The role of rational number density knowledge in mathematical development

Abstract

Many students still have not developed a robust understanding of rational number concepts at the end of primary school, despite several years of instruction on the topic. The present study aims to examine the patterns, predictors, and outcomes of the development of rational number knowledge in lower secondary school. Latent transition analysis revealed that rational number development from primary to lower secondary school (N = 362) appears to follow similar patterns as in younger students. In particular, a majority of students had poor knowledge of the density of the rational number set. Whole number magnitude knowledge appeared to be an important predictor of the development of rational number size knowledge, but not density knowledge. Finally, fraction density knowledge appeared to be related to concurrent algebra knowledge. Together these results point to an important role for density knowledge in mathematical development.