Children’s Magnitude Representations Of Common Fractions And Decimal Fractions And Their Development

Current numerical development theories, generally based on whole number studies, propose different hypotheses about magnitude representations of common fractions or decimal fractions. Previous studies addressing fraction representations yielded contradicting results. Moreover, these studies explored magnitude representations of these two types of fractions in isolation, while it is particularly important for both cognitive science and educational science to examine and compare magnitude representations of common fractions and decimal fractions. The present study examined and compared, from a developmental perspective, children’s magnitude representations of and translation between common fractions and decimal fractions. The present study, using a pretest-training-posttest design, also examined which training is more effective in improving children’s fraction representations and performance in fraction translation. The present study also examined international differences in magnitude representations of these two types of fractions.The present study yielded the following results. First, like whole numbers, both common fractions and decimal fractions could be represented on a mental number line. Second, knowledge of common fractions and decimal fractions and their translation developed with age. Third, substantial differences were observed between magnitude representations of common fractions and those of decimal fractions (e.g. accurate magnitude representations developed more often and earlier for decimal fractions than for common fractions; children were more likely to underestimate the magnitudes of common fractions than those of decimal fractions). Fourth, in addition to development, appropriate trainings could also improve children’s magnitude representations of common fractions and decimal fractions. Fifth, correlational, even causal, relationships were observed between children’s fraction representations and their performance in fraction translation. Last, Chinese fourth graders gained better magnitude representations for decimal fractions while American peers gained better magnitude representations for common fractions.These findings have profound implications for revising current numerical development theory, improving fraction instructions, and evaluating the traditional approach of teaching common fractions before teaching decimal fractions.