The contribution of working memory, conceptual knowledge and calculation principles to the individual and group differences in arithmetic competency of elementary school children

Abstract

Research findings from previous studies have suggested the importance of working memory and conceptual and procedural knowledge to the development of children’s arithmetic competency. However, their influences on children’s arithmetic competency have rarely been studied together and most of the findings in these areas are from overseas studies. Given the national and cultural differences and the variations in curriculum design and classroom instructions, the applicability of international studies to the local population has yet to be confirmed. This current study is a cross-sectional study to assess working memory capacity, understanding of fundamental arithmetic concepts and use of calculation principles simultaneously, as they contribute to individual and group differences in competency in early elementary arithmetical learning. In the current study, a variety of measures were administered to 160 primary 1 to 3 children from a local mainstream school, in order to assess the functioning of different components as well as general resource of children’s working memory, conceptual understanding of place-value and commutativity and the application of calculation principles. Results from analyses of variance ANOVA indicated that children of different grades and levels of arithmetic competency showed differences in performances in most of the measures of working memory with a few exceptions. Although the higher ability group of all grades outperformed their lower ability peers in the understanding of place-value and commutativity concepts, and the uses of calculation principles, the differences between the performances of the two arithmetic ability groups tended to decrease as grade levels increased. Hierarchical regression analyses revealed that the relationship between working memory functioning and children’s arithmetical competency was not mediated by children’s conceptual or procedural knowledge and vice versa. Hierarchical analyses also revealed the pattern of interaction of different components of working memory, as they contribute in explaining variance in children’s arithmetic competency. Al the three cognitive aspects in question were shown to have significant unique contribution and interaction in their influences on the arithmetic competency in each grade. However, it was found that these influences tended to decrease with schooling.