Devolution of a problem and construction of a conjecture, the case of the sum of the angles of a triangle

Nicolas Balacheff (1)

1 LIG - Laboratoire d'Informatique de Grenoble

Edited and augmented translation of Balacheff N. (1987) Dévolution d'un problème et construction d'une conjecture, le cas de la somme des angles d'un triangle. Cahiers de Didactique des Mathématiques n°37. Paris : IREM - Université de Paris VII. This study is part of the research project I conducted during the 80s on junior high school students’ conceptions of proof in mathematics before the teaching of mathematical proof [in French: démonstration]. The first part of this project resulted in the identification of different types of proofs students may rely on. The second part investigated the principle of design of situations which could support an evolution of students’ conceptions of proofs likely to serve as a basis for teaching mathematical proof; this paper reports on two case studies carried out within this project. It details the principles of design, the implementation and the analysis of a sequence of situations aimed at generating debate on proofs and refutations. It takes up the challenge of rejecting empirical proofs to open the way to intellectual proofs on which teaching could ground the introduction of mathematical proof. This translation of the report includes comments, notes (Note2020) and new references in order to facilitate the reading and understanding of the contemporary reader.

Mots clés: Learning mathematical proof; Didactic of Mathematic; Geometry; Sum of the angles of a triangle; Teaching mathematical proof

Domaines: Histoire et perspectives sur les mathématiques [math.HO]

Nicolas Balacheff. Devolution of a problem and construction of a conjecture, the case of the sum of the angles of a triangle. 2020, 50 p. ⟨hal-01117320⟩