EDIT 590 Research Proposal

8/11/2019 EDIT 590 Research Proposal

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Running head: INCREMENTAL THEORY TRAINING EFFECT 1

Incremental Theory Training Effect on Attitudes Toward Mathematics Practice

in Middle School Pre-Algebra Students

Kimberlie Fair

George Mason University

Author Note

Submitted in partial fulfillment of the requirements for EDIT 590, Summer 2014


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INCREMENTAL THEORY TRAINING EFFECT 2

Abstract

This study seeks to determine if teaching middle school pre-algebra mathematics students

to think of intelligence as malleable changes their attitudes toward practice. The research will use

a qualitative mixed method, two-stage explanatory design (QUANT qual). The first stage will

be a quantitative single-group pretest-posttest study consisting of an assessment of participants

attitudes toward practice, a lesson on the malleability of intelligence, and a second assessment on

attitudes toward practice. Descriptive statistics will be used to compare pretest and posttest

results. The second stage will be a constructivist grounded theory study consisting of in-depth

interviews with participants whose attitudes toward mathematics practice change significantly

and with participants whose attitudes did not change, to determine the reasons they continued to

hold or changed their attitudes toward mathematics practice.

Keywords: growth mindset, fixed mindset, middle school, mathematics, practice, entity,

incremental, goal orientation


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Incremental Theory Training Effect on Attitudes Toward Mathematics Practice

in Middle School Grade Pre-Algebra Students

Introduction

Middle school is a time of great social, academic, and personal change for students.

There are the physiological changes that come with adolescence, combined with a less controlled

social environment. This can lead students to feel less safe and to exhibit social behavior that is

less mature than exhibited by older elementary students (Rockoff & Lockwood, 2010). For some

it is a time of declining motivation and increasing school-related behaviors that can lead to

academic failure (Eccles et al., 1993). Academic achievement can falter and perceptions of

overall academic rigor can fall. Students mathematics test scores often decline from their

elementary school levels (Rockoff & Lockwood, 2010). Pre-algebra coursework begins for many

students in middle school. They are faced with the rigor and practice that this level of

mathematics requires for success at the same time they are experiencing vast changes in

themselves and their environment.

Literature Review

Research has demonstrated that the level in which middle school mathematics students

think of intelligence as malleable (incremental theory), as opposed to intelligence as fixed (entity

theory), has been predicative of later upward trends in their achievement (Aronson, Fried, and

Good, 2002; Blackwell, Trzesniewski, & Dwek, 2007).

A five-year study, the first part of a two-part study, by Blackwell, Trzesniewski, and

Dweck (2007) followed four waves of students as they progressed through the seventh and

eighth grades. They surveyed 373 seventh grade students at a public secondary school in New

York City to assess the students theory of intelligence, goals, beliefs about effort, and responses


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to failure. The students measured responses were compared to their levels of achievement over

their middle school years. The results indicated that students who held an incremental theory of

intelligence belief at the beginning of middle school achieved higher mathematics grades at the

end of the eighth grade than students who held an entity view. The grades of the students who

held an entity perspective dropped less than one percent while the grades of the students who

held an incremental view of intelligence saw an average increase of three percentage points.

Students who held an incremental view started two percentage points higher at the beginning of

seventh grade. The effect was that the incremental group pulled significantly ahead of the entity

group in mathematics achievement by the end of eighth grade. Positive motivational beliefs

about work correlated with students who held an incremental theory perspective. Researchers

concluded that these motivational beliefs were a mediating factor.

The second part of the Blackwell et al. (2007) study was a nonequivalent-groups pretest-

posttest experimental design. Ninety-one seventh grade students were divided into two groups:

48 in the experimental group and 43 in the control group. The pretest was the same survey used

in the first study. The experimental group was given training in the incremental theory of

intelligence. There was a small, but significant positive change in the trajectory of the grades of

the experimental group, and no change in the non-experimental group. Though all students in the

experimental group increased their incremental theory score, the students who endorsed more of

an entity theory at the start benefited the most.

Two studies compare theory of intelligence perspective to goal orientation perspective

(Dweck & Legget, 1988; Kaplan & Maehr, 2006). Students with a mastery goal orientation focus

on learning content and increasing skill. Students with a performance goal orientation work to

create an impression of high ability and avoid the impression of low ability (Kaplan & Maehr,


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2006). Dweck and Legget (1988) found that children who have an entity view are more likely to

set performance goals and more likely to withdraw their effort when faced with challenges.

Children who had an incremental view were more likely to set mastery goals and take on

challenges even if it carried the risk of failure. Their quality of engagement was higher and they

persisted longer. Kaplan and Maehr (2007), in a convergent study of both quantitative and

qualitative research, found strong support for the relationship between entity theory beliefs and

performance-approach/performance-avoidance goals, and incremental theory beliefs and mastery

goals. A third study that compared achievement levels with results of a survey on motivation and

effort in middle school students found that goal orientation had a greater impact on outcomes

than motivation or effort (Brookhart, Walsh, & Zientarski, 2006).

There were several limitations in the current research. The role of social and economic

factorsinfluence on the development of belief systems in students was not addressed. Parents

and home environment play a formative role in self-schemas and may have a large effect on

whether students ascribe to an incremental or entity theory of intelligence. Also, previous

positive experience with the effects of work may have influenced the students attitudes about

the malleability of intelligence. The length of longitudinal studies is limited, and results of long-

term effects have not been included.

Students with an incremental theory of intelligence orientation are more likely to hold a

mastery goal orientation and are more likely to continue work even with the risk of failure.

Though training in incremental theory changed the trajectory of achievement in middle school

mathematics students the possible mediating factors were not studied.

Practice improves performance, and repetition leads to efficiency not only in physical

activities, but also in working memory cognitive activities (Sayala, Sala, & Courtney, 2005). The


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present study seeks to determine if a change in attitudes toward practice in middle school

students is a possible mediating factor in improved performance following training in

incremental theory.

Research Purpose and Questions

The purpose of this study is to determine if changes in attitudes toward practice are a

possible mediating factor in increased mathematics performance in middle school students

following incremental theory training. A correlation between an incremental theory orientation

and a belief in the value of effort has been shown (Blackwell et al., 2007). Teaching students

about incremental theory increased their performance (Blackwell et al., 2007). Does the

instruction change attitudes toward practice? What caused participants to either change or not

change their attitudes toward mathematics practice after incremental theory training?

Method

Research Design

This study is a qualitative mixed method, two-stage explanatory design using a QUANT

qual model. This model was selected because the purpose of this study is not only to identify

changes in attitudes toward mathematicspractice, but also to explore the participants

perspective on why their attitudes did or did not change. The quantitative data attained from the

first phase of the study will be used to select individuals to interview in the second phase of the

study.

The initial stage is an experimental single-group pretest-posttest design consisting of a

Likert scale assessment to determine attitudes toward practice, its efficacy, and whether they

avoid or seek opportunities to practice. A lesson on incremental theory will be delivered to the

subjects, and a second assessment of attitudes toward practice will be administered.


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A constructivist grounded theory study was selected for the second phase because it will

focus on the perspectives of the participants and emphasize how participants have or have not

changed their perceptions and insights (McMillian, 2002, p. 283). In-depth interviews will take

place with participants whose assessment scores changed significantly and with participants

whose assessment scores changed very little or did not change.

Stage I

Participants

The target population for this study is middle school pre-algebra students. A minimum of

25 participants will be recruited before the study will begin. The participants in the first stage of

the study will be a typical case sampling of middle school pre-algebra students recruited from

families who are members of Fair Studio, a teaching studio in Fairfax County, VA. Because Fair

Studio provides both music and mathematics training, not all studio members receive private

mathematics instruction. Additional subjects will be recruited from classmates and siblings of

students from the studio to increase variability and reduce bias associated with studio training.

Students and their families will be informed of this educational research study at the

studio and on the website. Participants will be volunteers and will not necessarily be associated

with membership in the studio. Allparticipants results will remain anonymousin the reporting.

Signed consent forms will be obtained from all volunteers and their legal guardians before the

study begins.

Setting

The pretest will be administered online at FairStudio.com. An online training course on

incremental theory will be developed for the site that will include a self-assessment and allow for


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participants to check for understanding of the concepts. The posttest will also be administered on

the site.

Variable/Data Sources/Measures

The independent variable in this stage is a categorical variable with two characteristics:

the participant has completed training in incremental theory or the participant has not completed

training in incremental theory. The dependent variable is a continuous measure ofparticipants

attitudes toward mathematics practice measured with a Likert type scale from one (very

negative) to five (very positive). A ten-item survey will contain five positive and five negative

items. Positive items will measure students beliefs that mathematics practice leads to positive

outcomes. Negative items will measure the belief that practice has a negative relationship to

ability.

Instruments/Validity and Reliability

Since there is not an instrument in current use that measures attitudes toward

mathematics practice an instrument will be developed for this study. Questions will need to be

carefully constructed to make sure that the participants understand what mathematics practice

means in this context. The internal structure of the questionnaire will be checked to confirm that

all questions specifically refer to mathematics practice, and not general attitudes toward effort or

mathematics.

To support content validity, experts with experience in measuring motivation will review

the questionnaire to judge whether it adequately measures attitudes toward math practice. All

elements of the questionnaire must pass review.

A split-half reliability test will be done to compute internal consistency reliability

estimates for the pretest and the posttest. The two forms of the survey will be tested for


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equivalence with a separate group of individuals that match the characteristics of the target

population.

The instrument will be pilot tested to minimize the problems of response set and faking.

In order to mitigate the response set tendency of subjects to respond the same way to the each of

the questions, questions will be designed with both positive and negative perspective and the

order of the response set will be varied from least to greatest and from greatest to least. Faking

will be addressed in the initial instructions to the participants, informing them of their role in

increasing understanding of their own perspectives and the possible impact of the general

understanding gained from the research.

The instruments will be available as soon as the participant has completed each step to

minimize the time between the pretest and the posttest, and to reduce threats to internal validity.

Intervention

The intervention will be an online lesson in incremental theory. It will be self-paced and

continuously available to the participants. Participants will be taught that intelligence is

malleable and can be developed. The key message will be that learning changes the brain by

forming new connections and that learners have control of the process. Analogies will be made

to building muscles though stress and examples of the learning process of babies. The

intervention will be modeled on the theory-altering experimental materials developed for the

Blackwell et al. (2007) study. A self-graded quiz with infinite chances will be available online as

a knowledge check for the participant.

Data Collection Procedures

Once the consent forms have been received from the participants and their guardians, and

the survey has been tested and approved, it will be made available via the FairStudio.com site.


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pretest and the posttest. Three participants with a large change in attitudes toward practice, and

three participants with little or no change in attitudes toward practice will be interviewed.

Setting

The researcher will conduct one-on-one in-person interviews with the participants at the

office of Fair Studio. Interviews will be scheduled during at a time convenient for the student

and the interviewer. In order to minimize the effect of a possible participant-studio relationship,

the interview will take place at a neutral location apart from the space normally used for

teaching.

Central phenomenon and measures

The second stage will be a constructivist grounded theory study that will focus on the

perspectives of the participants selected. Using a qualitative research approach, a designed set of

structured questions will address the central phenomenon of what aspects of the training either

did or did not change their attitudes about mathematics practice. Follow-up unstructured

questions will allow the participant to expand on their responses, providing insight into their

attitudes, motivations, and history. The researcher will take notes during the interview, and an

audio recording will be made with a computer or other digital device.

Researcher's identity

The researcher/interviewer is the owner and teacher at Fair Studio. Her relationship with

students can span years. Over that time close bonds can form. The studio teaches from an

incremental theory orientation to intelligence and prior training has been given in the

malleability of intelligence. Many of the current students were not members at the time and did

not receive the instruction. The possible close relationship between the researcher and the

participants will provide a comfortable, familiar environment for the participant to express their


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feelings and experiences. Because of the halo effect, the role of the researcher as participant

observer may affect the interpretation of what is observed and should be accounted for in the

field notes. Descriptive notes should include the history between the researcher and the

participant. Though the bias threat is there, the possible prolonged trusting relationship between

the researcher and the participant may be a rich resource for insight in the observer comments

and strengthen the credibility of the findings.

Data Collection

The participant and the participants guardian will sign a consent form that will describe

the purpose of the interview, how the participant was selected, the voluntary nature of

participation, that participation will have no impact on the participants relationship with the

studio or the researcher, and that the participant will remain anonymous in all reports associated

with the study.

An interview protocol will be designed with a scripted introduction that restates the

conditions on the consent form, the length of the interview (thirty minutes), the material that will

be covered, and a thank-you to the participant for agreeing to take part in a study that increases

knowledge and understanding.

The interview will begin with structured questions that include:

What aspects of the training caused you to change or hold your attitudes toward

mathematics practice?

How did this training relate to your experiences with practice?

What prior experiences have affected your attitudes toward practice?

Follow-up unstructured questions will be asked to allow the participant to explain fully

their attitudes and beliefs about practice and its possible effect on their intelligence.


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Data will be recorded with a digital recording device, interviewers observational field

notes, and interviewers reflections following the interview.

Validity and Reliability

Training of the interviewer in unstructured interview techniques will be given before the

interviews take place. Training will include techniques for recording detailed field notes of

observations and reflections, and the generalizability of data. Because of the close relationship

the researcher may have with the participants, the halo effect will need to be accounted for and

addressed in the training.

The internal validity and reliability of the findings will be verified through data

triangulation using the following sources: posttest results, transcripts of the interview, detailed

field notes, and member checking.

External validity will be addressed by choosing participants with varying results in the

posttest and by including participants who do not have a relationship with the researcher. There

will be an emphasis on interview questions and observations that can be generalized to the

population of middle school pre-algebra students.

Data Analysis

Emic data will be obtained through verbatim transcripts of the interview and through the

interviewers description of nonverbal behavior. Eticdata will be obtained from the observers

comments.

Iterative methods will be used to identify themes that emerge from the etic and emic data.

The transcripts of the interviews and the interviewers notes will be coded for salient words or

events. These codes will be organized into families including major themes that emerge


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(codes),and logical divisions of the major codes (sub codes). Consistencies and inconsistencies

will be identified and major codes will be clustered for the final review.

The final interpretation of the data will be based on the themes that emerge from the data

analysis.

Limitations

Generalizing from the results will be limited to populations who closely match the

participants in age, level of mathematics, and socio-economic circumstances. Because the

participants come from a region with a highly educated, highly compensated population, they are

not a representative sample of the general population of middle school math students and results

may only apply to the population that matches these parameters.

The high likelihood of the participants involvement in Fair Studio may impact the results

of the experimental study because of the possibility of the participant having received prior

training in incremental theory. Also the close relationship with the researcher creates an

environment with a possible high degree of bias on the part of the researcher.

Further research should include a longitudinal study correlating attitudes toward practice

with achievement as this is not within the scope of this study.


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References

Aronson, J., Fried C.B., Good, C., (2002). Reducing the effects of stereotype threat on African

American college students by shaping theories of intelligence.Journal of Experimental

Social Psychology 38, 113125 doi:10.1006/jesp.2001.1491

Blackwell, L. S., Trzesniewski, K. H., Dweck, C. S. (2007). Implicit theories of intelligence

predict achievement across an adolescent transition: A longitudinal study and an

intervention. Child Development, 78(1), 246263. doi:10.1111/j.1467-

8624.2007.00995.x

Brookhart, S.M., Walsh, M.W., Zientarski, W.A., (2006). The dynamics of motivation and effort

for classroom assessments in middle school science and social studies. Applied

Measurement in Education, 19(2), 151184. DOI: 10.1207/s15324818ame1902_5.

Dweck, C. S., & Leggett, E. L. (1988). A social-cognitive approach to motivation and

personality.Psychological Review, 95, 256273. Retrieved from

https://web.stanford.edu/dept/psychology/cgi-bin/drupalm/system/files/A%20social-

cognitive%20approach_0.pdf

Eccles, J. S., Wigfield, A., Midgley, C., & Reuman, D, Iver, and Feldlaufe. (1993). Negative

effects of traditional middle schools on students motivation. Elementary School Journal,

93, 553574. Retrieved from http://www.jstor.org/stable/1001828

Kaplan, A., Maehr, M., (2007). The Contributions and Prospects of Goal Orientation Theory.

Educational Psychology Review19:141184 DOI 10.1007/s10648-006-9012-5

McMillan, J. H. (2012). Educational research: Fundamentals for the consumer (6th

ed.). Boston,

MA: Pearson.


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Rockoff, J.E., Lockwood, B.B. (2010). How and why middle schools harm student achievement.

Education Next, Fall 2010. Retrieved from

http://educationnext.org/files/ednext_20104_68.pdf

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EDIT 590 Research Proposal