Early detection and stimulation of precursors and foundations of … · 2018-09-17 · Södervik, & Aino Mattinen (University of Turku, Finland): Stimulating SFON, cardinality and

Scientific Research Community: WO.008.14N Developing competencies in learners: From

ascertaining to intervening

Fifth meeting

October 17 – 19, 2018

Irish College, Leuven

Early detection and stimulation of precursors and foundations of competencies

Programme and abstracts

2



Fifth meeting

October 17 – 19, 2018



Scientific Programming Committee

X. Vamvakoussi (University of Ioannina, Greece)

W. Van Dooren (University of Leuven, Belgium)

L. Verschaffel (University of Leuven, Belgium)

Local Organizing Committee

K. Dens (University of Leuven, Belgium)

F. Depaepe (University of Leuven, Belgium)

J. Elen (University of Leuven, Belgium)

D. Gijbels (University of Antwerp, Belgium)

K. Struyven (University of Brussels, Belgium)

J. Torbeyns (University of Leuven, Belgium)

H. Van Keer (Ghent University, Belgium)

W. Van Dooren (University of Leuven, Belgium)

L. Verschaffel (University of Leuven, Belgium)

3



Fifth meeting

October 17 – 19, 2018



List of participants

Daniel Ansari The University of Western Ontario (Canada)

Merel Bakker University of Leuven (Belgium)

de Groot Renate Open University (The Netherlands)

Ton de Jong University of Twente (The Netherlands)

Laure De Keyser University of Leuven (Belgium)

Bert De Smedt University of Leuven (Belgium)

Fien Depaepe University of Leuven (Belgium)

Jo Eaves Loughborough University (UK)

Jan Elen University of Leuven (Belgium)

Esther Gheyssens University of Brussels (Belgium)

Camilla Gilmore Loughborough University (UK)

Brian Greer Portland State University (USA)

Júlia Griful Freixenet University of Brussels (Belgium)

Minna Hannula-Sormunen University of Turku (Finland)

Sofie Heirweg Ghent University (Belgium)

Matthew Inglis Loughborough University (UK)

Paul Kirschner Open University (The Netherlands)

Erno Lehtinen University of Turku (Finland)

Despina Lepenioti University of Athens (Greece)

Irena Y. Maureen University of Twente (The Netherlands)

Jake McMullen University of Turku (Finland)

Emmelien Merchie Ghent University (Belgium)

Andreas Obersteiner Freiburg University of Education (Germany)

Greet Peters University of Leuven (Belgium)

Jayne Pickering Loughborough University (UK)

Sanne Rathé University of Leuven (Belgium)

Frank Reinhold Technical University of Munich (Germany)

Kristina Reiss Technical University of Munich (Germany)

Amélie Rogiers Ghent University (Belgium)

Michael Schneider University of Trier (Germany)

Sanne Schreurs Maastricht University (The Netherlands)

Elke Sekeris University of Leuven (Belgium)

Jon Star Harvard University (USA)

Anselm Strohmaier Technical University of Munich (Germany)

Anne-Sophie Supply University of Leuven (Belgium)

Joke Torbeyns University of Leuven (Belgium)

4

Xenia Vamvakoussi University of Ioannina (Greece)

Wim Van Dooren University of Leuven (Belgium)

Hilde Van Keer Ghent University (Belgium)

Jeroen Van Merrienboer Maastricht University (The Netherlands)

Stefanie Vanbecelaere University of Leuven (Belgium)

Kiran Vanbinst University of Leuven (Belgium)

Elien Vanluydt University of Leuven (Belgium)

Sandy Verbruggen University of Leuven (Belgium)

Ludo Verhoeven Radboud University Nijmegen (The Netherlands)

Lieven Verschaffel University of Leuven (Belgium)

Theresa Elise Wege Loughborough University (UK)

Nore Wijns University of Leuven (Belgium)

Iro Xenidou-Dervou Loughborough University (UK)

5



Fifth meeting

October 17 – 19, 2018



Address conference venue

The Leuven Institute for Ireland in Europe

Janseniusstraat 1

3000 Leuven

Belgium

Phone: + 32 16 31 04 30

Fax: + 32 16 31 04 31 Email: [email protected]

Website: http://www.leuveninstitute.eu/site/index.php

Google Maps

From Leuven train station to the conference venue:

https://goo.gl/maps/cKbMv

From the conference venue to the Faculty Club:

https://goo.gl/maps/cWNXv

From the conference venue to the Hotel school VTI:

https://goo.gl/maps/6eKMZGFG1U52

Address CIP&T

Centre for Instructional Psychology and Technology

Dekenstraat 2, postbox 3773

3000 Leuven

Belgium

Phone: +32 16 32 62 03

Fax: +32 16 32 62 74

E-mail secretariat: [email protected] Link to website conference: http://ppw.kuleuven.be/o_en_o/CIPenT/WOGCONF2018

mailto:[email protected]

http://www.leuveninstitute.eu/site/index.php

https://goo.gl/maps/cKbMv

https://goo.gl/maps/cWNXv

https://goo.gl/maps/6eKMZGFG1U52

mailto:[email protected]

http://ppw.kuleuven.be/o_en_o/CIPenT/WOGCONF2017

6



Fifth meeting

October 17 – 19, 2018



Programme

Wednesday 17.10.2018

13.00-15.00: Arrival

15.00-15.10: Welcome and general introduction (chair: Lieven Verschaffel)

15.10-16.40: Invited lecture 1 – Daniel Ansari (University of Western Ontario, Canada): Building

blocks of mathematical competence: evidence from brain & behavior (chair: Bert De Smedt)

16.40-17.00: Coffee break

17.00-19.00: Paper session 1: Early detection of precursors and foundations of competencies

(chair: Kristina Reiss)

Iro Xenidou-Dervou1, Johannes E. H. Van Luit2, Evelyn H. Kroesbergen3, Ilona Friso-van

den Bos2, Lisa M. Jonkman4, Menno van der Schoot5, & Ernest C.D.M. van Lieshout5

(1Loughborough University, United Kingdom, 2Utrecht University, The Netherlands, 3Radboud University Nijmegen, The Netherlands, 4Maastricht University, The

Netherlands, 5Vrije Universiteit Amsterdam, The Netherlands): Early predictors of

children’s individual growth rates in mathematical achievement

Kiran Vanbinst¹, Elsje van Bergen2, Pol Ghesquière1, & Bert De Smedt1 (¹KU Leuven,

Belgium & 2VU Amsterdam, The Netherlands): Arithmetic and reading in 5-year olds:

Related cognitive correlates

Sanne Rathé, Joke Torbeyns, Bert De Smedt, & Lieven Verschaffel (KU Leuven, Belgium):

The role of spontaneous focusing on Arabic number symbols in young children’s early

mathematical development

Jake McMullen¹, Erno Lehtinen¹, Minna M. Hannula-Sormunen¹, & Robert S. Siegler2

(¹University of Turku, Finland & 2Carnegie Mellon University, USA): Spontaneous

focusing on multiplicative relations predicts the development of complex rational

number knowledge

20.00: Dinner (Faculty Club, Groot Begijnhof 14, Leuven)

7

Thursday 18.10.2018

9.00-10.30: Invited lecture 2 – Ludo Verhoeven (Radboud University, Nijmegen,

The Netherlands): Precursors and foundations of reading development (chair: Hilde Van Keer)


11.00-12.30: Paper session 2: Development of competencies: the role of the teacher and the

curriculum (chair: Fien Depaepe)

Xenia Vamvakoussi & Lina Vraka (University of Ioannina, Greece): Quantification in early

instruction: An analysis of the Greek kindergarten mathematics curriculum

Renate H. M. de Groot (Open University of the Netherlands, The Netherlands): It’s the

teacher with their didactics that counts!

Esther Gheyssens & Katrien Struyven (Vrije Universiteit Brussel, Belgium): Differentiated

instruction in primary and secondary schools: from noticing to adapting teaching

12.30-13.30: Lunch

13.30-15.00: Invited lecture 3 – Matthew Inglis (Loughborough University, UK): Precursors and

non-precursors of advanced mathematical competencies (chair: Wim Van Dooren)

15.00-16.30: Interactive poster session 1: Detection and stimulation of competencies in various

content domains (chair: Joke Torbeyns)

Amélie Rogiers, Emmelien Merchie, & Hilde Van Keer (Ghent University, Belgium):

Fostering students’ text-learning strategies secondary education: the impact of explicit

strategy-instruction

Sofie Heirweg, Mona De Smul, Geert Devos, & Hilde Van Keer (Ghent University,

Belgium): Profiling upper primary school students’ self-regulated learning through self-

report questionnaires and think-aloud protocol analysis

Despina Lepenioti¹ & Stella Vosniadou¹,2 (¹National and Kapodistrian University of

Athens, Greece & 2Flinders University, Australia): Developing fraction knowledge with

the support of a fraction tutor

Joanne Eaves, Camilla Gilmore, & Nina Attridge (Loughborough University, United

Kingdom): Understanding and misconceptions of the order of operations

Stefanie Vanbecelaere, Katrien Van den Berghe, Frederik Cornillie, Bert Reynvoet,

Delphine Sasanguie, & Fien Depaepe (KU Leuven, Belgium): Effects of an educational

game on young children’s cognitive and affective factors underlying math and reading

Júlia Griful-Freixenet, Katrien Struyven, Wendelien Vantieghem, & Esther Gheyssens

(Vrije Universiteit Brussel, Belgium): Towards conceptual clarity in the interrelationship

between Universal Design for Learning (UDL) and Differentiated Instruction (DI)


17.00-18.30: Paper session 3: Detection of precursors and foundations of competencies:

measurement issues (chair: Erno Lehtinen)

8

Camilla Gilmore & Sophie Batchelor (Loughborough University, United Kingdom): What

do numeral order processing tasks measure?

Emmelien Merchie & Hilde Van Keer (Ghent University, Belgium): Uncovering

elementary students’ cognitive processes during informative text and mind map learning.

Combining eye tracking and retrospective interviews

Sanne Schreurs1, Kitty Cleutjens1, Arno M. M. Muijtjens1, Jennifer Cleland2 & Mirjam G.

A. oude Egbrink1 (1Maastricht University, The Netherlands & 2University of Aberdeen,

UK): Selection into medicine: The predictive validity of an outcome-based procedure

19.30: Dinner (Hotel School VTI, Brabançonnestraat 22, Leuven)

Friday 19.10.2018

9.00-10.30: Interactive poster session 2: Analysis of early core mathematical competencies

(chair: Jan Elen)

Theresa Elise Wege1, Bert De Smedt2, Camilla Gilmore1 & Matthew Inglis1

(1Loughborough University, United Kingdom & 2KU Leuven, Belgium): What counts as a

unit? Investigating the developmental trajectory of unit-flexibility

Nore Wijns, Joke Torbeyns, Bert De Smedt, & Lieven Verschaffel (KU Leuven, Belgium):

Development and stimulation of early mathematical patterning competencies in four- to

six-year olds

Elke Sekeris, Lieven Verschaffel, & Koen Luwel (KU Leuven, Belgium): The development

and stimulation of computational estimation from kindergarten to third grade of primary

school

Elien Vanluydt, Lieven Verschaffel, & Wim Van Dooren (KU Leuven, Belgium): Mapping

the emergence of proportional reasoning – initial results from a longitudinal study

Anne-Sophie Supply, Wim Van Dooren and Patrick Onghena (KU Leuven, Belgium):

Probabilistic reasoning in primary school

Merel Bakker, Joke Torbeyns, & Bert De Smedt (KU Leuven, Belgium): Determinants of

individual differences in the development of early numerical competencies


11.00-12.30: Paper session 4: Early stimulation of precursors and foundations of competencies

(chair: Jon Star)

Minna Hannula-Sormunen, Cristina Nanu, Milja Heinonen, Anne Sorariutta, Ilona

Södervik, & Aino Mattinen (University of Turku, Finland): Stimulating SFON, cardinality

and counting skills at day care

Irena Y. Maureen, Hans van der Meij, & Ton de Jong (University of Twente, The

Netherlands): Supporting literacy and digital literacy development in early childhood

education using (digital) storytelling lessons

Frank Reinhold1, Kristina Reiss1, Andreas Obersteiner2, Stefan Hoch1, Bernhard Werner1,

& Jürgen Richter-Gebert1 (1Technical University of Munich, Germany & 2Freiburg

9

University of Education, Germany): Drawing on children’s intuitive knowledge to enhance

fraction concepts: An intervention study with tablet-PCs

12.30-13.00: General conclusions and discussion (Chair: Xenia Vamvakoussi & Wim Van Dooren)

10

Conference formats

1. Invited lecture. Invited lectures are keynote presentations given by experts from the field

from outside or within the network. Invited lectures last 90 minutes. Each invited lecture

starts with a brief introduction of the speaker by the chair, followed by the keynote

presentation + 60 minutes) and a discussion with the audience (+ 30 minutes).

2. Paper session. Paper sessions provide the opportunity to present theoretical and/or

empirical work related to the major conference theme. Paper sessions last 90 or 120

minutes, depending on the number of papers in the session (resp. 3 or 4). Each paper is

presented during max. 15 minutes, followed by + 10 minutes for questions and discussion.

3. Poster session. The interactive poster sessions, which last 90 minutes, will be organized as

follows:

o Short plenary introduction of each poster by the poster presenters (30 minutes, i.e. 5

minutes per poster)

o Roundtable per poster (30 minutes), wherein the poster presenter can present his/her

work in greater detail and raise issues for the discussion (max. 10 minutes), followed by

a roundtable discussion (+ 20 minutes)

o Short plenary reflection on the poster and the discussion by an invited participant (30

minutes, i.e., 5 minutes per poster)

11

Abstracts keynotes

Building blocks of mathematical competence: evidence from brain & behaviour

Daniel Ansari (Department of Psychology and Brain & Mind Institute, Western University)

It is well established that early math skills are a strong predictor of later mathematics achievement. Moreover, low numerical and mathematical skills in childhood have been shown to relate to low socio-economic outcomes in adulthood. Against this background it is critical to better understand the early predictors of numerical and mathematical skills and to use this information to inform early mathematics education.

In this talk I will provide an overview of what insights have been gained from recent research in Developmental Psychology and Developmental Cognitive Neuroscience on the building blocks of mathematical competence. Specifically, I will discuss research that has shown that basic number processing (such as comparing which of two numbers is larger) is related to individual differences in children’s arithmetic achievement. Furthermore, children with mathematical difficulties have been found to perform poorly on basic number processing tasks. In this talk I will review evidence for an association between basic number processing and arithmetic achievement in children with and without mathematical difficulties. By doing so, I will also discuss whether individual differences in mathematical abilities are driven by innate differences in a ‘number sense’ that humans share with other species or whether such variability is related to the acquisition of uniquely human, symbolic representations of number (e.g. Arabic numerals). I will draw on evidence from both brain and behavior and discuss the implications of this research for assessment, diagnosis and intervention.

Precursors and foundations of reading development

Ludo Verhoeven (Behavioural Science Institute, Radboud University Nijmegen)

For school success and participation in society, learning to read is obviously of utmost importance. In learning to read, children are confronted with the task of acquiring implicit knowledge of how a writing system works—how the written word reveals meaning through a layer of graphic forms. Given the nature of writing and particularly the language constraints on writing, reading is universally grounded in both language and writing systems. Defined narrowly, reading is the decoding of language forms from written forms and spelling is the encoding of linguistic forms into written forms. Learning to decode print into spoken language marks the transition from language to literacy and the literate use of language as a window for thinking. In this lecture, I will discuss precursors and foundations of reading development, highlighting possible universals—including operating principles on the part of the learner - in perspective of early detection and intervention.

Precursors and non-precursors of advanced mathematical competencies

Matthew Inglis (Mathematics Education Centre, Loughborough University)

A fundamental goal of mathematics education at higher levels is to develop students' understanding

of mathematical proof. Unfortunately, a great deal of research has demonstrated that many students

at secondary and undergraduate levels find proof and proving to be extremely challenging. Two main

12

accounts have been proposed. Both suggest that students have inadequate precursor knowledge.

One focuses on epistemic cognition, arguing that students do not know how to reliably establish

knowledge in mathematics. The other focuses on students' poor logical skills. My goal in this talk is to

review some of my research on each of these topics. In both cases I will argue that successful

mathematicians often exhibit behaviour that, if exhibited by students, would be interpreted as a lack

of necessary precursors for engaging with proof. I conclude by arguing that either the research

community has inadequate conceptualisations of these supposed precursors, or that they are not in

fact precursors at all.

13

Abstracts paper sessions

PAPER SESSION 1 – paper 1

Early predictors of children’s individual growth rates in mathematical achievement

Iro Xenidou-Dervou1, Johannes E. H. Van Luit2, Evelyn H. Kroesbergen3, Ilona Friso-van den Bos2, Lisa

M. Jonkman4, Menno van der Schoot5, & Ernest C.D.M. van Lieshout5

1Loughborough University, United Kingdom, 2Utrecht University, The Netherlands, 3Radboud University

Nijmegen, The Netherlands, 4Maastricht University, The Netherlands, 5Vrije Universiteit Amsterdam,

The Netherlands

Research has identified various domain-general and domain-specific cognitive abilities as early

predictors of children’s individual differences in mathematics achievement. However, we know very

little about which abilities predict children’s individual growth rates, namely between-person

differences in intra-individual change in mathematics achievement. We conducted a three-year long

longitudinal study starting when the children were at the kindergarten stage. We assessed 334

children’s performance on an IQ measure, various domain-general and mathematics-specific WM

measures covering all components of WM, their counting skills, and their nonsymbolic and symbolic

magnitude comparison and arithmetic abilities. We also collected data on their general mathematics

achievement performance longitudinally across four time-points within the first and second grades of

primary school.

Latent growth modeling showed that, as expected, a constellation of multiple cognitive abilities

contributed to the children’s starting level of mathematical success. Specifically, WM abilities, IQ,

counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained

individual differences in the children’s initial status on a curriculum-based general mathematics

achievement test. Surprisingly, however, only one out of all of the assessed cognitive abilities was a

unique predictor of the children’s individual growth rates in mathematics achievement: their

performance in the symbolic approximate addition task. In this task, children were asked to estimate

the sum of two numbers (from 6 up to 70) and decide if this estimated sum was smaller or larger

compared to a third number.

Our findings demonstrate the importance of multiple domain-general and mathematics-specific

cognitive skills for identifying early on children at risk of struggling with mathematics and highlight the

significance of early approximate arithmetic skills for the development of one’s mathematical success.

Symbolic approximate arithmetic – otherwise known as computational estimation - was the only

predictor of children’s growth in mathematics achievement, even beyond WM capacities and exact

arithmetic. Lastly, a striking finding of this study is the fact that, despite the wide range of early

cognitive factors that we assessed, and even though our latent growth model explained sufficient

variance (52%) in the initial status factor (i.e., mathematics achievement in middle of grade 1), it only

explained 11% of the variance in children’s individual mathematics growth rates. So far research has

been focusing on the predictors of children’s performance; but what about their learning and

developmental growth? We argue the need for more research focus on identifying the predictors of

children’s individual growth rates in mathematics achievement.

14


Arithmetic and reading in 5-year olds: Related cognitive correlates

Kiran Vanbinst¹, Elsje van Bergen2, Pol Ghesquière1, & Bert De Smedt1

1 Parenting and Special Education Research Unit, KU Leuven, Belgium 2 Netherlands Twin Register, VU Amsterdam, The Netherlands

Arithmetic and reading constitute two quintessential building blocks of children’s elementary school

education. Prior cognitive research has predominantly focused on identifying the cognitive

underpinnings of (future) individual differences in arithmetic or reading. This research has revealed

distinct domain-specific cognitive correlates for each learning domain separately. Studies from the

reading research field, have repeatedly demonstrated that, phonological awareness underlies

individual differences in learning to read (i.e., Melby-Lervåg et al., 2012). Interestingly, phonological

awareness, considered a reading-specific cognitive correlate, has also been associated to individual

differences in arithmetic learning (i.e., Fuchs et al., 2005). Arithmetic and reading are consistently

found to be highly correlated (i.e., Simmons & Singleton, 2008) and it has even been suggested that

these academic abilities share genetic influences (so-called “generalist genes”) (i.e., Kovas et al., 2007).

Additionally, learning difficulties characterized by specific deficits in arithmetic (dyscalculia) or reading

(dyslexia) co-occur frequently (e.g., Boets & De Smedt, 2010; Simmons & Singleton, 2008). It is

consequently surprising that research on arithmetic and reading has mostly occurred in isolation from

each other. Against this background, the present study aims to investigate individual differences in

arithmetic and reading simultaneously, in order to reveal underlying cognitive mechanisms that are

shared between these learning abilities, rather than focusing on what sets arithmetic and reading

development apart. Firstly, this study explored associations between levels of early arithmetic as well

as early reading before formal instruction. We further investigated how early arithmetic and early

reading levels correlate with cognitive skills known to predict future fluency in arithmetic and/or

reading. This allowed us to reveal specific and shared cognitive skills for arithmetic and reading.

Participants were 188 children (101 girls, 87 boys) in the last year of Kindergarten in Flanders (M = 5

years, 8 months; SD = 4 months), who had not yet received formal education. Early arithmetic was

assessed with concrete materials and with symbols (2 + 3 = ?). Early reading was tested with an active

letter knowledge task. The measured cognitive skills were: Symbolic and non-symbolic comparison,

numeral recognition and phonological awareness (end-phoneme identification; end-rhyme

identification). Regression analyses and Bayesian hypothesis testing revealed strong associations

between levels of early arithmetic and early reading, even after controlling for age, sex and intellectual

ability. Numeral recognition appeared the most important cognitive correlate of early arithmetic and

early reading. Phonological awareness correlated with symbolic arithmetic and early reading, but not

with concrete arithmetic. The current findings indicate that especially preschoolers’ ability to identify

abstract symbols (i.e., Arabic numerals) represents an important and shared cognitive correlate of

learning to calculate, but also to read. It consequently constitutes a risk factor for developing

difficulties in arithmetic as well as reading. Screening this shared cognitive correlate might be useful

to detect preschoolers at risk for learning difficulties.

http://www.tweelingenregister.org/en/

15


The role of spontaneous focusing on Arabic number symbols in young children’s early

mathematical development

Sanne Rathé1, Joke Torbeyns1, Bert De Smedt2, & Lieven Verschaffel1

1Center for Instructional Psychology and Technology, KU Leuven, Belgium 2Parenting and Special Education Research Unit, KU Leuven, Belgium

Identifying early markers of individual differences in children’s mathematical development is an

important goal of studies in the domain of cognitive and educational psychology. Up until now,

research on young children’s early mathematical development has mainly focused on the importance

of early mathematical abilities, such as counting or magnitude comparison skills, in the prediction of

concurrent and later mathematics achievement (e.g., Geary & VanMarle, 2016; Nguyen et al., 2016;

Vanbinst, Ghesquière, & De Smedt, 2015).

However, another line of research proposes that children’s tendency to spontaneously focus their

attention on the aspect of exact number in their everyday environment, without explicitly prompted

to do so (i.e., SFON), is also an important component of their early mathematical development

(Hannula-Sormunen, 2015; Rathé, Torbeyns, Hannula-Sormunen, De Smedt, & Verschaffel, 2016).

Many studies have identified SFON as an unique predictor of concurrent early mathematical abilities

in kindergarten and later arithmetical skills in primary school (see Rathé et al., 2016, for a review). One

important characteristic of these previous studies is that they used stimuli in which numbers are

presented in a non-symbolic format, with the result that children’s spontaneous attention for Arabic

number symbols has not yet been addressed in this research.

In the present study, we aimed to address this gap by exploring children’s tendency to spontaneously

focus on Arabic number symbols (i.e., SFONS) in relation to their SFON, numerical abilities (i.e., Arabic

numeral identification, counting objects, verbal counting, and mapping), and mathematics

achievement, taking into account child and family characteristics. Participants were 159 children (77

boys, Mage fall = 4y5m) from the second year of Flemish kindergarten. All children completed measures

of SFON, SFONS, and numerical abilities in the fall, and measures of non-verbal IQ, language ability,

and mathematics achievement in the spring of the same school year. Family characteristics (i.e.,

parents’ education level) were measured via a parent questionnaire.

In line with previous findings (Rathé, Torbeyns, De Smedt, & Verschaffel, 2017), we found a small but

significant association between children’s SFONS and SFON scores, but the correlation further

decreased once age (in months), parental education, non-verbal IQ, and language ability were

controlled for. Furthermore, children’s SFONS, but not their SFON, was significantly associated with

numerical abilities (except for verbal counting) and mathematics achievement, also when age, parental

education, non-verbal IQ, and language ability were taken into account. These findings suggest that

SFONS is a relevant component of children’s early mathematical development.

16


Spontaneous focusing on multiplicative relations predicts the development of complex

rational number knowledge

Jake McMullen¹, Erno Lehtinen¹, Minna M. Hannula-Sormunen¹, & Robert S. Siegler2

¹University of Turku, Finland 2Carnegie Mellon University, USA

The theory of adaptive expertise suggests that a routine understanding of a topic is not sufficient for

high level success, regardless of the strength of the routine knowledge (Hatano & Oura, 2012). Instead,

adaptive expertise requires more malleable, fluid knowledge that is readily applicable to novel

situations. In other topics in mathematics, especially whole number arithmetic, adaptive expertise has

been found to be a strong predictor of later learning (e.g. Baroody & Rosu, 2004). The present study

aims to examine adaptivity with rational number knowledge and to examine sources of individual

differences in such knowledge, including Spontaneous Focusing On quantitative Relations (SFOR).

Adaptive number knowledge with whole numbers involves “a rich network of knowledge about

characteristics of numbers and the relations between numbers, which can be flexibly applied in solving

novel arithmetic tasks” (McMullen, Brezovszky, et al., 2016, pg. 172). The present study is the first to

investigate such knowledge with rational numbers, which is expected to bridge students’

understanding of rational number sizes, notations, and arithmetic, as well as procedural skills with

rational number arithmetic.

Integrated knowledge of rational number concepts and procedures may depend on factors beyond the

skills and knowledge developed in traditional mathematics classrooms. Students who recognize and

utilize multiplicative relations in and out of the classroom contexts – as indexed by SFOR tendency

(McMullen, Hannula-Sormunen, & Lehtinen, 2014) – may have an advantage in acquiring advanced

knowledge of rational numbers.

Over a year-and-a-half, students from the 7th and 8th grades of a school in the southeastern US

(N=395; 53% female) completed measures of SFOR tendency, rational number knowledge, including

adaptive rational number knowledge, and other mathematical and cognitive measures.

Latent profile analysis (Figure 1) revealed that adaptive number knowledge is a unique feature of

rational number knowledge and skills, and that it is related to, but not entirely dependent on,

knowledge of the magnitudes, operations, and representations of rational numbers.

17

Figure 1. Mean scores for latent profiles for each aspect of rational number knowledge. Error

bars: ±2 S.E.

Structural equation modelling revealed that SFOR tendency predicts adaptive rational number

knowledge (β=.23, p<.001) even after taking into account other types of conceptual knowledge of

rational numbers, procedural fluency with rational number arithmetic, overall mathematical

achievement, interest in mathematics, spatial reasoning, and guided focusing on quantitative

relations.

Students with a high SFOR tendency may benefit from seeing the quantitative relations in everyday

life. Detecting such quantitative relations might be useful in acquiring adaptive rational number

knowledge because everyday settings often require integration of multiple aspects of rational number

knowledge, for example, integrating understanding of the size of the fraction 1/4 (“I am ¼ of my way

home) and the multiplicative relation among 1/4, 4, and 1 (“It will take me three times as long to get

home as I have traveled so far”). These experiences with integrating different aspects of rational

number knowledge in everyday situations may explain why SFOR tendency is related to adaptive

rational number knowledge.

18


Quantification in early instruction: An analysis of the Greek kindergarten mathematics

curriculum

Xenia Vamvakoussi & Lina Vraka

University of Ioannina, Greece

In this paper we present results of a systematic analysis of the Greek kindergarten mathematics

curriculum with respect to quantification. Our analysis draws on P. Thompson’s (1993, 2010)

perspective on quantification as “the analysis of a situation into a quantitative structure - a network of

quantities and quantitative relationships” (1993, p. 165). Quantities are, by definition, measurable:

given a unit of measurement, the numerical value of the quantity can be determined. Importantly, this

value represents a multiplicative relation between the unit and the measured quantity. However, non-

numerical and numerical quantification are not the same--one can identify quantities and relations

between quantities without using numbers (Nunes & Bryant, 2015; Sophian, 2004; Thompson, 2010).

We draw on this distinction to highlight a problem with early quantification through instruction. We

argue that early instruction favors the quantification of situations that involve discrete quantities,

additive relations, and where concepts and processes pertaining to natural numbers are applicable.

This asymmetry limits the development of quantification competencies and may contribute to

students’ difficulties with multiplicative/proportional reasoning; and also with non-natural numbers.

(Vamvakoussi, Christou, Vosniadou, in press).

We analyzed the Greek kindergarten mathematics curriculum with respect to the kinds of quantities

(discrete vs. continuous) and relations (equivalence and order relations; additive and multiplicative

relations) that are explicitly studied; and with respect to numerical quantification (i.e., which quantities

and relations are expressed numerically, and how).

With respect to non-numerical quantification, we found that discrete quantities (represented as

collections of objects) and continuous quantities (length, area, and volume) are treated quite similarly:

Comparison, ordering, and additive composition/decomposition of quantities are explicitly required.

Numerical quantification is introduced in the context of discrete quantities, via the act of counting. All

proposed activities refer to situations where units conflate with physical objects, thus the relation of

the size of the unit to the counting outcome is not relevant (Sophian, 2004). Additive relations and also

additive comparison between discrete quantities are explicitly required, also numerically.

On the other hand, numerical quantification for continuous quantities is introduced via measurement

with non-standard units. Two processes are proposed: a) composing the quantity with multiple copies

of the unit and then counting the number of units; b) iterating one single copy of the unit. The latter

could highlight the multiplicative character of measurement; however this is not explicitly addressed.

The possibility that both processes may not “come out even” is also not addressed. Thus, measurement

can be reduced to single-unit counting (“how many units?”, “how many iterations”?).

19

Finally, multiplicative situations are included in the curriculum only in the context of discrete quantities

(equal grouping/fair sharing). Surprisingly, not even the simplest multiplicative relations (half/double)

are explicitly mentioned.

Such an approach to quantification in early instruction may contribute to older students’ tendency to

over-rely on additive and natural-number–based reasoning in situations where this is not appropriate

(Vamvakoussi et al., in press). This claim may be further substantiated, if early mathematics

educational programs addressing these issues prove to be effective in the long run.


It’s the teacher with their didactics that counts!

Prof. dr. Renate H. M. de Groot

Welten institute, Research Centre for Learning, Teaching and Technology, Open University of the

Netherlands, The Netherlands

Learning is not simply an isolated cognitive experience in the learner’s brain. In addition to a person’s

personal learning capacity (i.e., genetics and personal characteristics), the extent to which learning

occurs is highly dependent on the context in which and the conditions under which a person tries to

learn. We define context as the (learning) environment in which learning takes place (e.g., school,

workplace, everyday life) and conditions as those variables that directly influence the biopsychology of

the learner in a negative (e.g., feelings of inferiority, stress, fatigue, illness) or positive (e.g., self-

confidence, motivation, learning strategies, exercise, healthy diet, enough sleep) way. Collectively,

context and conditions can be seen as prerequisites for learning.

In 2010, Sameroff posited his ‘Unified theory of development’. Sameroff states that every person has

her/his own biology and psychology. However, biology and psychology overlap, influence each other,

and interact with each other. Together they form the individual learner (i.e., the blueprint made by the

architect). However, the learner is not a static entity. (S)he is dynamic, changes over time, develops

and matures. This development is again influenced by the learner’s own biology and psychology, but

is also strongly influenced by the context and conditions in which and under which a learner exists (see

social ecology as discussed by Bronfenbrenner (1977).

Thompson et al. (2001), for example, showed that identical twins (i.e, with 100% identical genetic

material), eventually exhibit significant differences in the outgrowth of their brains. Thus, the

prerequisites for learning (including gene-environment interactions; epigenetics) determine at least

part of the outgrowth of a person’s brain.

In sum, genetics, context, and conditions play important roles in learning and their underlying learning

processes. All three influence the growth and maturation of the brain and influence learning. To

understand how and when context and conditions subsequently influence learning it is essential to

further study the quality of educational practice in order to improve it. All learners have the right to

reach their own potential. If we want our children to reach what they can, we have to acknowledge

that ultimate performance starts at the first day of (prenatal) life and that parents and then teachers

20

are critical in this process. Learning can be seen as teamwork between the architect (i.e., the learner’s

psychobiology) and the contractors (e.g., parents, teachers, peers). Context and conditions (i.e.,

environmental factors created by parents, teachers, and peers) are thus essential to come to an

optimal learning process. Identification of (context and condition specific) sensitive periods for learning

are a prerequisite.

The presentation will explain Sameroff’s theory and provide many examples from the scientific

literature to illustrate the important role of the teachers with their didactics (i.e., educational tools and

techniques) for optimal development of the learner to achieve optimal development of the learner’s

competencies.


Differentiated instruction in primary and secondary schools: from noticing to adapting

teaching

Esther Gheyssens & Katrien Struyven Vrije Universiteit Brussel, Belgium Differentiated Instruction (DI) is proven to be a valid and reliable approach for teachers to meet the

needs of diverse learners. Several empirical studies confirm the impact of DI on student learning in

terms of students’ academic achievements and students’ attitudes about learning in both primary and

secondary education. However, DI is also a complex concept. It is considered as both an approach to

teaching and as a philosophy, influenced by the beliefs of teachers (Coubergs et al., 2017; Latz &

Adams, 2011; Tomlinson, 2005). Thus, measuring teachers’ knowledge and especially teachers’

practice of DI is less evident. This study aims to gain a broader perspective of teachers’ perceptions,

noticing and reasoning of DI by using triangulation method. More specifically two different valid

instruments are used to measure this: the DI-Quest instrument and the e-PIC videography tool. Both

methods are adopted to investigate the connection between thinking and acting on DI. The DI-Quest

instrument measures self-reported beliefs and practices of DI (Coubergs et al., 2017). The e-PIC tool

measures teachers’ noticing and reasoning of DI (Roose et al., 2017), which is a promising approach to

establish a theory-practice connection (Stürmer, Seidel & Schäfer, 2013). Drawing on the hypothesis

that the more teachers notice, the higher adaptive practices of DI are reported, two research questions

were investigated: (1) Can we distinguish teacher profiles based on the noticing and reasoning? (2)

How do these profiles relate to teachers the self-reported practices and beliefs of DI? Results reveal

two profiles of teachers based on their noticing and reasoning. The first group of teachers have strong

notice abilities and find DI strategies such as flexible grouping, active learning, adaptive teaching and

instructional clarity important. The second group are less able to notice DI and find the related

reasoning arguments about DI also less important. Moreover, the positioning of the teacher in one of

these profiles also predicts their self-reported practices. The hypothesis that teachers with stronger

notice abilities of DI, have also stronger abilities to implement DI practices is confirmed in this study.

Surprisingly, there was also a relationship found between the noticing and reasoning capabilities of

teachers and their beliefs about DI. This study validates the complexity of DI as a multi-layered model,

nevertheless it also demonstrates that all these different layers are interrelated with each other.

21


What do numeral order processing tasks measure?

Camilla Gilmore & Sophie Batchelor

Loughborough University, United Kingdom

Background

The past two decades have seen an increased interest in understanding the basic skills associated with individual differences in mathematics performance. Recent attention has focused on symbol knowledge and the role of symbol-symbol mappings in explaining mathematics differences. In particular, an increasing number of studies have explored performance on numeral order processing tasks. These tasks typically involve showing participants triplets of numerals and asking participants to decide whether the triplets are in numerical order (e.g. 4 5 6) or not (e.g. 4 6 5). Studies have demonstrated that performance on numeral order tasks is associated with mathematics performance, typically measured with an arithmetic task, in both adults (e.g. Lyons & Beilock, 2009, 2011; Vos et al., 2017) and children (e.g. Lyons & Ansari, 2015; Lyons et al., 2014). However, to date, the mechanism underlying this relationship is unclear.

Some researchers have suggested that the relationship between numeral order processing and arithmetic arises because order information is a fundamental property of symbolic numerical representations. We tested an alternative explanation, that the relationship between numeral order processing and arithmetic could be driven by verbal count sequence knowledge.

Method

Sixty-two children aged 6 to 8 completed 4 tasks:

1) Numeral order processing task (based on Lyons et al., 2014).

2) Verbal count sequence task in which children were asked to complete a series of 4 ascending and 4 descending count sequences.

3) The color and number subtests of the Rapid Automatized Naming (RAN) test.

4) A shortened version of the WIAT II-UK Numerical Operations subtest to assess arithmetic performance.

Results

We ran a series of hierarchical regression models to explore the extent to which numeral order processing and verbal count sequence knowledge were associated with arithmetic performance. In the first set of models we tested whether numeral order processing was associated with arithmetic over and above age, verbal count sequence knowledge and RAN. This revealed that count sequence knowledge was a significant independent predictor of arithmetic (β = .48, p < .001). Adding numeral order accuracy or RT to the model did not improve the fit (ΔR2 = .01, p = .167; ΔR2 = .02, p = .083).

In the second set of models we tested whether verbal count sequence knowledge was associated with arithmetic performance over and above age, numeral order processing and RAN. Count sequence knowledge substantially and significantly improved the fit of the model over and above numeral order processing accuracy (ΔR2 = .14, p < .001) or RT (ΔR2 = .11, p < .001).

22

Discussion

Our findings demonstrate that performance on a typical numeral order processing task did not

predict concurrent arithmetic performance once children’s verbal count sequence knowledge had

been taken into account. This suggests that order information may not be a fundamental aspect of

symbolic number representations. Moreover, insufficient attention may have been paid to the role

of verbal number knowledge in explaining differences in symbolic arithmetic performance.


Uncovering elementary students’ cognitive processes during informative text and mind map

learning. Combining eye tracking and retrospective interviews.

Emmelien Merchie & Hilde Van Keer

Ghent University

Background

The ability to strategically process and learn informative text is of vital importance for future personal

and professional success making successful text-based learning a highly relevant research topic (Ponce

& Mayer, 2014). It is crucial from elementary grades on to initiate students into successful learning

from text. Research however points at elementary graders’ lack of necessary strategies to learn from

complex informative texts (Merchie, Van Keer & Vandevelde, 2014; Tielemans, Vandenbroeck, Bellens,

Van Damme & De Fraine, 2016). In this respect, the beneficial effects of graphic organizers (i.e., spatial

text arrangements) to facilitate this text-based learning has repeatedly been proven in literature

(Nesbit & Adesope, 2006; Merchie & Van Keer, 2016). The present study focusses on mind maps

(Buzan, 2005) as specific GO types, frequently used in practice, though seriously understudied in

scientific research. Given that uncovering specific difficulties when learners work with texts and mind

maps are indispensable to attune strategies instruction (Hilbert & Renkl, 2008), insights into this

matter are of high importance.

Aims

The study specifically focusses on students’ covert, non-observable cognitive processes during text and

mind map learning and their relationship with learning outcomes. More specifically, the following

research questions are under investigation:

(1) What cognitive processes do elementary students apply when (a) learning from text and (b)

learning from mind maps?

(2) Does the presentation of mind maps as study aids presented either beforehand or afterwards

prime different cognitive processing when learning from text?

(3) How are cognitive processes during text and mind map learning related to learning outcomes?

Methodology

Sixty late elementary school students will be randomly assigned to three conditions: text group, text-

mind map group or mind map-text group. All groups will study global warming in the text and mind

23

map while their eye movements will be registered. Students will answer a multilayered knowledge

acquisition test afterwards. Furthermore, they will be retrospectively interviewed concerning their

learning behavior. Data will be gathered during May 2018 and analyzed in the subsequent months.

Results

The following eye tracking measures will be selected for further data analysis: total reading time, first-

pass reading time, second-pass reading time, fixation duration on particular areas of interest (AOI),

sequence of eye movement (i.e., scan path analysis) (Jian, 2016). Independent t-tests will be performed

to understand differences in cognitive processes and their relationship with learning outcomes.

Retrospective interviews will be transcribed verbatim and thematically analyzed (McCrudden &

Kendeou, 2014).

Discussion

This study is highly relevant, since the lack of research investigating empirical links between text and

mind map learning. During the paper session, the results of this study will be extensively discussed.

Evidence-based didactical guidelines will be provided to attune strategy instruction in text-based

learning.


Selection into medicine: The predictive validity of an outcome-based procedure

Sanne Schreurs1, Kitty Cleutjens2, Arno M. M. Muijtjens1, Jennifer Cleland3, & Mirjam G. A. oude

Egbrink4

Departments of 1Educational Development and Research, 2Pathology and 4Physiology, Institute for

Education and School of Health Professions Education, Faculty of Health, Medicine and Life Sciences,

Maastricht University, The Netherlands, 3Institute of Education for Medical and Dental Sciences,

University of Aberdeen, United Kingdom

As there are many more applicants than places, medical schools need to select students from a large

pool of suitably qualified candidates. An important issue is ensuring that selection tools assess the

attributes considered important by key stakeholders, including students, medical schools and patients.

Schools must ensure they admit those candidates most likely to succeed in the curriculum and,

crucially, to become good doctors. Up to now, however, the choice of selection procedures for medical

school admissions is often pragmatic, based on available tools rather than desired outcomes (1-4).

An alternative approach is to start with the end goal, educating a good doctor, and develop an

outcome-based selection procedure through backward chaining. Furthermore, the context for which

the selection procedure is meant should be taken into account, e.g. learning environment (see Figure

1).

24

Figure 1, developing an outcome-based selection procedure.

The aim of this study was to examine if an outcome-based, holistic selection procedure is predictive of

study success in a medical bachelor curriculum.

Methods

The selection procedure as well as the curriculum and assessment program under study are aligned

with the CanMEDS framework of competences. For the selection procedure, the outcome

competences were translated to a ‘talent’-level. Due to the selection processes in the Netherlands, we

had the unique opportunity to compare the study results of students who were selected to those of

students who were rejected in the same selection procedure, but still got into medical school via a

national weighted lottery procedure (the control group). Using data from three cohorts (2011-13), we

examined the relationship between performance on an outcome-based selection procedure and study

success across a three-year medical bachelor program.

The outcomes were grouped into categories: cognitive (e.g. block tests and progress tests),

(inter)personal (e.g. professional behavior, consulting and reflecting skills), combined (OSCEs), and

general (drop-out and study delay). Linear and logistic regression analysis was applied to the different

outcome variables. Age and cohort were controlled for in the analysis, if needed. Controlling for pre

university grade point average was not necessary as this was equal in both groups.

Results and conclusion

The Maastricht University selection procedure satisfied basic psychometric demands, e.g. interrater

reliability and internal reliability. The selected students significantly outperformed their rejected

counterparts on most aspects of the program, including cognitive and (inter)personal outcomes and

assignments calling on both aspects (i.e. OSCEs). The predictive value of selection was most

pronounced for OSCE performance.

Unlike traditional medical school selection procedures, our outcome-based procedure used backward

chaining to select for the end product, good doctors. While the evidence for the predictive validity of

traditional procedures is mixed (1-4), we found good evidence for predictive value for performance on

different assessments over the three-year program. All in all, we have shown that an outcome-based,

25

holistic selection procedure is predictive of study success across a variety of cognitive, (inter)personal

skills and mixed assessments.


Stimulating SFON, cardinality and counting skills at day care

Minna Hannula-Sormunen, Cristina Nanu, Milja Heinonen, Anne Sorariutta, Ilona Södervik, & Aino

Mattinen

University of Turku, Finland

This presentation describes a naturalistic 2 - 5 –year-old children’s intervention study aimed at

promoting children’s Spontaneous Focusing On Numerosity (SFON) and early numerical skills. The

enhancement activities in both small-group and whole-group settings were conducted at day care by

early educators. The interventions consisted of a quasi-experimental pretest-posttest design with a

delayed posttest, active skill-, age-, and SES-matched control groups and a professional development

program.

Björklund and Barendregt, (2016) point out that even though preschool teachers engage children in

communication about mathematical phenomena, they do not systematically use the physical

environment as a point of departure for directing children’s attention to specific mathematical

concepts or principles. Our intervention program is based on the idea that early educators should be

guided to use number talk, questions and activities that stimulate mathematical thinking among

children both in guided activities and as part of everyday situations so that children learn to see the

world through numerical lenses (Hannula, Mattinen & Lehtinen, 2005; Mattinen, 2006; Saebbe &

Mosvold, 2016). Learning to recognize early mathematical thinking and skills in children’s activities are

the basis on which an early educator and the child can start building more elaborated numerical

activities and interpretations. In the current project we developed specific methods of how this can be

accomplished in day care.

SFON-based intervention 1 (One, two, how many –program) with (n = 32) 2.5-3-year-old, and SFON-

based intervention 2 (Let’s count, how many –program) with (n = 43) 3-5-year-old children had similar

methods to enhance SFON but they differed in the level of cardinality related skills trained, 1 was

focused on cardinality recognition on small numbers, while 2 on object counting skills. Pre-, post- and

delayed post-tests included parallel sets of SFON tasks and cardinality recognition, listening

comprehension and vocabulary tasks. Two control groups (ntotal = 61) matched at the group level in

SFON and cardinality related skills in both interventions participated in a listening comprehension

intervention (Let’s read and discuss – program) with corresponding structure and professional

development program as the SFON interventions. All conditions had 6 weeks of intensive training

phase including 3 small-group sessions combined with whole group special transfer activities in each

week, followed by 4-month rehearsal phase, when intervention activities were integrated to normal

day care.

26

Figure 1. Examples activities in the SFON interventions: SFON baits, Vegetable market, How many –

boxes and Counting boards with which were used to stimulate children’s focusing on numerosities and

number recognition skills.

Preliminary ANCOVA results on SFON interventions combined vs. control group show that children of

the SFON interventions had higher scores in their SFON tendency F(1,132) =6.706, p <.05, 𝜂𝑝2=.05 and

cardinality related skills F(1,132) =3.413, p <.05, 𝜂𝑝2=.02 in the post-test than the control group when

pre-test scores were controlled for. Similar comparisons of all three intervention types revealed that,

intervention type had a significant effect on both SFON F(2,130) =3.265, p <.05, 𝜂𝑝2=.05 and cardinality

related skills at post-test F(2,131) =4.810, p <.05, 𝜂𝑝2=.06 when age and pre-test skills were controlled

for. Planned contrasts revealed that it was specifically SFON intervention 2 (Count, how many –

program), which resulted better performance in the post-tests than the control group. Delayed post-

tests will be finished in May, and these results will be presented in the workshop.

Presentation will further detail the theoretical and practical implications on SFON and early numeracy

development and education. So far it seems the developed interventions and professional

development courses can be used as basis for pre- and in-service training of early educators.


Supporting Literacy and Digital Literacy Development in Early Childhood Education using (Digital) Storytelling Lessons

Irena Y. Maureen, Hans van der Meij, & Ton de Jong

University of Twente, The Netherlands

Children’s success in school, and later in life, is to a great extent dependent upon literacy skills

development especially in reading and writing during early childhood years (NAEYC, 2018). The

increased attention for achieving such (digital) literacy goals in early childhood education has been

accompanied by more formalized educational practices. In line with the emerging critique on this

movement, the present study investigated the design and the effectiveness of a storytelling approach

aimed to stimulate the (digital) literacy skills. Storytelling can be characterized as a narrative play that

can develop literacy (Collins, 1999). The storytelling approach was systematically structured in the

lesson plans being based on the widely accepted ‘events of instruction’ from Gagné (Smith & Ragan,

2005). An experiment was performed on three classes in a public kindergarten (forty-five 5- and 6-

year-old children) with three conditions. Assignment to conditions was random. In the control

condition, regular classroom lessons on literacy were given. One experimental condition received

27

storytelling lessons, while the other experimental condition received digital storytelling lessons. Each

experimental condition received one lesson related to (digital) literacy in a week for a total three

lessons (and weeks). Each lesson plan composed of 150-minute instruction, including the 30-minute

storytelling session. The effects of the lessons were assessed with (digital) literacy skills tests

administered before and after the lessons. The administration of a pre-test not only afforded the

assessment of learning gains but also provided a test of the comparability of the children’s starting

levels of (digital) literacy skills across classrooms. Pre-test scores indicated that there were no

differences in the mean skills levels in classrooms/conditions at the start of the lessons. The findings

indicated that the (digital) storytelling lessons increased the children’s literacy skills significantly more

than that of the control condition. Exploratory analyses further suggested that the (digital) storytelling

lessons also enhanced digital literacy skills development. All in all, the study indicates that the

integration of the storytelling approach with the didactic approach of Gagné’s nine events of

instruction is a promising approach for (digital) literacy development in early childhood education.


Drawing on Children’s Intuitive Knowledge to Enhance Fraction Concepts: An Intervention

Study with Tablet-PCs

Frank Reinhold1, Kristina Reiss1, Andreas Obersteiner2, Stefan Hoch1, Bernhard Werner1, & Jürgen

Richter-Gebert1

1Technical University of Munich, Germany 2Freiburg University of Education, Germany

An understanding of fraction concepts is a key facet of mathematical literacy. There is empirical

evidence that understanding fractions is predictive of later achievement in higher mathematics such

as algebra (Bailey, Hoard, Nugent, & Geary, 2012). Unfortunately, many students struggle with learning

of fraction concepts as well as with higher mathematics (e.g., Lortie-Forgues, Tian, & Siegler, 2015).

Therefore, some researchers suggest that fractions could be the “gatekeepers” of higher mathematics

(Booth & Newton, 2012).

Although students’ difficulties with learning fractions are well documented, studies show that pre-

school children already have a fundamental understanding of ratios and proportions (Boyer & Levine,

2015). It seems that traditional school instruction does not draw sufficiently on children’s early

abilities. Instead, it often emphasizes symbolic fraction arithmetic that appears meaningless to many

students.

The aim of our research project ALICE:fractions was to develop and evaluate a learning environment

that draws on intuitive and perceptual abilities with non-symbolic fraction representations and links

them to symbolic fractions. The learning environment consists of a digital textbook for use on iPads

that includes interactive and adaptive exercises. The exercises focus on transitions between various

non-symbolic and symbolic representations and provide intuitive pathways to core fraction concepts

such as fraction magnitude. Hands-on activities and adaptive feedback allow students to explore non-

symbolic fractions (e.g., tape diagram) before introducing more formal representations (e.g., number

line with fraction symbols).

28

The effectiveness of the learning environment was evaluated during a fifteen-lessons intervention

study in which N=736 sixth grade students participated (476 in German “Gymnasium” – higher-

achieving students, and 260 in German “Mittelschule" – lower-achieving students). Students were

assigned to one of three groups: An iPad group worked with the iPad-assisted learning environment,

a paper-copy group received the same material as a regular paper-based book (treatment groups), and

a control group used conventional textbooks (see Reinhold, Hoch, Werner, Richter-Gebert, & Reiss,

2017). At pretest, initial fraction concepts were assessed (10 items, McDonald’s =.82). A posttest

measured conceptual knowledge of fractions (11 items, =.67, focusing specifically on transitions

between iconic and symbolic representations, or on the manipulation of iconic representations of

fractions) and procedural knowledge of fractions (8 items, =.71, symbolic representation of fractions

where no transitions between representations are necessary).

For the higher-achieving students, both treatment groups scored significantly better in the posttest

than the control group, =.03, without a significant difference between the treatment groups.

Furthermore, these differences were limited to conceptual knowledge, =.07, with no significant effect

for procedural knowledge (see Reinhold et al., 2017). However, regarding lower-achieving students,

learners from the iPad group achieved significant better results than learners from both other groups,

=.08. In particular, children who were taught with iPads showed higher conceptual knowledge, =.07,

and higher procedural knowledge, =.06 (see Reinhold, 2018).

The results of this study suggest that students benefit from a teaching approach for fraction concepts

that links children’s intuitive knowledge to formal mathematics. The study also shows how

technology can support teaching mathematics in an interactive and adaptive way, which seems to be

particularly beneficial for lower-achieving students.

29

Abstracts poster sessions

INTERACTIVE POSTER SESSION 1 – poster 1

Fostering students’ text-learning strategies secondary education: the impact of explicit

strategy-instruction

Amélie Rogiers, Emmelien Merchie, & Hilde Van Keer

Ghent University, Belgium

Context

As text-learning is a complex and demanding task, text-learning strategy instruction is indispensable at

the beginning of secondary education. Here, students are faced with more complex academic

demands, more autonomous learning situations, and increased expectations for independent text

study (Meneghetti et al., 2007). Especially learning from informative texts is crucial at this point in

students’ school careers, since demanding textbooks across different curriculum subjects are asking

for the effective use of text-learning strategies (i.e., strategies to select, organize, condense, and retain

text information in a more memorable form; Merchie et al., 2014; Vermunt & Vermetten, 2004).

Educational research should therefore provide teachers with evidence-based guidelines for teaching

text-learning strategies in daily practice. In this respect, the present study examines the effectiveness

of explicit strategy instruction (ESI) to provide students with a text-learning strategy repertoire. With

explicit instruction, teachers (a) introduce learning strategies by modelling (i.e., explaining, verbalizing,

and demonstrating their thoughts, actions, and reasons while processing text), (b) providing

knowledge on the how, when, and why to apply strategies, and (c) providing various practice

opportunities while providing feedback and gradually releasing guidance to internalize the strategies

(Weinstein et al., 2011).

Participants and design

In total, 22 Dutch language teachers and their 680 seventh-grade students (55.1% girls and 44.9% boys,

Mage=12.09) from 36 classes in Flanders (the Dutch-speaking part of Belgium) participated in the study.

A switching replication design (Shadish et al., 2002) with two groups and three measurement occasions

(Table 1) was set up in which students followed an eight-lesson teacher-delivered instructional

treatment. All lessons were embedded in the learning to learn cross-curricular standards for secondary

education (Flemish Ministry of Education and Training, 2010) and addressed the development of a

strategic repertoire.

30

Table 1: Design with a switching replication including 2 groups and 3 measurement occasions (M1, M2,

M3).

M1

January 2018

Phase 1

(3 weeks)

M2

March 2018

Phase 2

(3 weeks)

M3

May 2018

Group 1

(18 classes)

Pretest

ESI-program Posttest Regular

program

Retention test

Group 2

(18 classes)

/ Regular

program

Pretest

ESI-program Posttest

Measures

All data were collected within the classroom context during regularly scheduled class hours. At the

three measurement occasions, students’ spontaneous text-learning strategy use was assessed by (1) a

learning task, (2) a task-specific self-report inventory (Text-Learning Strategies Inventory; Merchie et

al., 2014), and (3) a cued recall test.

Data analysis

Currently, the intervention is ongoing. Multilevel piecewise growth analysis (Hox, 2002) will be used

to examine differences between classes and students, as well as the growth in students’ text-learning

strategy use and its relationship with class-level (i.e., instructional approach) and student-level (i.e.,

gender and achievement level) characteristics. Detailed results will be presented at the WOG

meeting.


Profiling upper primary school students’ self-regulated learning through self-report

questionnaires and think-aloud protocol analysis

Sofie Heirweg, Mona De Smul, Geert Devos, & Hilde Van Keer

Ghent University

During the last decades, self-regulated learning (SRL) received increasing attention in educational

practice and research due to the clear relation between students’ SRL skills and their academic success.

Students that efficiently adopt cognitive (e.g., rehearsing, rereading, summarizing), metacognitive

(e.g., planning, setting goals, monitoring and self-evaluating) and motivational strategies (e.g., self-

efficacy, task interest) during their learning process indeed outperform their peers on tests (Kistner et

al., 2010; Mega, Ronconi, & De Beni, 2014; Paloş, Munteanu, Costea, & Macsinga, 2011; Pintrich & De

Groot, 1990). Moreover, SRL provides students with the competences necessary for lifelong learning

and is thus vital for success after initial schooling (Zimmerman, 2008). Unfortunately, different studies

31

show that many students struggle to regulate their learning (e.g., Perry et al., 2004; Pintrich, 2004),

underlining the need to investigate and promote students’ SRL at a young age. In this regard, most

research nowadays examines SRL by means of a group-based comparison of separate SRL variables,

rather than focusing on how cognitive, metacognitive, and motivational SRL strategies come together

in individual students or subgroups of students. The current study aims to fill this gap by exploring the

occurrence of different SRL profiles in upper primary school children (N=2023) using a general self-

report questionnaire (Vandevelde, Van Keer, & Rosseel, 2013) and think-aloud protocol analysis

(Vandevelde, Van Keer, Schellings, & Van Hout-Wolters, 2015) on a subsample of students (N=105).

Further, it investigates the relation of students’ SRL profile with their general achievement level and

gender for the complete sample and with cued recall test performance for the subsample.

Cluster analysis on the self-report questionnaire showed the presence of four SRL profiles: active

learners with high quantity motivation (AHQN), active learners with high quality motivation (AHQL),

passive learners with low quantity motivation (PLQN), passive learners with low quality motivation

(PLQL). AHQN and AHQL learners are both characterized by high scores on cognition and

metacognition, but differ with regard to their motivation. While AHQN learners score high on both

autonomous (i.e. engaging in schoolwork for pleasure, interest) and controlled (i.e., engaging in

schoolwork because of external pressure) motivation, AHQL students have a high autonomous and low

controlled motivation. In contrast, passive learners are characterized by low scores on cognition and

metacognition, in combination with a disadvantageous motivational profile. While PLQN students have

low scores on both autonomous and controlled motivation, PLQL score low on autonomous and high

on controlled motivation. As expected on the basis of prior research (e.g., Kistner et al., 2010;

Vandevelde et al., 2013), a significant relation could be found between students’ profile, their gender

and general achievement level. Results show that boys and low achieving students more often belong

to the passive learner clusters than respectively girls or (above) average achieving students.

On the other hand, cluster analysis on the think-aloud protocols only distinguished between two SRL

profiles: low and high SRL learners. A significant relation could be found between students’ profile and

their scores on a cued recall test.

Implication of the profiles for research and practice will be discussed.


Developing fraction knowledge with the support of a fraction tutor

Despina Lepenioti¹ & Stella Vosniadou¹,2

¹National and Kapodistrian University of Athens, Greece & 2Flinders University, Australia

We designed and implemented a game-like, online fraction tutor for elementary school students

(grades 4-5-6) who have had minimal exposure to fractions. The tutor focuses on the conceptual

understanding of fractions and (i) utilizes the number line as an external representation and (ii) bases

its teaching sequence on empirical evidence regarding the order of acquisition of the fraction concept.

External representations have been shown to support the understanding of the different facets of the

fraction concept (Bright, Behr, Post & Wachsmuth, 1988). It has been argued that the number line is a

32

preferred external representation compared to other representations such as pies because it can

support improper fractions that cannot be supported using other external representations. In addition,

it represents the numbers on a continuum which can encourage the understanding of the relationship

between fractions and integers (Siegler, Thompson & Schneider, 2011) and of number density (Bright

et al., 1988).

The fraction tutor was designed to include magnitude fraction comparison problem sets the sequence

of which corresponds to the explanatory frameworks for the development of the fraction concept, as

described by Stafylidou & Vosniadou (2004). The students begin by connecting representations with

with fractions that share common denominators and later with fractions that share common

numerators. The next set of problems includes fractions consistent with the whole number bias and

later problems that include fractions inconsistent with the whole number bias. The last set of problems

includes fractions equal to the unit and then improper fractions. Students must successfully connect

the representations in order to move to the next problem.

This design of the teaching sequence guides students to explore how and in which instances they can

successfully apply their existing knowledge and in which instances this knowledge needs to be

reconsidered. We hypothesized that this design of the teaching sequence can support students

overcome the resulting misconceptions of the incompatibility of their existing knowledge for the

integers and the new knowledge for fractions (Vosniadou, 2014).

The fraction tutor was tested in a first intervention with 6th-grade students. 78 students were assigned

to two experimental groups, a number line and a pie training group and a control which received no

intervention. The experimental groups participated in 3 hourly sessions of training in connecting

representations for fractions with the fraction tutor. Students’ performance before and after the

intervention was assessed with a pretest and a posttest that included tasks regarding both the

conceptual and the procedural understanding of fractions. A repeated measures ANOVA revealed a

significant pretest/posttest improvement of the number line experimental group in comparison to the

pie and the control group overall, and specifically in fraction equivalence tasks and in tasks assessing

the interpretation of fractions as a measure

We are now in the process of running a second experiment which manipulates experimentally the

sequence of presentation of the different fraction tasks.


Understanding and misconceptions of the order of operations

Joanne Eaves, Camilla Gilmore, & Nina Attridge

Loughborough University, United Kingdom

Knowledge of the order in which arithmetic operations can be performed is key for success with

mathematics in secondary-school (ages 11+) and bridging the transition from arithmetic to algebra. A

correct understanding consists of knowing that multiplication and division have precedence over

addition and subtraction, that multiplication and division have equal precedence, and that addition

and subtraction have equal precedence. In countries such as the UK, USA and Australia, the order of

33

operations is often taught with the aid of acronyms such as BIDMAS (Brackets, Indices, Division,

Multiplication, Addition and Subtraction).

Many children have difficulty understanding the order of operations. Some individuals have no

awareness that operations have different precedence (Linchevski & Livneh, 1999; Pappanastos et al.,

2002), and routinely operate in a left-to-right manner regardless of the operations that problems

contain. Others have a literal interpretation of the acronyms they were taught, i.e. incorrectly assigning

precedence to division over multiplication and addition over subtraction (Kieran, 1985; Banerjee &

Subramaniam (2005). These misunderstandings are still prevalent in adulthood, even in teachers

(Ameis, 2011; Zakis & Rouleau, 2017).

Despite this, no attempt has been made to quantify individuals’ understanding of the order of

operations, or investigate the extent to which misconceptions exist. Our studies filled this gap, by

exploring the extent to which a University educated sample understood the order of operations, and

the extent to which they held misconceptions that could be attributed to the procedures taught in

school (e.g. BIDMAS).

We developed a new tool to measure knowledge of the order of operations, which was validated on

27 mathematics students. The measure consisted of a 20-item multiple choice questionnaire, where

individuals were asked to select, without calculating, the parts of arithmetic problems that could be

performed first. Following the validation phase, 76 students on non-mathematics programmes

completed the questionnaire, and a cluster analysis was performed on their data.

Five distinct clusters emerged, each with a different type of understanding of the order of operations.

One cluster fully understood operation order, although they were a minority (n = 12) while the

remaining clusters demonstrated different misunderstandings. The largest group (n = 21) had a literal

interpretation of acronyms (e.g. BIDMAS) and consistently indicated that addition had precedence

over subtraction; as a result, their answers to the majority of the problems were incorrect. Others

possessed a left-to-right understanding (n = 13), a mixed understanding (n = 17) and no understanding

(n = 13), and cluster-membership was associated with scholastic maths achievement.

These findings demonstrate that even in a well-educated sample, there are more individuals who

misunderstand the order of operations than there are individuals who have a good understanding.

Given that misunderstandings impede the development of advanced mathematical competencies

(Booth & Koedinger, 2008), we urge that scholars and education practitioners identify and diagnose

knowledge of the order of operations early on. This could be achieved quickly with the measure we

have developed, and allow remediation strategies to be deployed efficiently. Ultimately this could ease

the difficulties that many face when transitioning from arithmetic to algebra.

34


Effects of an educational game on young children’s cognitive and affective factors

underlying math and reading

Stefanie Vanbecelaere2,3, Katrien Van den Berghe3, Frederik Cornillie3, Bert Reynvoet1,3, Delphine

Sasanguie1, & Fien Depaepe2,3

1Brain and Cognition, KU Leuven, Belgium 2Centre for Instructional Psychology and Technology, KU Leuven, Belgium 3ITEC, KU Leuven, Belgium

The development of number sense (a set of early numerical abilities), phonological awareness and

letter knowledge have been shown to be key predictors of the future math and reading abilities of

children1,3,5, and are given significant prominence in the initial years of formal education. In today’s

diverse classrooms, intensive and personalized training of number sense and early reading can be

supported through adaptive educational games, as these games comprise activities adapted to the

level of the pupil, immediate feedback, and an attractive narrative8. These games might result not only

in positive cognitive but also non-cognitive learning outcomes (e.g., increase of motivation, reduction

of anxiety). However, previous research of (adaptive) games on cognitive and non-cognitive outcomes

is scarce2,6 and inconclusive7. The current study, a longitudinal, quasi-experiment with 335 first graders,

examined the cognitive and affective effects of two educational games, namely Dudeman and Sidegirl:

Operation clean world (NSG) and Lezergame (LG). Children were randomly assigned to an experimental

condition (N=222), comprising 8 weeks of intensive game-based training, or a control condition

(N=113) in which children took part in regular education that lacked game-based practice. The number

sense game contained digit comparison and number line tasks that increased in difficulty, while the

reading game supported emergent reading as it trained auditory and visual skills through the learning

of the letters. A pre- and posttest design measured the effects of the treatment on number sense skills

(digit comparison task, number line task), letter knowledge, and math and reading anxiety. The impact

on math and reading competence was assessed through validated curriculum-based assessments and

a fluency test, both immediately after the intervention and delayed after a period of two months.

Results showed significant improvements for the children of the experimental condition for the

number line task and the letter knowledge task immediately after the intervention. For digit

comparison the children improved equally in the two conditions. On neither of the post-tests did math

scores of curriculum-based assessment or the fluency test show any differences between the

experimental and control condition. Interestingly, the posttest scores of reading fluency were found

to be significantly better for the children in the experimental condition compared to the control

condition immediately after the intervention. Two months later only a positive effect remained on the

word reading fluency test in favour of the experimental condition. Math anxiety decreased equally in

both conditions, language anxiety did not differ across both conditions and was equal before and after

the intervention. This study has shown that educational games are beneficial in comparison to

conventional teaching methods when training cognitive factors underlying math and reading.

Regarding the NSG training, children improved only for tasks similar to the game, they did not score

better on general math abilities immediately after the training or on retention tests. Regarding the LG

training, children improved in tasks similar to the game, but also scored significantly higher on general

reading tests immediately after the training and on the delayed test compared to the control condition.

35

Positive effects on affective factors in favour of using educational games were not found compared to

the control condition.


Towards conceptual clarity in the interrelationship between Universal Design for

Learning (UDL) and Differentiated Instruction (DI)

Júlia Griful-Freixenet, Katrien Struyven, Wendelien Vantieghem, & Esther Gheyssens

Vrije Universiteit Brussel, Belgium

Researchers in the field are calling for a more accessible and inclusive approach that meets the learning

needs of all students, and that replaces the inflexible traditional model based on a “onesize-fits-all”

curriculum. The Universal Design for Learning (UDL) and the Differentiated Instruction (DI) models

offer a promising alternative. The UDL model was developed by the Center for Applied Special

Technology (CAST, 1998) following the legislation for the inclusion of individuals with disabilities in the

American educational system. UDL has been defined as a framework that ‘proactively builds in features

to accommodate the range of human diversity’ (McGuire et al., 2006; p.173) by encouraging teachers

to anticipate the students’ learning needs at the beginning of the lesson instead of modifying materials

as an afterthought (CAST, 2004). Recently, several authors argue strongly for implementing UDL as “an

ideal to aspire to” (Burgstahler & Cory, 2008), rather than a framework to adopt unilaterally. On the

other hand, the DI model has been developed and continuously refined by Tomlinson (1999), a teacher

working in the field of gifted education. Tomlinson’s DI model is rooted in the belief that variability

exists in any group of learners and teachers should expect student diversity and adjust their instruction

accordingly. In 2001, DI was described as a form of “adaptive teaching”, with the aim of providing all

students with optimal learning. More recently, Tomlinson (2005) conceived DI as both teaching

philosophy and approach in which teachers need to be proactive and responsive to all their learners’

needs in the same classroom. More and more, both UDL and DI are being presented in the literature

as two similar and interrelated models within the inclusive education paradigm. Nevertheless, we find

a broad proliferation of theories about the interrelationship between both. This review aims to bring

conceptual clarity by identifying previous peer-reviewed studies that related both UDL and DI.

A systematic literature review in five scientific databases was conducted to explore the peer-reviewed

evidence. In total, 27 scientific articles were included and analysed. For each interrelationship,

conceptual similarities and differences of both UDL and DI models were described and analysed. Three

theoretical interrelationships between the UDL and DI models were found in the literature. Firstly, the

complementary interrelationship, perceived interdependency between UDL and DI, and therefore,

proposed to combine them in an integrated way. Secondly, the embedded interrelationship, perceived

that DI was encompassed within the UDL framework. Lastly, the distinctive interrelationship, perceived

both UDL and DI as two separate entities with some similarities but also important, or even

incompatible, differences. The discussion highlights the origin, evolution and refinement of these two

models during the last two decades. We can see that both most recent theories are converging towards

each other, making it increasingly difficult to distinguish between both UDL and DI models. Finally,

future directions of research are discussed.

36


What counts as a unit? Investigating the developmental trajectory of unit-flexibility

Theresa Elise Wege1, Bert De Smedt2, Camilla Gilmore1, & Matthew Inglis1

1Loughborough University, United Kingdom 2Parenting and Special Education Research Unit, KU Leuven, Belgium

With this research we introduce the concept of unit-flexibility, which refers to the ability to flexibly

and task-dependently switch between different units of enumeration for the same objects. Previous

research shows that pre-schoolers struggle with deviation from single-object units for counting and

especially struggle to count conceptual groups containing multiple objects. Throughout primary school

mathematics education, different units become more relevant in the form of place-value and

partitioning.

We developed a new task to measure children's unit-flexibility. In this task, children have to make one-

to-one correspondence matches for grouped dot arrays based on the number of dots and also the

number of groups. Using this task, we explored the developmental trajectory of this ability, testing 110

children between 4 and 12 years old.

We find that throughout the full age range some children express unit-flexibility and others don't and

that this is mostly determined by their performance when grouping multiple objects into one unit.

Children, who express unit-flexibility perform better on a conceptual counting measure and the

correlation between conceptual counting and unit-flexibility remains after controlling for children's

age.

Given that working with different levels of units is central to many mathematical operations, these

findings suggest a new lens for mathematical cognition and education research.


Development and stimulation of early mathematical patterning competencies in four- to

six-year olds

Nore Wijns, Joke Torbeyns, Bert De Smedt, & Lieven Verschaffel

Centre for Instructional Psychology and Technology, KU Leuven, Belgium

The potential of children’s early mathematical patterning competencies as a precursor for later

mathematical development has recently gained a lot of research interest. In several longitudinal

studies an association was found between children’s patterning abilities in preschool and their

mathematical abilities up to fifth grade (e.g., Lüken, Peter-Koop, & Kollhoff, 2014; Rittle-Johnson, Fyfe,

Hofer, & Farran, 2017; Schmerold et al., 2017). Moreover, children following a patterning intervention

developed better numerical or mathematical abilities than children who did not follow the intervention

(Kampmann & Lüken, 2016; Papic, Mulligan, & Mitchelmore, 2011).

In our longitudinal study we are currently following a group of 400 kindergartners’ competencies

regarding repeating and growing patterns. We selected three patterning activities that are often used

37

in research and that are assumed to cover a range of patterning abilities, namely extending (i.e., What

comes next?), generalizing (i.e., Make the same pattern using different materials.), and identifying (i.e.,

Reconstruct the pattern when hidden.). The three activities were each implemented with six repeating

and six growing pattern items, resulting in an assessment measure consisting of 36 patterning items.

Besides this assessment measuring children’s patterning ability, they are also given a task to measure

their spontaneous focusing on patterns and structures. In this task children are asked to create a tower

using all the provided blocks (i.e., 15 blocks in three different colors). These tasks were individually

administered at the end of second and third year of kindergarten (i.e., age 4 & 5), and will be

administered again at the end of first grade (i.e., age 6).

Our longitudinal study has three main aims. First, we aim to extend the learning trajectory for

repeating patterns proposed by Clements and Sarama (2014) by including another type of patterns,

namely growing patterns. Growing patterns receive only little attention in kindergarten, but are often

used in primary school to teach functions and algebra (e.g., Moss & McNab, 2011). Early insight in

growing patterns might therefore be another important contributor to later mathematical

development. Second, we aim to unravel the mutual developmental relations between children’s

patterning ability and their spontaneous focusing on mathematical patterns and structures. The idea

that children can have “a tendency to seek and analyse patterns” has already been suggested by

Mulligan and Mitchelmore (2009, p. 38), but so far no tasks have been developed to measure such a

spontaneous focusing on mathematical patterns and structures. Third, we are interested in the mutual

developmental relations between early patterning competencies and general numerical abilities as

well as in the association between early patterning competencies and general mathematical ability in

primary school.

The tentative results of the first and second data collection (i.e., at age 4 & 5) with respect to the three

above-mentioned research aims will be presented.


The development and stimulation of computational estimation from kindergarten to third grade of primary school

Elke Sekeris1, Lieven Verschaffel1, & Koen Luwel2,1

1Centre for Instructional Psychology and Technology, KU Leuven, Belgium 2Centre for Educational Research and Development, KU Leuven – Campus Brussels, Belgium

Computational estimation is defined as providing an approximate answer to an arithmetic problem

without calculating the actual exact answer (Dowker, 1997). In addition to its practical relevance in

everyday life (e.g., estimating how much you would have to pay for your groceries at the check-out

register), it has an educational relevance to other specific aspects of mathematical ability, such as

knowledge of place-value and mathematical fluency (Sowder, 1992; van den Heuvel-Panhuizen, 2000).

For these reasons, it is considered as an important goal in the mathematics curriculum in primary

schools (NCTM, 2000). Despite its importance for primary school mathematics, computational

estimation is typically taught and investigated from age 8 onwards. So, little is known about the

development of this skill at younger ages (for a review see Sekeris, Verschaffel, & Luwel, submitted).

38

With the current PhD project we want to investigate the early emergence and development of

computational estimation. Therefore, we are longitudinally following a group of children starting from

the age of 5 (i.e., fall 2017) until the age of 8 (i.e., fall 2020). The first wave of data collection had

already taken place in third grade of kindergarten (fall 2017, Sekeris, Verschaffel, & Luwel, in

preparation) and we are currently in our second wave of data collection in the first year of elementary

school (fall 2018). In line with Dowker's (1997, 2003) notion of the “zone of partial knowledge and

understanding” related to computational estimation, children receive estimation problems just

outside their performance level of exact arithmetic in each wave. In their zone of partial knowledge

and understanding children’s knowledge is thought to be insufficient to exactly compute mathematical

problems, but they can be solved already by means of estimation (Dowker, 1997, 2003). In the third

year of kindergarten, a non-verbal estimation task was used since children were not familiar with the

number symbols in the number range in which the estimation problems were given. Results of the first

wave showed that 5-year-olds can already meaningfully solve estimation problems in an inexact way

and that their estimation accuracy is positively correlated with their performance on exact arithmetic.

In the current wave in the first year of primary school, both the nonverbal and a verbal estimation task

are being used, while in the second and third grade of primary school only the verbal estimation task

will be used.

In a second part of the current PhD project, we will investigate whether we can stimulate

computational estimation in 5-year-olds by training either their exact arithmetic abilities or their

estimation skills. We will investigate the effect of both interventions on children’s exact arithmetic and

computational estimation performance respectively, and the transfer from the exact intervention on

computational estimation and vice versa.

39


Mapping the emergence of proportional reasoning – initial results from a longitudinal study

Elien Vanluydt, Lieven Verschaffel, & Wim Van Dooren

Centre for Instructional Psychology and Technology, KU Leuven, Belgium

Proportional reasoning is a major goal in mathematics education. It is crucial for understanding many

important mathematical ideas and for various daily-life situations. Therefore proportional reasoning

receives a lot of instructional attention in elementary mathematics education, typically from third

grade on. However, the concept of proportion is traditionally thought to be hard to apprehend for

children (Resnick & Singer, 1993).

The development of proportional reasoning has been widely studied. Piaget and Inhelder (1975) stated

that the development of proportional reasoning is a rather late achievement and that children cannot

reason proportionally until the age of eleven. Many studies support these claims about proportional

reasoning (Noelting, 1980; Schwartz & Moore, 1998). Along this line of reasoning, the traditional view

of Piaget and colleagues (Inhelder & Piaget, 1958) considers additive reasoning as a developmental

precursor to proportional reasoning. This assumption is supported by numerous developmental

studies that revealed that children erroneously use additive approaches to solve proportional

problems (Kaput & West, 1994). However recent studies start to question the sequential development

of additive and proportional reasoning. One indicator is that Van Dooren et al. (2005, 2010)

documented the frequent occurrence of the inverse mistake as well, namely that of older children

erroneously using multiplicative reasoning to solve additive problems or over-using both methods

simultaneously. A second indicator are recent studies supporting the early presence of proportional

reasoning ability (Nunes and Bryant, 2010; Boyer and Levine, 2012; Resnick & Singer, 1993).

Therefore more and more questions are raised about the assumptions that proportional reasoning can

only be achieved at a later age, and that it is preceded by additive reasoning. The present PhD project

focuses on mapping and stimulating proportional reasoning ability at a much younger age than is

typically done (i.e. from the age of 5). Additionally, besides proportional reasoning ability, we will map

a dispositional aspect, children’s preference for additive vs. multiplicative reasoning, as well.

The mapping of the development of proportional reasoning will be addressed within the context of a

longitudinal study about the early development of various core mathematical competencies. We will

measure children’s proportional reasoning ability and disposition, between the last grade of

Kindergarten and Grade 3 of primary education. Children’s ability is measured in a set of missing-value

proportional reasoning tasks, whereas their preference is measured with open mathematical tasks that

can be answered correctly proportionally or additively. Both sets of tasks are non-symbolic, because

the youngest children are not yet familiar with symbolic number representations.

In this longitudinal study we will also relate the development of proportional reasoning ability and

preference to competencies that are expected to develop earlier and that can be considered as

important precursors of proportional reasoning, such as patterning and structure, estimation,

numerical abilities.

40

To investigate the impact of early instructional attention on proportional reasoning, an intervention

study will be conducted in the second grade of primary school, specifically aimed to stimulate

proportional reasoning at an earlier age than is typically done, and explicitly make the distinction and

similarity with additive reasoning.


Probabilistic Reasoning in Primary School

Anne-Sophie Supply1, Wim Van Dooren1, & Patrick Onghena2

1Centre for Instructional Psychology and Technology, KU Leuven, Belgium 2Centre for Methodology of Educational Sciences, KU Leuven, Belgium

Randomness and uncertainty are omnipresent in children’s lives through sports and play. At the

playground you might, for example, see children use rock-paper-scissors as a randomizer to ensure

fairness in deciding which team can initiate the game. Despite of the implicit presence of uncertainty

in children’s lives, probability and its different components as a subject is hardly mentioned in the

standards for primary schools in Flanders (Vlaams Ministerie van Onderwijs en Vorming, 2010).

Langrall (2018) shows that this limited attention on probability as a study domain is not unique to

Flemish primary schools. While elementary school children in all countries learn about exact

arithmetic, the concept of probability is not introduced to pupils under the age of 11 in, for example,

England, France, Japan or The United States. In the current PhD project we aim to critically question

whether a late focus on probability in schools is justified, by conducting a longitudinal and intervention

study on the development of probabilistic reasoning in young children.

Literature on the development of probabilistic reasoning in children is considerably inconclusive.

Piaget and Inhelder (1951/1975) suggest that children are unable to grasp the distinction between

uncertain and certain events before the concrete operational stage, which is not generally reached

before the age of 8. Furthermore, they state that formal operations (obtained from the age of 12) are

required to properly manage probabilities, which might explain the absence of probability in primary

school mathematics in many countries (Jones & Thornton, 2005). However, Fischbein (1975) argues

that children from the age of 7 possess different types of intuitions about chance and some intuitions

can be reshaped through instruction, also in primary school. More recent literature suggests that even

infants are able to use probabilistic information in their decision-making (e.g., Denison & Xu, 2014),

casting more doubt on the limited attention on probability in elementary school.

The current PhD project aims to develop a more accurate view on the development of probabilistic

reasoning in children. A longitudinal study is set up to map the development of different abilities

concerning probabilistic reasoning in children from the age of 5 to 9. First, in each wave participating

children are presented with a set of binary choice tasks adapted from a study of Falk and Yudilevich-

Assouline (2012) to investigate their abilities to 1) distinguish certain from uncertain events, 2)

compare two probabilities, and 3) understand independent events. Second, children receive a task

with manipulatives based on Falk and Wilkening (1998) to investigate their ability to 4) generate equal

probabilities.

41

A second aim of the current PhD project is to investigate whether it is possible to stimulate probabilistic

reasoning at a younger age than is currently the case in Flemish schools. For this reason an intervention

study will be conducted with a group of children in their second year of elementary school and with

participants of the longitudinal study acting as controls.


Determinants of individual differences in the development of early numerical competencies

Merel Bakker1,2, Joke Torbeyns1, & Bert De Smedt2

1Centre for Instructional Psychology and Technology, KU Leuven, Belgium 2Parenting and Special Education Research Unit, KU Leuven, Belgium

There are large individual differences in children’s development of early math skills (Dowker, 2005).

An important goal in educational and developmental science is to specify the determinants of these

differences (De Smedt, 2016). Studies on individual differences in math achievement have largely

narrowed their focus on (non-symbolic) numerical magnitude processing as a determinant of these

individual differences, while other potentially important determinants, such as domain-general

correlates, have been largely ignored. Building upon previous studies, we will longitudinally follow the

development of a wide range of early numerical competencies in a large sample of 4-9-year-olds in the

critical transition from non-formal to formal math education. We aim to address two major goals,

namely (1) analyzing the contribution of gender, cognitive factors, and environmental factors to

individual differences in early numerical competency and (2) examining the developmental trajectories

of children’s early numerical competencies, focusing specifically on children with a delayed

development (dyscalculia) as well as children who excel in math (math-gifted children).

The first study of this PhD project focused on gender differences in early numerical competencies of

children attending the second year of preschool. There is little research examining gender differences

in early numeracy at preschool age, and the current literature shows mixed findings (Lindberg et al.,

2010). We examined eight numeracy tasks and we used Bayesian statistics to quantify the evidence

for the hypotheses of gender differences and gender equality. Results revealed substantial support for

the null hypothesis of gender equality for seven of the eight numeracy tasks. In view of the observation

that these early numerical competencies provide the foundation for acquiring more complex math

skills, the current finding of gender equality suggests that girls and boys are equally competent in

acquiring more complex math skills.

The second focus of my PhD will be on cognitive determinants of individual differences in the

development of numerical competencies. We will examine the role of critical domain-general cognitive

skills, such as language, working memory or executive functions. In addition to the cognitive

determinants, we will examine child and home environment predictors of individual differences in

numerical development (LeFevre et al., 2009). Lastly, we will focus on children with atypical

developmental trajectories. Although an atypical trajectory is most often associated with a

developmental trajectory that is delayed or disturbed, as in dyscalculia, we are also interested in math-

gifted children (Geary & Brown, 1991) - a group of children that are particularly important for the

STEM-agenda.

Documents

Early detection and stimulation of precursors and foundations of … · 2018-09-17 · Södervik, & Aino Mattinen (University of Turku, Finland): Stimulating SFON, cardinality and