Individual Differences in Academic Trajectories from Elementary toLate Middle School: Influences of Gender, Ethnicity, and Income Open Access

Abstract

Abstract Individual Differences in Academic Trajectories from Elementary to Late Middle School: Influences of Gender, Ethnicity, and Income By Molly Embree Longitudinal academic data for a cohort of elementary to middle school students from a small diverse (50% Caucasian, 44% African American, 5% other ethnicity) Southeastern public school were analyzed with hierarchical modeling (HM). The influences of and interactions among gender, ethnicity, and income on academic growth were examined. The hypotheses tested included: 1) achievement gaps exist at 3rd grade, 2) gaps grow from 3rd to 8th grades, and 3) gender differences are more apparent in analyses of the tail distributions than in averages of the overall distribution. Performance data were scale scores for language arts, math, and science domains, from a widely-used standardized test. Ethnicity and income were strongly correlated ( r(630)= 0.79, p<.01). Performance gaps by ethnicity were found at 3rd grade in language arts (02 = -20.61, p<.05) and science (02 = -17.58, p<.05), and differences in linear and quadratic growth by ethnicity and income opened a performance gap in math by 8th grade (22=-2.42, p < .05; 32=0.19, p < .05), with African American students averaging lower than Caucasians. Influences of ethnicity and income were large and stable in the tails, with low income and African American children over-represented in the bottom tail and nearly absent from the top tail over time. A significant interaction between gender and ethnicity showed African American boys scoring significantly lower in science than their peers at 3rd grade (04=-20.90, p<.05). The HM results predicted a significant acceleration in science growth by boys relative to girls after 6th grade (21=-2.89, p<.05; 31=0.25, p<.05). Analyses of the tail distributions make clear that average differences obscure important information: sex differences differed by academic domain, by tier of performance, and changed with time. These complex results preclude simple generalizations of "male advantage" or "female advantage" by academic domain.

Table of Contents

Table of Contents Introduction ..................................................................................................................... 1

Review of Educational Achievement Literature ............................................................. 6 Rationale ..................................................................................................................... 11 Research Questions and Hypotheses ......................................................................... 13 Complete distribution ............................................................................................... 14 Tail distributions ....................................................................................................... 15 Method ........................................................................................................................... 16 Student Sample ........................................................................................................... 16 Measures ..................................................................................................................... 17 Procedures .................................................................................................................. 19 Data collection and de-identification ........................................................................ 19 Data selection criteria .............................................................................................. 19 Design .........................................................................................................................21 Model Specification...................................................................................................... 21 Unconditional model ................................................................................................ 22 Conditional model .................................................................................................... 23 Estimation and inference ......................................................................................... 26 Results ........................................................................................................................... 27 Descriptive Statistics.................................................................................................... 27 Model Fitting ................................................................................................................ 28 Main Findings .............................................................................................................. 30 Hypothesis 1: Gaps by sex, ethnicity, and income already exist at 3rd grade ....... 30 Hypothesis 2: Ethnicity and/or income account for more variance in performance by domain than does sex ......................................................................................... 30 Hypothesis 3: Ethnicity and income are correlated within the sample .................... 30 Hypothesis 4: Boys' achievement in all three domains across all time points is characterized by greater variance............................................................................ 31 Hypothesis 5: Performance at third grade is an important predictor of eighth grade performance in that domain ..................................................................................... 31 Hypothesis 6: Changes in achievement growth rates are greatest during middle school (grades 6-8) .................................................................................................. 31

Hypothesis 7: Gaps by sex, ethnicity, and income are maintained or increase from third to eighth grades ............................................................................................... 32 Hypothesis 8: An interaction of gender and ethnicity, or gender and income, accounts for significant variance in initial status and/or growth rate ........................ 33 Hypothesis 9: Within the tails of the distribution, significant differences in academic performance by ethnicity, sex, and/or income already exist at third grade .............. 33 Hypothesis 10: Within the tails of the distribution, gaps present at third grade are maintained or increase by eighth grade, with the exception of a gender gap in math and science which reverses..................................................................................... 36 Hypothesis 11: At all time points, differences by predictors are larger in the tails than in the middle distribution .................................................................................. 38 Discussion .....................................................................................................................39 Variance and Variability ............................................................................................... 39 Early Differences ......................................................................................................... 41 Ethnicity and Income................................................................................................ 41 Gender ..................................................................................................................... 42 Differences by Ethnicity/Income Widen Over Time ..................................................... 43 Gender Effects Differ Over Time by Domain and Performance Level ......................... 44 Examining differences in growth by curved averages and average curves ............. 45 Examining differences in growth by performance tiers ............................................ 49 Limitations and Implications for Theory, Method, and Practice ................................... 50 References.....................................................................................................................57 Appendix A .................................................................................................................... 68 Appendix B .................................................................................................................... 70 Appendix C .................................................................................................................... 76 Model Evaluation ......................................................................................................... 76 Normality.................................................................................................................. 76 Homoscedasticity..................................................................................................... 77

List of Tables Table 1

. Results of Fitting Multilevel Model M for Change to Language arts, Mathematics, and Science data ............................................................78 Table 2. Effect Sizes, Coefficient of Variance Ratios, and Odds Ratios by Gender and Grade for Three Academic Domains......................................................84 Table 3. Language Arts Effect Sizes and Student Ratios by Quintile..........................85 Table 4. Mathematics Effect Sizes and Student Ratios by Quintile.............................88 Table 5. Science Effect Sizes and Student Ratios by Quintile....................................91

List of Figures Figure 1

. Conceptual model.............................................................................94 Figure 2. Mean scale score by grade for ITBS overall language arts, mathematics, and science domains..............................................................................95 Figure 3. Overall distribution curves by grade level for language arts, mathematics, and science..........................................................................................96 Figure 4. Distribution curves by gender by grade level for language arts, mathematics, and science....................................................................................99 Figure 5. Distribution curves by gender and ethnicity subgroups by grade level for language arts, mathematics, and science............................................102 Figure 6. Average performance over time by gender and ethnicity subgroups in language arts, mathematics, and science............................................105 Figure 7. Random 20% samples of individual raw data trajectories for language arts, mathematics, and science................................................................106 Figure 8. Predicted score as a function of grade, gender, and ethnicity in language arts, mathematics, and science................................................................107 Figure 9. Language arts: effect size change over time for ethnicity, income, gender ..108 Figure 10. Language arts: student ratio change over time for ethnicity, income, gender ..................................................................................................109 Figure 11. Mathematics: effect size change over time for ethnicity, income, gender ..110 Figure 12. Mathematics: student ratio change over time for ethnicity, income, gender ..................................................................................................111 Figure 13. Science: effect size change over time for ethnicity, income, gender...........112 Figure 14. Science: student ratio change over time for ethnicity, income, gender.......113

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School	Laney Graduate School
Department	Psychology
Subfield / Discipline	Neuroscience and Animal Behavior
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Psychology, Physiological Psychology, Developmental Psychology, Cognitive
Keyword	math multilevel analysis ethnicity language arts longitudinal cognitive abilities gender difference hierarchical model science free or reduced lunch neurodevelopment puberty elementary and middle school academic performance male or female variability income sex difference
Committee Chair / Thesis Advisor	Wallen, Kim, Emory University
Committee Members	Walker, Elaine, Emory University Fivush, Robyn, Emory University Bliwise, Nancy, Emory University Maney, Donna, Emory University Furlow, Carolyn, CDC

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