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

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 its decimal expansion(s). The students in the control group made substantially less progress. Résumé:De nombreusesétudes ont montré que lesétudiants de tous les niveaux, y compris les futurs enseignants au primaire et au premier cycle du secondaire,éprouvent de sérieuses difficultésà saisir la relation qui unit un nombre rationnel (une fraction ou un entier relatif) et son développement décimale, y compris par exemple la notion que 0.9 = 1. Cet article présente un compte-rendu de la performance mathématique d'un groupe de futurs enseignants au primaire et au premier cycle du secondaire qui venaient de terminer une unité pédagogique portant spécifiquement sur la répétition décimale, fondée sur la théorie APOS et mise en pratique grâce au Cycle d'enseignement de l'ACE. Les participantsà la rechercheétaient desétudiants inscritsà un cours théorique sur les nombres et les opérations dans une grande université du sud. Deux sous-groupes ont pris part au cours expérimental, et trois ont suivi une approche traditionnelle. Les résultats quantitatifs indiquent que lesétudiants du groupe expérimental ont amélioré considérablement leur niveau de compréhension de l'égalité spécifique entre 0.9 et 1, de même que la relation plus générale qui existe entre un nombre rationnel

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

“…Students in the experimental group performed better than those from the control group. We believe this might be due to the following reasons: Writing computer programs with Maple helped students in the experimental group to develop their geometric interpretation of derivative in their mental constructions (Weller et al, 2009). This was one of our goals in designing and implementing the ACE cycle.…”

“…The focus of these tasks is to promote reflective abstraction rather than to obtain correct answers. This is often achieved by having students write short computer programs using a mathematical programming language (Weller, Arnon, & Dubinsky, 2009.…”

“…The class discussions and in-class work give students an opportunity to reflect on their work, particularly the activities done in the lab. As the instructor guides the discussion, he or she may provide definitions, offer explanations, and/or present an overview to tie together what the students have been thinking about and working on (Weller et al, 2009(Weller et al, , 2011.…”

An Investigation into the Preparedness of Teachers to Teach Grade 12 Mathematics: A Case Study

“…APOS theory postulates that a mathematical concept develops as one tries to transform existing physical or mental objects. The descriptions of action, process, object and schema given are based on those given by Weller et al (2009) and Maharaj (2010Maharaj ( , 2013Maharaj ( , 2014Maharaj ( , 2015.…”

An APOS Analysis of students’ understanding of the concept of a limit of a function

“…Design and implementation of teaching Collection and analysis of data descriptions of action, process, object and schema; given below; are based on those given by Weller, Arnon and Dubinsky (2009).…”