Differences in High- and Low-Performing Students’ Fraction Learning in the Fourth Grade

Abstract

The aim of this longitudinal study was to examine the differences between high- and low-performing students’ development of fraction proficiency over a school year and to investigate how those differences were related to instruction in fractions versus instruction in other mathematics topics. The data for this study were drawn from a group of (n = 398) students from 21 fourth-grade classes, from which we formed two subgroups: the 25% highest performing students (n = 99) and the 25% lowest performing students (n = 100), based on their Danish national test scores. The students’ fraction proficiency levels were studied over eight months at five measurement time points. A multiple linear regression analysis with random effects was used to model the test scores. The results showed that the high-performing students developed their fraction proficiency during most of the school year—both when instructed in fractions and, more surprisingly, when instructed in other mathematics topics. In contrast, low-performing students only developed their fraction proficiency while being instructed in fractions. Finally, the gap between high- and low-performing students’ fraction proficiency widened both when the students were taught lessons on fractions and when they were taught other topics in mathematics.