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

Authors

  • Nicolas Balacheff Directeur de recherche CNRS émérite, Equipe MeTAH, Modèles et Technologies pour l'Apprentissage Humain Laboratoire d’informatique de Grenoble Univ. Grenoble Alpes, CNRS, Grenoble INP https://orcid.org/0000-0001-7084-3482
  • Saddo Ag Almouloud Pontifícia Universidade Católica de São Paulo https://orcid.org/0000-0002-8391-7054
  • Méricles Tadeu Moretti Universidade Federal de Santa Catarina

DOI:

https://doi.org/10.23925/1983-3156.2022v24i1p872-950

Keywords:

Devolution, Triangle, Sum of the angles of a triangle, Conception of proof.

Abstract

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 to facilitate the reading and understanding of the contemporary reader.

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Author Biographies

Nicolas Balacheff, Directeur de recherche CNRS émérite, Equipe MeTAH, Modèles et Technologies pour l'Apprentissage Humain Laboratoire d’informatique de Grenoble Univ. Grenoble Alpes, CNRS, Grenoble INP

Nicolas Balacheff received the PhD degree in mathematics education. He is now senior scientist emeritus at the French National Centre for Scientific Research (CNRS). He was the cofounder of the journal Recherches en Didactique des Mathématiques in 1980. He served as the president of the International Group for the Psychology of Mathematics Education (1988–1990). In the recent years, he served as director of the computer-science and discrete mathematics Laboratory Leibniz (2000–2006). He was the founder and first scientific director of Kaleidoscope, European network of excellence on Technology Enhanced Learning (2004–2007)

Saddo Ag Almouloud, Pontifícia Universidade Católica de São Paulo

Doutorado em Mathematiques et Applications - Université de Rennes 1 em 1992 - frança. Assistente doutor - pontifícia universidade católica de São Paulo, e assistente doutor da fundação Santo André. Consultor ad hoc da fundação de amparo a pesquisa do estado de são Paulo, da capes, bolsista pesquisador de CNPQ, foi coordenador do programa de estudos pós-graduados em educação matemática da PUC-SP de 2007 à 2009 e de 01/08/2013 a 31/07/2017. Atualmente é vice coordenador do referido programa. Foi coordenador do curso de especialização em educação matemática da PUC-SP de 2006 a 2017. Publicou mais de 50 artigos em periódicos especializados e mais de 83 trabalhos em anais de eventos. Possui 5 capítulos de livros e 12 livros publicados. Possui 1 software e mais de 62 itens de produção técnica. Participou de vários eventos no exterior e mais de 112 no brasil. Orientou mais 77 dissertações de mestrado e teses de doutorado na área de educação matemática entre 1996 e 2016. Participou de mais de 200 bancas de defesa de dissertações e doutorados. Coordenou mais de 5 projetos de pesquisa. Atualmente coordena 2 projetos de pesquisa. Atua na área de educação, com ênfase em educação matemática. É avaliador do prêmio victor civita desde 2013. Em suas atividades profissionais interagiu com mais 70 colaboradores em coautorias de trabalhos científicos. Em seu currículo lattes os termos mais frequentes na contextualização da produção científica, tecnológica e artístico-cultural são: ensino-aprendizagem, geometria, educação matemática, matemática, demonstração, ensino básico, formação de professores, geometria dinâmica, TIC.

Méricles Tadeu Moretti, Universidade Federal de Santa Catarina

Doutorado em Didática da Matemática

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Published

2022-04-22

How to Cite

BALACHEFF, N.; ALMOULOUD, S. A.; MORETTI, M. T. Devolution of a problem and construction of a conjecture, the case of the sum of the angles of a triangle. Educação Matemática Pesquisa, São Paulo, v. 24, n. 1, p. 872–950, 2022. DOI: 10.23925/1983-3156.2022v24i1p872-950. Disponível em: https://revistas.pucsp.br/index.php/emp/article/view/57669. Acesso em: 20 dec. 2024.

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Vol. 24 No. 1 (2022): Volume 24 -1-2022

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