Considerations Concerning
Balacheff’s 1988 Taxonomy of
Mathematical Proofs
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Northern Alberta Institute of Technology, Edmonton, CANADA
Publication date: 2011-06-21
EURASIA J. Math., Sci Tech. Ed 2011;7(3):181-192
KEYWORDS
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.