013). Thinking efficiency was
studied in a mental arithmetic task using two different testing conditions (static and
interactive) with short and long sums (7 or 11 numbers). Thinking efficiency was measured
as a ratio of accuracy over the time invested to complete the sums. There was a significant
interaction between condition and the set size and therefore it was confirmed that by allowing
the participants to manipulate the tokens the accuracy and efficiency was enhanced.
However, for the shorter sums the subjects performed better without manipulating the tokens
which indicated that performance is relative to the degree of task difficulty and cognitive
ability of the individual (Vallée-Tourangeau, 2013).
Finally, Vallée-Tourangeau, Sirota, and Villejoubert (2013) concluded that there was
a strong negative correlation between maths anxiety and mental arithmetic performance only
in a static condition. There were two conditions used in the study to complete a set of simple
sums: a static condition where the participants were not allowed to use their hands and an
interactive condition where a set of tokens were used to assist with the calculations. The
participants’ working memory capacity was also measured with a computation span task.
There was a statistically significant relationship between maths anxiety and working memory
capacity. Additionally, there was a statistically significant interaction between maths anxiety
level and the level of interactivity. With increased maths anxiety levels, there were fewer
errors in the interactive condition than in the static condition (Vallée-Tourangeau, Sirota, &
Villejoubert, 2013).
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2.2 The Present Experiment
In sum, many studies have looked at the benefits of external representations and how
to use interactivity to increase maths performance (accuracy and latency to solution). This is
particularly important when participants are highly maths-anxious or face negative
stereotyping in a mathematical context. Both constructs can place additional pressures on
working memory. However, if candidates can be given the chance to combine the resources
of their working memory with external resources (e.g., by using pen and paper), it can lead to
a stronger cognitive system that can increase the capacity of working memory resources and
reduce the overall demands of working memory. Although previous investigations have
shown that negative stereotypes about girls’ maths performance can lead to lower maths
performance, there are no studies that have tried to alleviate these effects with the help of
increased interactivity. Additionally, state maths anxiety is not typically measured in a
stereotype threat context. The present study focused on these two aspects. The experiment
reported here explored whether increased interactivity might alleviate the impact of negative
stereotyping about women’s maths performance on difficult mental arithmetic tasks, working
memory, and maths anxiety. Difficult multi-digit mental arithmetic tasks were completed in a
stereotype threat or control condition crossed with interactivity or no interactivity.
In line with previous research, our first hypothesis (Hypothesis 1) was that
interactivity would increase maths performance (accuracies and latencies to solution). Our
second hypothesis (Hypothesis 2) was that negative stereotyping about women’s maths
ability would impair the performance of the difficult mental arithmetic tasks. However, these
mental arithmetic performance decrements could be alleviated with the help of increased
interactivity (e.g., using pen and paper). Third, we hypothesized that there would be a
reduction of working memory capacity when the negative stereotype about women’s maths
performance was made salient. It was also expected that reduced working memory capacity
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would have a causal role in the reduced mental arithmetic performance. In other words, a
reduction in working memory would mediate the effect of stereotype threat on girls’ mental
arithmetic performance (Hypothesis 4). We also hypothesized that that participants would
feel more maths anxious in the stereotype condition than in the control condition (Hypothesis
5). Our final hypothesis (Hypothesis 6) was that the participants who were allowed to utilise
distributed cognition while computing the maths tasks than those who were not allowed
would feel less maths anxious after the experiment.
2.3 Method
2.3.1 Participants
Eighty-four 16-year-old girls participated in this study. The participants were
recruited from secondary schools in the south of England and were year 12 pupils. The
testing took place in an educational setting. After consenting to participate in the study, the
subjects were randomly assigned to one of the experimental conditions (stereotype threat or
control crossed with interactivity or no interactivity). The participants were briefed after the
experiment. A statistical power analysis (GPower, a priori) was performed for sample size
estimation. With an alpha = .05 and power = 0.80, the projected sample needed with the
medium effect size of 0.09 (partial eta squared) was N = 80.
2.3.2 Materials
Arithmetic skill. Basic arithmetic skill (BAS) was measured with the help of 45
simple expressions in a 60-second period (e.g., 10-5). The participants were asked to
complete as many mathematical expressions as they could in 60 seconds.
Mathematics self-efficacy. Mathematics self-efficacy was tested with the help of
Mathematics Self-efficacy and Anxiety Questionnaire (MSEAQ, shortened) by May (2009).
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This test is administered with seven questions (e.g., I believe I am the kind of person who is
good at mathematics) which are measured on scale of 1 to 5 (May, 2009).
Arithmetic task. The participants completed 10 difficult multi-digit mental arithmetic
tasks in primed conditions (stereotype threat or control, crossed with interactivity or no
interactivity). The mental arithmetic tasks included all 4 operands of mathematics (adding,
subtraction, division, and multiplication) and the tasks were up to 3-digit numbers (e.g., 433
+ 288, 93-37, 168/4 and 7x29). Multi-digit arithmetic requires the candidates to maintain
intermediate results as well as managing the carry or borrow demands of the calculation
(DeStefano & LeFevre, 2004). The mental arithmetic tasks were completed in Qualtrics to
measure time (latencies) and accuracy (percentage correct).
Computation span (C-span). Working memory capacity was measured with the help
of a computation-based span test by Salthouse and Babcock (1990). The participants were
asked to read a simple arithmetic expression and announce their answer aloud to the
researcher. Additionally, the subjects were asked to remember the second number of each
equation (e.g., 5+2=?) to be recalled later. The sequences of the simple arithmetic tasks
varied from 1 to 7 tasks (Salthouse & Babcock, 1990). According to Ashcraft and Kirk
(2001), people with maths anxiety have smaller working memory spans. This smaller span
can lead to increased reaction times and errors when mental mathematics is completed at the
same time as a memory load task.
Maths anxiety (state). Maths anxiety was measured with the 23-item Mathematics
Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This test has been
designed to measure maths anxiety levels of UK undergraduates. The test comprises
statements that relate to everyday situations that have a mathematics component (e.g., adding
up a pile of change). The participants are expected to respond by confirming the level of
anxiety that they feel on a 5-point Likert-type scale. This scale ranges from not at all to very
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much. MAS-UK measures three levels of anxiety: maths evaluation anxiety, everyday maths
anxiety, and maths observation anxiety (Hunt et al., 2011).
2.3.3 Procedure
The subjects were asked two weeks before the experimental session to complete a
pre-testing session that comprised of a timed basic arithmetic test and a mathematics self-
efficacy measurement. The data from the two tasks were used as covariates in the main
statistical analysis of the dependent variables due to their known effects on the variables.
Additionally, latencies were used as a covariate in order to avoid any speed-accuracy trade-
off. The participants were tested individually and the pre-testing session lasted approximately
5 minutes. The current study was a 2 (experimental condition: stereotype threat or control) x
2 (level of interactivity: interactivity or no interactivity) between-groups study. In the
stereotype condition, participants were told that the test was diagnostic of mathematical
ability and it had shown gender differences previously. The participants were also told that
girls performed worse than boys in these type of tests (explicit stereotype threat activating
cue). The participants were asked to provide their gender before starting the experimental
session. In the control condition, the participants were advised that the test measured the
capacity of their working memory. All participants were informed that that they could receive
feedback at the end of the experimental session.
Participants assigned to the interactive condition were given the option of using pen
and paper to write down interim totals to complete the mental arithmetic tasks (interactive
condition), whereas those assigned to the control condition did not utilise any external
artefacts. The experimental session started with the difficult mental arithmetic tasks. The
participants were randomly assigned to one of the experimental conditions (stereotype threat
or control crossed with interactivity or no interactivity). The mental arithmetic task was
administered in Qualtrics so that the performance of these tasks (accuracy and time) could be
69
measured. Finally, the experimental session concluded with the computation span test
(working memory) and the maths anxiety measurement. The participants were tested
individually in an educational setting and the testing session took approximately 20 minutes.
The dependent variables of the research reported here were accuracies of the mental
arithmetic tasks, solution latencies, working memory capacity, and maths anxiety. Participant
accuracy was assessed with the help of Qualtrics where the mental arithmetic tasks were
computed by both participant groups (interactive or non-interactive). This allowed us to
record accuracy and time to complete the mental arithmetic tasks. Latency to solution was
calculated based on the page submit function of Qualtrics (the time from first click to the time
of the final click). Working memory was assessed by the performance of the simple mental
arithmetic expressions (e.g., 10-5) that were computed at the same time with a memory load
task (second digit of the expression). Finally, measures of participants’ level of maths anxiety
were obtained from the questionnaire which is described in the materials section.
2.4 Results
2.4.1 Data Analysis Plan
To investigate the hypotheses, four separate 2 (experimental condition: stereotype
threat or control) x 2 (level of interactivity: interactivity or no interactivity) between-groups
analysis of covariance (ANCOVA) were conducted with percentage correct, latencies,
working memory (computation span), and maths anxiety as dependent variables. The
covariates were basic arithmetic skills and mathematics self-efficacy (measured during the
pre-testing phase) and were chosen specifically because of their known effects on the
dependent variables. The mean values and standard deviations of these variables can be seen
in Table 1. It is of importance to mention here that whilst it was only the mental arithmetic
tasks that were computed in the interactive condition, the study expected to see carry-on
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effects of both stereotype threat and interactivity on working memory capacity and maths
anxiety that were measured after the mental arithmetic tasks.
A detailed correlational analysis was conducted for all of the four dependent variables
across the different experimental conditions. Additionally, if there was an effect of stereotype
threat on maths performance, then a mediation analysis would be conducted (to confirm that
a reduction in working memory capacity would mediate the effect of stereotype threat on
girls’ maths performance). Before the actual statistical analysis was conducted, it was
reported that there were no group differences between the stereotype-threatened participants
and the participants in the control group condition on the basic arithmetic skills (F < 1) that
was measured during the pre-testing phase. It was therefore confirmed that the groups did not
differ in their ability to complete mental arithmetic tasks under timed conditions.
Additionally, there were no group differences on the mathematics self-efficacy measure
either (F < 1) confirming that the participants did not differ in their levels of mathematic self-
efficacy.
2.4.2 Percentage Correct (Solution Accuracy)
To test the first and second hypotheses, the percentage correct of the mental
arithmetic tasks was examined. The mental arithmetic performance was elevated with
distributed cognition. Table 2 shows the performance of the mental arithmetic tasks in the
interactive condition (M = 74.80%, SE = 4.20%) and in the non-interactive condition (M =
43.20%, SE = 4.20%). A 2 (stereotype threat or control) x 2 (interactivity or control)
between-groups analysis of covariance (ANCOVA) was conducted. The scores from the
basic arithmetic skills test (pre-test) were used as a covariate. The covariate, basic arithmetic
skills, was significantly related to the percentage correct, F(1, 78) = 23.23, p < .001, ŋp2 = .23.
Additionally, the covariate (latencies) was significantly related to the percentage correct, F(1,
78) = 7.90, p = .006, ŋp2 = .09. Confirming the first hypothesis, the main effect of interactivity
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was significant, F(1, 78) = 64.34, p < .001, ŋp2 = .45. The main effect of experimental
condition was not significant (F < 1) failing to support the second hypothesis. Finally, the
interaction between the experimental condition and level of interactivity was not significant
as F < 1.
Table 1
Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data)
M SD
Basic arithmetic skills 23.12 8.87
Maths self-efficacy 20.43 5.31
Note. Participants were not primed to complete the pre-testing tests. The pre-testing was completed two weeks
before the actual experiment. The pre-testing comprised of a basic arithmetic skills test and a mathematics self-
efficacy questionnaire. The scale for basic arithmetic skills is from 0 to 45 and the scale for mathematics self-
efficacy is from 0 to 35.
Table 2
Descriptive Statistics: Means and Standard Errors (Post-Testing Data)
STI STNI NSTI NSTNI
n = 21 n = 22 n = 19 n = 22
Performance scores M SE M SE M SE M SE
Percentage correct 78.40 4.20 40.30 4.30 74.80 4.20 43.20 4.20
Latencies (seconds) 32.83 2.89 38.72 2.91 32.33 2.89 39.30 2.89
Working memory 21.22 1.28 19.62 1.29 24.62 1.28 21.63 1.28
Mathematics anxiety 57.24 3.01 60.73 3.00 64.00 3.00 57.84 3.00
Note. STI = stereotype threat, interactive; STNI = stereotype threat, non-interactive;
NSTI = non-stereotype threat, interactive; NSTNI = non-stereotype threat, non-interactive.
The scale for the working memory measure is 0 to 56 and the scale for mathematics anxiety is from 0 to 115.
Only the mental arithmetic tasks were completed in the interactive or non-interactive conditions.
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2.4.3 Latency to Solution
We next looked at the latency to solution of the difficult mental arithmetic tasks to
test the first and the second hypotheses. Clearly, interacting with physical resources allowed
participants to complete the mental arithmetic tasks more quickly. Table 2 shows the
performance of the girls in the interactive condition (M = 32.33 s, SE = 2.89 s) and in the
non-interactive condition (M = 39.30 s, SE = 2.89 s). A 2 (stereotype threat or control) x 2
(interactivity or control) between-groups analysis of covariance (ANCOVA) was conducted.
The scores from the basic arithmetic skills test (pre-test) were used as a covariate. The
covariate, basic arithmetic skills, was significantly related to latency to solution, F(1, 79) =
18.34, p < .001, ŋp2 = .19. There was a main effect of interactivity, F(2, 79) = 4.97, p = .03, ŋp
2
= .06 supporting the first hypothesis. There was no effect of experimental condition (F < 1)
which failed to support the second hypothesis. Finally, the interaction between the
experimental condition and level of interactivity was not significant as F < 1.
2.4.4 Working Memory
We next examined the effects of negative stereotyping on working memory
(third hypothesis). Table 2 shows the performance of participants in the non-stereotype
condition (M = 21.63, SE = 1.28) and in the stereotype condition (M = 19.62, SE = 1.29). A 2
(stereotype threat or control) x 2 (interactivity or control) between-groups analysis of
covariance (ANCOVA) was conducted. The scores from the basic arithmetic skills test (pre-
test) were used as a covariate. The covariate, basic arithmetic skills, was significantly related
to working memory, F(1, 79) = 27.53, p < .001, ŋp2 = .26. There was a main effect of
experimental condition, F(2, 79) = 4.49, p = .04, ŋp2 = .05 confirming the third hypothesis.
There was no main effect of interactivity as F < 1. Finally, the interaction between the
experimental condition and level of interactivity was not significant as F < 1.
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Mediation analysis for the fourth hypothesis could not be conducted as there was no
statistically significant effect of stereotype threat on the mental arithmetic performance.
2.4.5 Mathematics Anxiety (State)
To test the fifth hypothesis, a 2 (stereotype threat or control) x 2 (interactivity or
control) between-groups analysis of covariance (ANCOVA) was conducted for maths
anxiety. The scores from the maths self-efficacy measure were used as a covariate to control
for individual differences. The covariate, maths self-efficacy, was significantly related to
maths anxiety, F(1, 79) = 7.20, p = .009, ŋp2 = .08. However, there was no significant effect of
experimental condition on maths anxiety (F < 1) failing to confirm the fifth hypothesis. There
was no effect of interactivity on maths anxiety (F < 1) failing to support the final hypothesis.
Finally, the interaction between the experimental condition and level of interactivity was not
significant as F < 1.
2.4.6 Correlational Analysis
A correlational analysis was conducted on the four primary dependent variables
(percentage correct, solution latencies, working memory, and mathematics anxiety) across the
experimental conditions (stereotype threat or control, crossed with interactivity or no
interactivity). As expected, working memory capacity was a strong predictor of mental
arithmetic performance in the stereotype threat condition without interactivity (Table 4),
r(84) = .64, p = .01 confirming existing empirical findings (Allen & Vallée-Tourangeau,
2016; Vallée-Tourangeau, 2013). However, when the stereotype-threatened participants were
given the opportunity to reconfigure the environment (with the help of pen and paper) this
same pattern could not be found anymore (Table 3). The potential working memory
limitations were compensated by externalizing the internal cognitive process to the outside
world. Additionally, there was a strong negative correlation between working memory
capacity, and maths anxiety (Table 4), r(84) = - .46, p = .03 in the stereotype threat condition
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without interactivity confirming existing literature (Ashcraft, 2002). This same pattern did
not exist in the interactive condition as interactivity allowed the individual to rely on the
extended working memory resources. Additionally, there was a strong positive correlation
between working memory capacity and accuracy in the non-interactive condition (without
stereotype threat), r(84) = .56, p = .01 (Table 6). However, this same pattern could not be
found in the interactive condition (Table 5). When the coupling of internal and external
resources was not allowed both the stereotype-threatened individuals and the control group
participants relied solely on their working memory resources. Working memory predicted the
mental arithmetic performance of the participants in both participant groups but more so for
the stereotype-threatened individuals. This same pattern could not be found in the interactive
condition. Interactivity provided the role of working memory by reducing the demands on the
working memory resources and allowing it to be augmented.
Table 3
Correlation Matrix for the Performance Measures (Percentage Correct, Latencies, Working
Memory, and Mathematics Anxiety) in the Stereotype Threat, Interactive Condition
1 2 3 4
% Correct Latencies WM MAS
1 1 .01 .22 -.03
2 1 -.12 .27
3 1 -.10
4 1
Note. % Correct = accuracy in the mental arithmetic tasks in percentage; Latencies = the time it took for the
participants to complete the task in seconds; WM = Working memory measurement (computation span); MAS =
maths anxiety measure.
** Correlation is significant at the 0.01 level, * Correlation is significant at the 0.05 level.
***The Bonferroni cut-off is 0.0125.
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Table 4
Correlation Matrix for the Performance Measures (Percentage Correct, Latencies, Working
Memory, and Mathematics Anxiety) in the Stereotype Threat, Non-Interactive Condition
1 2 3 4
% Correct Latencies WM MAS
1 1 -.09 .64** -.39
2 1 -.40 -.13
3 1 -.46*
4 1
Note. % Correct = accuracy in the mental arithmetic tasks in percentage; Latencies = the time it took for the
participants to complete the task in seconds; WM = Working memory measurement (computation span); MAS =
maths anxiety measure.
** Correlation is significant at the 0.01 level, * Correlation is significant at the 0.05 level.
***The Bonferroni cut-off is 0.0125.
Table 5
Correlation Matrix for the Performance Measures (Percentage Correct, Latencies, Working
Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Interactive Condition
1 2 3 4
% Correct Latencies WM MAS
1 1 -.14 .33 -.40
2 1 -.13 .26
3 1 .03
4 1
Note. % Correct = accuracy in the mental arithmetic tasks in percentage; Latencies = the time it took for the
participants to complete the task in seconds; WM = Working memory measurement (computation span); MAS =
maths anxiety measure.
** Correlation is significant at the 0.01 level, * Correlation is significant at the 0.05 level.
The Bonferroni cut-off is 0.0125.
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Table 6
Correlation Matrix for the Performance Measures (Percentage Correct, Latencies, Working
Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Non-Interactive
Condition
1 2 3 4
% Correct Latencies WM MAS
1 1 .26 .56** -.40
2 1 -.13 .07
3 1 -.26
4 1
Note. % Correct = accuracy in the mental arithmetic tasks in percentage; Latencies = the time it took for the
participants to complete the task in seconds; WM = Working memory measurement (computation span); MAS =
maths anxiety measure.
** Correlation is significant at the 0.01 level, * Correlation is significant at the 0.05 level.
***The Bonferroni cut-off is 0.0125.
2.5 Discussion
The current study explored the cognitive mechanisms governing stereotype threat in a
mathematical context. In this study, girls completed difficult multi-digit mental arithmetic
tasks in stereotype threat or control condition, crossed with interactivity or no interactivity.
The primary dependent variables were performance on the mental arithmetic test (accuracy
and latencies), working memory capacity, and maths anxiety. Accuracy was substantially
improved with elevated interactivity confirming our first hypothesis. The participants who
were given the opportunity to externalize their internal cognitive process, performed better
and were quicker than the participants in the non-interactive condition. Clearly, recruiting
artefacts (e.g., using pen and paper) can transform mental arithmetic performance. Past
research findings by Kirsh (1995a) and Carlson et al., (2007) have confirmed that elevated
interactivity increased both accuracy and speed to come to the solution. Clearly, there was no
cost in time to improve accuracies. The increased speed of the current study contrasts with
Neth and Payne (2011) study which failed to confirm a significant result regarding speed. It
77
failed to confirm that there might be a trade-off between accuracy and speed. When a
participant tries to improve the accuracy of the calculations, there might be a cost in time.
There were no significant effects of stereotype threat on maths performance (accuracies and
latencies) failing to confirm our second hypothesis set in the introduction. This finding is in
contrast with existing studies that have confirmed that negative stereotyping impairs maths
performance (Schmader & Johns, 2003; Beilock et al., 2007).
However, there was a performance decrement in the working memory performance
for the participants in the stereotype condition confirming the third hypothesis. According to
Schmader and Johns (2003), stereotype threat reduces the capacity of working memory
available to complete mathematical computations (e.g., mental arithmetic tasks). In their
study, stereotype threat led to poorer maths performance for women and Latinx participants
in the stereotype condition; this impaired performance was mediated by working memory
capacity. Stereotype threat can also co-opt working memory resources, particularly verbal
resources (Beilock et al., 2007). Additionally, the detailed correlation analysis of the current
study revealed that working memory capacity was a strong predictor of mental arithmetic
performance in both conditions (stereotype threat or control) and in particular when
stereotype threat was made salient. The lack of this correlational pattern in the interactive
condition, allowed us to draw the conclusion that distributed cognition allowed the
participant to extend their working memory capacity and that is why this correlation could
not be seen in the interactive condition.
However, the current study failed to support the causal role of working memory in
reducing maths performance under stereotype threat (Hypothesis 4). One possible reason for
this is that the candidates of the current investigation were 16-year-old girls who had recently
completed the GCSE assessments (General Certificate of Secondary Education, British)
where mathematics is one of the compulsory subjects. Mental arithmetic skills play an
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important role in the mathematics part of the examination. The students had the required skill
and experience to manage the type of mental arithmetic tasks that were utilised in the current
experiment and were not affected by the negative stereotyping while completing these tasks,
unlike the working memory assessment that was used. The working memory test did not
follow the expected format of testing and the candidates felt the extra burden of not being
expected to succeed. Therefore, there was a performance decrement in the working memory
performance but not a significant effect on the maths performance as measured by accuracies
and latencies.
Finally, maths anxiety was not affected by the manipulation of the experimental
condition (stereotype threat or control). In other words, stereotype threat did not increase the
participants’ feeling of being more maths anxious, failing to confirm Hypothesis 5. It is
evident that the participants conformed to social expectations about their maths abilities and
thus their working memory capacity was reduced. However, this reduction in working
memory capacity was not because of increased levels of maths anxiety. It is possible that
there were no significant statistical effects of stereotype threat on maths anxiety because the
maths anxiety measure that was used comprised of statements that related to everyday
situations that have a mathematics component rather than the actual task in hand.
Additionally, the research reported here did not find any carry-over effects of interactivity on
maths anxiety. The participants who interacted with physical resources while completing the
mental arithmetic tasks, were not less maths anxious at the end of the experiment compared
to their non-interactive counterparts. It is possible that these types of carry-on effects of
interactivity can only be felt immediately after the interactive task. It is also possible that self-
reported maths anxiety measures like the one used as part of this experiment do not
successfully detect correct anxiety levels and in particular when interactivity has been
utilised. Past interactivity research has not measured state maths anxiety.
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2.6 Limitations
Whilst the findings of the research reported here were encouraging, there were
limitations to the study. This study employed only 10 difficult mental arithmetic tasks and it
is possible that it was not enough to demonstrate any statistically significant findings. The
current research only employed one type of maths task and it is clear that the study would
have benefited in having additional maths tasks in different formats in order to compare the
effects of stereotype threat on mental arithmetic performance. This study also utilised a task
that was in a known format to the participants. By being in a known format, it could be
argued that it was not measuring what it was supposed to measure as the students were more
automated with these types of mental arithmetic tasks. Whilst the level of working memory
processing was not measured as part of this investigation, it was evident that the automation
of completing the tasks, allowed the participants to rely less on the working memory
resources than if they had been in a format that required deeper processing. Additionally, the
current study only utilised one level of interactivity (the use of pen and paper). Past empirical
studies have employed various forms of interactivity (e.g., use of pointing and adding up
wooden tokens) to further explore the positive effects of distributed cognition on maths
performance. Finally, it is possible that the priming that was given to the control participants
(when told that the test was a measure of working memory capacity) triggered performance-
approach goals. It is possible that the participants felt pressure to perform well in comparison
to others doing the same test.
2.7 Future Studies
In summary, this study has provided evidence that interactivity enhances maths
performance and particularly accuracies and latency to solution. Additionally, it has been
shown that working memory resources are compromised from stereotype threat for 16-year-
old girls in an educational setting. In other words, an increase in negative comments about
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girls’ maths performance caused the participants in the stereotype threat condition to have a
lower working memory performance compared to the control participants. However, there
was no causal role of working memory in reduced maths performance under stereotype
threat. Therefore, it is suggested that for future studies, modular arithmetic tasks should be
used as the mental arithmetic problems (e.g., 5 mod 3 ≡ 2 which means 2 is the remainder
when you divide 5 by 3). Modular arithmetic tasks rely heavily on working memory
resources but are in a format not easily recognised by participants and therefore would
require different processing skills than the ones that were used in the current experiment. And
it is therefore anticipated that there will be a reduction of maths performance in the stereotype
condition and this performance decrement will be mediated by reduced working memory
performance. The mental arithmetic tasks of the current study were in a format that was
easily recognized by the candidates. Future studies would also benefit from measuring trait
maths anxiety as part of the pre-testing phase to be able to use it as a covariate when the state
maths anxiety analysis is conducted. This would be a more accurate analysis of the maths
anxiety levels of the participant at the end of the experiment.
Chapter 3: The Effects of Stereotype threat on Female University Students’ Maths
Performance: The Role of Distributed Cognition
Previous research (Study 1) indicated that there were no mental arithmetic
performance decrements when stereotype threat about girls’ and maths was made salient to
16-year-old girls. In other words, stereotype threat about girls’ maths performance did not
cause the participants to perform worse in the difficult mental arithmetic tasks compared to a
non-stereotype threat condition. It was assumed that the students had the required skill and
experience to deal with the type of mental arithmetic tasks that were utilised and were not
affected by the negative stereotyping while completing the tasks. However, negative
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stereotyping caused working memory performance to be lower than when negative
stereotyping was not made salient without reduced mental maths performance. It is possible
that the working memory test did not follow the expected format of testing and therefore it
was suggested that the participants felt the extra burden of not being expected to succeed
(situation-induced stress). It was therefore plausible to suggest that the combination of not
recognising the format of the working memory measure and the additional stress caused by
the stereotype threat caused a working memory performance drop. Finally, interactivity
elevated the mental arithmetic performance (percentage correct and solution latency) when
stereotype threat about girls’ maths performance was not present (control condition).
Based on the findings of the first study, it was concluded that the format of the mental
arithmetic tasks should be in a format not easily recognisable by the participants. Modular
arithmetic tasks were suggested because they are based on common mathematical procedures,
but are in an uncommon format. Thus, previous task experience is controlled because most
students have not seen the format before (Beilock & Carr, 2005). The participants need to
learn the required steps to complete the tasks first and to store this information in working
memory.
Finally, the aim of the study reported here (Study 2) was to look at the effects of
negative gender related stereotypes (female maths performance) on mental arithmetic
performance (known format) and modular arithmetic performance that was in a novel format
(low WM load and high WM load), and working memory. There were two levels of difficulty
of modular arithmetic tasks to further explore the impact of stereotype threat on maths
performance. We further explored whether the negative effects on the mental arithmetic
performance and modular arithmetic performance could be mitigated with the help of
distributed cognition. Additionally, the current study investigated whether there were any
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carry-over effects of stereotype threat and interactivity on maths anxiety that was measured at
the end of the experiment.
3.1.1 Maths Anxiety and Interactivity
Maths anxious individuals’ thoughts are dominated by fears of mathematical tasks
and how to compute them successfully; this can have a causal effect on the individual’s
overall working memory capacity. This preoccupation functions as a secondary task (dual
task set-up) that is heavily working memory resource demanding. Maths anxiety is
significantly correlated with working memory capacity. When there is an increase of maths
anxiety levels, there is a drop on the working memory capacity (Ashcraft, 2002). Due to the
additional worries, the highly maths-anxious individual is faced with two simultaneous tasks:
the worry about the successful completion of the task and the actual task requirement
(including possible borrowing or carrying over), (Ashcraft & Krause, 2007). Higher levels of
maths anxiety causes a transitory disruption of working memory, causing diminished working
memory resources to deal with maths tasks. This reduced working memory capacity is an on-
line effect that disrupts information processing in maths tasks. This reduced level of working
memory capacity of high maths anxious individuals is partially responsible for the maths
performance decrements. (Ashcraft & Kirk, 2001). However, the benefits of interactivity for
the highly maths anxious individual are well established (Allen & Vallée-Tourangeau, 2016;
Vallée-Tourangeau et al., 2016). When a participant is interacting with the external
environment it allows the individual to access greater cognitive resources which in turn can
mitigate the effect of maths anxiety on maths performance. However, what is less clear is
whether maths anxiety itself is mitigated in the interactive condition. The study reported here
aims to answer this question by measuring maths anxiety at the end of the experiment.
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3.2 Pilot Study
Before the actual experiment, a pilot study with ten participants was conducted to
further understand the right difficulty level of modular arithmetic tasks for the second study.
Clearly, attempts to determine the effectiveness of externalising the internal cognitive process
to the outside world in helping individuals to solve mathematical problems must be
relativized to the cognitive abilities of the individual and to the difficulty of the task (Vallée-
Tourangeau & Wrightman, 2010). The original Beilock and Carr (2005) study employed up
to two-digit modular arithmetic tasks because all of the participants were required to
complete the experiment without any external artefacts: the low load tasks used single-digit
numbers and high load tasks employed two-digit numbers (Beilock & Carr, 2005). The
experiment reported here allowed half of the participants to utilise interactivity (i.e., to use
pen and paper) to reach a solution and therefore the tasks needed to be at the right difficulty
level for the participants to make use of this option. Kirsh (2010) reported that interactivity
changes the cost structure of the required cognitive process and therefore people will do
whatever is easier to perform the task. If the task is too easy, the participant will not feel the
need to externalize the process to complete the tasks. Instead, the participant will work out
the answer by relying on their internal cognitive resources only (Kirsh, 2010).
3.3 Method
3.3.1 Participants
Ten female undergraduate psychology students from the University of Surrey (M =
19.30, SD = 0.95) participated in this study for exchange of SONA credits. After consenting
to participate in the study, the subjects were randomly assigned to one of the experimental
conditions (stereotype threat or control crossed with interactivity or no interactivity). The
experimental sessions (both pre-testing and post-testing) were conducted in a psychology lab
at the University of the Surrey.
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3.3.2 Material and Measures
Arithmetic skill. Basic arithmetic skill (BAS) was measured with the help of 45
simple expressions in a 60-second period (e.g., 10-5). The participants were asked to
complete as many expressions as they could in 60 seconds.
Mathematics self-efficacy. Mathematics self-efficacy was tested with the help of
Mathematics Self-efficacy and Anxiety Questionnaire (MSEAQ, shortened) by May (2009).
This test is administered with seven questions (e.g., “I believe I am the kind of person who is
good at mathematics”) which are measured on scale of 1-5 (May, 2009).
Mathematics anxiety (trait). Maths anxiety was measured with the 23-item
Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). The test
comprises statements that relate to everyday situations that have a mathematics component
(e.g., adding up a pile of change). The participants are expected to respond by confirming the
level of anxiety that they feel on a 5-point Likert-type scale. This scale ranges from not at all
to very much. MAS-UK measures three levels of anxiety: maths evaluation anxiety, everyday
maths anxiety and maths observation anxiety (Hunt et al., 2011). This measurement and the
two previous ones constituted the pre-test.
Computation span. Working memory capacity was measured with the help of a
computation-based span test by Salthouse and Babcock (1990). The participants were asked
to read a simple arithmetic expression (e.g., 5 + 2 = ?, 9 – 6 = ?) and announce their answer
aloud to the researcher (7, 3). Additionally, the participants were asked to remember the
second number of each equation to be recalled later (2, 6). The sequences of the simple
arithmetic tasks varied from 1 to 7 tasks. The computation span task requires both on-line
processing for the problem solution which is simultaneous with storage and maintenance of
information in working memory for serial recall (Salthouse & Babcock, 1990). According to
Ashcraft and Kirk (2001), people with maths anxiety have smaller working memory spans.
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This smaller span can lead to increased reaction times and errors when mental mathematics is
completed at the same time as a memory load task (Ashcraft & Kirk, 2001).
Arithmetic task. The arithmetic task of the pilot study consisted of 30 modular
arithmetic tasks that relied heavily on working memory resources. The tasks were adapted
from Beilock and Carr, (2005) original study. The purpose of these type of modular
arithmetic tasks is to judge the validity of maths problems like 61 ≡ 18 (mod 4). The middle
number is subtracted from the first number (i.e., 61-18) and then the difference is divided by
4. If the answer is a whole number the maths problem is true (Beilock & Carr, 2005).
Modular arithmetic tasks as laboratory tasks are advantageous because although the tasks are
based on common mathematical procedures, most students have not seen them before and
therefore previous task experience is controlled.
The participants in the pilot study solved modular arithmetic problems that varied as a
function of the demands on the working memory (low WM demand or high WM demand).
Fifteen problems were low-demand problems where single-digit numbers were used [e.g., 8 ≡
2 (mod 2)], while the remaining 15 problems were high-demand problems where two-digit
numbers were utilised [e.g., 32 ≡ 8 (mod 6)]. It was assumed that if situation-induced
pressure (e.g., stereotype threat) impacted working memory capacity, then mental arithmetic
performance should be more likely to decline on high-demanding problems in comparison to
low-demanding problems. The dependent variable of the modular arithmetic tasks was the
number of true responses.
The modular arithmetic tasks of the pilot study were presented in a horizontal format. The
horizontal presentation of the maths problems is more reliant on phonological resources (the
verbal resources) because individuals maintain the required problem steps in their memory
verbally. The anxiety of stereotype threat put extra burden on the working memory
(phonological loop, in particular), and together with the horizontally presented maths
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problems there can be maths performance decrements under stereotype threat (Beilock et al.,
2007). The mental arithmetic tasks were completed in Qualtrics to measure time (latencies)
and accuracy (percentage correct). The mental arithmetic tasks that were used as part of the
first study, were not utilised as part of the pilot study.
Maths anxiety (state). Maths anxiety was measured with the 23-item Mathematics
Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). The state maths
anxiety was measured with the same questions as the trait anxiety measure, but this time the
questionnaire referred to the current time (now), (Hunt et al., 2011). This measure and the
previous two measures constituted the post-test.
3.3.3 Procedure
There was a pretesting sessions two weeks before the actual experiment comprising of
basic arithmetic skills test, maths-self efficacy questionnaire, and maths anxiety (trait)
measurement. During the actual experiment, the participants started with the computation
span which was followed by the modular arithmetic tasks. This was followed by the state
maths anxiety measurement.
3.4 Pilot Study Findings
We did not conduct any statistical analysis of the pilot study data, only qualitative
observations were made during the experiment. The main purpose of the pilot study was to
investigate the right difficulty level of the modular arithmetic tasks for the interactive option
to work. If the task is too easy, there are no benefits of combining internal and external
resources (Kirsh, 2010). The qualitative observations were done by monitoring the
participants while they were completing the maths tasks. We had predicted that there would
be limited benefits in employing interactivity with the low WM load tasks due to these tasks
utilising single-digit numbers and therefore there would be limited use of borrowing and
carrying that tax working memory. It was therefore assumed that these types of tasks would
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be quicker and easier to be computed in the head only. The behaviour of the pilot participants
was observed during the experiment and particularly whether the participants utilised the pen
and paper option to compute the tasks. Some of the pilot study participants did not make use
of the interactive option when working on the tasks. Perhaps the external artefacts that were
offered to the participants were in their way and distracting the performance. This was
particularly evident during the single-digit tasks. Hence, the pilot study concluded that the
second study would require a higher level of difficulty of the modular arithmetic tasks that
was employed in the original Beilock and Carr (2005) study.
Whilst it was not directly measured, it seemed that the participants did not feel the
need to employ the interactive option to complete the tasks. It was assumed that they had the
required skill and the internal cognitive resources e to compute the tasks without the
externalising of the internal cognitive process. Similar findings have been made by Vallée-
Tourangeau and Wrightman (2010) who examined these factors in a simple word production
task utilizing letter tiles. Two sets of letter tiles were used with differing word production
difficulty. The participants were told to produce as many words as they could from the letter
tiles. There was an interactive condition where the participants were encouraged to touch and
rearrange the tiles when producing words. In the non-interactive condition, the participants
could not point to the tiles or interact with them in any way. There was also a distinction
between a low and high verbal fluency group as a function of the participants’ score on the
Thurstone word fluency test. For the high-fluency participants the word production
performance was not enhanced with the interaction of the letter tiles. However, in the low
verbal fluency group, letter rearrangement elevated the word production performance (both in
the hard and easy set of tiles). The benefits of the external restructuring of the letter tiles was
more beneficial for the participant with lower cognitive abilities and with a more taxing task
(Vallée-Tourangeau & Wrightman, 2010). Based on the findings of the pilot study, it was
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suggested that up to three-digit numbers would be employed in the high WM load to better
allow for the benefits of increased interactivity in the actual experiment. The low WM load
would consist of numbers that were up to two-digits and the high load tasks would use
numbers that were up to three-digits.
3.5 The Current Study
Based on the findings of the first study, the first hypothesis for the second experiment
(Hypothesis 1) was that the externalising of the internal cognitive process to the outside
world by using pen and paper would increase maths performance in terms of accuracy
(percentage correct) of the mental arithmetic tasks and modular arithmetic tasks (high WM
load and low WM load). Furthermore, it was predicted that increased accuracy would be
stronger for the high WM load modular arithmetic tasks than the low WM tasks. The second
hypothesis (Hypothesis 2) stated that interactivity would reduce the solution latencies
(allowing the participant to complete the tasks faster) for the mental arithmetic tasks and the
modular arithmetic tasks (low WM load and high WM load) as per findings of the Study 1.
The third hypothesis (Hypothesis 3) was that negative stereotyping about women’s maths
ability would impair the performance of the modular arithmetic tasks and not the mental
arithmetic task performance as per findings of the Experiment 1. However, these modular
arithmetic performance decrements were expected to be alleviated with the help of increased
interactivity (e.g., using pen and paper), (Hypothesis 4) as per existing empirical findings
(Vallée-Tourangeau, 2013). Additionally, it was expected that interactivity would be most
beneficial for the high WM load modular arithmetic tasks. We hypothesized that there would
be a reduction of working memory capacity when the negative stereotype about women’s
maths performance was made salient (Hypothesis 5) as per existing findings by Schmader
and Johns (2003). It was also expected that the reduced working memory capacity would
have a causal role in the reduced modular arithmetic performance (Hypothesis 6).
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Additionally, we predicted that interactivity would reduce the participants’ state maths
anxiety levels (Hypothesis 7) as per existing findings on interactivity allowing the maths
anxious individuals to improve their maths performance (Allen & Vallée-Tourangeau, 2016;
Vallée-Tourangeau et al., 2016). We expected the participants to feel more maths anxious
(state) in the stereotype condition than in the control condition when tested at the end of the
experimental session (Hypothesis 8). Finally, our final hypothesis was that there would be a
two-way interaction in that interactivity would reduce the levels of maths anxiety (state) in
the stereotype threat condition (Hypothesis 9).
3.6 Method
3.6.1 Participants
Ninety-six female undergraduate psychology students from the University of Surrey
(M = 23.70 SD = 7.60) participated in this study for exchange of (SONA) credits. After
consenting to participate in the study, the subjects were randomly assigned to one of the
experimental conditions (stereotype threat or control crossed with interactivity or no
interactivity). Both the pre-testing and post-testing took place in a psychology lab, at the
University of Surrey. A statistical power analysis (GPower, a priori) was performed for
sample size estimation. With an alpha = .05 and power = 0.80, the projected sample needed
with the medium effect size of 0.09 (partial eta squared) was N = 80.
3.6.2 Material and Measures
Arithmetic skill. Basic arithmetic skill (BAS) was measured with the help of 45
simple expressions in a 60-second period (e.g., 10-5).
Mathematics self-efficacy. Mathematics self-efficacy was tested with the help of
Mathematics Self-efficacy and Anxiety Questionnaire (MSEAQ, shortened) by May (2009).
Mathematics anxiety (trait). Maths anxiety was measured with the 23-item
Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This
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measurement and the two previous ones constituted the pre-test which were identical with the
pre-testing measures of the pilot study.
Computation span. Working memory capacity was measured with the help of a
computation-based span test by Salthouse and Babcock (1990). The participants were asked
to read a simple arithmetic expression (e.g., 5 + 2 = ?, 9 – 6 = ?) and announce their answer
aloud to the researcher (7, 3). Additionally, the participants were asked to remember the
second number of each equation to be recalled later (2, 6). The sequences of the simple
arithmetic tasks varied from 1 to 7 tasks. This task was identical with the pilot study.
Arithmetic tasks. The participants completed two sets of mental arithmetic tasks.
The first one consisted of 10 difficult multi-digit mental arithmetic tasks in primed conditions
(stereotype threat or control, crossed with interactivity or no interactivity). The first task was
identical to the task used in the Study 1. The mental arithmetic tasks included all 4 operands
of mathematics (adding, subtraction, division and multiplication) and the tasks were up to 3-
digit numbers (e.g., 433 + 288, 93-37, 168/4 and 7x29). Multi-digit arithmetic requires the
candidates to maintain intermediate results as well as managing the carry or borrow demands
of the calculation (DeStefano & LeFevre, 2004).
The second mental arithmetic task consisted of modular arithmetic tasks (30 tasks, in
primed conditions) that relied heavily on working memory resources, adapted from Beilock
and Carr (2005). The participants of the current study had to solve modular arithmetic
problems that varied as a function of the demands on working memory (low WM demand or
high WM demand). Fifteen problems were low-demand problems where two-digit numbers
that required a carry were used [e.g., 83 ≡ 27 (mod 8)] while the remaining 15 problems were
high-demand problems where up to three-digit numbers requiring a carry were utilised [e.g.,
135 ≡ 69 (mod 6)]. If situation-induced pressure impacts working memory capacity, then
modular arithmetic performance should be more likely to decline on high-demanding
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problems [e.g., 135 = 69 (mod 6)] in comparison to low-demanding problems [e.g., 83 ≡ 27
(mod 8)] of the present study.
Like the pilot study, the modular arithmetic tasks of the current experiment were
presented in a horizontal format (rather than vertical format). The horizontal presentation of
these types of problems is more reliant on phonological resources (the verbal resources)
because the required problem steps are stored in the memory verbally. The distractive
thoughts of stereotype threat can put extra burden on the working memory (phonological
loop, in particular), and together with the horizontally presented maths problems there can be
depleted maths performance under stereotype threat (Beilock et al., 2007).
Maths anxiety (state). Maths anxiety was measured with the 23-item Mathematics
Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This questionnaire
(which was identical with the pilot study) and the two previous tasks constituted the post-test.
3.6.3 Procedure
Two weeks before the experimental session participants completed a pre-testing
session that comprised of the basic arithmetic test, Mathematics Self-Efficacy Questionnaire,
and Mathematics Anxiety Scale (trait). The participants were tested individually in a
psychology testing lab for 5 minutes. The participants were randomly assigned to one of the
experimental conditions (stereotype threat or control crossed with interactivity or no
interactivity). When the actual experimental session started, the participants in the stereotype
threat condition were advised that the test was diagnostic of their mathematical ability and
that the tests had shown gender differences previously. The participants were also told that
girls performed worse than boys in these type of tests (explicit stereotype threat activating
cue). The participants were asked to provide their gender before starting the experimental
session. The participants in the non-stereotype threat condition were advised that the study
was testing the participants’ working memory capacity. After the priming of negative gender
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stereotypes, the participants completed the computation span test (measure of working
memory) and this was followed by the 10 mental arithmetic tasks and 30 modular arithmetic
tasks (low and high WM load). Participants assigned to the interactive condition were
allowed to use pen and paper to write down interim totals to complete the mental arithmetic
tasks and modular arithmetic tasks (interactive condition), whereas those assigned to the
control condition could not do so. The mental arithmetic tasks and the modular arithmetic
tasks were administered in Qualtrics so that the performance of these tasks (accuracy and
time) could be measured. Finally, the experimental session was concluded with the Maths
Anxiety Scale (state). The participants were tested individually in the psychology testing lab
for approximately 30 minutes.
The primary dependent variables of the current study were working memory capacity,
accuracies of the mental arithmetic tasks (known format) and modular arithmetic tasks (novel
tasks), solution latencies (for both types of maths tasks), and maths anxiety (state) with trait
maths anxiety as a covariate. As before, working memory was assessed by the performance
of the simple mental arithmetic expressions (e.g., 10-5) that were computed at the same time
with a memory load task (second digit of the expression). The accuracy of the maths tasks
was assessed with the help of Qualtrics where the mental arithmetic tasks and modular
arithmetic tasks were computed by both the interactive and non-interactive participants. This
allowed us to record accuracy and time to complete both types of math tasks. Latency to
solution was calculated based on the page submit function of Qualtrics (the time from first
click to the time of the final click). Finally, measures of participants’ level of maths anxiety
(state) were obtained from the questionnaire which is described in the materials section. The
maths anxiety measure (trait) that was measured during the pre-testing phase was used as a
covariate.
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3.7 Results
3.7.1 Data Analysis Plan
To investigate the hypotheses, three separate 2 (experimental condition: stereotype
threat or control) x 2 (level of interactivity: interactivity or control) between-groups analysis
of covariance (ANCOVA) were conducted with percentage correct (accuracies), latencies,
and state maths anxiety as dependent variables. There was an equal number of participants in
each condition (n = 24). The covariates were basic arithmetic skills and maths anxiety (trait)
that were measured during the pre-testing phase. Additionally, latencies were used as a
covariate to avoid speed-accuracy trade-off when the maths tasks were computed. They were
chosen specifically because of their known effects on the dependent variables. Past research
has found a positive correlation between basic arithmetic skills and working memory capacity
(Guthrie & Vallée-Tourangeau, 2018). Additionally, the pre-existing arithmetic skills
(measured with the help of basic arithmetic skills test) were expected to affect the maths
performance of the actual experiment. It was noted during the first study that one of the
limitations of the study was that trait maths anxiety was not measured during the pre-testing
phase and therefore our state maths anxiety measure did not reflect the pre-existing levels of
maths anxiety. The level of maths anxiety (trait) that the participant felt prior to the
experiment was expected to affect the state maths anxiety at the end of the experiment. We
also conducted a one-way (experimental condition: stereotype threat or control) between
groups analysis of variance (ANOVA) with working memory capacity as the dependent
variable.
The order of the second study was different to the first study in that working memory
was measured directly after the priming. In the first study, the mental arithmetic tasks were
completed before the working memory measure. Only the mental arithmetic tasks and the
modular arithmetic tasks were computed in the interactive condition and hence a one-way
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ANOVA was conducted for working memory capacity. Additionally, the current study
profiled participants in relation to their basic arithmetic skills, maths self-efficacy, maths
anxiety (trait), and working memory. A detailed correlational analysis was conducted to
explore the degree to which the individual differences correlated with mean modular
arithmetic performance (both low WM load and high WM load) in the interactive condition
and in the non-interactive condition. Finally, a mediation analysis (to confirm that a reduction
in working memory capacity would mediate the effect of stereotype threat on maths
performance) could not be conducted (to test hypothesis seven) because negative stereotyping
about the female students’ maths performance did not significantly affect participants’ mental
arithmetic performance and modular arithmetic performance.
3.7.2 Group Differences
Before the statistical analyses related to the hypotheses were completed, baseline
analyses were conducted. There were no group differences between the stereotype-threatened
participants and the participants in the control condition on the basic arithmetic skills that was
measured during the pre-testing phase, F < 1. The groups did not differ in their ability to
complete mental arithmetic tasks under timed conditions. Furthermore, there were no group
differences on the mathematics self-efficacy measure either, F(1, 92) = 3.27, p = .07, ŋp2
= .03. Finally, there were no group differences between the two experimental conditions
(stereotype threat or control) on the trait maths anxiety measure (F < 1) confirming that the
individuals did not differ on their pre-existing maths anxiety levels.
3.7.3 Percentage Correct (Mental Arithmetic Tasks)
To test the first, third, and fourth hypotheses, percentage correct (accuracy) of the
mental arithmetic tasks was examined. As predicted, participants were more accurate in the
interactive condition (M = 78.12%, SE = 3.50%) than in the non-interactive condition (M =
59.43%, SE = 3.50%). A summary of the descriptive statistics can be seen in Table 7 (pre-
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study) and Table 8 (post-study). A 2 (experimental condition: stereotype threat or control) x 2
(level of interactivity: interactive or non-interactive) between-groups analysis of covariance
(ANCOVA) was conducted and the scores from the basic arithmetic skills test (pre-test) were
used as a covariate. The covariate, basic arithmetic skills, was significantly related to the
percentage correct, F(1, 90) = 28.11, p < .001, ŋp2 = .24. The covariate (latencies) was not
significantly related to the percentage correct as F < 1. Confirming the first hypothesis, the
main effect of interactivity was significant, F(1, 90) = 16.81, p < .001, ŋp2 = .16. However, the
main effect of experimental condition (stereotype threat or control) was not significant, F < 1,
failing to confirm the third hypothesis. The interaction between the experimental condition
and the level of interactivity was not significant either, F < 1 which did not support the fourth
hypothesis.
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Table 7
Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data)
M SD
Basic arithmetic skills 27.63 10.73
Maths self-efficacy 20.62 5.80
Maths anxiety (trait) 52.64 11.62
Note. Participants were not primed to complete the pre-testing tests. The pre-testing comprised of basic
arithmetic skills, mathematics self-efficacy, and mathematics anxiety (trait). The scale for basic arithmetic skills
is from 0 to 45. The scale for mathematics self-efficacy is from 0 to 35 and the scale for mathematics anxiety is
from 0 to 115.
Table 8
Descriptive Statistics: Means and Standard Errors (Post-Testing Data)
STI STNI NSTI NSTNI
Performance scores M SE M SE M SE M SE
Percentage correct (MAT) 74.12 3.60 64.21 3.40 78.12 3.50 59.43 3.50
Latencies (s) 30.93 2.13 30.62 1.92 31.14 2.02 31.32 2.02
Percentage correct (MA LL) 90.00 2.70 87.30 2.70 90.00 2.70 84.90 2.60
Latencies (s) 17.92 1.12 14.45 1.00 18.34 1.00 16.43 1.02
Percentage correct (MA HL) 78.00 2.90 72.70 2.90 81.70 2.80 69.00 2.80
Latencies (s) 26.63 1.82 18.94 1.74 26.03 1.84 23.24 1.83
Working memory N/A N/A 26.03 1.13 N/A N/A 25.22 1.12
Mathematics anxiety (state) 54.12 2.42 60.72 2.34 52.25 2.43 63.13 2.41
Note. STI = stereotype threat, interactive; STNI = stereotype threat, non-interactive; NSTI = non-stereotype
threat, interactive; NSTNI = non-stereotype threat, non-interactive. MAT = mental arithmetic tasks, MA LL =
modular arithmetic tasks, low load; MA HL = modular arithmetic tasks, high load.
The scale for working memory is from 0 to 56 and the scale for mathematics anxiety is from 0 to 115.
Working memory test was not completed in an interactive condition.
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3.7.4 Percentage Correct (Modular Arithmetic Tasks, Low WM Load)
To test the first, third and fourth hypotheses, percentage correct (accuracy) of the
modular arithmetic tasks (low WM load) was examined. Table 7 (pre-study) and Table 8
(post-study) display the descriptive statistics of the current study. As expected, the maths
performance was elevated with increased interactivity (M = 90.00%, SE = 2.70%) compared
with no interactivity (M = 84.90%, SE = 2.60%). A 2 (experimental condition: stereotype
threat or control) x 2 (level of interactivity: interactive or non-interactive) between-groups
analysis of covariance (ANCOVA) was conducted. The scores from the basic arithmetic
skills test (pre-test) were used as a covariate. The covariate, basic arithmetic skills, was
significantly related to the percentage correct, F(1, 90) = 17.00, p < .001, ŋp2 = .16.
Additionally, the covariate (latencies) was significantly related to the percentage correct, F(1,
90) = 5.53, p = .02, ŋp2 = .06. Confirming the first hypothesis, the main effect of interactivity
was statistically significant, F(1, 90) = 2.00, p = .02, ŋp2 = .02. There was no significant main
effect of experimental condition (stereotype threat or control), F < 1, failing to confirm the
third hypothesis. Additionally, the interaction between the experimental condition and the
degree of interactivity was not statistically significant, F < 1 which did not support the fourth
hypothesis.
3.7.5 Percentage Correct (Modular Arithmetic Tasks, High WM Load)
To test the first, third, and fourth hypotheses, percentage correct (accuracy) of the
modular arithmetic tasks (high WM load) was examined. The descriptive statistics can be
seen in Table 7 (pre-study) and Table 8 (post-study). Interactivity increased the accuracy of
the modular arithmetic tasks (M = 81.70%, SE = 2.80%) compared with the maths
performance in non-interactive condition (M = 69.00%, SE = 2.80%). A 2 (experimental
condition: stereotype threat or control) x 2 (level of interactivity: interactive or non-
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interactive) between-groups analysis of covariance (ANCOVA) was conducted. The scores
from the basic arithmetic skills test (pre-test) were used as a covariate. The covariate was
significantly related to the percentage correct, F(1, 90) = 24.21, p < .001, ŋp2 = .15.
Additionally, the covariate (latencies) was significantly related to percentage correct, F(1, 90)
= 8.93, p = .004, ŋp2 = .09.Confirming the first hypothesis, the main effect of interactivity was
statistically significant F(1, 90) = 9.35, p = .003, ŋp2 = .09. The main effect of experimental
condition (stereotype threat or control) was not statistically significant, F < 1, failing to
confirm the third hypothesis. The interaction between the experimental condition and the
level of interactivity was not statistically significant, F(1, 90) = 1.78, p = .19, ŋp2 = .02 which
did not support the fourth hypothesis.
3.7.6 Latencies (Mental Arithmetic Tasks)
To test the second, third and fourth hypotheses, solution latency was examined. A 2
(experimental condition: stereotype threat or control) x 2 (level of interactivity: interactive or
non-interactive) between-groups analysis of covariance (ANCOVA) was conducted. The
descriptive statistics can be seen in the Table 7 (pre-study) and Table 8 (post-study). The
scores from the basic arithmetic skills test (pre-test) were used as a covariate. The covariate
was significantly related to the latency to solution, F(1, 91) = 24.62, p < .001, ŋp2 = .21. The
main effect of interactivity was not statistically significant, F < 1 and it failed to confirm the
second hypothesis. The main effect of experimental condition (stereotype threat or control)
was not statistically significant either, F < 1, failing to support the third hypothesis.
Additionally, the interaction between the experimental condition and the level of interactivity
was not statistically significant, F < 1 which did not support the fourth hypothesis.
3.7.7 Latencies (Modular Arithmetic Tasks, Low WM Load)
To test the second, third, and fourth hypotheses, solution latency was examined. Table
7 (pre-study) and Table 8 (post-study) summarize the descriptive statistics. Interactivity
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slowed the participants down when completing the low WM load modular arithmetic tasks
(M = 18.34 s, SE = 1.00 s) compared with the latency to solution in the non-interactive
condition (M = 16.43 s, SE = 1.02 s). A 2 (experimental condition: stereotype threat or
control) x 2 (level of interactivity: interactive or non-interactive) between-groups analysis of
covariance (ANCOVA) was conducted and the scores from the basic arithmetic skills test
(pre-test) were used as a covariate. The basic arithmetic skills (covariate), was significantly
related to the latency to solution, F(1, 91) = 53.72, p < .001, ŋp2 = .37. Confirming the second
hypothesis, the main effect of interactivity was statistically significant F(1, 91) = 6.99, p
= .01, ŋp2 = .07. The main effect of experimental condition (stereotype threat or control) was
not significant, F < 1, failing to support the third hypothesis. The interaction between the
experimental condition and the level of interactivity was not significant either, F < 1 which
did not support the fourth hypothesis.
3.7.8 Latencies (Modular Arithmetic Tasks, High WM Load)
To test the second, third, and fourth hypotheses, latency to solution was examined for
the high WM load modular arithmetic tasks. The summary of the descriptive statistics can be
seen in the Table 7 (pre-study) and Table 8 (post-study). Interactivity slowed the participants
down when completing the high WM load modular arithmetic tasks (M = 26.03 s, SE = 1.84
s) compared with the latency in the non-interactive condition (M = 23.24 s, SE = 1.83 s). A 2
(experimental condition: stereotype threat or control) x 2 (level of interactivity: interactive or
non-interactive) between-groups analysis of covariance (ANCOVA) was conducted. The
scores from the basic arithmetic skills test (pre-test) were used as a covariate. The covariate,
basic arithmetic skills, was significantly related to the latency to solution, F(1, 91) = 14.12, p
< .001, ŋp2 = .13. Confirming the second hypothesis, the main effect of interactivity was
statistically significant F(1, 91) = 9.00, p = .003, ŋp2 = .09. The main effect of experimental
condition (stereotype threat or control) was not statistically significant, F < 1, failing to
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confirm the third hypothesis. Finally, the interaction between experimental condition and the
level of interactivity was not significant either, F < 1 which did not support the fourth
hypothesis.
3.7.9 Working Memory
To test hypothesis five, working memory capacity (computation span) was examined. Table 7
(pre-study) and Table 8 (post-study) summarize the descriptive statistics. A one-way
(experimental condition: stereotype threat or control) between-groups analysis of variance
(ANOVA) was conducted. The main effect of experimental condition was not significant, F <
1 which did not support the hypothesis five. Additionally, the main effect of interactivity was
not significant as F < 1. Finally, the interaction between experimental condition and level of
interactivity was not significant either as F < 1.
3.7.10 Maths Anxiety (State)
To test the seventh, eighth, and ninth hypotheses, maths anxiety levels after the
experimental session were examined. Table 7 (pre-study) and Table 8 (post-study) outline the
descriptive statistics of the current study. A 2 (experimental condition: stereotype threat or
control) x 2 (level of interactivity: interactive or non-interactive) between-groups analysis of
covariance (ANCOVA) was conducted and the scores from the maths anxiety (trait anxiety
that was measured during the pre-test) were used as a covariate. Maths anxiety (trait), the
covariate, was significantly related to maths anxiety (state), F(1, 91) = 65.23, p < .001, ŋp2
= .42. The participants who were in the interactive condition were less maths anxious (M =
52.25, SE = 2.43) than the participants in the control condition (M = 63.13, SE = 2.41).
Confirming the seventh hypothesis, the main effect of interactivity was statistically
significant F(1, 89) = 13.63, p < .001, ŋp2 = .13. The main effect of experimental condition
(stereotype threat or control) was not statistically significant, F < 1, failing to confirm the
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eigth hypothesis and the interaction between the experimental condition and the level of
interactivity was not not significant either, F < 1 which did not support the final hypothesis.
3.7.11 Individual Differences
We profiled participants in terms of their basic arithmetic skills (BAS), maths self-
efficacy, maths anxiety (trait), and working memory (measured with a computation-span).
Because half of the participants were conditioned to the stereotype threat condition during the
experimental session, their working memory data could not be used for the detailed
correlation analysis explained here. Therefore, only the data (basic arithmetic skills, maths
self-efficacy, state maths anxiety, and working memory) from the control group (n = 48) was
employed for this part of the analysis. Additionally, only the modular arithmetic tasks (both
low and high load) were part of the analysis. In line with previous research (Guthrie &
Vallée-Tourangeau, 2018), the measure of basic arithmetic skills (BAS) was correlated with
working memory capacity, r(96) = .54, p < .001. Additionally, there was a positive
correlation between maths self-efficacy and basic arithmetic skills (BAS), r(96)= .30, p = .04
confirming previous literature (e.g., Pajares & Graham, 1999). And as expected, maths self-
efficacy and maths anxiety (trait) were moderately correlated, r(96) = -.46, p < .001
confirming previous findings (e.g., Lee, 2009).
Of greater interest was the degree to which the individual differences correlated with
mean modular arithmetic performance (both low WM load and high WM load) in the
interactive condition and in the non-interactive condition. Correlational analyses indicated
that in the non-interactive condition, participants’ maths performance (accuracy) reflected
their arithmetic skill. Basic arithmetic skills (BAS) was a moderate predictor of modular
arithmetic performance for both the low WM load, r(96)= .48, p = .02 and high WM load,
r(96) = .39, p = .06 modular arithmetic performance. As expected, basic arithmetic skills
(BAS) was not correlated with the modular arithmetic performace in the interactive
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condition. Interactivity allowed the participant to externalize the internal cognitive process to
the outside world. The participant became more effective, was able to deal with more difficult
problems, and to compute more deeply and precisely.
In the non-interactive condition, participants’ latencies to solution reflected their basic
arithmetic skills and working memory capacity. Basic arithmetic skills (BAS) was a strong
predictor of low WM load latencies, r(96) = -. 63, p < .001 and a moderate predictor of high
WM load latencies, r(96) = -.40, p = .05. Additionally, working memory was moderately
correlated with low WM load latencies, r(96) = -.41, p = .05. However, only the basic
arithmetic skills (BAS) predicted the latencies in the low WM load, r(96) = -.56, p = .004 and
high WM load, r(96) = -.43, p = .04, in the interactive condition. These results suggest that
interactivity allowed working memory capacity to become augmented in the interactive
condition and therefore WM was not a predictor of latencies to solution any more.
When looking at maths anxiety (state) in the non-interactive condition, there was a
moderate correlation between maths self-efficacy and maths anxiety (trait), r(96) = -.56, p
= .005. Additionally, there was a strong positive correlation between the participant’s trait
maths anxiety levels (measured during the pre-testing phase) and the state maths anxiety
levels that were measured at the end of the experiment, r(96) = .71, p < .001. Level of maths
anxiety (state) was predicted by the level of maths self-efficacy and pre-existing maths
anxiety levels. However, this same pattern could not be found in the interactive condition
which suggested that interactivity offered the participant the opportunity to feel less maths
anxious (this same pattern has also been shown by Vallée-Tourangeau, 2013).
3.8 Discussion
The purpose of the current experiment was to investigate the effects of stereotype
threat on mental arithmetic performance and modular arithmetic performance (accuracies and
latency to solution), working memory, and maths anxiety. Additionally, the experiment
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investigated the role of distributed cognition in reducing the negative effects of stereotype
threat on maths performance, and on maths anxiety. It was hypothesised that the female
students would feel more state maths anxious after the situational manipulation of stereotype
threat. The intrusive thoughts and worry about being able to succeed with the required task
would consume valuable cognitive resources, and particularly working memory resources. It
was predicted that there would be a dual-task set up whereby the additional worry and the
cognitive task would compete for the same existing working memory resources. As
mentioned in the introduction, working memory is seen as a short-term memory system with
a limited capacity (Miyake & Shah, 1999) and therefore the combination of the additional
worries and task requirement would put pressure on the limited working memory resources.
Additionally, working memory capacity can be seen as the ability to focus one’s attention on
a given task while keeping task-irrelevant thoughts at bay (Engle, 2002). Hence, stereotype
threat might put an extra burden on the female participants’ cognitive resources, and on
working memory. Clearly, individuals with high working memory are better at suppressing
task-irrelevant information (e.g., stereotype threat priming) than individuals with low
working memory (Engle, 2002). Finally, the depleted working memory capacity, caused by
stereotype threat was predicted to have a causal role in reduced mental arithmetic
performance and modular arithmetic performance. Moreover, it was hypothesised that the
participants in the stereotype threat condition would feel more maths anxious (state) after the
experiment. However, it was predicted that allowing the participant to externalise the internal
cognitive process to come to the solution would reduce the negative effects of the stereotype
threat on maths anxiety.
Maths anxiety (state) measured after the experiment, confirmed that the participants
did not feel more worried or anxious about their maths abilities in the stereotype threat
condition. Maths anxiety (state) levels were not elevated and therefore there was no
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additional burden on working memory. The fact that working memory capacity was predicted
by the participant’s basic arithmetic skills rather than stereotype threat priming, is an
indicator that it was the level of the maths skill that contributed to working memory capacity
rather than the stereotype threat priming. The participants did not feel a threat because their
ability in maths was strong enough. There was no need for the participants to doubt their
abilities when in the stereotype threat condition.
Unlike the first study, this experiment failed to show reduced working memory
capacity in the stereotype threat condition. This is in contrast with Schmader and Johns
(2003) who showed that priming self-relevant negative stereotypes reduced women’s
(Experiment 1) and Latinx participants’ (Experiment 2) working memory capacity. In their
final study, it was confirmed that a reduction in working memory capacity mediated the
effect of stereotype threat on women’s maths performance (Schmader & Johns, 2003). In the
current study, the working memory capacity score was predicted by strong basic arithmetic
skills rather than by negative stereotyping about female maths performance, confirming a
previous finding by Guthrie and Vallée-Tourangeau (2018) where arithmetic skills were also
a predictor of working memory capacity (Guthrie & Vallée-Tourangeau, 2018). What is
more, the current study failed to show reduced maths performance (mental arithmetic and
modular arithmetic tasks) when stereotype threat was made salient. Clearly, there was no
causal link between reduced working memory capacity and reduced maths performance.
However, it was confirmed that interactivity elevated maths performance (accuracy)
when stereotype threat was not present (control condition) confirming previous research (e.g.,
Guthrie & Vallée-Tourangeau, 2018; Vallée-Tourangeau, 2013). Additionally, as predicted
maths anxiety (state) was reduced for participants who were allowed to externalize their
internal cognitive process, by using pen and paper (interactive condition). The dual task set
up (maths anxiety and task requirement) did not exist anymore. The agent did not need to
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fight for the same working memory resources; the increased interactivity had provided the
additional cognitive resource. Previous studies have shown that working memory is
negatively associated with maths anxiety (Ashcraft & Kirk, 2001). Vallée-Tourangeau and
his colleagues have concluded that interactivity improves mental arithmetic performance in
maths anxious participants (Allen & Vallée-Tourangeau, 2016; Vallée-Tourangeau et al.,
2016). However, the Vallée-Tourangeau studies have only looked at trait maths anxiety. The
current study explained here has measured state maths anxiety after the experimental session
and has shown reduced maths anxiety in the interactive condition (without stereotype threat).
To our knowledge, this is the first study that has measured maths anxiety (state), after
allowing the participants to complete the maths tasks in an interactive setting.
3.9 Limitations
Whilst the findings of this study are encouraging, the research reported here has some
limitations to it. The findings in this report are subject to at least two limitations. First,
examination of the wording of the control condition (when the control participants were told
that the experiment measured their working memory capacity) suggests that it may not have
functioned as a neutral control condition as planned. Instead, the control condition might
have been primed for performance-approach goals and to the idea that working memory is
fixed (Dweck, 1986) rather than being a true control. Endorsing an entity theory of
intelligence can lead to performance-approach goals. Indeed, this might serve as an
alternative explanation for the lack of a significant difference in maths performance between
the two conditions (stereotype threat or control). Second, the study lacks external validity as
it was conducted in a lab-based setting rather than in a more applied context (e.g., in an
educational setting) in which mental arithmetic tasks are regularly computed.
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3.10 Future Studies
To sum up, Study 1 and 2 reported that girls’ maths performance was not depleted
with negative stereotyping compared to a control condition. However, because the control
condition might have primed performance-approach goals, achievement goals were examined
in more detail in the final two studies (Studies 3 and 4). Additionally, it would be of interest
to investigate whether distributed cognition could be used as an innovative way of reducing
the negative effects of evaluative pressure caused by the achievement goals.
Chapter 4: Achievement Goals and Mental Arithmetic: The Role of Interactivity
Findings from Study 1 and 2 of this programme of research indicated that stereotype
threat about women’s maths performance did not negatively affect their academic
performance. Participants’ mental arithmetic performance did not suffer while the
participants were primed with negative stereotypes pertaining to women’s maths ability.
Studies 1 and 2 failed to find any statistically significant differences in the mental arithmetic
performance between the stereotype threat condition and the control group. However, in the
first study, working memory capacity was reduced with stereotype threat about girls’ maths
performance, but this had no effect on mental arithmetic performance. Consistent with this
view, Pennington et al., (2018) also reported that stereotype threat did not impair women’s
inhibitory control or mathematical performance. Given no negative effects of stereotype
threat on mental arithmetic performance in Studies 1 and 2 of this thesis, there were no
benefits of using distributed cognition when stereotype threat had been made salient either.
One reason that women in the stereotype threat may not have seen decrements in
performance compared to those in the control condition is that the control condition may have
inadvertently primed performance goals. Similar to stereotype threat, achievement goals, and
performance-approach goals in particular, can have detrimental effects on the existing
working memory resources (due to worries about outperforming others), (Crouzevialle &
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Butera, 2013). If performance-approach goals and the distractive thoughts of performing
better than others handicaps working memory resources, then interactivity could be used as
an innovative way of mitigating these negative effects. The aim of the present study was to
further understand how mastery-approach goal and performance-approach goal engage
working memory resources, and whether distributed cognition (e.g., use of pen and paper)
could be used to defuse any of the negative effects of performance-approach goals on maths
performance. Additionally, we wanted to further our understanding whether the mastery-
approach goal individuals would benefit in externalising internal cognitive processes. The
current study (Study 3) acted as a Pilot Study to Study 4 to further investigate whether there
were any detrimental effects of performance-approach goals on maths performance. The
study only focused on maths performance and did not have any additional measurements. The
sample size for this study was small (41 participants) as the main purpose of the study was to
see that whether there was an effect of achievement goals on maths performance and whether
interactivity could be used to alleviate the possible negative effects before investigating with
a bigger sample.
4.1.1 Achievement Goals
Achievement goals reflect the aim of an individual’s achievement pursuits. They are
frameworks that can help to understand how individuals react to various achievement
situations (Poortvliet & Darnon, 2010). There is a wealth of research on achievement goals
and their effects on academic performance. However, much less is known about the effects
on working memory. The present study examined how motivational approach goals
differentially impact upon working memory capacity. Additionally, we studied the role of
distributed cognition in relation to achievement goals (mastery-approach goal and
performance-approach goal) and maths performance.
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4.1.2 Mastery-Approach Goals and Performance-Approach Goals
There is a widely supported conceptualisation of achievement goals that distinguishes
between mastery-approach goals where the individual is aiming for knowledge acquisition
and task mastery and performance-approach goals where demonstrating competence in the
subject field and aiming for outperforming others is the main goal (Crouzevialle & Butera,
2017). When individuals focus on performance, they strive to look good in front of peers.
Due to the focus of outperforming others rather than concentrating on the actual learning
process and knowledge acquisition, there are behavioural patterns individuals follow when
they are focused on performance goals in order to reach their academic targets. When
pursuing performance-approach goals, individuals listen to the cues about the future
academic assignments and adjust their learning based on these cues. Students’ academic
achievements are higher when focusing on areas that are deemed important by the teacher
and tested as part of the curriculum (Broekkamp et al., 2007). Additionally, students focusing
on performance concentrate on memorisation rather than elaboration and knowledge
construction of the topic (Entwistle, 1988). Unfortunately, this type of exam preparation can
lead to surface learning and rote learning (Harackiewicz & Linnenbrink, 2005).
Normative comparisons allow the individual to compete with people around them and
to outperform others doing similar tasks. Additionally, the individual focusing on
performance has outcome goals that are focused on attaining a positive outcomes in the form
of good exam grades (Grant & Dweck, 2003). However, striving for academic success and
the worry to rise above others might cause elevated feelings of pressure (Crouzevialle &
Butera, 2013). Pressure can create mental distractions that compete for existing working
memory resources. Additionally, the pressure can reduce working memory capacity that
would normally be allocated to skill execution (Beilock & Carr, 2005). Hence, the
programme of research reported here is focusing on performance-approach goals only (with
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mastery approach-goals functioning as a comparison group). If there is additional taxation on
the working memory, then it is the individuals who are pursuing performance-approach goals
who would benefit from combining the internal and external cognitive resources.
4.1.3 Achievement Goals and Modular Arithmetic Tasks
We utilised modular arithmetic tasks as our testbed. Modular arithmetic tasks [e.g., 52
≡ 16 (mod 8)] involve judging mathematical equations’ true value. When the answer to the
equation is a whole number, the answer to the problem is true. Clearly, these equations can be
computed in different ways with varying levels of working memory taxation. Whilst these
tasks can be computed by executing working memory demanding procedures [e.g., (52 –
16)/8 = true or false] there are also less working memory resource demanding shortcuts that
can be employed. It could be assumed that modular arithmetic problems employing even
numbers are true because dividing two even numbers is not normally associated with
remainders and the purpose of the MA tasks is to judge whether the answer is a whole
number or not (i.e., no remainders). On the contrary, when dividing two numbers of different
parity, it is more likely that there are reminders, and therefore the answer would be false. It is
possible that even numbers can produce the correct answer [e.g., 34 ≡ 18 (mod 8)] in some
cases but not always [e.g., 52 ≡ 16 (mod 8)], (Beilock, 2008). The pursuit of performance-
approach goals allows for a more implicit way of dealing with the modular arithmetic tasks.
One the contrary, the mastery-focused individual focuses on the explicit processing of the
tasks that are more resource demanding rather than using quick shortcuts to come to the
solution (Avery et al., 2013).
4.1.4 Achievement Goals and Working Memory
Performance-approach goals may produce distraction and therefore have negative
consequences on task focus and performance. The concerns about competition and peer
comparisons of the more performance-focused goal can distract individuals from the task
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focus (Brophy, 2005). Beilock, Holt, Kulp and Carr, (2004) tested this in a laboratory setting,
under either low or high evaluative pressure. The study concluded that the high-pressure
scenario taxed a large part of the working memory resources and as a consequence there was
a performance decrement for the most demanding maths problems (high WM load tasks)
compared with the low WM load tasks (Beilock et al., 2004). Similar findings have been
made by Crouzevialle and Butera (2013) whose results revealed that there was impaired
maths performance in the performance-approach goal environment. As before, this reduced
maths performance could only be observed with the highly demanding problems.
Performance-approach goals distract participants from full engagement of the task
(Crouzevialle & Butera, 2013). Additionally, the pressure to perform better than others
consumes the verbal resources of the working memory. It is like an inner language that is
focused on concerns about the evaluative situation and which in turn impairs the overall
cognitive performance (Decaro, Rotar, Kendra, & Beilock, 2010.) This is like a dual-task set-
up where the distractive thoughts and task execution compete for the same working memory
resources. Additionally, Avery and Smillie (2013) examined the influence of achievement
goal pursuits on working memory with varying levels of executive load. Under the high
executive load, there was poorer working memory processing during the performance-
approach goal than when mastery-approach goal or a no-goal control were used (Avery &
Smillie, 2013).
4.1.5 The Benefits of Interactivity
Interacting with external representations elevates and transforms thinking and
mathematical problem solving. Internal cognitive processes go to wherever they are more
cost effective. In other words, if an agent has a pen and paper available and if the sentence is
complex enough, it might be more beneficial to draw a picture of the information held
internally in the head which might in turn reduce the overall cognitive cost of the sense
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making (Kirsh, 2010). Additionally, by creating these external structures, individuals can
compute more efficiently, and create forms that allow the individual to share their internal
thoughts (Kirsh, 2010).
However, there are factors that can determine whether the reshaping of the physical
environment in problem solving is beneficial. The experience of the reasoner and cognitive
abilities of the individual determine the possible benefits of the external manipulation. Webb
and Vallée-Tourangeau (2009) explored this further with an interactive word production task
with dyslexic children (with less efficient working memory abilities) and typically
developing children (aged between 9 and 11 years). The children were asked to create words
from two different word tiles (with a varying difficulty: difficult and easy) in an interactive
condition (where the children were allowed to touch the tiles and physically manipulate
them) and in a non-interactive condition (where the manipulation of tiles was not allowed).
By allowing physical interaction with the tiles the dyslexic children were able to enhance
word production with the easy set of word tiles but not with the more difficult set. However,
typically developing children did not benefit from the external manipulation of the tiles to
produce words. Instead, there was a performance drop with the easy letter set when
interactivity was employed. Thus, the effectiveness of the physical problem space is relative
to the level of task difficulty as well as the cognitive abilities of the reasoner (Webb &
Vallée-Tourangeau, 2009).
In another word production study, participants were required to generate words with
any length (with seven different letter sets) for a period of 5 minutes. The experiment allowed
the hands group to manipulate the tiles (interactive condition) and in the non-hands group
(non-interactive condition) this externalisation of internal cognitive process was not
employed. When a word was generated the participant said the word and then spelled it. The
experimenter then wrote down the answer. The word production performance was different
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for participants who were classified as either low or high fluency group (measured by their
performance on the Thurstone word fluency test). For the high-fluency group, there were few
benefits of restructuring the external environment to produce the words. The individuals had
the cognitive abilities to deal with the demands of the task. However, for the low-fluency
group interactivity significantly enhanced the word production. The task was more working
memory resource taxing and by the external manipulation of the word sets, enhancement of
the performance was achieved (Vallée -Tourangeau & Wrightman, 2010)
4.2 Present Study (Pilot Study to Study 4)
The aim of the experiment reported here was to further examine the influence of
achievement goal states on working memory and whether interactivity could be used to
mitigate any of the possible negative effects of achievement goals on maths performance. If
the working memory is loaded due to outcome related worry then there is additional taxation
on working memory (Crouzevialle & Butera, 2013). Together with the horizontally presented
maths problems (modular arithmetic tasks) there can be maths performance decrements when
in the performance-approach goal condition (Beilock, 2008). We reasoned that, if worries of
outperforming others lead to poor maths performance, then giving students the opportunity to
externalize the internal cognitive process would reduce internal working memory demands
and enhance task performance. Additionally, if the working memory capacity of individual
with a mastery-approach goal is unaffected by the lack of distractive thoughts, there might be
little benefits to manipulate the external world.
4.2.1 Hypotheses of the Study
Based on the findings of the first two studies of this programme of research, the first
hypothesis for the current study (Hypothesis 1) was that externalising the internal cognitive
process to the outside world would enhance accuracy of the modular arithmetic tasks. The
second hypothesis (Hypothesis 2) stated that interactivity would increase the solution
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latencies (allowing the participant to complete the tasks slower) for the modular arithmetic
tasks as per findings of the Study 2.
Additionally, we predicted that the participants of the mastery-approach goal
condition would have higher maths performance (higher accuracy) than the participants in the
performance-approach goal condition (Hypothesis 3). And at the same time, the maths
performance of the individuals in the performance-approach goal condition was expected to
suffer (Hypothesis 4). It has been suggested that there are less worries in the mastery-
approach goal environment and therefore the working memory of the individual is not as
heavily taxed as when performance-goal has been made salient (Crouzevialle & Butera,
2013). However, these performance decrements of the performance-focused individuals were
expected to be alleviated with the help of external artefacts (e.g., using pen and paper),
(Hypothesis 5) as per existing empirical findings (Vallée-Tourangeau, 2013).
Additionally, it was predicted that the individuals in the mastery-approach goal
condition would not benefit from interactivity due to less taxation of the working memory. In
fact, it was predicted that their performance would be poorer when they were allowed to use
pen and paper to come to the solution than when they were not (Hypothesis 6). If an
individual has the cognitive abilities or resources (e.g., working memory) to complete the
task, interactivity can cause a performance drop (Vallée-Tourangeau & Wrightman, 2010;
Webb & Vallée-Tourangeau, 2009). If there are less distractive thoughts in the mastery-
approach goal environment, then there is more capacity available for the task in hand
(Crouzevialle & Butera, 2013). Hence, interactivity might not bring the same benefits to the
mastery-focused participant as to the performance-focused participant.
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4.3 Method
4.3.1 Participants
Forty-one female undergraduate psychology students (M = 21.88, SD = 3.90)
participated in this study for exchange of SONA credits. After consenting to participate in the
study, subjects were randomly assigned to one of the experimental conditions. The
participants were tested individually in a psychology lab, at the University of Surrey (UK).
4.3.2 Material and Measures
Arithmetic task. There were two blocks of 24 modular arithmetic tasks that relied
heavily on working memory resources, adapted from Beilock and Carr (2005). The task
comprised of high WM load tasks only. As mentioned before, the purpose of the tasks is to
judge the validity of maths problems like [61 ≡ 18 (mod 4)]. The middle number is subtracted
from the first number (i.e., 61-18) and then the difference is divided by 4. If the answer is a
whole number the maths problem is true (Beilock & Carr, 2005). Modular arithmetic tasks as
laboratory tasks are advantageous because most students have not seen them before and
therefore previous task experience is controlled. Additionally, the performance is not
proceduralized and therefore working memory resources are required to assist in solving the
tasks.
High-demand problems [e.g., 42 ≡ 27 (mod 3)] requiring a double-digit subtraction
operation were used because they required borrowing, resulting in using more working
memory resources. Half of the maths problems required a true response by the participant.
The order of the questions was randomized and each question was asked only once. The
original tasks used by Beilock and Carr (2005) were a mixture of high demand problems
(two-digit numbers requiring borrowing) and low-load questions (single-digit numbers,
without borrowing), (Figure 1). The study reported here utilised the high-demand problems
only because of limited benefits of employing interactivity with low-demand tasks.
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Figure 1. Examples of low-load and high-load modular arithmetic tasks. This figure is
adapted from (Beilock, 2008).
The modular arithmetic tasks were presented in a horizontal format as opposed to a
vertical format (also called column subtraction), (Figure 2). The horizontal presentation of the
maths problems is more reliant on phonological resources (the verbal resources) because
individuals maintain the required problem steps (e.g., interim totals) in their memory verbally
(DeStefano & LeFevre, 2004). In the case of modular arithmetic tasks, the possible worries of
performing better than others places much heavier demands on working memory
(phonological loop, in particular).
Figure 2. Examples of vertical and horizontal modular arithmetic problems. This figure is
adapted from (Beilock, 2008).
Experimental manipulations. Participants were informed after completing the
baseline block of modular arithmetic tasks (24) that they were required to complete a second
block (24) of modular arithmetic tasks; this time their performance would be recorded. The
participants in the performance-approach goal condition read the following instructions
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Vertical MA tasks: 52
≡ 24 (mod 3)
Horizontal MA tasks:52 ≡ 24 (mod 3)
Low-load tasks:9 ≡ 3 (mod 2)
High-load tasks:52 ≡ 24 (mod 3)
before starting the task that were aimed at activating performance-approach goals based on
previous research:
During the recorded part of the task, the experimenters will assess your performance.
It is important for you to be proficient, to perform well and obtain a high score, in
order to demonstrate your competence. You should know that a lot of students will do
this task. You are asked to keep in mind that you should try to distinguish yourself
positively, that is, to perform better than majority of students. In other words, what we
ask you here is to show your competencies, your abilities. (Darnon, Harackiewicz,
Butera, Mugny, & Quiamzade, 2007, p. 816 )
The participants in the mastery-approach goal condition read instructions that were
designed to activate mastery-approach goals. There was no social comparison and the
instructions were aimed to create task interest. Additionally, there was no mention of scores
or task performance:
In previous research, we have observed that practice of the arithmetic task you are
solving right now has benefits to cognitive functioning and leads to a progressive
improvement of mental processes. Hence, this task solving can be proven to be
beneficial in the long-term. It is however necessary that you focus your attention on
calculation mastery, so as to quickly and accurately solve each problem, in order to
experience these benefits. Try to master this task as much as you can; keep in mind its
practice can be beneficial to you. (Crouzevialle et al., 2015, p. 7 )
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Interactivity. The participants in the interactive condition were allowed to use pen
and paper while computing the mental arithmetic tasks. When using the pen and paper the
participants first worked out the answers on the paper and then transferred the answers to
Qualtrics. The participants in the non-interactive condition were not allowed to use any
external artefacts to come to the solution. They answered all the questions directly in
Qualtrics.
4.3.3 Procedure
Participants were tested individually in a testing laboratory (School of Psychology) at
the University of Surrey. The experimenter remained in the testing room across all of the
experimental conditions. After consenting to participate in the study, participants were
randomly assigned to one of the experimental conditions (performance-approach goal or
mastery-approach goal crossed with interactivity or no interactivity). There was a short
training session consisting of two modular arithmetic tasks before starting the first block. The
first block of questions (24) functioned as a baseline and the performance (accuracy and
latencies) was recorded in Qualtrics. However, the participants were told that it was a training
block, and that their performance was not recorded to avoid any achievement goal activation.
Before starting the second block, the participants were told that their performance was
recorded this time. The priming of the participants was done between the training block and
actual block of maths tasks. The order of the maths tasks was counterbalanced in both blocks.
Finally, the participants were briefed and thanked for their participation at the end.
The current study had two primary dependent variables: accuracy of the tasks and
solution latency (in seconds). Accuracy of the participants was measured during the first
block and second block (percentage correct) and a difference score (B2 – B1) was calculated.
The accuracy of the maths tasks was assessed with the help of Qualtrics where the modular
arithmetic tasks were computed by both the interactive and non-interactive participants. This
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allowed us to record accuracy and time to complete the required tasks. Latency to solution
was calculated based on the page submit function of Qualtrics (the time from first click to the
time of the final click). Additionally, solution latency (with the help of a difference score, B2
– B1 solution latency) also functioned as a covariate when the primary statistical analysis was
being conducted. Studies 3 and 4 are based on the same study design as the original paper by
Crouzevialle and Butera (2013) and therefore the solution latencies were only used as
covariates in these studies, rather than dependent variables.
4.4 Results
4.4.1 Data Analysis Plan
To investigate the hypotheses, two separate 2 (instruction: performance-approach goal
or mastery-approach goal) x 2 (level of interactivity: interactivity or control) between-groups
analysis of covariance (ANCOVA) were conducted with percentage correct (accuracies) and
latencies, as primary dependent variables. Accuracy difference score was calculated by
subtracting the modular arithmetic performance of block 1 from block 2. Furthermore, a
difference score in latencies was used as a covariate to avoid any speed-accuracy trade-offs
for the participants.
4.4.2 Group Differences
Before concentrating on the actual performance measures of the study, it was
concluded that there were no group differences between the participants in the mastery-
approach goal condition and performance-approach goal condition on the baseline modular
arithmetic performance (block 1), F(1, 36) = .08, p = .78, ŋp2 = .002 confirming that the
groups did not differ in their ability to complete the modular arithmetic tasks. Additionally,
there were no group differences on the baseline (block 1) latencies to solution either, F(1, 36)
= .17, p = .69, ŋp2 = .004 confirming that the participants did not vary in their speed to
complete the modular arithmetic tasks, during the baseline assessment.
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Table 9 summarises the descriptive statistics and standard errors of modular
arithmetic performance in block 1. Table 10 is a summary of the mean accuracies for block 2
(only in the interactive condition, for comparison). Table 11 is a summary of descriptive
statistics for block 2 across the different experimental conditions.
Table 9
Descriptive Statistics and Standard Errors of Modular Arithmetic Performance (Accuracy
and Latencies to Solution) in Block 1
Interactive Non-Interactive
M SE M SE
Accuracy (%) 91.62 2.20 82.83 2.20
Latency (seconds) 14.33 1.11 15.13 1.10
Note. There was no priming of achievement goals (mastery-approach goal or performance-approach goal) in
block 1. Participants completed the modular arithmetic tasks in interactive or non-interactive condition only.
Table 10
Descriptive Statistics and Standard Errors of Modular Arithmetic Performance (Accuracy
and Latencies to Solution) in Block 2 (Interactive Condition)
Interactive Non-Interactive
M SE M SE
Accuracy (%) 87.43 2.20 82.34 2.20
Latency (seconds) 12.82 0.86 13.16 0.84
Note. This is the interactive condition only in order to get a comparison with block 1.
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Table 11
Descriptive Statistics and Standard Errors of Modular Arithmetic Performance (Accuracies
and Latencies to Solution) in Block 2
PAG-INT PAG-NI MAG-INT MAG-NI
n = 10 n = 12 n = 9 n = 10
M SE M SE M SE M SE
Accuracy (%) 85.93 3.20 74.74 3.20 88.92 3.20 90.02 3.10
Latency (seconds) 13.22 1.21 12.33 1.21 12.56 1.21 14.03 1.16
Note. PAG-INT = performance-approach goal with interactivity; PAGNI = performance- approach goal without
interactivity; MAG-INT = mastery-approach goal with interactivity; MAG-NI = mastery-approach goal with no
interactivity. Priming of achievement goals was utilised during block 2. Participants were also in either
interactive or non-interactive condition.
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4.4.3 Accuracy
Our main performance measure was accuracy of the modular arithmetic tasks (high
WM load). Accuracy difference score was calculated by subtracting the modular arithmetic
performance of block 1 from block 2 (B2 - B1). Furthermore, a difference score in latencies
was used as a covariate in order to avoid any speed-accuracy trade-off of the participants.
A 2 (instruction: performance-approach goal or mastery-approach goal) x 2 (level of
interactivity: interactivity or control) between-groups analysis of covariance (ANCOVA) was
conducted. The covariate (difference score in latencies) was significantly related to the
modular arithmetic accuracy, F(1, 36) = 5.76, p =.02, ŋp2 = .14. There was no statistically
significant main effect of interactivity as interactivity did not improve the overall modular
arithmetic performance, F(1, 36) = 1.13, p = .30, ŋp2 = .03 which failed to support the first
hypothesis.
There was a main effect of instruction (mastery-approach goal or performance-
approach goal), F(1, 36) = 9.70, p = .004, ŋp2 = .21 . As we had anticipated, the modular
arithmetic performance (accuracy difference score, S2 – S1) of the mastery-approach goal
participants was higher (M = 1.53, SE = 1.72) than the performance-approach goal
participants’ performance (M = -6.16, SE = 1.76), (Figure 4), confirming the third and fourth
hypotheses.
Additionally, there was a statistically significant interaction of interactivity and
instruction on problems solved correctly, F(1, 36) = 4.39, p = .043, ŋp2 = .11. As expected, the
participants in the mastery-approach goal condition performed better (M = 5.44, SE = 2.38)
than performance-focused participants (M = -7.43, SE = 2.50) when interactivity was not
used (Figure 3) confirming the third hypothesis, F(1, 18) = 11.08, p = .004, ŋp2 = .38.
Additionally, the individuals in the mastery-approach goal condition had a performance drop
in the interactive condition (M = -2.37, SE = 2.50) compared with their performance in the
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non-interactive condition (M = 5.44, SE = 2.38) (Figure 3), confirming the sixth hypothesis,
F(1, 18) = 4.90, p = .04, ŋp2 = .21 (Table 12).
Table 12
Descriptive Statistics and Standard Errors of Modular Arithmetic Performance Difference
(B2 - B1) across the Experimental Conditions
PAG-INT PAG-NI MAG-INT MAG-NI
M SE M SE M SE M SE
Accuracy (%) -4.89 -2.50 -7.43 -2.50 -2.37 -2.50 5.44 2.38
Latency (seconds) -1.26 -0.90 -2.02 -0.90 -1.61 -0.90 -1.99 -0.85
Note. PAG-INT = performance-approach goal with interactivity; PAGNI = performance- approach goal without
interactivity; MAG-INT = mastery-approach goal with interactivity; MAG-NI = mastery-approach goal with no
interactivity.
Interactive Non-Interactive
-10
-8
-6
-4
-2
0
2
4
6
8
-4.89
-7.43
-2.37
5.44
Interactivity x Instruction (Accuracy Difference Score, B2 - B1)
Performance-Approach Goal Mastery-Approach Goal
Mod
ular
Arit
hmet
ic P
erfo
rman
ce (%
)
Figure 3. Mean difference in modular arithmetic performance (%) as a function of
experimental condition (performance-approach goal or mastery-approach goal crossed with
interactivity or control).
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Performance-Approach Goal Mastery-Approach Goal
-7.0
-6.0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
-6.16
1.53
Instruction (Accuracy Difference Score, B2 - B1)M
odul
ar A
rithm
etic
Per
form
ance
(%)
Figure 4. Mean difference in modular arithmetic performance (%) as a function of
experimental condition (performance-approach goal or mastery-approach goal).
4.4.4 Latencies
Our second dependent variable was solution latency as part of the overall maths
performance of the modular arithmetic tasks. As before, a difference score was calculated by
subtracting the solution latency of block 1 from block 2 (B2 - B1). A 2 (instruction:
performance-approach goal or mastery-approach goal) x 2 (level of interactivity: interactivity
or control) between-groups analysis of variance (ANOVA) was conducted. There was no
main effect of instruction (mastery-approach goal or performance-approach goal) as F < 1,
failing to support the third and fourth hypotheses set in the beginning. Additionally, there was
no main effect of interactivity on the time it took for the participants to complete the task (F
< 1) which did not support the second hypothesis. Additionally, there was no two-way
interaction of instruction and interactivity (F < 1) which did not support the fifth and sixth
hypotheses that were set in the beginning. It is important to mention here that solution latency
(difference score, B2 - B1) was used as a covariate when the accuracy of maths tasks was
computed as part of the main statistical analysis.
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4.5 Discussion
The current study examined how motivational approach goals differentially impact
upon working memory resources. Additionally, the study aimed to further investigate how
interactivity influenced the effects of achievement goals on modular arithmetic performance.
We wanted to find out whether the detrimental effects of performance-approach goals on
academic performance could be alleviated with the help of distributed cognition and whether
there would be benefits in utilising distributed cognition for the mastery-focused individual.
The provision of a performance-approach goal reduced the modular arithmetic performance
compared to the mastery-approach group. Additionally, mastery-focused individuals suffered
a larger decrement than the performance-focused individuals in their modular arithmetic
performance when the participants were allowed to interact with external resources (with the
use of pen and paper).
There were no significant main effects of interactivity when looking at the modular
arithmetic performance of the current study, failing to support Hypothesis 1 and 2. Similar
findings have been reported in the Vallée-Tourangeau (2013) study where distributed
cognition allowed elevated performance only for the longer sums (11 single-digit numbers)
but not for the shorter sums (7 single-digit numbers). Participants performed marginally
better when they only relied on their internal cognitive resources. The degree to which the
design of an extended cognitive system can elevate cognitive performance is clearly relative
to the actual degree of task difficulty. With shorter sums, participants did not feel the need to
externalise the internal cognitive process as they were more efficient when relying on their
own internal cognitive resources and working memory. There was less effort required to
complete the task in the head alone (Vallée-Tourangeau, 2013). Similarly, the modular
arithmetic tasks of the current study were easy enough to be completed in the head alone and
there were no benefits to externalising this process.
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Earlier on, Study 1 of this PhD thesis reported a statistically significant main effect of
interactivity on modular arithmetic performance. The modular arithmetic tasks used in Study
1 had a higher level of difficulty; the numbers used were either double-digit or triple-digit
numbers and like the present study the tasks were presented in a horizontal format.
Distributed cognition allowed the participants to reach higher accuracy and efficiency.
However, there were no effects of stereotype threat on the maths performance but
interactivity allowed the participants to increase modular arithmetic performance.
We found that when women were primed into a performance-approach goal, there
was a drop in the mental arithmetic performance compared to a mastery-approach goal,
confirming the fourth hypothesis. One explanation for these findings was that when the
mastery-focused individuals showed higher mental arithmetic performance (confirming the
third hypothesis), it was assumed that these differences were related to the lack of the
outcome related anxiety confirming existing findings by Crouzevialle and Butera (2013).
Mastery-focused learning allows the individual to focus on their own learning and not
compare their academic performance to others. Hence, the lack of performance-based anxiety
may allow the participant to have higher mental arithmetic performance. Previous research
has suggested that the anxiety of outperforming others can tax working memory. Together
with the high-load working memory tasks, working memory resources may be further
compromised by performance-focused goals (Crouzevialle & Butera, 2013). Additionally,
under high working memory load, when a performance-approach goal has been made salient,
there is poorer working memory processing than in the mastery-approach goal environment
or when there is no go-goal control, leading to a performance drop (Avery & Smillie, 2013).
Another explanation for the reduced maths performance of the performance-focused
individual might be due to the implicit processing that is less working memory resource
demanding of the modular arithmetic tasks (Avery & Smillie, 2013). Perhaps there is more
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working memory capacity available to deal with the distractive thoughts which reduce task
focus and overall cognitive performance. Additionally, the mastery-focused individuals may
rely more on the WM resources due to explicit processing (deeper level of processing),
(Avery et al., 2013) and therefore their cognitive performance might deteriorate. However,
the current findings run contrary to the existing findings by Avery et al., (2013). The mastery-
approach goal participants’ maths performance in the present study was higher than the
performance-approach goal individuals and therefore does not support the findings of Avery
et al., 2013.
Interactivity did not allow any augmented maths performance for the participants in
the mastery-approach goal condition, confirming the final hypothesis (Hypothesis 6). On the
contrary, the maths performance of the mastery-approach goal participants was lower with
the use of pen and paper compared to when they did not use interactivity (control). This
finding suggests that there was a limited need to extend the current working memory
resources of the mastery-focused individual. It was assumed that their working memory
resources were not compromised due to the outcome related distractive thoughts or anxiety.
As mastery-focused individuals do not tend to worry about other people’s academic
performance and only focus on the benefits of their own learning, working memory is not as
heavily taxed as performance-focused individuals’ working memory. In other words, there is
no dual-task set-up for the mastery-focused individual. Interactivity may allow the agent to
extend their working memory resources when there is a need for this. Similarly, in another
study, dyslexic children (aged between 9 – 11 years) benefited the most from rearranging the
letter tiles (interactive condition) in a word production task. By reshaping the physical
presentation of the letters, their less efficient working memory capabilities could be
compensated. The control group (typically developing children) did not benefit from
externalising the internal cognitive process. In fact, their performance was poorer (with the
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easy set of letters) when they manipulated the tiles to produce words than when they did not
(Webb & Vallée-Tourangeau, 2009).
Finally, the study reported here used high WM load tasks only to see the possible
benefits of employing distributed cognition. The high-load tasks require the participant to
rely heavily on working memory resources to compute the task. There are computational
steps that need to be recalled (subtraction and division) and interim totals that require storing
in the working memory in order to compute the task efficiently. In the original Beilock and
Carr (2005) study, a mixture of low-load and high-load tasks were used to see the effects on
the cognitive performance, and in particular on working memory. Their study concluded that
the performance of the high-load tasks deteriorated if there were feelings of evaluative
pressure caused by situation-laden environments (e.g., stereotype threat) while working on
the required tasks. Similarly, the current study found that the performance-focused
individuals’ performance was lower in the non-interactive condition than in the interactive
condition.
4.6 Limitations of the Study
Whilst the findings of this study are encouraging, there are various limitations. The
current study only looked at the effects of distributed cognition on mental arithmetic
performance in relation to two different achievement goals. It could be argued that it is
actually the performance-avoidance goal that is more taxing on working memory due anxious
thoughts about not being able to complete the task in hand (Avery & Smillie, 2013). Whilst
the study reported here talked about increasing levels of anxiety of the performance-focused
students, there were no anxiety measures taken to show that performance goal individuals felt
more anxious, and that their working memory resources were taxed by this additional worry.
The current study has utilised existing empirical findings in this field. There was also no
measurement of working memory resources in the beginning of the study to show that the
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groups did not differ in their levels of working memory capacity measured before the priming
of the candidates.
Additionally, this study did not utilise any manipulation checks to make sure that the
priming of the achievement goals worked the way that they had been designed to work,
lacking internal validity. The present experiment, only utilised the statistical evidence to
demonstrate the findings of the study. Finally, the priming of the performance-approach goal
could be misunderstood as a performance-avoidance goal but as there were no manipulation
checks in place, this could not be investigated further.
4.7 Future Studies
Future studies would benefit in measuring maths anxiety of the participants both
before the experiment (trait maths anxiety) and after (state maths anxiety). If maths anxiety is
elevated when performance-approach goals are made salient then there should be more
benefits of externalizing the internal cognitive process to the outside world (interactivity) for
the performance-focused individual. Interactivity allows the agent to extend their working
memory capacity by allowing the use of external artefacts (e.g., pen and paper). It would also
be of interest to further understand the positive and negative effects that the participants
might experience after being allowed to use interactivity to compute the modular arithmetic
tasks. Interestingly, not all of the participants make use of the external artefacts; some of the
students compute the tasks without the help of a pen and paper. Hence, it could be argued that
even the thought of knowing that the option of writing things down (if needed to) could make
the participants feel more positive, and that on its own might help to improve the maths
performance. Future studies would also benefit in measuring basic arithmetic skills, and
working memory as an individual difference measurement to see that what generally drives
modular arithmetic performance, and to show that there are no group differences in the levels
of arithmetic skills and working memory.
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Chapter 5: Achievement Goals, Maths Performance, and Interactivity
The previous study of this PhD thesis (Study 3) found that the maths performance of
the participants in a mastery-approach goal condition was higher than that of individuals in a
performance-approach goal condition when interactivity was not employed. Additionally, the
mental arithmetic performance of the mastery-focused participants was compromised when
the use of pen and paper was allowed. We therefore concluded that there were no benefits of
externalizing the internal cognitive process to the outside world for this group of individuals.
The purpose of the present experiment is to further our understanding about
achievement goals and how they differently affect working memory resources. As before, we
are looking at the role of distributed cognition and whether both of the achievement goal
groups would benefit in interacting with the external world. Finally, one omission in Study 3
is that we did not measure maths anxiety. The current study will measure state maths anxiety
at the end of the experiment to see that if there are any maths anxiety differences between the
two achievement goal endorsements. We will also measure positive and negative affect in
order to see that if there are any positive effects of interactivity on maths performance.
Additionally, we will conduct a mediation analysis to investigate whether an increase in the
state maths anxiety levels will mediate the effect of achievement goals on maths
performance, in interactive or non-interactive condition.
5.1.1 Maths Anxiety
Maths anxiety is defined as a feeling of tension, apprehension, or fear that interferes with
maths performance. Maths anxious individuals often have less practice than low maths
anxious individuals because of negative thoughts, the avoidance of the subject, and any
maths-related situations. Individuals who are maths anxious get less practice and exposure in
mathematics because they avoid maths (Ashcraft, 2002). However, general achievement tests
show no competence differences between the highly maths anxious individuals and the low
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maths anxious individuals. However, when tests are timed the maths anxiety affects whole-
number arithmetic problems (e.g., 46 + 27), (Ashcraft, 2002). Additionally, individuals who
are maths anxious have negative attitudes towards mathematics and they have negative self-
perceptions about their skills in maths. However, there is only a weak link between maths
anxiety and overall intelligence (a small correlation of -.17). Highly maths anxious
individuals score high on other anxiety tests. The strongest link is between test anxiety and
maths anxiety (.52 correlation). Women report more feelings of maths anxiety. However, this
might be due to the fact that women are more honest about their feelings (Ashcraft, 2002;
Hembree, 1990).
Arithmetic problems with larger numbers (e.g., multiplication problems and two-column
additions) have shown two important maths anxiety effects. First, individuals with higher
levels of maths anxiety respond quicker to maths tasks than do individuals with lower levels
of maths anxiety. The quicker responses are typical of avoidance behaviour whereby
responding quickly, the highly maths anxious individuals reduce the amount of time that they
deal with the maths tasks. However, by doing the tasks quickly, there is a sharp increase in
errors. Secondly, the addition problems that have a carrying element are difficult for the
highly maths anxious individuals because of the extra burden on the working memory
(Ashcraft, 2002).
5.1.2 Maths Anxiety and Working memory
Individuals who have higher levels of maths anxiety demonstrate smaller working
memory spans (Ashcraft & Kirk, 2001). This is particularly evident with a computation-based
span task, similar to the task that this study has used. There is an increase of reaction times
and errors when mental additions are performed concurrently with a memory load task.
Maths anxiety causes a transitory disruption of working memory. The lower working
memory capacity of high maths anxious individuals is partially responsible for the maths
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performance decrements. This reduced working memory capacity is on on-line effect that
disrupts information processing in maths tasks (Ashcraft & Kirk, 2001).
Mathematics anxiety affects performance by overloading working memory (Hopko et
al., 1998). According to the processing efficiency theory, when a person is anxious about
something, worrying thoughts may distract attention from the task and therefore overload
working memory. General anxiety is also associated with working memory deficits. The
intrusive thoughts compete with the ongoing cognitive task for the limited working memory
resources. Intrusive thoughts can cause slowing of performance or reduced accuracy (lower
cognitive efficiency), (Eysenck & Calvo, 1992). Similarly, maths anxious individual might be
preoccupied with the dislike of mathematics and the previous bad experiences of this area,
and as a consequence working memory gets taxed. These intrusive thoughts act like a
secondary task, reducing the attention from the task (Ashcraft, 2002).
5.1.3 Achievement Goals and Maths Anxiety
There is a wealth of research about achievement goals and their effects on academic
performance but much less is known about the associations with anxiety, and maths anxiety
in particular. Butler (2013) reported that when people pursue performance goals (not mastery
goals) there are concerns about demonstrating superior abilities (performance-approach
goals) and masking any possible inferior abilities (performance-avoidance goals) that the
individual might have (Butler, 2013). According to Bong (2009), having a performance-
approach goal (not a mastery-approach goal) was correlated with maths anxiety (Bong, 2009;
Skaalvik, 1997). In another study, Linnenbrink (2005) reported that performance-approach
goals were detrimental for academic achievement and test anxiety, in particular (Linnenbrink,
2005). Additionally, Skalvik (1997) found that mastery goals predicted lower levels of maths
anxiety supporting the earlier findings. However, performance goals were not related to
anxiety. When an individual places the emphasis on avoiding a negative performance
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outcome, it can lead to increased anxiety. These are somewhat inconsistent findings in this
area and further research is required to fully understand the effects of achievement goals on
academic performance, and maths anxiety in particular. Anxiety is generally measured with
self-reported questionnaires and as such there can be inconsistent findings due to variety of
responses.
5.1.4 Positive Affect and Working Memory
There are various studies that have demonstrated a beneficial role of positive affect on
working memory. The current study examines if the use of interactivity during a mental
arithmetic task allows the individual to feel positive affect which in turn might allow
enhanced working memory resources and maths performance. In the Carpenter et al., (2013)
study, participants completed a computer administered card task (complex decision-making
task) in which they could gain monetary rewards if they chose from gain decks and lose
money if they chose from lose decks. The participants in the positive-feeling condition chose
generally better and made more money than the neutral-feeling participants. The participants
in the positive-feeling condition improved working memory capacity (Carpenter, Peters,
Västfjäll, & Isen, 2013). In another study, positive affect compared with neutral affect
enhanced working memory and controlled processing, in particular (measured with an
operations span task), (Yang, Yang, & Isen, 2013).
5.1.5 The Current Study
Study 3 reported that interactivity did not benefit the mastery-approach goal
participants. One explanation for the findings of Study 3 could be that mastery-focused
individuals did not feel the need to extend their existing working memory resources because
of lack of outcome related concerns. These worrying thoughts can tax working memory and
leave less capacity available to compute the mental arithmetic tasks (Crouzevialle & Butera,
2013). Solving mental arithmetic tasks at the same time with the worrying thoughts can place
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heavy demands on the limited working memory storage. Clearly, the taxing of working
memory seems to be more pronounced for performance-focused students than mastery-
focused students. Therefore, our first hypothesis (Hypothesis 1) is that mastery-approach goal
participants will have higher maths performance than performance-approach goal participants
because of lack of anxious thoughts about other people’s maths performance. It is predicted
that the maths performance of the performance-focused individuals will suffer in the non-
interactive condition (Hypothesis 2) because there are additional demands caused by anxiety
on working memory resources. We also predict (Hypothesis 3) that it will be the
performance-approach goal participants who will benefit more from distributed cognition
than the mastery-approach goal participants. Additionally, it is expected (as shown in Study
3) that the mastery-focused individuals will have a drop in their performance in the
interactive condition compared to those in the non-interactive condition (Hypothesis 4). One
reason that endorsing performance-approach goals (during the Study 3) may have led to a
greater decrement in performance compared to pursuing mastery-approach goals was because
of concerns about academic and maths performance because participants desired to achieve
better than others. Unfortunately, however, Study 3 failed to measure maths anxiety levels
(both before and after the experiment). Performance-focused individuals might show higher
levels of maths anxiety because of outcome related concerns in a mathematical domain
(Hypothesis 5). Experiment 4 therefore measured maths anxiety of the participants both
before the experiment (trait maths anxiety) and after (state maths anxiety). The pre-existing
maths anxiety levels were used as a covariate in the state maths anxiety statistical analysis to
show the actual effect of achievement goals on the maths anxiety level. Additionally, it was
argued that if the state maths anxiety is elevated when performance-approach goal is made
salient then clearly there should be more benefits of externalizing the internal cognitive
process to the outside world (interactivity) for the performance-focused individual
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(Hypothesis 6). Our seventh hypothesis was that the effects of achievement goal
endorsements on maths performance in the non-interactive condition would be mediated by
the increased state maths anxiety levels (Hypothesis 7).
We also hypothesized that participants in the mastery-approach goal conditions would
show higher levels of positive affect than participants in the performance-approach goal
condition due to lack of task-irrelevant thoughts and these thoughts not occupying the
working memory (Hypothesis 8). Linnebrink et al., (1999), reported that negative affect
mediated the positive relation between mastery-approach goals and working memory. There
was reduced negative affect for the mastery goal individuals. This in turn was related to
enhanced working-memory functioning. Performance goals had a negative indirect relation to
working memory by increasing negative affect (Linnenbrink et al., 1999). Another
explanation for the increased maths performance for the more performance-focused
individual in the interactive condition might be that there are more feelings of positive affect
with the help of the externalization of the internal cognitive process (Hypothesis 9). This
might consequently allow elevated working memory capacity, and mental arithmetic
performance. Finally, the research reported here also measured basic arithmetic skills (BAS)
and working memory capacity (computation span) before the modular arithmetic tasks in the
primed conditions to show that there were no pre-existing group differences between the
participants in the two different achievement groups.
5.2 Method
5.2.1 Participants
Seventy-eight female undergraduate psychology students (M = 19.12, SD = 1.60)
participated in this study for course credits. As in the Study 3, the current study only included
women because they evidence higher levels of maths anxiety than men (Hembree, 1990).
After consenting to participate in the study, the participants were randomly assigned to one of
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the experimental conditions (performance-approach goal or mastery-approach goal crossed
with interactivity or control). The participants were tested individually in a psychology lab at
the University of Surrey (UK), and the experimental session lasted 40 minutes. A statistical
power analysis (GPower, a priori) was performed for sample size estimation. With an alpha =
.05 and power = 0.80, the projected sample needed with the medium effect size of 0.09
(partial eta squared) was N = 80.
5.2.2 Material and Measures
Mathematics anxiety (trait). Maths anxiety was measured with the 23-item
Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). The test
comprises statements that relate to everyday situations that have a mathematics component
(e.g., adding up a pile of change). The participants respond by confirming the level of anxiety
that they feel on a 5-point Likert-type scale. The scale ranges from not at all to very much.
MAS-UK measures three levels of anxiety: maths evaluation anxiety, everyday maths
anxiety, and observation anxiety.
Basic arithmetic skills. Basic arithmetic skill (BAS) was measured with the help of
45 simple expressions in a 60-second period (e.g., 10-5). The participants were asked to
complete as many expressions as they could in 60 seconds.
Computation span (Working memory). Working memory capacity was measured
with the help of a computation-based span test. The participants were asked to read a simple
arithmetic expression (e.g., 5 + 2 = ?, 9 – 6 = ?) and announce their answer aloud to the
researcher (7, 3). Additionally, the participants were asked to remember the second number
of each equation to be recalled later (2, 6). The sequences of the simple arithmetic tasks
varied from 1 to 7 tasks. The computation span task requires both on-line processing for the
problem solution which is simultaneous with storage and maintenance of information in
working memory for serial recall. People with maths anxiety have smaller working memory
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spans than people who are not maths anxious. This smaller span can lead to increased
reaction times and errors when mental mathematics is completed at the same time as a
memory load task (Ashcraft & Kirk, 2001).
Arithmetic task. The modular arithmetic tasks used here were identical to Study 3.
There were two blocks of 24 modular arithmetic tasks that relied heavily on working memory
resources, adapted from Beilock and Carr (2005). The purpose of the tasks is to judge the
validity of maths problems like 61 ≡ 18 (mod 4). The middle number is subtracted from the
first number (i.e., 61-18) and then the difference is divided by 4. If the answer is a whole
number the maths problem is true (Beilock & Carr, 2005). Modular arithmetic tasks as
laboratory tasks are advantageous as most students have not seen them before and therefore
previous task experience is controlled.
High-demand problems [e.g., 42 ≡ 27 (mod 3)] requiring a double-digit subtraction
operation were used as they required borrowing, resulting in using more working memory
resources. Half of the maths problems required a true response by the participant. The order
of the questions was randomized and each question was asked only once. The original tasks
used by Beilock and Carr (2005) were a mixture of high WM demand problems (two-digit
numbers requiring borrowing) and low-load questions (single-digit numbers, without
borrowing), (Figure 5). The study reported here utilised the high-demand problems only
because of limited benefits of utilising interactivity with low-demand tasks as shown with the
Pilot study before. Additionally, the tasks were in a horizontal format as opposed to a vertical
format (Figure 6).
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Low-load tasks:9 ≡ 3 (mod 2)
High-load tasks:52 ≡ 24 (mod 3)
Figure 5. Examples of low-load and high-load modular arithmetic tasks. This figure is
adapted from (Beilock, 2008).
Figure 6. Examples of vertical and horizontal modular arithmetic problems. This figure is
adapted from (Beilock, 2008).
Positive and Negative Affect Schedule (PANAS). The PANAS consists of two 10-
item mood scales and provides brief measures of positive affect. Respondents are asked to
rate the extent to which they have experienced each particular emotion within a specified
time period, with reference to a 5-point scale (from 1 to 5). A number of different time-
frames can be used with the PANAS, but in the current study the time-frame adopted was
right now (Watson, Clark, & Tellegen, 1988).
Mathematics anxiety (state). Maths anxiety was measured with the 23-item
Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This
test was the same as the trait measurement used earlier during the experiment but this time
referring to present time (now). The participants responded by confirming the level of anxiety
that they felt after completing the experiment.
Experimental manipulations. The priming instructions were identical to Study 3.
Participants were informed after completing the baseline block of modular arithmetic tasks
(24) that they were required to complete a second block (24) of modular arithmetic tasks and
this time their performance would be recorded. The participants in the performance-approach
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Vertical MA tasks: 52
≡ 24 (mod 3)
Horizontal MA tasks:52 ≡ 24 (mod 3)
goal condition read the following instructions before starting the task that were aimed at
activating performance-approach goals:
During the recorded part of the task, the experimenters will assess your performance.
It is important for you to be proficient, to perform well and obtain a high score, in
order to demonstrate your competence. You should know that a lot of students will do
this task. You are asked to keep in mind that you should try to distinguish yourself
positively, that is, to perform better than majority of students. In other words, what we
ask you here is to show your competencies, your abilities. (Darnon et al., 2007, p. 7)
The participants in the mastery-approach goal condition read instructions that were
designed to activate mastery-approach goals. There is no social comparison being made and
the instructions are aimed to create task interest, use for everyday life, and there is no
mention about scores or task performance:
In previous research, we have observed that practice of the arithmetic task you are
solving right now benefits to cognitive functioning and leads to a progressive
improvement of mental processes. Hence, this task solving can be proven to be
beneficial on the long-term. It is however necessary that you focus your attention on
calculation mastery, so as to quickly and accurately solve each problem, in order to
experience these benefits. Try to master this task as much as you can; keep in mind its
practice can be beneficial to you. (Crouzevialle et al., 2015, p. 816)
Interactivity. As before the participants in the interactive condition were allowed to
use pen and paper to come to the solution. In other words, interactivity allowed the individual
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to off-load the working memory content to the external world. On the contrary, the
participants in the non-interactive condition were not allowed to use any external artefacts,
and were required to rely on their internal cognitive resources only.
5.2.3 Procedure
After consenting to participate in the current study, the participants commenced with
the trait maths anxiety questionnaire. This was then followed by the timed basic arithmetic
skills test where the participants were told to complete as many questions as they could in 6o
seconds. Before starting with the modular arithmetic tasks in primed conditions, computation
span (working memory capacity) was assessed. The working memory assessment was done
in an oral format with the researcher. The assessment required on-line processing and
maintenance of computation-based information. After that, there was a short training session
(2 questions) before starting the first block of the modular arithmetic problems (24) that acted
as a baseline. Only high-demand problems requiring a double-digit subtraction operation
[e.g., 42 ≡ 27 (mod 3)] were used as they required more of the working memory resources
compared to low-demand problems (single-digit operation, and no carrying required),
(Ashcraft & Kirk, 2001). The participants were primed to either performance-approach goal
condition or mastery-approach goal condition crossed with interactivity or control (during
block 1 and block 2 only). If in the interactive condition, the use of pen and paper was
allowed. After completing the second block of arithmetic tasks, the participants were required
to complete the PANAS questionnaire. Finally, the experimental session was concluded with
the state maths anxiety measurement that was the same measurement that was used earlier
(trait maths anxiety) but this time referring to the current time (now). The participants were
briefed and thanked after their participation in the experiment.
5.3 Results
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5.3.1 Data Analysis Plan
To investigate the hypotheses, three separate 2 (instruction: performance-approach
goal or mastery-approach goal) x 2 (level of interactivity: interactivity or control) between-
groups analysis of covariance (ANCOVA) were conducted with percentage correct
(accuracies), solution latencies, and state maths anxiety as dependent variables. Accuracy
difference score was calculated by subtracting the modular arithmetic performance of block 1
from block 2. Furthermore, a difference score in latencies was used as a covariate to avoid
any speed-accuracy trade-off of the participants. We also conducted, a 2 (instruction:
performance-approach goal or mastery-approach goal) x 2 (level of interactivity: interactive
or control) between-groups analysis of variance (ANOVA) with PANAS as the dependent
variable. Additionally, a detailed correlational analysis was included as part of the results
section. Finally, we conducted a mediation analysis to confirm whether an increase in the
state maths anxiety levels would mediate the effect of achievement goals on maths
performance in the non-interactive condition.
5.3.2 Group Differences
There were no group differences between the participants in the two achievement goal
groups on the baseline modular arithmetic performance (block 1), F(1, 74) = 1.77, p = .19, ŋp2
= .02, confirming that the groups did not differ in their ability to complete the modular
arithmetic tasks. Additionally, there were no group differences on the baseline (block 1)
latencies to solution either, F(1, 74) = 0.42, p = .52, ŋp2 = .006 indicating that the participants
did not vary in their speed to complete the modular arithmetic tasks during the baseline
assessment. Additionally, the two achievement goal groups did not have different levels of
working memory capacity, F(1 ,74) = 1.17, p = .28, ŋp2 = .02 when tested before priming to
the experimental conditions. Similar findings were made for basic arithmetic skills, F(1, 74)
= .28, p = 0.60, ŋp2 = .006 and trait maths anxiety, F(1, 74) = 0.39, p = .27, ŋp
2 = .02 (Table
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13). Table 14 summarises the block 1 means and standard errors and Table 15 is the means
and standard errors for block 2 (for comparison).
Table 13
Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data)
M SD
Maths anxiety (trait) 52.54 10.34
Basic arithmetic skills (BAS) 22.82 8.35
Computation span (WM) 23.64 6.06
Note. Participants were not conditioned to complete the pre-testing tests. All the tests were
completed before priming. The pre-testing comprised of mathematics anxiety (trait), basic
arithmetic skills (BAS), and working memory. The scale for mathematics anxiety is from 0 to
115, basic arithmetic skills is from 0 to 45, and the scale for computation span is from 0 to
56.
Table 14
Descriptive Statistics and Standard Errors of Modular Arithmetic Performance (Accuracy
and Latencies to Solution) in Block 1
Interactive Non-interactive
M SE M SEAccuracy (%) 92.10 1.30 87.90 1.30
Latency (seconds) 16.62 0.80 13.15 0.80Note. There was no priming of achievement goals (mastery-approach goal or performance-
approach goal) in block 1. Participants completed the modular arithmetic tasks in interactive
or non-interactive condition only.
Table 15
Descriptive Statistics and Standard Errors of Modular Arithmetic Performance (Accuracy
and Latencies to Solution) in Block 2
Interactive Non-interactive
M SE M SE
Accuracy (%) 92.10 1.30 91.10 1.30
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Latency (seconds) 14.87 0.65 12.04 0.65
Note. This is the interactive or control condition only in order to get a comparison with block
1.
5.3.3 Accuracy
To test the hypotheses, accuracy difference score (block 2 - block 1) of the modular
arithmetic tasks was examined. A 2 (instruction: performance-approach goal or mastery-
approach goal) x 2 (level of interactivity: interactivity or control) between-groups analysis of
covariance (ANCOVA) was conducted with latency difference score as a covariate (Table 16
includes the means and standard errors based on the difference score of B2 – B1). To begin
with, the two main effects (interactivity or instruction) did not reach statistical significance
failing to support hypotheses 1 and 2. There was no significant difference in accuracy
between the participants in the interactive condition and the participants in the non-interactive
condition, F(1, 73) = 2.35, p = .13, ŋp2 = .03. Additionally, the main effect of instruction
(mastery-approach goal or performance-approach goal) did not reach statistical significance
(F < 1).
However, there was a significant two-way interaction of instruction (mastery-
approach goal or performance-approach goal) and interactivity (interactivity or control), after
controlling for a difference score in latencies, F(1, 73) = 10.04, p = .002, ŋp2 = .12. As
anticipated, the participants in the performance-approach goal condition benefited from
interactivity as their maths performance was higher (M = 3.70, SE = 1.80) than the
participants in the mastery-approach goal condition (M = -3.30, SE 1.90), confirming
Hypothesis 3 (Figure 5), F(1, 36) = 6.82, p = .01, ŋp2 = .16. As already shown in Study 3, the
maths performance of the participants in the mastery-approach goal condition was lower in
the interactive condition (M = -3.30, SE = 1.90) than in the non-interactive condition (M =
5.40, SE = 1.90) confirming the fourth hypothesis, (Figure 7), F(1, 36) = 10.67, p = .002, ŋp2
= .23.
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Interactive Non-Interactive
-4.00-3.00-2.00-1.000.001.002.003.004.005.006.00
3.70
0.60
-3.30
5.40
Interactivity x Instruction (Accuracy Difference Score, B2 - B1)
Performance-Approach Goal Mastery-Approach Goal
Mod
ular
Arit
hmet
ic P
erfo
rman
ce (%
)
Figure 7. Mean difference in modular arithmetic performance (%) as a function of
experimental condition (performance-approach goal or mastery-approach goal crossed with
interactivity or control).
Table 16
Descriptive Statistics and Standard Errors of the Primary Dependent Variables (Based on a
Performance Difference Score, B2 – B1)
PAG-INT PAG-NI MAG-INT MAG-NIn = 20 n = 21 n = 19 n = 18
M SE M SE M SE M SE
Accuracy (%) 3.70 1.80 0.60 1.80 -3.30 1.90 5.40 1.80
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Latency (seconds) -0.86 0.56 -1.50 0.57 -2.65 0.58 -0.71 0.56
PANAS (positive) 23.50 1.68 24.32 1.72 26.05 1.72 25.05 1.68
PANAS (negative) 17.25 1.32 16.32 1.35 15.68 1.35 16.45 1.32
Maths anxiety (state) 57.14 2.76 54.92 2.83 46.86 2.86 51.32 2.76Note. PAG-INT = performance-approach goal with interactivity; PAGNI = performance-
approach goal without interactivity; MAG-INT = mastery-approach goal with interactivity
and MAG-NI = mastery-approach goal with no interactivity. Only the modular arithmetic
tasks employed interactivity (accuracy and latency to solution).
5.3.4 PANAS
PANAS (positive affect) scores were analysed with the help of a 2 (level of
interactivity: interactivity or control) x 2 (instruction: performance-approach goal or mastery-
approach goal) between-groups analysis of variance (ANOVA). The two main effects of
interactivity or instruction did not reach statistical significance. There was no significant
difference in positive affect between the participants in the interactive condition and the
participants in the non-interactive condition, F < 1. Additionally, the main effect of
instruction (mastery-approach goal or performance-approach goal) did not reach statistical
significance (F < 1) failing to support Hypothesis 8. There was no significant two-way
interaction of interactivity (interactivity or control) and instruction (mastery-approach goal or
performance-approach goal) either, F < 1, failing to support Hypothesis 9 (Table 16).
PANAS (negative affect) scores were also analysed with a 2 (level of interactivity:
interactivity or control) x 2 (instruction: performance-approach goal or mastery-approach
goal) between-groups analysis of variance (ANOVA). The two main effects (interactivity or
instruction) did not reach statistical significance. There was no significant difference in
negative affect between the participants in the interactive condition and the participants in the
control condition, F < 1. Additionally, the main effect of instruction (mastery-approach goal
or performance-approach goal) did not reach statistical significance (F < 1). Finally, there
145
was no significant two-way interaction of interactivity (interactivity or control) and
instruction (mastery-approach goal or performance-approach goal) as F < 1.
5.3.5 Maths Anxiety (State)
A two-way between groups analysis of covariance (ANCOVA) was conducted to
compare the effects of interactivity on two levels of instructions that were given to the
participants (mastery-approach goals or performance-approach goals) when completing the
modular arithmetic tasks. After adjusting for pre-existing maths anxiety levels (trait maths
anxiety), there was a significant main effect of instruction (mastery-approach goal or
performance-approach goal) on state maths anxiety, F(1, 73) = 6.07, p = .02, ŋp2 = .08. The
participants in the performance-approach goal condition showed higher levels of maths
anxiety after completing the experiment in primed conditions (M = 56.03, SE = 1.98) than the
participants in the mastery-approach goal condition (M = 49.09, SE = 1.98) confirming the
Hypothesis 5 (Figure 6). The main effect of interactivity did not reach statistical significance
(F < 1) nor did the two-way interaction of instruction and interactivity, F (1, 73) = 1.42, p
= .24, ŋp2 = .02 failing to confirm Hypothesis 6.
Performance-Approach Goal Mastery-Approach Goal44
46
48
50
52
54
56
5856.03
49.09
Maths Anxiety (State)
Mat
hs A
nxie
ty
Figure 8. Mean difference in state maths anxiety levels as a function of experimental
condition (performance-approach goal or mastery-approach goal).
146
5.3.6 Mediation
We conducted a mediation analysis to further understand whether an increase in the
state maths anxiety levels in the non-interactive condition would mediate the effect of
achievement goals on maths performance. The mediation analysis was conducted as a
function of interactivity (interactive condition or control). There was no evidence of direct or
indirect mediation of state maths anxiety on maths performance in the non-interactive
condition as p = .17 [in path a (between achievement goal instruction and state maths
anxiety), b (between state maths anxiety and maths performance) and c (between
achievement goal instruction and maths performance)] failing to support the Hypothesis 7. In
the interactive condition, there was a direct effect of instruction (performance-approach goal
or mastery-approach goal) on the maths performance, t(78) = -2.89, p = .007. However, there
was no evidence of direct or indirect mediation as p = .15 (in path a and b) failing to support
Hypothesis 7.
5.3.7 Correlations
A correlational analysis of the performance-focused individuals was conducted to
further explore what was driving the mental arithmetic performance, and the state maths
anxiety levels for the more maths-anxious individuals (trait), (Table 17 and 18). Only the
participants in the performance-approach goal condition were included in the analysis here as
they were the more maths-anxious (state) participants. Additionally, it was these individuals
who benefited the most from coupling of the internal cognitive resources with the external
environment. We compared the correlations in the interactive condition with the control
condition to see any possible differences. As we anticipated, trait maths anxiety was strongly
correlated with the state maths anxiety in the interactive condition, r(78) = .59, p = .006.
Additionally, there was a strong correlation between trait maths anxiety and basic arithmetic
skills, r(78) = -.51, p = .02. In the non-interactive condition, there was a strong correlation
147
between trait maths anxiety and state maths anxiety, r(78) = .60, p = .007. Additionally, trait
maths anxiety was strongly correlated with working memory, r(78) = -.50 p = .007. But more
importantly, the correlations revealed that in the non-interactive condition, there was a
marginally significant correlation of working memory capacity and state maths anxiety,
r(78) = -.41, p = .08. However, this same pattern could not be found in the interactive
condition suggesting that interactivity functioned as extended working memory capacity in
the interactive condition for the more maths-anxious performance-focused individual.
Interactivity allowed the more maths-anxious participant to extend their existing working
memory capacity.
Table 17
Summary of Correlations in the Performance-Approach Goal and Non-Interactive Condition onlyMeasure 1 2 3 4
1. Maths anxiety (trait) 1 -.34 -.50* .60**
2. Basic arithmetic skills -.34 1 .17 -.40
3. Working memory -.50* .17 1 -.41
4. Maths anxiety (state) .60** -.40 -.41 1
Note. * = correlation is significant at the .05 level, ** = correlation is significant at the .01 level.
***The Bonferroni cut-off is 0.0125.
Table 18
Summary of Correlations in the Performance-Approach Goal and Interactive Condition only
Measure 1 2 3 4
1. Maths anxiety (trait) 1 -.51* -.12 .59**
2. Basic arithmetic skills -.51* 1 .39 -.14
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3. Working memory -.12 .39 1 .14
4. Maths anxiety (state) .59** -.14 .14 1
Note. * = correlation is significant at the .05 level, ** = correlation is significant at the .01 level.
***The Bonferroni cut-off is 0.0125.
6 Discussion
The purpose of this study was to further our understanding on the effects of
interactivity on the maths performance of mastery-approach goals. We also wanted to
investigate whether the adverse effects of performance-approach goals on mental arithmetic
performance could be alleviated with the use of distributed cognition. We considered the role
of maths anxiety (state) and whether interactivity could be used as an innovative way of
defusing the possible impact of maths anxiety on mental arithmetic performance. We found
that participants in the two achievement goal conditions did not differ in their levels of
modular arithmetic task (block 1), latency (block 1), working memory, basic arithmetic skills,
and trait maths anxiety levels. Thus, the performance differences that were found as part of
the main analysis were not due to pre-existing achievement group differences.
As found in the Study 3, there was lower maths performance for the participants in the
mastery-approach goal condition with interactivity compared to the non-interactive condition,
supporting Hypothesis 4. Mastery-focused individuals did not feel the benefits of
externalising the internal cognitive process of computing the maths tasks. On the contrary,
there was a clear performance drop when interactivity was employed, replicating the finding
of Study 3 in this thesis. Similar findings have been made by Webb and Vallée-Tourangeau
(2009) who reported that dyslexic children (aged between 9 – 11 years) benefited the most
(compared to typically developing children) from rearranging letter tiles (interactive
condition) in a word production task. By allowing dyslexic children to reshape the physical
presentation of the letters, their less efficient working memory capabilities could be
compensated. There were no benefits of externalising the internal cognitive process for the
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typically developing children (control group), they had the required working memory
resources and capabilities to compute the tasks. In fact, their performance deteriorated (with
the easy set of letters) when they manipulated the tiles to produce words (Webb & Vallée-
Tourangeau, 2009).
There can be cognitive cost implications in relation to how beneficial and successful
the use of interactivity is. Sometimes it is quicker and easier to rely on the internal resources
only (Kirsh, 2010). The mastery-approach goal endorsement of the current study did not
affect the cognitive resources of the participants in a way that it would have been beneficial
to utilise the external resources to complete the task. However, as expected, the participants
in the performance-approach goal condition had higher maths performance compared to the
participants in the mastery-approach goal condition in the interactive condition supporting
Hypothesis 3. There were more benefits for the more performance-focused individual than
the mastery-focused individual to utilise the external resources that were provided to
complete the task. Clearly, the internal cognitive resources (including working memory) were
adversely affected by the performance-approach goal endorsement and there were clear
benefits of coupling the internal and external resources of the individual to come to the
solution. These findings are in line with Avery and Smillie (2013) who concluded that the
pursuit of performance-approach goals can have an adverse effect on the working memory
processing of the participants and can cause a performance drop (Avery & Smillie, 2013).
The current study added to this finding in that the opportunity to externalise the internal
cognitive process has allowed the extension of working memory resources (the processing
part in particular) and caused a positive effect on the maths performance.
We also found that the individuals in the performance-approach goal condition felt
higher levels of state maths anxiety after completing the maths tasks (supporting Hypothesis
5). This is in contrast with the Avery and Smillie (2013) study where it was reported that
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there were no heightened state anxiety levels in the performance-approach goal condition.
The same authors concluded that under high load, the endorsement of performance-approach
goals resulted in poorer working memory processing (N-Back working memory task) than the
pursuit of mastery-approach goals or no-goal condition. The adverse effects on working
memory processing were only felt under high executive load (3-back) but not under the less
demanding tasks (1-back or 2-back), (Avery & Smillie, 2013). Additionally, there was no
direct measure of state maths anxiety in the Butera and Crouzevialle (2013) study either. A
performance drop of the performance-approach goal individuals was explained by distractive
thoughts (Study 1 and 2) that were due to the activation of performance-approach goal related
thoughts during the task solving (Study 3) rather than increased state anxiety levels. Study 3
used thought suppression manipulation to investigate this. When an individual tries to get rid
of a particular thought, an opposite reaction happens and there can be an increase in its
accessibility (Wegner, 1994). This effect is generally caused by a disruption of the
monitoring process. Additionally, there is a supervision process that searches for the
unwanted thought presence to point out a failure of suppression (not easily disrupted by
additional load). This disruption of monitoring thoughts can trigger accessibility to the
unwanted content (e.g., normative goal attainment concerns), (Wegner, 1994). Activation of
performance-approach goal-related content has been found to be responsible for distractive
effects (Crouzevialle & Butera, 2013) .
Additionally, the study reported here did not find a two-way interaction between
achievement goal endorsements and interactivity on state maths anxiety. Whilst it is evident
that performance-approach goal condition allowed the participants to feel higher levels of
maths anxiety, there was no evidence to suggest that the anxiety levels were reduced with the
help of interactivity and as a consequence, the working memory extended and maths
performance enhanced. Clearly, the endorsement of the achievement goals was still felt post-
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priming but not the interactivity that was utilized during the mental arithmetic tasks. The
participants in the performance-approach goal condition showed higher levels of maths
anxiety after the experiment but this anxiety was not reduced with coupling of the agent and
the environment. Finally, it is important to mention that the participants completed the
PANAS measurement straight after the mental arithmetic tasks in primed conditions. This
was then followed by the state maths anxiety measure.
There were no effects of interactivity that carried on to the subsequent tests (i.e.,
PANAS and state maths anxiety) in the experiment reported here. To our knowledge, there
are no empirical studies on interactivity that have measured maths anxiety post-experiment.
Most of the existing studies on interactivity have concentrated on the differences of low and
high maths anxious individuals and how their maths performance is affected by the increased
levels of interactivity. These studies have concluded that there are more benefits of
externalising the internal cognitive process to the outside world for the more maths anxious
individual (e.g., Allen & Vallée-Tourangeau, 2016).
Unlike the current study, Study 2 reported that there were strong carry-on effects of
distributed cognition on state maths anxiety after completing maths tasks in primed
conditions. Participants who were allowed to extend their existing working memory resources
felt less maths anxious after the experiment than before. The level of difficulty of the mental
arithmetic tasks that were utilised in Study 2 were higher (modular arithmetic tasks that were
up to three-digit numbers) than the current study (two-digit numbers) and would therefore
possibly explain the statistically significant result of interactivity reducing the levels of trait
maths anxiety. There were more benefits of using interactivity with the higher difficulty
level, and this had a causal effect on the trait maths anxiety levels too. Similar findings have
been found in Vallée-Tourangeau (2013) where increased interactivity allowed increased
performance only for the longer sums (11 single-digit numbers) but not for the shorter sums
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(7 single-digit numbers). Participants performed marginally better when they only relied on
their internal cognitive resources (Vallée-Tourangeau, 2013).
Additionally, we conducted a mediation analysis to investigate the role of state maths
anxiety on maths performance. The mediation analysis indicated that achievement goals did
not have a direct or indirect mediation effect of state maths anxiety on the maths performance
when in the non-interactive condition. In other words, the change in the state maths anxiety
levels did not mediate the maths performance when the maths tasks were not completed
without the assistance of interactivity. Instead, there was a direct effect of achievement goals
on maths performance in the interactive condition. This pattern could not be found in the non-
interactive condition.
This study failed to show any statistically significant results of positive affect. The
mastery-focused individuals did not feel more positive affect than the performance-focused
individuals failing to confirm hypothesis 8. It was predicted that the coupling of the internal
cognitive resources with the external environment would enhance the level of positive affect
for the participants in the interactive condition. This would consequently extend working
memory resources and increase the mental arithmetic performance, particularly for the
performance-goal participants. Interactivity did not increase the levels of positive affect
failing to confirm Hypothesis 9. We predicted that if the participants would show higher
levels of positive affect in the interactive condition, this affect would be more beneficial for
the performance-focused individual as part of their working memory resources were occupied
by worry about outperforming the others. If interactivity allowed the participants to feel more
positive affect, this affect would allow working memory to be augmented and maths
performance enhanced.
A correlational analysis (performance-approach goal only) revealed that in the non-
interactive condition, working memory was correlated with state maths anxiety. However,
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this correlation was not statistically significant in the interactive condition. This finding lends
its support to the important role of interactivity for the more maths anxious individual. With
elevated working memory resources, there was a reduction of state maths anxiety in the non-
interactive condition, for the performance-approach goal participant. In other words,
interactivity functioned as extended working memory capacity in the interactive condition for
the more maths-anxious performance-focused individual.
Finally, the mental arithmetic tasks that this study utilised relied heavily on working
memory resources in that only high working memory load tasks were employed (Beilock &
Carr, 2005). Thus, interactivity allowed working memory to be extended when performance-
approach goals were made salient but not for the less anxious mastery-focused individual. In
conclusion, distributed cognition hindered maths performance for the mastery-focused
individual who was less maths anxious after the experiment but allowed the more maths-
anxious individual (performance-approach goal) to improve mental arithmetic performance.
7 Limitations
Whilst the findings of this study are encouraging, the current experiment has only
looked at two of the four achievement goals. The experiment did not investigate the effects of
mastery-avoidance goals and performance-avoidance goals on mental arithmetic performance
and whether distributed cognition could be used as an innovative way of elevating maths
performance. According to Elliott and McGregor (2001) both of the avoidance goals are
linked to test anxiety (Elliot, & McGregor, 2001). If the avoidance goal participants
(performance-avoidance goal or mastery-avoidance goal) were the more anxious individuals,
then there might be more benefits of interactivity for this group of participants.
8 Future Studies
Future studies would benefit in further understanding the reasons behind the increased
maths anxiety levels. Written protocols could be included in any further experiments to
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further explore what is causing the anxiety in relation to the different achievement goals. It
would also be of interest to use different difficulty levels of the modular arithmetic tasks. As
was shown earlier, the more complicated tasks that were used in Study 2 allowed the benefits
of externalising the internal cognitive process to be more visible. Additionally, the current
study only had female participants. Future studies would benefit in having both males and
females to investigate gender differences in relation to the effects of achievement goals on
working memory.
Chapter 6: Discussion
Across four empirical studies, this thesis investigated the role of distributed cognition,
and whether interactivity could be employed as an innovative way to maintain working
memory capacity and mental arithmetic performance while experiencing evaluative pressure.
This evaluative pressure can be caused by negative stereotypes about girls’ maths
performance (Study 1 and 2) or achievement goals, and performance-approach goals in
particular (Study 3 and 4). Whilst there are various other situation-induced pressure
situations, the current programme of research focused on negative stereotypes and
achievement goals because both of these pressure situations may contribute to the same type
of cognitive mechanisms when it comes to depleting working memory capacity caused by a
stressful situation. In order to address these questions, this thesis had the following three
research objectives: 1) to examine the impact of interactivity on mental arithmetic
performance, 2) to examine how working memory and maths performance are affected by
situation-induced stress caused by priming (a) negative gender-related stereotypes (girls and
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mathematics) or (b) achievement goals (performance-approach goals and mastery-approach
goals), and 3) to examine the role of interactivity on maths performance and maths anxiety in
evaluative pressure situations caused by stereotype threat or achievement goals. The
following section will focus on presenting the findings of the four studies that contributed to
this thesis. We will begin by presenting a summary of the findings followed by a detailed
discussion based on the similarities and differences of the studies and limitations. This
section will conclude with theoretical and practical contributions of the findings and
recommendations for future studies.
1.1 Summary of the Findings
The purpose of this PhD programme of research was to investigate the role of
distributed cognition in mathematical problem solving, in evaluative pressure situations (i.e.,
stereotype threat and achievement goals in mathematical problem solving). As expected,
interactivity increased maths accuracy and reduced solution latencies (Study 1) confirming
existing findings (Guthrie, Harris, & Vallée-Tourangeau, 2015; Guthrie, Mayer, & Vallée-
Tourangeau, 2014). When girls were negatively primed about their maths performance, there
was a reduction in their working memory performance. However, the priming did not reduce
mental arithmetic performance. This study also found that participants’ maths anxiety levels
were not affected by the priming of negative stereotypes about girls’ maths performance.
As before, in the second study, interactivity increased accuracy in all of the three
different maths tasks. However, there were more benefits of interactivity for the tasks
requiring more working memory (i.e., MA tasks). Additionally, the individuals became
slower with the more demanding, novel modular arithmetic tasks. Participants spent more
time in getting the tasks correct at the expense of time (speed-accuracy trade-off). Unlike the
first study, this study found no effects of stereotype threat on working memory. There were
no effects of stereotype threat on the maths performance of the female university students.
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Finally, combining the internal and external resources of the reasoner allowed the participants
to feel less state maths anxiety when the difficulty level of the maths tasks was high and
when maths anxiety was measured straight after the primed maths tasks.
As predicted, the third study found that the individuals in the performance-approach
goal setting had a drop in their MA performance compared to participants in the mastery-
approach goal condition. Whilst it was not measured as part of the investigation, it is possible
that the drop in the performance was due to additional concerns about outperforming the
other participants (Crouzevialle & Butera, 2013; Crouzevialle et al., 2015). Perhaps also there
was less taxation of the working memory because of the strategies employed by the
participants in the performance-approach condition (implicit processing) to compute the
maths tasks compared to participants in the mastery-approach goal condition. As a
consequence of the implicit processing, more space in working memory was used to
concentrate on competing with others. Another explanation for the impaired maths
performance of the participants in the performance-approach condition could be that there is
impaired working memory processing of the performance-focused participants suggested by
Avery and Smillie (2013), resulting in impaired cognitive performance. An unexpected
finding was that the maths performance of the mastery-approach goal participants was
hampered with the interaction of external artefacts (with the use of pen and paper). Clearly,
the working memory of the participants in the mastery-approach goal condition was not
negatively affected because of the pursuit of the mastery-approach goal and therefore there
was no cognitive need to interact with the external artefacts to reduce the overall cognitive
load, confirming existing findings (Cox, 1999; Kirsh, 1995; Vallée-Tourangeau &
Wrightman, 2010; Webb & Vallée-Tourangeau, 2009).
Finally, Study 4 replicated the findings of the performance drop of the mastery-
approach goal participants. In contrast to Study 3, however, individuals in performance-
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approach goal condition benefited from the use of distributed cognition. We found that the
individuals in the performance-approach goal condition showed higher levels of state maths
anxiety at the end of the experiment than the individual in the mastery-approach goal
condition. However, after conducting a mediation analysis, we found that state maths anxiety
levels did not mediate the maths performance when interactivity was not employed
suggesting that interactivity had allowed the individuals in the performance-approach
condition to increase maths performance but not because of reduced anxiety levels as
originally thought. Whilst not measured as part of the investigation, it is possible that the
maths performance of the participants in the performance-approach goal condition was
elevated because interactivity allowed improved working memory processing required to
solve mental arithmetic tasks. Clearly, concerns about outperforming others had made the
participants more maths anxious as shown with the significant main effect of interactivity of
performance-focused individuals. However, there were no effects of increased interactivity
on state maths anxiety levels after priming of the participants. Hence, it looks like the
participants of the performance-approach goal condition may have benefited from
interactivity by allowing the participant with the reduced working memory processing to
increase their maths performance.
1.2 The Effects of Interactivity on Maths Performance
Across the two first studies, the accuracy of the mental arithmetic tasks was markedly
improved with increased interactivity, addressing the first research objective. Similar findings
have been made before (Carlson, Avraamides, Cary, & Strasberg, 2007; Kirsh, 1995; Vallée-
Tourangeau, 2013). Individuals who had the opportunity to externalize their internal
cognitive process benefited vastly in doing so. Recruiting external artefacts (the use of pen
and paper in this case) allowed the participants to transform their mental arithmetic
performance. The task difficulty level of the mental arithmetic tasks of the two first studies
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was high enough to clearly experience the benefits of employing distributed cognition. If a
task is too easy and there are no benefits of externalising the process, individuals will rely on
the internal processes only (Kirsh, 2010). Additionally, participants might be more accurate
and faster when relying on their own internal cognitive abilities. This same pattern of
increased accuracy could be found when the modular arithmetic tasks were employed during
the second study. When looking at the means of the modular arithmetic tasks with
interactivity, there was a higher percentage increase for the high WM load modular arithmetic
tasks than the lower WM load modular arithmetic tasks. For the low load tasks, interactivity
increased the performance by 5.70% and for the high load tasks, interactivity allowed an
increase of 11.30%. The high load tasks benefited more from the endorsement of distributed
cognition.
When it came to solution latencies, the participants in the interactive conditions of
Study 1 were quicker than participants in the non-interactive conditions. However,
interactivity made the participants slower when modular arithmetic tasks (both the low WM
load and high WM load tasks) were completed during Study 2. There was a speed-accuracy
trade-off with novel and more working memory dependent tasks. The participants’ focus on
increasing maths accuracy resulted in increased solution latencies. In other words, the cost of
improving accuracy was the increased latency to solution when novel tasks were computed.
1.3 The Impact of Stereotype Threat on Mental Arithmetic Performance
Across the two studies, it was found that there were no significant main effects of
stereotype threat on mental arithmetic performance (accuracies and latencies), addressing the
second research objective. Thus, negative stereotyping about women’s maths performance
did not hamper the participants’ maths performance in terms of accuracy and how quickly the
participants completed the tasks. Whilst there were similar findings made about the effects of
stereotype threat on maths performance in the first two studies, the statistically non-
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significant results of these studies may have resulted from different reasons. Participants in
the first study were Year 12 students who had recently completed the General Certificate of
Secondary Education (GCSE) maths assessment where mental arithmetic is one of the
mandatory sections of the maths syllabus. Thus, they were well-rehearsed in mental
arithmetic tasks and the processes of computing these tasks in an efficient manner due to
extensive preparations for the GCSE maths assessment. The girls had the required skill and
experience to manage the type of mental arithmetic tasks that were utilised in the Study 1 and
were not affected by the negative stereotyping while completing these difficult mental
arithmetic tasks.
While completing the mental arithmetic tasks, the participants of the first study were
clearly utilising strategies that did not rely too heavily on existing working memory
resources. They were following automated processes that did not put additional pressure on
the working memory. This was in line with Beilock et al., (2007) who reported that
stereotype threat about females’ maths performance harmed maths performance (high WM
load modular arithmetic tasks) that relied heavily on working memory resources and the
phonological parts of the system in particular. However, it was found that by heavily
practising the mental arithmetic tasks, the negative effects of stereotype threat could be
alleviated. There is less pressure on the working memory resources when the tasks have been
actively rehearsed. When the tasks are heavily practiced, they are retrieved from the long-
term memory rather than from the working memory (Beilock et al., 2007). A good example
of this type of memory retrieval would be multiplication tasks. When multiplication tasks are
computed, the process is fully automated.
Although the university students in Study 2 were not as trained on the quick mental
maths strategies as the participants of the first study because of not having the same
immediate need to use these quick strategies, the university sample was a highly selected
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sample in relation to their academic achievements. When comparing the pre-testing data of
these two samples, the university students had considerably higher levels of basic arithmetic
skills (M = 27.60, SD = 10.70) compared to the school sample where the same average
figures were much lower (M = 23.10, SD = .97). The high levels of basic arithmetic skills
could be seen as a level of confidence in the participants’ maths performance. The existing
mental arithmetic skills were high enough to deal with the extra pressures of negative
stereotyping about the maths performance. The basic arithmetic skills test is a beneficial task
as it allows the participants to complete as many simple mental arithmetic tasks during a 60-
second period as they can. The participants are scored on the number of correct answers
provided in the required time frame. Being able to be both accurate and quick when
completing the mental arithmetic tasks, can be seen as evidence to show that the individual is
also able to deal with the additional anxiety caused by the gender related stereotype threat
about maths performance. It is possible that the effects of negative stereotyping endorsement
were felt but as the mental arithmetic skills were high enough, it did not affect students’
overall maths performance. Furthermore, previous studies have shown that maths accuracy
deteriorates when individuals are timed. Additionally, maths anxiety can be induced by
regular arithmetic problems presented in timed tasks (Ashcraft, 2002). Finally, there were no
variations when it came to maths self-efficacy between the two samples confirming that the
two groups felt similarly about maths as a topic. Hence, it was concluded that the level of
maths self-efficacy did not heighten the individuals’ susceptibility to stereotype threat.
Another explanation is that the university students believed that females and males
performed at the same level on the required tasks (working memory task and maths tasks). In
other words, students in the stereotype threat condition might have doubted the accuracy of
the stereotype of women performing worse than men on the various maths related tasks and
this may have masked any possible performance differences in the maths performance or
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working memory performance. Pennington et al., (2019) made similar findings with
stereotype threat not impairing women’s inhibitory control or maths performance in the form
of modular arithmetic performance (Pennington, Litchfield, McLatchie, & Heim, 2018).
The two first studies of this thesis confirmed that there were no statistically significant
findings of stereotype threat on mental arithmetic performance using tasks that were in a
recognizable format and hence not relying heavily on working memory resources.
Furthermore, the 10 mental arithmetic tasks in known format might not have been enough to
show the effects of stereotype threat of girls’ maths performance. The reason for the 10 tasks
only was time as the first study was conducted at an educational setting and required the girls
to not miss too much of the time for teaching. Additionally, the fact that there was no effect
of stereotype threat on the modular arithmetic performance (used during the second study)
that were in a novel format, is a strong indicator that the students in the stereotype threat
condition might not have believed that there were any gender related maths performance
differences.
Finally, after careful examination of the wording of the control condition of the two
first studies (when the control participants were told that the experiment measured their
working memory capacity rather than being advised that the test was diagnostic of their
maths ability) suggests that the control condition may not have functioned as a neutral control
condition as originally anticipated. Instead, the control condition of the first two studies
might have unintentionally primed for performance-approach goals and particularly to the
idea that an individual’s working memory capacity is fixed (Dweck, 1986). Hence, pursuing
an entity theory of intelligence could lead to performance-approach goals. Indeed, this might
serve as an alternative explanation for the lack of a significant difference in maths
performance between the stereotype threat condition and the control condition of the two first
studies.
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1.4 Stereotype Threat and State Maths Anxiety
Across the two studies, it was found that maths anxiety was not affected by the
manipulation of the experimental condition (stereotype threat or control). In other words, the
participants’ maths anxiety levels were not elevated after being told that females were
expected to do worse than males in maths tasks. However, individuals in the first study
conformed to social expectations about their maths abilities and thus, their working memory
capacity was reduced compared with the control group. Nevertheless, this depletion in
working memory capacity was not because of elevated levels of maths anxiety. There may
not have been statistically significant effects of stereotype threat on maths anxiety during the
first two studies because the type of maths anxiety measure that was utilised only comprised
of statements that related to everyday situations with a mathematics component rather than
the actual task in hand. The maths anxiety measure is a self-reported measure and as such, it
does not always capture the exact feelings of the participants, and particularly if the questions
are not directly linked to the task. Perhaps, as the maths anxiety measure was taken last (after
priming, mental arithmetic tasks, and working memory measure), the effects of stereotype
threat were not felt anymore. The effects may not last that long, maybe until the next task but
not after several tasks. So rather than measuring the effects of priming into stereotype threat,
it measures the participants’ maths anxiety levels after completing the maths tasks and
working memory measure.
1.5 The Role of Interactivity on State Maths Anxiety
Study 1 found no carry-over effects of interactivity on maths anxiety. The participants
in the interactive condition (while doing the mental arithmetic tasks) did not feel less maths
anxious at the end of the experiment. One possible reason for this finding is the order of the
tasks; the maths anxiety measure was taken after the mental arithmetic tasks and working
memory measure which did not involve interactivity. The positive effects of interactivity may
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not have been felt at the end of the experiment any more. Additionally, the tasks that the
study employed did not tax working memory heavily due to being heavily practiced.
However, there was reduced state maths anxiety for the participants in the second
study who were allowed to externalize their internal cognitive process by using pen and
paper. Allowing the participants to make use of external artefacts while computing the maths
tasks reduced the effects of state maths anxiety that was measured at the end of the
experiment. There were strong carry-over effects of distributed cognition. The interactive
participants were allowed to externalise their internal cognitive process during the mental
arithmetic tasks and modular arithmetic tasks. The positive effects of interactivity carried on
to the subsequent task, to state maths anxiety. According to Ashcraft and Kirk (2001) there is
a negative association between working memory and maths anxiety. Increased maths anxiety
reduces the available working memory resources (Ashcraft & Kirk, 2001). The reasoning
agent did not need to fight for the same working memory resources, the elevated interactivity
had provided the additional cognitive resource, and as a consequence the participant was less
maths anxious. To our knowledge, this is the first study that has measured maths anxiety
(state), after allowing the participants to complete a maths tasks in an interactive setting.
There is a wealth of studies that have looked at how distributed cognition can be employed to
elevate the maths performance of highly maths anxious participants (Allen & Vallée-
Tourangeau, 2016; Guthrie & Vallée-Tourangeau, 2018; Vallée-Tourangeau, 2013).
However, these studies have not measured state maths anxiety. The studies have measured
trait maths anxiety of the participants during the experiment and investigated the maths
performance according to the participant’s trait maths anxiety levels (high maths anxious vs.
low maths anxious). The study explained here has measured maths anxiety after the
experimental session and has showed reduced maths anxiety in the interactive condition.
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Whilst it was not measured as part of the Study 2, when the participants were allowed
to employ the pen and paper option to compute the maths tasks, the participants wrote down
the required steps of the modular arithmetic tasks to come to the solution and not just the
interim totals of the individual tasks. This pattern could not be found for the mental
arithmetic tasks that were in the known format. Additionally, there were some candidates that
chose not to fully utilise the interactive option for the calculations but as a minimum,
generally opted for the writing down of the instructions. It is also important to mention that
for the high WM load tasks (this study used up to three-digit numbers), there were large
benefits of employing external artefacts to come to the solution (with a large effect size, ŋp2
= .16). The second experiment had a much larger maths component as part of the study
comprising of mental arithmetic tasks similar to the first study and modular arithmetic tasks
(high WM load). Additionally, the modular arithmetic tasks were in a novel format that
required the participant to learn the required computation first and then hold this information
in working memory to be used later on. It is therefore easy to understand that why the
participants in the interactive condition would feel less maths anxious compared to the
individuals in the control condition.
In Study 1, this similar effect could not be found as the tasks were in an easily
recognisable format with four operands of maths (up to three-digit numbers). Additionally,
the participants in the first study had learned quick strategies to compute the mental
arithmetic tasks due to extensive GCSE revision practice. The process was automated and
therefore it was assumed that it did not affect the maths anxiety levels of the participants
either. We argued that interactivity did not allow the participants to feel less maths anxious,
as there was no need for this during the first experiment. Finally, it is of importance to
remember that there was a difference in the order of the tasks between the two studies. The
state maths anxiety was measured straight after the required maths tasks (that allowed
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interactivity or control) in the second experiment and might therefore explain the statistically
significant result of reduced maths anxiety in the interactive condition, unlike Study 1 where
it was measured after the working memory measure.
1.5 Stereotype Threat and Working Memory
Stereotype threat affected the working memory capacity of the participants of Study 1
and Study 2 differently, focusing on the second research objective. The statistically
significant effect of stereotype threat on working memory capacity during the first study
showed evidence that the participants endorsed the primed stereotypes to the point that it had
an effect on their existing cognitive resources, and working memory in particular. Similar
findings have been made by Schmader and Johns (2003) who found that stereotype threat
reduced the capacity of working memory available to complete mathematical computations
(e.g., mental arithmetic tasks) for women and Latinx participants but not for groups that were
not targeted by stereotype threat (e.g., men and European-Americans). Additionally, the same
authors reported that reduced working memory capacity under stereotype threat mediated the
reductions in performance on standardized tests (e.g., quantitative section of GRE). Taken
together, these findings suggest that when the negative stereotype has been made salient,
members of stigmatized groups perform poorly on cognitive tests because this added
information about their maths performance interferes with their working memory resources
and the attentional resources in particular (Schmader & Johns, 2003).
We suspected that during the first study, working memory was mainly utilised for
storing the interim totals and for borrowing and carrying over of numbers that were required
for later on due to the familiar format of the tasks. In other words, working memory was not
used to store complicated instructions or difficult steps of the calculations. When a
computational task is in a novel format, there is additional taxation of the working memory as
the new instructions need to be stored in the working memory. The type of tasks that were
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used as part of Study 1 did not require the level of processing that required more of these
cognitive resources. The mental arithmetic tasks in Study 1 used the four operands of
mathematics (i.e., addition, subtraction, multiplication and division) that were known to the
participant. The tasks were made more demanding by increasing the size of the expressions;
there were up to 3-digit-numbers. In other words, the difficulty of the problem was not made
greater with the help of increasing the number of steps required. A good example of tasks that
require multiple steps are modular arithmetic tasks where the calculations are based on
common concepts of mathematics but are in a novel format and require multiple steps to
completion. Additionally, modular arithmetic tasks require the individual to remember the
steps of the calculations as the initial format is new to the participant and has to be learned
first. Clearly, the strategies that are part of the GCSE syllabus make the students quick and
confident with the responses to allow a high level of achievement in the mental arithmetic
part of the GCSE curriculum.
The working memory test did not follow the expected format of testing (compared to
the mental arithmetic tasks in a known format) and it is therefore assumed that the candidates
of the first study felt the extra burden of not being expected to succeed (stereotype threat).
Whilst the actual calculations of the computation span were in an easily recognisable format
(e.g., 8 - 5 = 3), the fact that the participant had to remember the second digit of each
equation made it more challenging for the participants. Additionally, the working memory
assessment was in an oral format, and as such there was additional pressure of not forgetting
anything and not making any mistakes. The participants were not allowed to use any external
artefacts to come to the solution. The researcher conducted the working memory assessment
together with the participant. This is a dual-task working memory task whereby the
participant is expected to use working memory processing and storage simultaneously.
Additionally, both the processing and storing parts of the computation span involved
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mathematical equations. Clearly, when stereotype threat was made salient, the participants’
working memory capacity suffered as there were a multitude of aspects to be remembered at
the same time. The format of the working memory assessment was novel to the girls, and
therefore required more internal cognitive resources. This format of assessment could not
have been heavily practiced and therefore not automated as a process. It is therefore possible
that the effects of stereotype threat were felt as the format and the requirement of the working
memory assessment was hard.
Unlike the earlier experiment, the second study failed to report depleted working
memory capacity resources when stereotype threat was made salient, focusing on the second
research objective. The university students were not affected by the negative stereotyping of
women’s maths performance when the working memory measurement was taken. Clearly,
this is in contrast with existing empirical findings by Schmader and Johns (2003) and with
the findings of the earlier study. Operation Span Test (OSPAN), developed by Turner and
Engle (1989) was employed to measure working memory by Schmader and colleagues
(2013). This task requires the participant to evaluate simple mathematical equations (the
correctness of the answer) while simultaneously memorizing simple words to be recalled
later. After each mathematical equation, a word is presented for later recall (the mathematical
equation and the word at the end is seen as a set). At the end of each set of equations, the
participant is expected to verbally recall each of the words from the set in the correct order.
However, the maths equations were solely employed to make the participants to use certain
amount of internal cognitive processing. The actual working memory part of the operation
span test was measured with the number of words recalled correctly from each equation and
word set. Interestingly, when Schmader and colleagues (2003) looked at the maths
performance of the operations span test separately, there were no significant results of the
negative stereotype about females’ maths performance. In other words, there were no maths
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performance differences after the priming of students into stereotype threat condition or
control. The statistically significant results that were found, were the number of correctly
remembered words as part of the operation span test.
Study 2 found that the working memory capacity of the participants was predicted by
the participant’s basic arithmetic skills rather than stereotype threat priming. This indicates
that it was the arithmetic skill that contributed to working memory capacity rather than the
stereotype threat priming used during the experiment. Due to strong maths skills (measured
with the help of basic arithmetic skills test), the participants may not have felt the stereotype
threat being strong enough. It was assumed that the priming of the students into stereotype
threat did not make them feel doubtful about their maths performance. In other words, the
participants did not need to worry about their maths abilities and performance in the
stereotype threat condition.
Finally, the participants of the original Steel and Aronson (1995) study also tested
high performing university students who demonstrated decrements in performance (the test
comprised of items from the verbal Graduate Record Examination, GRE) so there may be
others reasons why the stereotype threat manipulation of the two first studies of this thesis did
not work. Many studies have failed to find effects of stereotype threat and there may be
publication bias in this literature (Nguyen & Ryan, 2008).
1.6 Achievement Goals
After concluding that the control condition of the first two studies might have
unintentionally primed for performance-approach goals, the following two studies (Study 3
and 4) concentrated on furthering our understanding of achievement goals and their effects on
working memory. These studies sought to explore motivational approach goals (i.e.,
performance-approach goals and mastery-approach goals) and how they differentially impact
upon working memory resources. As before, we aimed to further investigate how interactivity
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influenced the effects of achievement goals on modular arithmetic performance. We wanted
to further understand whether distributed cognition could be employed to reduce any of the
detrimental effects of performance-approach goals on mental arithmetic performance.
Additionally, we wanted to further our understanding of the benefits in utilising distributed
cognition for the mastery-focused individual. Study 3 found that the participants in the
performance-approach goal condition had a reduced modular arithmetic performance
compared to the mastery-approach group. However, this performance drop was improved
with the help of interactivity in the Study 4. The modular arithmetic performance of the
participants in the mastery-approach goal condition was reduced when allowed to interact
with the external resources (with the use of pen and paper) in Study 3 and 4, suggesting that
these two achievement goals differently impact upon working memory resources.
The goals of Study 4 were replicated and extended from Study 3. Hence, the purpose
of the fourth study was to further explore on the impact of distributed cognition on the maths
performance of the mastery-approach goal individual. Additionally, we investigated whether
the adverse effects of performance-approach goals on mental arithmetic performance could
be alleviated with the use of interactivity. We also considered the role of state maths anxiety
and whether interactivity could be used as a creative way of defusing the possible impact of
maths anxiety on the modular arithmetic performance. We argued that if there was elevated
maths anxiety in the performance-approach goal condition then there should be more benefits
of externalizing the internal cognitive process to the outside world. Finally, we looked at
whether participants experience positive and negative effects after being allowed to use
interactivity to compute the modular arithmetic tasks. Some of the participants computed the
tasks without the help of interactivity and that is why that we argued that even the thought of
knowing that the option of writing things down could make the participants feel more
positive about the task.
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1.7 The Impact of Interactivity on Maths Performance
Across the two final studies, there were no significant main effects of interactivity on
modular arithmetic performance, addressing the first research question. These findings are in
line with Vallée-Tourangeau (2013) who confirmed that when participants are allowed to
interact with the external world, there is elevated maths performance for the longer sums (11
single-digit numbers) but not for the shorter sums comprised of 7 single-digit numbers.
Additionally, an interesting observation was made, whereby the participants performed
marginally better when they only relied on their internal cognitive resources (non-interactive
condition). These findings suggest that the degree to which the design of an extended
cognitive system can increase cognitive performance is clearly relative to the actual degree of
task difficulty. In other words, there was no need for the participants to rely on the external
resources when calculating shorter sums as they were clearly more efficient when relying on
their own internal cognitive resources and working memory only. Additionally, there seemed
to be less effort required to complete the mental arithmetic task in the head alone (Vallée-
Tourangeau, 2013). The same way, the modular arithmetic tasks of the two final studies were
easy enough to be computed without the assistance of the external artefacts (the use of pen
and paper). Earlier, however, the second study reported a statistically significant main effect
of interactivity on modular arithmetic performance. However, the modular arithmetic tasks
that were employed as part of the second study had a much higher difficulty level. The
numbers were either double-digit or triple-digit numbers and were presented in a horizontal
format as opposed to the vertical format. Increased interactivity allowed the participants of
Study 2 to reach higher maths accuracy and efficiency when computing the required tasks
confirming existing findings by Kirsh (2010).
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1.8 Interactivity and the Impaired Maths Performance of the Participants in the
Mastery-Approach Goal Condition
An interesting finding was made across the two final studies of this thesis (addressing
the third research objective), the participants in the mastery-approach goal condition had a
performance drop when allowed to utilise the external artefacts to compute the maths task.
Clearly, there was no need to for the mastery-focused individual to extend their current
working memory resources. They had the required cognitive resources to deal with the task.
One explanation for this finding is that there was lack of outcome related thoughts and
anxiety as suggested by Butera and Crouzevialle (2013). Evidently, as the participants in the
mastery-approach goal condition focus on the benefits of their own learning and do not worry
about outperforming other people, their working memory is not as heavily taxed as the
performance-focused individuals’ working memory. In other words, there is no dual-task set-
up of completing the maths task combined with additional anxiety for the mastery-focused
individual, allowing high cognitive performance. Another explanation for the reduced maths
performance of the interactive mastery-focused participants might be linked to working
memory processing. Avery and Smillie (2013) suggested that the pursuit of performance-
approach goals might hamper the working memory processing that is required for successful
computation of simple mental arithmetic tasks. If this process is disrupted, cognitive
processing of the maths tasks is impaired and accuracy reduced. However, this reduced
working memory processing does not seem to affect the mastery-focused individuals and
therefore it seems that there are limited benefits of externalising the internal cognitive process
to this group of individuals.
In a similar vein, in another study, dyslexic children who were aged between 9 – 11
years benefited the most from rearranging the letter tiles (interactive condition) in a word
production task compared to a control group of typically developing children (Webb &
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Vallée-Tourangeau, 2009). Developmental dyslexics demonstrate impairments of working
memory and phonological processing difficulties in particular (Snowling, 1998). By
reshaping the physical presentation of the letters, the less efficient working memory
capabilities of the dyslexic participants could be compensated. The typically developing
children did not experience the same benefits from interacting with the external artefacts. In
fact, their task performance with the easy set of letters was poorer when they manipulated the
word tiles to produce words clearly demonstrating that the effectiveness of the manipulation
of the physical problem space is relative to the task difficulty as well as the cognitive abilities
of the reasoner (Webb & Vallée-Tourangeau, 2009).
Similarly, Cox (1999) introduced the notion of cognitive differences between
reasoning with self-constructed external representations and reasoning with presented
representations (e.g., textbook diagrams). Cox (1999) argued that there are three elements
that contribute to effective reasoning with the help of external representations. Interacting
with external representations is a three-way interaction between the cognitive properties of
the representation, the demands of the tasks and the effects of prior knowledge and cognitive
style of the reasoner (Cox, 1999). According to Kirsh (1995), it has to be cognitively cost
effective for the individual to interact with the external representations. If it is easier to solve
the problem mentally then this is clearly what the individual will do (Kirsh, 1995). A good
example of this is when a primary school aged child uses fingers to compute simple mental
arithmetic tasks. When the individual is older, this way of computing is not beneficial for the
reasoner anymore. It is quicker to compute the tasks in the head alone (Vallée-Tourangeau &
Wrightman, 2010).
1.9 The Maths Performance of the Performance-Approach Goal Participants
Study 3 found reduced maths performance of the performance-approach goal
participants in the non-interactive condition compared with the mastery-approach goal
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participants (addressing the second research objective). Whilst state maths anxiety was not
measured as part of Study 3, Study 4 found that the participants in the performance-approach
goal condition were more maths anxious than the mastery-focused individuals when
measured at the end of the experiment. It is possible that lower maths performance of the
performance-focused individuals is because of outcome related concerns about maths
performance that might reduce the existing working memory capacity available to compute
the task. Evidently, the performance-focused learning encourages the individual to focus on
social comparison and to outperform others leading to anxiety and lower maths performance.
And as a consequence, together with the high-load working memory tasks, working memory
resources may be further compromised by performance-focused goals (Crouzevialle &
Butera, 2013).
Poor working memory processing (measured with the help of an N-Back WM task) of
the performance-focused individuals might lead to impaired maths performance, (Avery &
Smillie, 2013). Working memory processing and central executive in particular, is an
important component when completing mental arithmetic tasks (Imbo & Vandierendonck,
2007). It has been suggested that under high working memory load, when a performance-
approach goal has been endorsed, there is poorer working memory processing available than
in the mastery-approach goal group or when there is no go-goal control, leading to a
cognitive performance drop (Avery & Smillie, 2013). N-Back task is a continuous WM
processing task rather than a mere WM storage task. N-Back is a task where a participant is
asked to confirm whether or not the position of a currently presented stimulus matches the
position on which a previous stimulus was shown. The load of the task is varied by increasing
the number of positions between the current and previous stimulus. Finally, when the N-Back
load increases, there is a bigger load on the central executive of the working memory (Kane,
Conway, Miura, & Colflesh, 2007). Finally, there was no measurement of working memory
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processing as part of the final two studies but it is possible that the reduced maths
performance of the more performance-focused individuals was due to reduced WM
processing as suggested by Avery and Smillie, 2013.
There are differing processing strategies of maths tasks for performance-focused
participants and mastery-focused individuals (Avery et al., 2013). Based on these differing
strategies of dealing with the maths tasks, Avery et al., (2013) suggested that it is the
mastery-approach goal individuals who have reduced maths performance compared to the
performance-approach goal individuals. The authors explained these results with the type of
strategies that the mastery-approach goal participants employed to come to the solution. A
motivated focus on developing self-referential skill of the mastery-approach goal individual
relied extensively on the existing working memory resources. This is caused by the use of
deliberative and step-by-step strategies during the achievement goal pursuit and as a
consequence, their cognitive performance is deteriorated. On the contrary, a focus on
demonstrating normative skill of the more performance-focused individual is less dependent
on working memory resources. These strategies are more heuristic and rely on short-cut
strategies and therefore do not tax the working memory as much as the deliberate strategies
employed by the mastery-focused individuals (Avery et al., 2013). However, our findings run
contrary to the existing findings by Avery et al., 2013. The individuals in the mastery-
approach goal condition demonstrated a higher maths performance than those in the
performance-approach goal condition (Study 3) when interactivity was not employed and
therefore does not support the findings of Avery et al., (2013). However, it is possible that
there might be more working memory capacity available to deal with the distractive thoughts
of the performance-focused individuals which reduce task focus and overall cognitive
performance when endorsing performance-approach goals. Performance anxiety may have a
more detrimental effect on working memory resources than the reduced processing of
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working memory. However, the third study of this programme of research failed to measure
maths anxiety and therefore we have limited knowledge of the anxiety levels of the
participants.
Additionally, written protocols of the non-interactive participants were not taken as
part of Study 3 and therefore, we currently have little evidence to suggest that the participants
in the performance-approach goal condition of Study 3 utilised the implicit processing of the
modular arithmetic tasks as suggested by Avery et al., (2013). It should also be noted here
that as half of the participants of the Study 3 were allowed the use of pen and paper
(interactive condition), we have written protocols of the way the modular arithmetic tasks
were computed for this group of participants. However, this information is not useful in this
part of the analysis as most of the participants seemed to employ explicit processing only,
regardless the achievement goal endorsement. Interactivity allowed the participants to extend
the current working memory resources and therefore explicit processing was possible for both
of the participant groups. This is similar to existing findings where it has been reported that
interactivity allows deeper and more efficient processing of maths tasks (Kirsh, 2010).
Finally, different strategies to solve the modular arithmetic tasks would be used depending
whether the task was computed relying on the internal resources only as in the original study
by Avery et al., (2013).
The pursuit of performance-approach goals (the goal to attain normative superiority
over peers) is particularly distractive for the students with high working memory capacity
(Crouzevialle et al., 2015). These are students who are used to being academic high achievers
because of their higher cognitive abilities to deal with demanding cognitive tasks. However,
the higher-level cognitive abilities might actually become a burden under performance-
approach goal pursuit as the high achievers aim to raise above others. This may represent an
opportunity to reaffirm their positive status of being the high academic achievers and
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therefore trigger disruptive outcome concerns that interfere with task processing. With
performance-approach goals as compared to mastery-approach goals (with no emphasis on
social comparison), the higher the individual’s working memory capacity, the lower their MA
performance. As part of their investigation, uncertainty was manipulated by providing bogus
feedback about score and ranking just before the completion of the evaluative modular
arithmetic block. The feedback was either very positive stating high score and ranking or
average which meant medium score and ranking. The feedback was designed to generate
confidence or uncertainty regarding the chance of getting a high score and outperform peers.
The increased uncertainty of outperforming the peers, reduced the MA performance of the
performance-approach goal individuals with high working memory capacity (Crouzevialle et
al., 2015).
Whilst the level of working memory capacity was outside the scope of the two
studies, some of the performance decrements of the performance-approach goal individuals
may have been caused because of increased levels of uncertainty of outperforming others.
The participants in the final two studies were psychology undergraduate students and as such
they represented a highly selective group of participants. It could be assumed that this group
of individuals demonstrate higher levels of working memory capacity and therefore a
stronger sense to attain normative superiority over other students. Thus, there might be an
even larger performance drop for this group of students due to increased uncertainty to
outclass others.
1.10 The Endorsement of Performance-approach Goals and Interactivity
As expected, the individuals in the performance-approach goal condition elevated
their maths performance in the interactive condition in Study 4, extending the finding that
was made in Study 3 (addressing the research objective 3). The earlier study found that the
maths performance of the performance-focused individuals was reduced without the use of
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interactivity. Study 4 has shown that there was clearly a cognitive need for this group of
participants to externalise the internal cognitive process to be able to deal with the task and
additional taxation of the working memory. Interacting with the external resources allowed
the individual in the performance-focused condition to increase their cognitive performance
of completing the modular arithmetic tasks. Working memory was adversely affected by the
pursuit of performance-approach goals and that is why there were clear benefits of
interactivity for the participants to come to the solution.
Whilst the two final studies did not measure working memory processing, it is
possible that the WM processing of the participants was impaired and therefore interactivity
allowed increased maths performance. Impaired central executive functioning can have
detrimental effects on maths performance. Central executive is responsible for planning and
sequencing of activities to complete the maths task (e.g., 34 + 56). It keeps track of which
parts of the calculation have been done and where to go next. It has executive functioning
responsibilities in deciding where to go next (DeStefano & LeFevre, 2004). Clearly, by
externalising some of these functions to the outside world, the individual can gain back some
of the lost processing required to complete the task. Finally, extending this research to
examine the impact of achievement goals on working memory processing and examining the
effects of distributed cognition, increase our understanding of how motivation drives
performance and how interactivity can be used to assist with this. This is an interesting
finding as distributed cognition is normally associated with working memory capacity which
is measured with the help of a computation span task rather than working memory
processing. However, more research is required in the area.
1.11 State Maths Anxiety
As expected, Study 4 found that the individuals in the performance-approach goal
condition felt higher levels of state maths anxiety after completing the maths tasks than the
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mastery-approach goal participants. This finding is not in line with Avery and Smillie (2013)
study where it was reported that there were no heightened state anxiety levels in the
performance-approach goal condition. The endorsement of performance-approach goals
resulted in poorer working memory processing under high load (N-Back working memory
task) than the pursuit of mastery-approach goals or no-goal condition. The adverse effects on
working memory processing were only felt under high executive load (3-back) but not under
the less demanding tasks (1-back or 2-back), (Avery & Smillie, 2013). Additionally, there
was no direct measure of state maths anxiety in the Butera and Crouzevialle (2013) study.
There was a performance drop of the performance-approach goal individuals because of
distractive thoughts that were due to the activation of performance-approach goal related
thoughts during the task solving rather than increased state anxiety levels as in the study
reported here. The authors used thought suppression manipulation to investigate the reduced
levels of performance. When an individual tries to suppress a particular thought, an opposite
reaction happens and there can be an increase in its accessibility (Wegner, 1994). The
activation of performance-approach goal-related content was actively responsible for the
distractive effect reported in the study (Crouzevialle & Butera, 2013).
1.12 State Maths Anxiety and Distributed Cognition
The final study predicted that there would be a two-way interaction of instruction
(performance-approach goal or mastery-approach goal) and interactivity. And in particular, it
was predicted that the performance-focused individuals would feel more maths anxious
because of their anxiety about outperforming others in the mathematical domain. This study
did not find a two-interaction between the achievement goal endorsements and interactivity,
on state maths anxiety. The pursuit of performance-approach goals allowed the participants
feel higher levels of maths anxiety, however, there was no evidence to suggest that the
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anxiety levels were reduced with the help of interactivity leading to extended working
memory and enhanced maths performance.
Clearly, the pursuit of the achievement goals was still felt post-priming but not the
distributed cognition that was utilized during the mental arithmetic tasks. Performance-
focused individuals showed higher levels of maths anxiety after the experiment but this
anxiety was not reduced with the externalisation of the internal cognitive process. Similarly,
to Study 1, the maths anxiety of the fourth study was not measured straight after the maths
tasks. The PANAS questionnaire was measured after the mental arithmetic tasks in primed
conditions, this was then followed by the state maths anxiety measure. It is possible that the
effects of interactivity could not be felt after the PANAS questionnaire any more. It was clear
that the priming instructions of performance-approach goals presented stronger carry-over
effects as they could still be experienced after the priming of the mental arithmetic tasks and
the PANAS measurement which was evidenced with a significant result of instruction
(performance-approach goal or mastery-approach goal) on state maths anxiety.
Unlike the fourth study, Study 2 found that there were strong carry-over effects of
interactivity on state maths anxiety after completing the required maths tasks in primed
conditions. The participants who were allowed to extend their existing working memory
resources felt less maths anxious after the experiment than before. However, there were clear
differences between Study 2 and Study 4 and how and when the maths anxiety was measured.
First, Study 2 utilized a higher level of difficulty of maths tasks (modular arithmetic tasks up
to three-digit numbers) than Study 4 (up to two-digit numbers). This might explain the
significant main effect of interactivity on state maths anxiety in the Study 2. Additionally, the
order of the tasks was different. The maths anxiety questionnaire was straight after the maths
tasks under primed conditions during the Study 2 unlike the Study 4 where the maths anxiety
was measured after the PANAS measurement.
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Finally, we conducted a mediation analysis to further explore the role of state maths
anxiety on the modular arithmetic performance. We found that achievement goals did not
have a direct or indirect mediation effect of state maths anxiety on the maths performance
when participants did not externalise the internal cognitive process. In other words, the
change in the state maths anxiety levels did not mediate the maths performance when the
maths tasks were computed without interactivity. Thus, increased levels of maths state
anxiety levels are not mediating the maths performance in the non-interactive condition. We
had argued that in the non-interactive condition, the achievement goals would affect the state
maths anxiety differently which would mediate the maths performance. We had also
predicted that this pattern could not be found in the interactive condition because interactivity
would have extended the diminished working memory resources needed to complete the task.
More research is required to fully understand the reasons for the performance drop of the
performance-approach goal participants, and why there is an increase with the performance
when interactivity is used.
2 Limitations and Future Studies
Whilst this PhD programme of research has made strong empirical findings in relation
to the impact of achievement goals on working memory and the role of distributed cognition,
there are limitations. We based our analysis on existing findings by Avery and Smillie (2013)
who reported reduced working memory processing for the more performance-focused
individual, causing impaired MA performance. Hence, any future studies on achievement
goals and the role of interactivity would benefit in measuring working memory processing in
performance-approach goal or mastery-approach goal environment, crossed with interactivity
or control to fully understand the role of working memory processing and interactivity.
Additionally, it would also be of interest to further explore achievement goals and the impact
of interactivity in an educational setting.
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3 Contributions of the Findings
When the literature review of the thesis was conducted a number of clear gaps in the
research were observed. The following paragraph will give an overview of these gaps and
how they have been dealt within the thesis. This paragraph is then followed by a section on
more detailed theoretical and practical implications of the findings. First, it was confirmed
that most of the research in the field of distributed cognition and the work of Kirsh in
particular, was based on research that mainly focused on everyday observations (Kirsh,
1995b; Kirsh, 2009; Kirsh 2010). With the help of experimental manipulations, this program
of study has shown clear evidence of the positive effects (increased accuracy and latencies
with a known task format) of transferring the internal cognitive process to the outside world
when computing mental arithmetic tasks. On the contrary to the findings of Kirsh (2010), the
current study also found evidence of speed-accuracy trade-off. When the maths tasks were in
a novel format (modular arithmetic tasks), the participants of the study became slower
because of speed-accuracy trade-off. It was also noted in the beginning of this research that
maths anxiety had not been measured directly (in relation to interactivity) in the work of
Vallée-Tourangeau (e.g., Allen & Vallée-Tourangeau, 2016; Vallée-Tourangeau et al., 2016).
Hence, the current study investigated the effects of interactivity on maths anxiety and found
that the interactive participants of the Study 2 had lower maths anxiety levels compared to the
control participants. When looking at the effects of stereotype threat, Steele and Aronson
(1995) stated that the African-American participants’ academic performance was negatively
affected by negative stereotyping and this was partly explained by reduced processing whilst
this was not actually measured. The current study therefore measured the levels of working
memory as one of the measures of the study to explain any possible performance decrements
caused by stereotype threat (girls and mathematics). Additionally, it can be difficult to draw
comparable conclusions of the stereotype threat effects because performance has been tested
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in various circumstances (Nguyen, 2008). Consequently, this study focused on understanding
the underlying mechanisms of stereotype threat instead. Hence, the research reported here is
focused on these mechanisms, and particularly on the effects of stereotype threat on working
memory. Finally, whilst there is ample evidence of four different achievement goals (e.g.,
Grant & Dweck, 2003; Harackiewicz & Barron, 2002), the current study employed two
achievement goals (performance-approach goals and mastery-approach goals) to further
investigate the effects of interactivity on maths performance. By employing these two
achievement goals only, allowed us to replicate the findings of Crouzevialle and Butera
(2013). Additionally, it added to the existing findings about the varying effects of
interactivity on achievement goals.
This thesis contributes to the research area of achievement goals and the role of
distributed cognition substantially. To our knowledge, this is the first programme of research
that has looked at this area. The following section will present theoretical and practical
implications of the findings. First, we started by investigating how motivational achievement
goals differently affect working memory resources, addressing the second research objective.
We confirmed existing findings of an impaired maths performance for the performance-
focused individual because of possible worries about outperforming peers (Crouzevialle &
Butera, 2013; Crouzevialle et al., 2015) or because of reduced working memory processing
(Avery & Smillie, 2013). We then extended this finding to show that this performance drop
could be reduced with the help of interactivity, addressing the third research question.
Interactivity encouraged the coupling of internal and external resources to create a cognitive
system that allowed the maths performance to get augmented for the performance-approach
goal individual. This is a substantial finding as it has not been investigated before.
We also found that maths anxiety levels of the performance-focused individuals were
elevated after the experiment compared to the mastery-approach goal individuals. However,
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maths anxiety was not reduced through distributed cognition. Interactivity allowed the
participant in the performance-approach goal condition to have a higher maths performance
compared to the control condition, however, this was not caused through reduced maths
anxiety levels. Past research has found that interactivity transformed working memory
capacity and increased its capacity and as a consequence, the resource drain that was caused
by maths anxiety, was diffused (Vallée-Tourangeau et al., 2013). The findings of this thesis
do not support these findings. We suggest that interactivity improves maths performance for
the participant who is focused on the academic performance but not through reduced anxiety
levels. It is possible that interactivity is supporting reduced working memory processing of
the individuals in the performance-approach condition. If the working memory processing of
computing maths tasks is disrupted then allowing the reasoning agent to externalise the
external cognitive process to compute the tasks, can lead to increased maths performance.
This thesis made an unexpected finding in relation to mastery-approach goal
participants’ maths performance (Study 3 and 4). These studies found that the mastery-
focused individuals’ maths performance was lower when permitted to reconfigure the
mathematical problem through using pen and paper when compared to the control condition,
addressing the third research objective. The mastery-approach goal individuals showed lower
levels of state maths anxiety compared to performance-focused participants in the final study
indicating that their working memory was not taxed with additional maths related worries.
According to Avery and Smillie (2013) the mastery-focused participants’ working memory
processing is not impaired by the endorsement of this achievement goal. Hence, it can be
concluded that their working memory was not affected and therefore there were no additional
benefits to interact with the external artefacts. As mentioned earlier, there needs to be a
cognitive need to combine the internal cognitive resources with the external resources. Thus,
there are opposite effects in which interactivity may cause performance decrements, like in
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the studies reported here and like existing research in the area (Webb & Vallée-Tourangeau,
2009). In order to create a beneficial distributed design of cognition we must understand the
full requirement of the task, the individuals who perform the task, as well as the nature of the
interaction with the external world (Cox, 1999; Kirsh, 1995; Vallée-Tourangeau &
Wrightman, 2010; Webb & Vallée-Tourangeau, 2009).
Another important finding was made in relation to state maths anxiety. We found that
interactivity allowed reduced state maths anxiety when novel and more working memory
dependent tasks were computed. There are currently no other studies that have made a similar
finding. As mentioned earlier, the existing studies have measured trait maths anxiety only and
therefore found that there are more benefits of interactivity for the more maths anxious
individual. The study reported here has concluded that state maths anxiety can be reduced
with the help of interactivity which is an important finding as it allows the more maths
anxious individual to have improved maths performance.
These findings have extended our understanding about achievement goals and their
differing effects of working memory, addressing the second research objective. Additionally,
we have found that the detrimental effects of performance-approach goals on maths
performance can be alleviated with the help of interactivity (addressing the third research
objective). These findings can contribute to practice, predominantly by providing evidence-
based guidance for policy-makers and teaching professionals. One suggestion would be that
maths education could utilise interactivity for more performance-focused individuals. By
allowing the individual to reconfigure the maths task by externalising the cognitive process,
their maths performance may be augmented. But equally for the participant who does not
have the same cognitive need to employ interactivity, it is acceptable to rely on the internal
cognitive resources only to compute the task. As individuals possess different motivational
achievement goals that lead to varying effects on the working memory, the distributed
185
cognitive system needs to be tailored to suit the individual needs of the reasoner in order for
them to be able to reach their full academic potential in an educational setting. As the current
educational system is focused on exam results and therefore heavily endorsing performance-
approach goals, these findings have implications for teaching and learning and in particular,
for mathematical education.
Finally, the findings of this PhD programme of research have shown strong empirical
evidence of the benefits of utilising interactivity in a mathematical domain when the reasoner
is feeling additional concerns about completing the task. The performance drop that has been
caused by performance-approach goal priming can be improved by using pen and paper
allowing the participant to gain higher maths performance. By allowing the participant to use
these relatively simple strategies (i.e., using pen and paper), maths performance can be
improved. In an educational setting, pupils should be allowed to utilise both the internal and
external cognitive resources depending on the level of their cognitive needs to solve a maths
task.
As mentioned earlier, this study has clearly shown that there are clear benefits of
using distributed cognition as a cognitive framework, in an academic setting. Whilst the work
of Kirsh is highly criticized for employing everyday observations only to show the benefits of
distributed cognition, the current study supports these original findings by using experimental
manipulations. The current study has allowed the participants to externalise their internal
cognitive process and by doing so the ability to think and to compute maths tasks has been
enhanced. This is clear evidence to show that people think with objects and with people
around them. Clearly, it is not an internal cognitive process only. People’s capacity to think
and reason well is clearly not only based on the cognitive abilities of the reasoner but also on
the artefacts that are used to support the thinking and decision making. As a consequence, the
186
school of distributed cognition should be supported when cognitive tasks are computed and
not only in an educational setting but in any everyday task requiring cognitive resources.
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Appendix A: Ethical Approval for Study 1
204
205
Appendix B: SAFE for Study 2
206
207
208
Appendix C: SAFE for Study 3
209
210
211
Appendix D: SAFE for Study 4
212
213
214
215
Appendix E: Basic Arithmetic Skills Test (BAS), Study 1, 2, and 4
216
Appendix F: Mathematics Self-Efficacy and Anxiety Questionnaire, Study 1 and 2
Please, answer the following 7 questions.
The scale is from 1-5 where
1 = I don’t agree and 5 = I strongly agree.
Please, circle around the number.
1. I believe I am the kind of person who is good at mathematics.
1 2 3 4 5
2. I believe I am the type of person who can do mathematics.
1 2 3 4 5
3. I believe I can learn well in a mathematics course.
1 2 3 4 5
4. I feel that I will be able to do well in future mathematics courses.
1 2 3 4 5
5. I believe I can understand the content in a mathematics course.
1 2 3 4 5
6. I believe I can get an “A” when I am in a mathematics course.
1 2 3 4 5
7. I believe I can do the mathematics in a mathematics course.
1 2 3 4 5
217
Appendix G: Maths Anxiety Scale (Trait), Study 2 and 4
How anxious would you feel in the following situations?
1. Having someone watch you multiply 12 x 23 on paper?Not at all A little A fair amount Much Very much1 2 3 4 5
2. Adding up a pile of change?Not at all A little A fair amount Much Very much1 2 3 4 5
3. Being asked to write an answer on the board at the front of a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5
4. Being asked to add up the number of people in a room?Not at all A little A fair amount Much Very much1 2 3 4 5
5. Calculating how many days until a person’s birthday?Not at all A little A fair amount Much Very much1 2 3 4 5
6. Taking a maths exam?Not at all A little A fair amount Much Very much1 2 3 4 5
7. Being asked to calculate £9.36 divided by 4 in front of several people?Not at all A little A fair amount Much Very much1 2 3 4 5
8. Being giving a telephone number and having to remember it?Not at all A little A fair amount Much Very much1 2 3 4 5
9. Reading the word ‘algebra’?Not at all A little A fair amount Much Very much1 2 3 4 5
10. Calculating a series of multiplication problems on paper?Not at all A little A fair amount Much Very much1 2 3 4 5
11. Working out how much time you have left before you set off work or place of study?Not at all A little A fair amount Much Very much1 2 3 4 5
218
12. Listening to someone talk about maths?Not at all A little A fair amount Much Very much1 2 3 4 5
13. Working out how much change a cashier should have given you in a shop after buying several items?Not at all A little A fair amount Much Very much1 2 3 4 5
14. Deciding how much each person should give you after you buy an object that you are all sharing the cost of?
Not at all A little A fair amount Much Very much1 2 3 4 5
15. Reading a maths text book?Not at all A little A fair amount Much Very much1 2 3 4 5
16. Watching someone work out an algebra problem?Not at all A little A fair amount Much Very much1 2 3 4 5
17. Sitting in a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5
18. Being given a surprise maths test in a class?Not at all A little A fair amount Much Very much1 2 3 4 5
19. Being asked to memorize a multiplication table?Not at all A little A fair amount Much Very much1 2 3 4 5
20. Watching a teacher/lecturer write equations on the board?Not at all A little A fair amount Much Very much1 2 3 4 5
21. Being asked to calculate three fifths as a percentage?Not at all A little A fair amount Much Very much1 2 3 4 5
22. Working out how much your shopping bill comes to?Not at all A little A fair amount Much Very much1 2 3 4 5
23. Being asked a maths question by a teacher in front of a class?Not at all A little A fair amount Much Very much1 2 3 4 5
219
Appendix H: Computation Span (Working Memory), Study 1, 2, and 4
You will be asked to read a simple expression and announce your answer. You will also be
asked to remember the second number for each equation.
Make sure to provide a correct answer to the arithmetic task. Accurate recall will only
be recorded if you have given a correct answer to the arithmetic task.
When the page is blank, without an equation, recall the second number from each equation –
for this practice sequence, the arithmetic answers would be 1 and 11, and the numbers to
recall would be 2 and 6:
3 – 2 = 1
5 + 6 = 11
Let’s practice with another set of two equations:
8 – 5 =
7 + 1 =
220
Arithmetic answer: 3 and 8
Recall answer: 5 and 1
Because the 2 equations were:
8 – 5 = 3
7 + 1 = 8
Expect to be asked to recall more than two numbers.
The test starts now.
221
9 – 1 =
Recall
222
5 + 2 =
Recall
223
9 – 5 =
8 + 9 =
Recall
224
1 + 3 =
8 – 2 =
Recall
225
8 + 1 =
6 – 2 =
5 + 9 =
Recall
226
7 – 2 =
3 + 7 =
5 + 9 =
Recall
227
7 + 2 =
6 – 2 =
8 – 5 =
5 + 7 =
Recall
228
7 + 6 =
8 – 1 =
1 + 2 =
9 – 5 =
1 + 7 =
Recall
229
9 + 2 =
9 – 6 =
9 – 5 =
6 + 7 =
6 – 1 =
Recall
230
3 + 4 =
8 – 3 =
5 – 1 =
1 + 7 =
4 + 9 =
9 – 6 =
Recall
231
4 + 5 =
8 + 2 =
8 – 1 =
7 + 8 =
7 – 5 =
4 + 7 =
Recall
232
3 + 2 =
5 + 1 =
8 + 9 =
7 – 4 =
9 – 5 =
1 + 6 =
4 – 3 =
Recall
233
8 – 7 =
1 + 5 =
8 + 4 =
2 + 8 =
7 – 2 =
2 + 9 =
4 – 3 =
Recall
234
Appendix I: Mental Arithmetic Tasks (Known Format), Study 1 and 2
Please, complete the following tasks:
1. 433 + 288 =
2. 93 – 37 =
3. 7 x 29 =
4. 168 / 4 =
5. (66 x 3) / 2 + 5 – 8 =
6. 548 + 695 =
7. 737 – 269 =
8. 13 x 77 =
9. 18 / 2 + 23 – (3 x 5) =
10. 486 + 843 =
235
Appendix J: Modular Arithmetic Tasks, Study 2
Welcome to the second part of the test!
You will be solving a series of problems on the computer. You are going to see problems on the screen that look like the following:
17 ≡ 5 (mod 6) Your job is to judge whether the problems are "true" or "false" as quickly and as accurately as possible.
Example 1: Is the following statement true? 35 ≡ 19 (mod 2) First we subtract 19 from 35: 35 - 19 = 16 Does 2 divide into 16 with 0 as the remainder? Yes, 2 goes into 16 eight times, with a remainder of zero. Thus our statement is true.
The test starts now.
1. 83 ≡ 27 (mod 8) =
2. 135 ≡ 69 (mod 6) =
3. 51 ≡ 19 (mod 4) =
4. 346 ≡ 229 (mod 9) =
5. 43 ≡ 27 (mod 7) =
6. 277 ≡ 139 (mod 3) =
7. 54 ≡ 36 (mod 7) =
8. 245 ≡ 59 (mod 3) =
9. 73 ≡ 37 (mod 7) =
10. 337 ≡ 149 (mod 4) =
11. 83 ≡ 35 (mod 4) =
12. 483 ≡ 297 (mod 4) =
236
13. 62 ≡ 38 (mod 6) =
14. 137 ≡ 69 (mod 8) =
15. 45 ≡ 27 (mod 4) =
16. 161 ≡ 79 (mod 6) =
17. 63 ≡ 48 (mod 4) =
18. 153 ≡ 77 (mod 6) =
19. 42 ≡ 27 (mod 3) =
20. 172 ≡ 84 (mod 8) =
21. 82 ≡ 55 (mod 8) =
22. 263 ≡ 98 (mod 8) =
23. 54 ≡ 18 (mod 6) =
24. 177 ≡ 69 (mod 4) =
25. 43 ≡ 18 (mod 3) =
26. 233 ≡ 196 (mod 9) =
27. 67 ≡ 18 (mod 6) =
28. 262 ≡ 175 (mod 9) =
29. 75 ≡ 59 (mod 4) =
30. 245 ≡ 189 (mod 6) =
237
Appendix K: Modular Arithmetic Tasks, Study 3 and 4
You will be solving a series of problems on the computer. You are going to see problems on
the screen that look like the following:
17 ≡ 5 (mod 6)
Your job is to judge whether the problems are "true" or "false" as quickly and as accurately as
possible.
Example 1: Is the following statement true?
35 ≡ 19 (mod 2)
First we subtract 19 from 35:
35 - 19 = 16
Does 2 divide into 16 with 0 as the remainder?
Yes, 2 goes into 16 eight times, with a remainder of zero. Thus our statement is true.
The test starts now.
238
Block 1:
31. 42 ≡ 27 (mod 3) =
32. 36 ≡ 27 (mod 3) =
33. 43 ≡ 27 (mod 8) =
34. 53 ≡ 26 (mod 4) =
35. 54 ≡ 36 (mod 7) =
36. 73 ≡ 37 (mod 7) =
37. 54 ≡ 26 (mod 6) =
38. 52 ≡ 17 (mod 4) =
39. 83 ≡ 27 (mod 9) =
40. 41 ≡ 27 (mod 6) =
41. 43 ≡ 27 (mod 7) =
42. 54 ≡ 36 (mod 6) =
43. 41 ≡ 27 (mod 7) =
44. 83 ≡ 27 (mod 8) =
45. 32 ≡ 14 (mod 6) =
46. 36 ≡ 27 (mod 4) =
47. 32 ≡ 14 (mod 7) =
48. 45 ≡ 29 (mod 8) =
49. 53 ≡ 26 (mod 3) =
50. 45 ≡ 29 (mod 9) =
51. 52 ≡ 17 (mod 7) =
52. 45 ≡ 27 (mod 3) =
53. 41 ≡ 23 (mod 4) =
54. 42 ≡ 27 (mod 4) =
239
Block 2:
1. 82 ≡ 55 (mod 9) =
2. 56 ≡ 38 (mod 4) =
3. 54 ≡ 27 (mod 9) =
4. 63 ≡ 48 (mod 4) =
5. 75 ≡ 59 (mod 4) =
6. 51 ≡ 19 (mod 4) =
7. 63 ≡ 15 (mod 6) =
8. 62 ≡ 38 (mod 6) =
9. 45 ≡ 27 (mod 4) =
10. 82 ≡ 55 (mod 8) =
11. 83 ≡ 35 (mod 4) =
12. 56 ≡ 38 (mod 3) =
13. 41 ≡ 23 (mod 3) =
14. 43 ≡ 18 (mod 5) =
15. 54 ≡ 27 (mod 8) =
16. 63 ≡ 48 (mod 3) =
17. 67 ≡ 18 (mod 7) =
18. 75 ≡ 59 (mod 5) =
19. 51 ≡ 19 (mod 3) =
20. 63 ≡ 15 (mod 7) =
21. 62 ≡ 38 (mod 7) =
22. 45 ≡ 27 (mod 3) =
23. 41 ≡ 23 (mod 4) =
24. 43 ≡ 18 (mod 3) =
240
Appendix L: Positive and Negative Affect Scale (PANAS), Study 4This scale consists of a number of words that describe different feelings and emotions. Read
each item and then mark the appropriate answer in the space next to that word. Indicate to
what extent you feel this way right now, that is, at the present moment.
Use the following scale to record your answers:
1 2 3 4 5
Very slightly or not at all A little Moderately Quite a bit Extremely
1.____Interested 11.____Irritable
2.____Distressed 12.____Alert
3.____Excited 13.____Ashamed
4.____Upset 14.____Inspired
5.____Strong 15.____Nervous
6.____Guilty 16.____Determined
7.____Scared 17.____Attentive
8.____Hostile 18.____Jittery
9.____Enthusiastic 19.____Active
10.____Proud 20.____Afraid
241
Appendix M: Maths Anxiety Scale (State), Study 1, 2, and 4
How anxious would you feel NOW in the following situations?
1. Having someone watch you multiply 12 x 23 on paper?Not at all A little A fair amount Much Very much1 2 3 4 5
2. Adding up a pile of change?Not at all A little A fair amount Much Very much1 2 3 4 5
3. Being asked to write an answer on the board at the front of a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5
4. Being asked to add up the number of people in a room?Not at all A little A fair amount Much Very much1 2 3 4 5
5. Calculating how many days until a person’s birthday?Not at all A little A fair amount Much Very much1 2 3 4 5
6. Taking a maths exam?Not at all A little A fair amount Much Very much1 2 3 4 5
7. Being asked to calculate £9.36 divided by 4 in front of several people?Not at all A little A fair amount Much Very much1 2 3 4 5
8. Being giving a telephone number and having to remember it?Not at all A little A fair amount Much Very much1 2 3 4 5
9. Reading the word ‘algebra’?Not at all A little A fair amount Much Very much1 2 3 4 5
10. Calculating a series of multiplication problems on paper?Not at all A little A fair amount Much Very much1 2 3 4 5
11. Working out how much time you have left before you set off work or place of study?Not at all A little A fair amount Much Very much1 2 3 4 5
12. Listening to someone talk about maths?Not at all A little A fair amount Much Very much1 2 3 4 5
13. Working out how much change a cashier should have given you in a shop after buying several items?
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Not at all A little A fair amount Much Very much1 2 3 4 5
14. Deciding how much each person should give you after you buy an object that you are all sharing the cost of?Not at all A little A fair amount Much Very much1 2 3 4 5
15. Reading a maths text book?Not at all A little A fair amount Much Very much1 2 3 4 5
16. Watching someone work out an algebra problem?Not at all A little A fair amount Much Very much1 2 3 4 5
17. Sitting in a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5
18. Being given a surprise maths test in a class?Not at all A little A fair amount Much Very much1 2 3 4 5
19. Being asked to memorize a multiplication table?Not at all A little A fair amount Much Very much1 2 3 4 5
20. Watching a teacher/lecturer write equations on the board?Not at all A little A fair amount Much Very much1 2 3 4 5
21. Being asked to calculate three fifths as a percentage?Not at all A little A fair amount Much Very much1 2 3 4 5
22. Working out how much your shopping bill comes to?Not at all A little A fair amount Much Very much1 2 3 4 5
23. Being asked a maths question by a teacher in front of a class?Not at all A little A fair amount Much Very much1 2 3 4 5
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