Preservice Teachers' Understanding of the Relation Between a Fraction or Integer and Its Decimal Expansion

Abstract

Abstract Many studies establish that students at all levels, including preservice elementary and middle school teachers, have considerable difficulty understanding the relationship between a rational number (fraction or integer) and its decimal expansion(s), including the idea that 0.9 = 1. This article reports on the mathematical performance of preservice elementary and middle school teachers who completed a specially designed unit on repeating decimals that was based on APOS theory and implemented using the ACE teaching cycle. Students enrolled in a content course on number and operation at a large southern university participated in the study. Two sections received the experimental treatment, and three sections followed a traditional approach. The quantitative results suggest that the students who received the experimental instruction made considerable progress in their development of an understanding of the specific equality between 0.9 and 1 and the more general relation between a rational number and...