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

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.RésuméDe nombreuses études ont montré que les étudiants de tous les niveaux, y compris les futurs enseignants au primaire et au premier cycle du secondaire, éprouvent de sérieuses difficultés à 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 0.9̄ = 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 participants à la recherche étaient des étudiants inscrits à 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 les étudiants du groupe expérimental ont amélioré considérablement leur niveau de compréhension de l’égalité spécifique entre 0.9̄ et 1, de mêe que la relation plus générale qui existe entre un nombre rationnel et son développement décimale. Les progrès des étudiants qui faisaient partie du groupe contrôle ont été beaucoup moins importants.

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