Teacher and education students’ knowledge of children’s understanding of arithmetic concepts

Abstract

Arithmetic concepts such as Equivalence (understanding the equals sign means that both sides of an equation are balanced), Inversion (understanding some pairs of operations are inversely related), and Associativity (understanding some problems can be solved in any order) are understood to give a deeper understanding of math (Wong, 2017). As well, the use of strategies that show an understanding of these concepts has been suggested to improve children’s accuracy on math problems (Chesney et al., 2013; Dubé & Robinson, 2010). Within this study, Teachers and Undergraduate Education students completed an online survey asking them to solve math problems that could be solved using a conceptually-based strategy. As well, participants were asked questions regarding their math anxiety and comfort teaching math. Finally, participants were asked to estimate at what grade 50% of children would apply a conceptually-based strategy to solve problems. Participants were only accurate estimating when 50% of children understood additive inversion. Participants overestimated children’s understanding of the concepts of associativity, equivalence, and multiplicative inversion. As well, it was found that higher math teaching anxiety was correlated with more conceptually-based strategy use, and higher maximum grade comfortable teaching math was correlated with less accuracy and conceptually-based strategy use. Overall, these findings indicated that more needs to be done to address education professionals estimates of children’s understanding.