Longitudinal Predictors of Conceptual Understanding of Arithmetic Principles

Abstract

A bidirectional relationship between conceptual and procedural understanding in the development of arithmetic skills has often been reported. We investigated whether domain-specific longitudinal predictors of procedural arithmetic performance at the beginning of primary school also predict conceptual understanding two years later. We assessed conceptual and procedural understanding of arithmetic and mathematical reasoning in 195 UK children (mean age 8 years 2 months) in Year 3. Conceptual understanding was defined as children’s understanding of principles underlying arithmetic procedures. Performance on a speeded arithmetic task was taken as an indicator of children’s procedural understanding of arithmetic. The same children had been assessed in Year 1 on potential cognitive and numerical predictors including number transcoding, symbolic and non-symbolic magnitude comparison, arithmetic performance, verbal and visuo-spatial working memory, and non-verbal reasoning. A structural equation model including arithmetic performance, number transcoding and non-verbal cognitive skills measured in Year 1 predicted 33% of the variance in conceptual understanding in Year 3. Arithmetic performance and number transcoding in Year 1 were also significant longitudinal predictors of both procedural arithmetic understanding and mathematical reasoning in Year 3. When we ran a second structural equation model without arithmetic performance in Year 1, number transcoding and non-verbal cognitive skills remained the only significant longitudinal predictors of conceptual understanding in Year 3. Our study highlights substantial similarities as well as some differences in the longitudinal predictors of conceptual versus procedural understanding of arithmetic in early primary school.