Using Quantile Regression to Examine the Relation Between Math Achievement and Math Self-Concept in Childhood

• In Event: Understanding Students' Math Self-Concept: Its Relation With Achievement, Development, and Educational Implications

Abstract

Researchers consistently find positive relations between math self-concept and math achievement (Marsh et al., 2005); however, some have found that the size of this relation may be weaker for lower-achieving students (Susperreguy et al., 2018). Importantly, this may impact the effectiveness of math self-concept intervention efforts for lower-achieving students, who may be most in need of intervention. In the current study, we examine whether math self-concept relates similarly to the math achievement of low-, middle-, and high-math-achieving elementary students. In addition, given research finding higher math self-concept in boys than girls (e.g., Ganley & Lubienski, 2016), we investigate these differential relations separately for boys and girls.

We collected data on math achievement (Schoen et al., 2021), math self-concept (adapted from Fredricks & Eccles, 2002), and student gender, with 1894 kindergarten to grade 3 students. We conducted overall ordinary least squares (OLS) regression analyses and quantile regression analyses at every .10 quantile of math achievement for boys and girls at each grade level. In each model, math self-concept predicted achievement.

Results are presented in Table 1 and Figure 1. OLS results indicated small-to-moderate, positive associations between math self-concept and achievement for every group except kindergarten boys (b=.02). In quantile analyses, we found non-significant associations for boys at the: .10-.20 quantiles in grade 1 (bs=.25-.43), .80-.90 quantiles in grade 2 (bs=.20-.24), and .10 quantile in grade 3 (b=.40). For girls, we found non-significant associations at the: .10-.20 and .90 quantiles in kindergarten (bs=.01-.16), .10-.20 and .60-.90 quantiles in grade 1 (bs=.12-.24), and .10-.20 quantiles in grade 2 (bs=.13-.24).

Next, we conducted pairwise ANOVA tests to compare differences in the strength of the relation across quantiles for each group. Stronger associations were found for boys in: kindergarten at the .50 quantile (b=.14) than at the .60 quantile (b=-.06), grade 1 at the .30-.90 quantiles (bs=.25-.43) than at the .10 quantile (b=-.03), grade 1 at the .40 (b=.32) and .60 quantiles (b=.43) than at the .20 quantile (b=.16), grade 2 at the .40-.60 quantiles (bs=.43-.47) than at the .80 quantile (b=.20), and grade 3 at the .90 quantile (b=.68) than at the .40-.50 quantiles (bs=.33-.35). Stronger associations were found for girls in grade 1 at the .40 quantile (b=.32) than at the .20 quantile (b=.12) and in grade 2 at the .90 quantile (b=.56) than at the .20-.30 quantiles (bs=.13-.20).

Our results suggest the math self-concept-achievement link is robust at grade 3 for most students and evident as early as kindergarten for girls and grade 1 for boys. We also provide preliminary evidence that targeting math self-concept as a means to improve concurrent achievement may not be beneficial to kindergarten boys, low-achieving grade 1 boys, and low-achieving grade 1 and 2 girls. In general, patterns showed either similar strength of relations across achievement levels or stronger connections between math self-concept and achievement for middle- and high-achieving students than their low-achieving counterparts. We will discuss the implications of this research and potential reasons for differences in the strength of this association across grades and gender.

Authors

• Connie Barroso Garcia, Texas A&M University

• Rachel A. Conlon, Florida State University

• Colleen M. Ganley, Florida State University