The development of the rational number concept from a conceptual change perspective

This paper starts from the basic assumption that learning rational numbers requires a ‘conceptual change’, given that there is a conflict between students’deeply rooted prior knowledge about natural numbers and the newly taught conceptualization about rational numbers. Three sets or research findings are discussed in support of this assumption. First, we discuss findings from a wide range of studies, showing how students’ errors on a variety of rational number tasks can be explained and predicted by the discrepancy between features of rational numbers and students’prior knowledge about natural numbers. Second, we show, by means of comparative studies, that regardless of curricular differences very similar difficulties and misconceptions can be observed in the development of rational number concepts in different countries, indicating that natural number prior knowledge plays the same role regardless of the curriculum. Third, we explain how even in students and experts who no longer commit errors to rational number tasks, indications of natural number interference can still be found in terms of reaction times. We conclude that one can speak of a gap in the development of the number concept as soon as rational numbers are involved, and natural number knowledge remains interfering. Research on the treatment of the transition from natural to rational numbers is treated in textbooks, however, indicates that differences between the rational and natural number system are rarely made explicit, while similarities are exploited. This may contribute to the difficulties that students experience in acquiring rational number understanding.status: publishe