Notes for a study of the didactic transposition of mathematical proof

TL;DR

This paper examines the historical and pedagogical evolution of mathematical proof in education, highlighting the didactical transposition process that shaped its current teaching status across all educational levels.

Contribution

It provides a chronological analysis of the didactical transposition of mathematical proof, offering insights into current educational challenges.

Findings

Proof's role in education has evolved from rote memorization to a fundamental learning content.

The didactical transposition of proof involves overcoming epistemic, didactical, logical, and mathematical constraints.

Understanding this evolution helps address current pedagogical issues in teaching mathematical proof.

Abstract

It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case either because following an old pedagogical tradition of rote learning proof was reduced to the formalism of a text and deprived from its meaning or, despiteits acknowledged presence anywhere in mathematics, proof did not get the status of something to learn for what it is. On the long way from its absence as such in the past to its contemporary presence as a content to be taught at all grades, proof has had to go through a process of didactical transposition to satisfy a number of different constraints either of an epistemic, didactical, logical ormathematical nature. I will follow a chronological order to outline the main features of this process with the objective to better understand the didactical problem that our current research is facing.