The relationship between executive function and arithmetic strategy in grades 4 to 6

Abstract

Current literature suggests that variance in conceptually-based strategy use on multi-term arithmetic problems is due to individual differences. The present study examined whether individual differences in conceptually-based strategy use was related to individual differences in executive function (EF). Through an additive and multiplicative problem-solving task, three arithmetic concepts were examined in 112 Grade 4-6 students: inversion (e.g., 2 + 5 – 5, or 7 x 4 ÷ 4), associativity (e.g., 2 + 29 – 27 or 7 x 9 ÷ 3), and equivalence (e.g., 4 + 2 + 7 = 4 + __ or 5 x 2 x 3 = 5 x __). An EF battery task was used to assess working memory, updating, inhibition, and switching components. Our primary hypothesis was that individual differences in arithmetic strategy use would be related to individual differences in EF. We also hypothesized that (1) participants would perform best and use inversion the most, followed by associativity, then equivalence, (2) there would be no grade differences (3) participants will perform better on additive than multiplicative problems. Correlational results indicated apparent links between EF capacities and arithmetic strategy use, with inversion correlating with inhibition, all three conceptual strategies correlating with updating, and equivalence correlating with all four EF components. ANOVA results indicated that participants perform best on inversion problems, but use equivalence strategies the most, individual rather than grade differences accounted for variance, and participants do better on additive problems. However, operation and concept ANOVA interactions suggest arithmetic strategy use may depend on operational and conceptual problem format.