Considerations Concerning Balacheff’s 1988 Taxonomy of Mathematical Proofs

Abstract

Current school curriculum documents require that justification and proof become a significant part of the mathematics classroom culture. In order to determine how well secondary level student teachers can complete a valid mathematical proof the researcher administered, the same mathematical task of Balacheff (1988) to a group of student teachers who were at the last semester of their teacher education program. The student teachers’ written responses were then classified using Balacheff’s Taxonomy of Proofs (BToMP). To assist in classifying student teachers’ work, the researcher generated examples corresponding to Balacheff’s taxonomy of proof. The purpose of this article is to confront the results of Balacheff and also to determine the various levels of proficiency with which the student teachers approached the task on the basis of BToMP. Along with the analysis of the results, the difficulties that the researcher encountered in categorizing student teachers’ written work according to BToMP, for the same task he administered in his study is also discussed in this article This study raises questions concerning the applicability of BToMP, especially with advanced level students who have preconceived ideas about what would constitute a “preferred” approach to the proving task. It also suggests a need for further research into the thought processes and cognitive skills that are necessary, no matter what one’s age, in solving mathematical proof tasks.