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Measuring Math Achievement and Self-Efficacy as Joint Developmental Processes: A Window Into the Male-Female Math Gap

Sun, April 7, 11:50am to 1:20pm, Metro Toronto Convention Centre, Floor: 200 Level, Room 201B

Abstract

Research shows that women are underrepresented in quantitative college majors and career fields (Dee, 2007; Fennema, 1990). This underrepresentation is often linked back to lower math achievement among female students (Robinson & Lubienski, 2011). Low achievement, in turn, can relate to students’ self-efficacy: the confidence they feel in their ability to successfully complete academic tasks (Bandura, 1993; Meyer, Wang, & Rice, 2018). Female students can have lower self-efficacy in mathematics, which may mean achievement gaps are partially a function of diminished self-confidence (Li, 1999).
Despite the importance of self-efficacy, we do not fully understand how students’ baseline levels of self-efficacy influence their growth in math achievement over time (and vice-versa), nor whether gains in self-efficacy over time are associated with gains in achievement (and vice-versa). Even less is known about how these developmental processes differ by biological sex. I begin to close that knowledge gap by asking three research questions:
1. Is there evidence that self-efficacy in mathematics develops consistently over time?
2. How do changes in self-efficacy affect growth in math achievement and vice-versa?
3. Does the relationship between self-efficacy and math achievement differ by biological sex?
I answer these questions using SEL survey data collected over three years in Santa Ana Unified, a high-poverty district serving a high proportion of English learners. Table 3.1 presents information on student demographics and Table 3.2 on the SEL measures. Each student also took the Measures of Academic Progress (MAP) Growth, a computer-adaptive vertically scaled achievement test in math.
Methodologically, for Question 1, I examined means and standard deviations of observed self-efficacy scores by grade and year to look for trends. Additionally, I tested the longitudinal measurement invariance of the scores to ascertain their suitability for use in a growth model. For Question 2, I compared the fit of the latent curve models (LCMs) detailed in path diagrams in Figures 3.1 and 3.2 (Curran, Howard, Bainter, Lane, & McGinley, 2014). The first is an LCM with a growth model for achievement and treating self-efficacy scores as time-varying covariates. The second is a multivariate LCM that models a separate growth curve for self-efficacy scores. The main difference between the models is whether self-efficacy is treated as idiosyncratic versus having a distinct developmental process (Curran et al., 2014). Finally, Question 3 introduces biological sex as a time-invariant covariate.
Turning to results, Table 3.3 shows a general downward trend in mean self-efficacy. Per Table 3.4, scores also met criteria for longitudinal configural, weak factorial, and strong factorial invariance (Meredith, 1993; Widaman, Ferrer, & Conger, 2010). Table 3.5 presents results from the multivariate LCM, which indicate that students with high starting math achievement also have high starting self-efficacy scores. Further, the higher a student’s initial self-efficacy, the higher the slope on growth in math achievement. Results also show that self-efficacy decreases faster among females, and the association between initial self-efficacy and mathematics growth is stronger for females. These results suggest that self-efficacy may be especially important for the math development of girls.

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