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

• Published in: Canadian journal of science, mathematics and technology education mathematics and technology education, 2009-01, Vol.9 (1), p.5-28
• Main Authors: Weller, Kirk, Arnon, Ilana, Dubinsky, Ed
• Format: Article
• Language: English
• Subjects: Decimals; Education; Engineering/Technology Education; Fractions; Mathematics Education; Science Education; Student teachers; Studies; Teacher education
• ISSN: 1492-6156; 1942-4051
• DOI: 10.1080/14926150902817381

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 0.9̄ = 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 0.9̄ and 1 and the more general relation between a rational number and its decimal expansion(s). The students in the control group made substantially less progresst.