A Cognitive Model of Algebra Achievement among Undergraduate College Students

Algebra has been called a gatekeeper because proficiency in algebra allows access to educational and economic opportunities. Many students struggle with algebra because it is cognitively demanding. There is little empirical evidence concerning which cognitive factors influence algebra achievement. The purpose of this study was to test a cognitive model of algebra achievement among undergraduate college students. Algebra achievement was defined as the ability to manipulate algebraic expressions which is a substantial part of many algebra curriculums. The model included cognitive factors that past research has shown relate to overall math achievement. Other goals were to compare a cognitive model of algebra achievement with a model of SAT-M performance and to test for gender differences in the model of algebra achievement. Structural equation modeling was used to test the direct and indirect effects of algebra experience, working memory, 3D spatial abilities, and computational fluency on algebra achievement. Algebra experience had the strongest direct effect on algebra achievement. Combined direct and indirect effects of computational fluency were as strong as the direct effect of algebra experience. While 3D spatial abilities had a direct effect on algebra achievement, working memory did not. Working memory did have a direct effect on computational fluency and 3D spatial abilities. The total effects of 3D spatial abilities and working memory on algebra achievement were moderate. There were differences in the cognitive models of algebra achievement and SAT-M. SAT-M scores were highly related to 3D spatial abilities, but moderately related to algebra experience. There were also gender differences in the cognitive model of algebra achievement. Working memory was highly related to computational fluency for males, but was not related to computational fluency for females. This study adds to the large body of evidence that working memory plays a role in computational abilities throughout development. The evidence that working memory affects higher level math achievement indirectly through computational fluency and 3D spatial abilities provides clarity to conflicting results in the few studies that have examined the role of working memory in higher level math achievement

Predicting Arithmetic Performance from Age and Executive Function Skills

The learning of mathematics can be a difficult process for many students. Understanding the cognitive components that contribute to arithmetic achievement may illuminate sources of difficulty and inform the development of better teaching and learning practices. Executive functions (EFs) have been implicated in the development of arithmetic skills in early childhood, but less is known about this relation across middle childhood and beyond. The current study included individuals ages 6-7, 9-10, 12-13, and 18+ years and examined the contributions of 3 components of EF, working memory (WM), inhibition, and set shifting (SS), to arithmetic skills in two domains. It was hypothesized that age, general cognitive ability, and EFs would have unique and combined influences on both domains of arithmetic: proficiency and fluency. Results from correlation, regression, and path analyses indicated that WM, inhibition, and SS differentially contributed to arithmetic proficiency and fluency. The implications for education and intervention are discussed