The Development and Initial Validation of an Abbreviated Instrument

198 Pages·2016·2.42 MB·English

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USF Tampa Graduate Theses and Dissertations USF Graduate Theses and Dissertations
4-7-2016
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Kenneth Lee Butler
University of South Florida, [email protected]
Follow this and additional works at: https://digitalcommons.usf.edu/etd
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Commons, and the Science and Mathematics Education Commons
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Butler, Kenneth Lee, "Motivation for Mathematics: The Development and Initial Validation of an
Abbreviated Instrument" (2016). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/6194
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Motivation for Mathematics: The Development and Initial Validation of an Abbreviated
Instrument

by

Kenneth L. Butler

A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
in Mathematics Education
Department of Teaching and Learning
College of Education
University of South Florida

Major Professor: Eugenia Vomvoridi-Ivanovic, Ph.D.
Robert Dedrick, Ph.D.
Ruthmae Sears, Ph.D.
Samuel Eskelson, Ed.D.

Date of Approval:
April 26, 2016

Keywords: Intermediate, Algebra, Developmental, Education, Survey, Intrinsic, Mastery,
Performance, Expectancy

Copyright © 2016, Kenneth L. Butler
DEDICATION

To my life partner and fellow researcher.
ACKNOWLEDGMENTS

I would like to thank Eugenia Vomvoridi-Ivanovic for her support throughout this
process, Robert Dedrick for pushing me to work towards a topic that may be beneficial to future
researchers, and Ruthmae Sears for being focused on quality writing and rigorous research. I
would also like to thank Anna Foster Butler for taking up my slack when I needed to work, and
my children for giving me hope for the future.
TABLE OF CONTENTS

List of Tables…………………………………………………………………………………….. iv

List of Figures…………………………………………………………………………………….. v

Abstract………………………………………………………………………………….……….. vi

Chapter One: Introduction………………………………………………………………………... 1
Background……………………………………………………………………………….. 1
Statement of Problem……………………………………………………………………... 6
Purpose of Study………………………………………………………………………… 10
Research Questions……………………………………………………………………… 11
Significance of Study……………………………………………………………………. 14
Definitions………………………………………………………………………………. 15
Engagement………………………………………………………………………15
Motivation……………………………………………………………………….. 15
Motivational Relationships and Structures……………………………………… 16
Motivation for Mathematics…………………………………………………….. 17
Assumptions…………………………………………………………………………….. 17
Limitations………………………………………………………………………………. 18
Traditional Concerns……………………………………………………………………. 19
Summary………………………………………………………………………………… 20

Chapter Two: Literature Review………………………………………………………………... 22
Motivation………………………………………………………………………………. 23
Self-Efficacy…………………………………………………………………….. 25
Self-Determination………………………………………………………………. 26
Achievement Goal Orientations………………………………………………… 28
Similarities between Frameworks………………………………………………. 31
Attribution Theory………………………………………………………………. 31
Motivational Relationships……………………………………………………………… 32
Achievement Goal Structures…………………………………………………… 32
Expectancy-Value……………………………………………………………….. 33
ARCS……………………………………………………………………………. 35
Questions for Mathematical Educators………………………………………………….. 37
What Motivates Mathematics Students? ………………………………………... 38
What Pedagogical Strategies Are Motivational? ……………………………….. 40
What Types of Curricula Are Motivational? …………………………………… 43
What Types of Assessments Are Motivational? ………………………………... 44
i
What Are the Relationships Between Student Motivation and Equity
in Mathematics Classrooms? …………………………………………………… 48
What Professional Development Is Needed to Train Educators in
Motivational Structures Known to Improve Student Engagement?…………….. 52
Theoretical Framework………………………………………………………………….. 54
Usher and Pajares (2009): Validation Study for a Motivation Related Instrument……... 57
Summary ………………………………………………………………………………... 59

Chapter Three: Method………………………………………………………………………….. 62
Sources of Validity Evidence…………………………………………………………….62
Three Phase Systematic Approach………………………………………………………. 66
Phase 1 in Detail….……………………………………………………………... 68
Participants and Data Collection for Phase 1……………………………. 70
Data Analysis for Phase 1……………………………………………….. 72
Phase 2 in Detail…….…………………………………………………………... 74
Participants and Data Collection for Phase 2……………………………. 74
Data Analysis for Phase 2……………………………………………….. 76
The coding process……………………………………………… 78
Selection of Items……………………………………………….. 80
Phase 3 in Detail………………………………………………………………… 81
Participants and Data Collection for Phase 3…………………………….81
Data Analysis for Phase 3……………………………………………….. 83
Summary...………………………………………………………………………………. 85

Chapter Four: Results…………………………………………………………………………… 87
Phase 1…………………………………………………………………………………... 88
Expert Replies to Emails………………………………………………….…….. 89
Expert Comments to Survey Sections……………………………………….….. 91
Popularity of Items by Factor………………………………………………….... 98
Phase 2…………………………………………………………………………………... 99
Phase 2 Participants……………………………………………………………. 100
Emergent Categories …….…………………………………………………….. 102
Selection of Items ……………………………………………………………... 109
Phase 3…………………………………………………………………………………. 114
Descriptive Statistics …………………………………………………………... 114
Exploratory Factor Analysis …………………………………………………... 118
Confirmatory Factor Analysis …………………………………………………. 121
Relationships between Motivation, Gender, and Achievement ……………….. 122

Chapter Five: Discussion ……………………………………………………………………… 128
Validity Evidence ……………………………………………………………………... 131
Evidence Based on Content …………………………………………………… 131
Evidence Based on Relationships to Other Variables ………………………… 134
Evidence Based on Internal Structure ………………………………………… 135
Limitations ……………………………………………………………………………. 137
ii
Implications of the Results for Practice ……………………………………………….. 138
Recommendations for Further Research ………………………………………………. 140
Conclusions …………………………………………………………………………..... 142

References ……………………………………………………………………………………... 144

Appendices ……………………………………………………………………………………. 157
Appendix A: Online Expert Surveys…………………………………………………... 158
Appendix B: Sources of Items and Original Participants……………………………… 164
Appendix C: Phase 3 Consent Form …………………………………………………... 169
Appendix D: Effect Sizes for Survey Comments……………………………………… 171
Appendix E: Phase 2 Intra-Respondent Matrix……………………………………….. 172
Appendix F: Expert Endorsement Percentage ………………………………………… 178
Appendix G: The Motivation for Mathematics Abbreviated Instrument ……………... 181
Appendix H: IRB Application for the Phase 1 Expert Reviews……………………….. 183
Appendix I: IRB Application for the Phase-three Instrument Administration………… 185

iii
LIST OF TABLES

Table 1: Summary of Research by Phase....…………………………………………………... 68

Table 2: Codes Used in Analysis...…………………………………………………………… 80

Table 3: Items Removed from the Phase 1 Instrument……………………………………… 112

Table 4: Descriptive Statistics for Phase-three instruments…………………………………. 115

Table 5: Internal Consistency for Phase 3 Four Factor Instrument ………………………… 116

Table 6: Internal Consistency for Phase 3 Intrinsic Motivation Instrument...………………. 117

Table 7: Internal Consistency for Phase 3 Mastery Orientation Instrument………………… 117

Table 8: Internal Consistency for Phase 3 Performance Orientation Instrument……………. 117

Table 9: Pattern Matrix from Exploratory Factor Analysis…………………………………. 120

Table 10: Structure Matrix from Exploratory Factor Analysis ………………………………. 120

Table 11: Summary Table for Measurement Invariance………………………………………124

Table 12: Regression of Achievement on Latent Variables Moderated by Gender………….. 125

Table B1: Sources of Items and Participants from Original Validation………………………. 164

Table D1: Effect Sizes for Survey Comments ………………………………………………... 171

Table E1: Effect Sizes per Code per Item ……………………………………………………. 172

Table F1: Percentage Endorsement per Item ……………………………………………….... 178

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LIST OF FIGURES

Figure 1: Scree plot displaying the result of an exploratory analysis of items from the
phase three administration of the MMAI ………………………………………….. 119

Figure 2: Parallel analysis plot demonstrating the four factor structure of the 16
relevant items from the phase three administration of the MMAI…………………. 119

Figure 3: Four factor confirmatory factor analysis for the MMAI…………………………… 122

Figure 4: Structural equation model showing relationship between latent factors
measuring motivation and achievement …………………………………………… 123

Figure 5: Regression equations for achievement (A) on intrinsic motivation (im),
mastery orientations (mo), performance orientations (po), and expectancy
(ex)…………………………………………………………………………………. 126

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ABSTRACT

This study outlines the development and initial validation of an abbreviated instrument
intended to measure motivation for mathematics of university students in developmental algebra
courses. I look across many of the predominant theories on motivation with the aim of
representing several of these theories as latent constructs in a single instrument that is short
enough to be administered in a reasonable amount of time, but inclusive enough that it could
incorporate subscales representing multiple distinct latent factors. This study answers a call by
researchers expressing a need to investigate relationships between disparate theories on
motivation and is a response to recent studies that have used several subscales from many
published instruments in whole or in part as lengthy combined instruments to measure
motivation across theories. The practice of utilizing many separate instruments to measure across
theoretical frameworks may be unwieldy leading to validity concerns based on response
processes, and the practice of taking individual items from separate instruments may potentially
be incomplete leading to validity concerns based on the internal structure of the instrument and
underrepresentation of the intended construct.
To answer these concerns and develop a tool for future research, I conducted a three
phase study. Phase one of this study asked experts in motivation to comment on and pick the best
items from a pool of 122 items sourced from several popular previously published instruments
that contained factors associated with self-determination, self-efficacy, achievement goals, and
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