Exploring proof in elementary schools within Research-Situations for the Classroom -The case of polyominoes
Résumé
Although there has been considerable interest in how students learn to prove, the elementary school is less studied than the other schooling levels. Several research in mathematics education points out the pressing need of research about proof and teacher's guidance in elementary school. This article proposes to implement a research situation coming from ongoing discrete mathematics involving polyominoes in two ordinary elementary classrooms. Such Research-Situations for the Classroom (RSCs) are designed and studied by mathematicians and researchers in education for twenty years in France. The aims for research with such an implementation which promotes an authentic mathematical activity are twofold: to identify what kinds of proving processes and arguments young students are able to produce within RSCs and to discuss the ways the teacher manages and supports students' proving processes in a RSC. A theoretical background is defined by taking three components into account: definitions of proof and arguments and their specificities in elementary school, characterization of RSCs, use of the Theory of Didactical Situations to implement and manage RSCs. The results of the experiment in both classrooms highlight the pragmatic arguments produced by the students, the obstacles overcome during the experiment, the teacher's guidance and the limits of the use of RSCs in ordinary elementary classrooms. Then, the article presents new perspectives for mathematics education regarding RSCs and their potentialities to foster the teaching and the learning of proof for lower grades and for teacher training.
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