Representations of and translation between common fractions and decimal fractions

Abstract

Recent years have seen a boom in research on the magnitude representations of common fractions and decimal fractions. However, previous studies generally only explored the magnitude representations of these two types of fractions in isolation. The present study, using a pretest-training-posttest design, examined and compared the magnitude representations of both types of fractions, and more importantly examined their relations to fraction translation and overall mathematical competence. The results showed that (1) accurate magnitude representations developed more often for decimal fractions than for common fractions; (2) individual differences in fraction magnitude representations predicted individual differences in fraction translation performance above and beyond initial knowledge of fraction translation; (3) mere exposure to visual representations of fractions on number lines improved children’s mental representations of fraction magnitudes more than exposure to visual representations of fractions on circles or reading a textbook section on fractions. The present findings suggest that, like whole numbers, both types of fractions are organized on a mental number line, which appears to provide a central conceptual structure for organizing a wide range of numerical knowledge. Educational implications of the findings are discussed.