Notes for a study of the didactic transposition of mathematical proof
DOI:
https://doi.org/10.23925/1983-3156.2025v27i3p309-354Keywords:
Proof, Demonstration, Didactic transposition, Teachiing, LearningAbstract
This article studies the long road between the absence of demonstration as such in the past and its contemporary presence as content to be taught in all grades. However, demonstration had to undergo a process of didactic transposition to satisfy a series of different restrictions, whether epistemic, didactic, logical, or mathematical in nature. The author therefore follows a chronological order in his study to outline the main characteristics of this process, with the aim of better understanding the didactic problem that our current research faces. Balacheff shows that proof is both a foundation and an organizer of knowledge. While learning, it contributes to reinforcing the evolution of knowledge and provides tools for its organization. In teaching, it legitimizes new knowledge and constitutes a system: knowledge and proof, interconnected, provide the knowledge base for a structure that can function as a precursor to the theoretical basis necessary for mathematics. The institutionalizing function of proof situations places explicit validation under the arbitration of the teacher, who is ultimately the guarantor of its mathematical character. This social dimension, in the sense that scientific functioning depends on a constructed and accepted organization, is at the heart of the difficulty of teaching proof in mathematics.
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