Development of mathematical concepts in grade 4 students

Abstract

Mathematical concepts help build a knowledge base for children to learn more complex mathematical skills, such as algebra (Alibali, Knuth, Hattikudur, McNeil, & Stephens, 2007). The goals of this study were to observe the development of mathematical concepts and study their relationship with working memory. The additive and multiplicative mathematical concepts investigated were inversion (a + b − b, d × e ÷ e), associativity (a + b − c, d × e ÷ f), and equivalence (a + b + c = a + _, d × e × f = d × _). The study was the first phase of a longitudinal study. The participants consisted of 50 students in Grade 4. Two sessions were completed: solving mathematical equations (12 additive problems, 12 multiplicative problems) and a working memorytest battery. Accuracy was highest on addditive and multiplicative versions of inversion, followed by associativity, then equivalence. There were significantly higher results for additive problems compared to multiplicative problems. Shortcut use was highest on additive versions of inversion, followed by equivalence, then associativity. When comparing scores for multiplicative problems to additive problems, equivalence was the only strategy to increase in shortcut use; inversion and associatively both decreased for multiplicative problems. The results showed that as working memory increased the accuracy increased. This research provides a better understanding of how mathematical concepts develop and allows for a clear portrayal of the differences between problem types at this developmental age.