Control, proof, and demonstration

Three regimes of validation

Authors

DOI:

https://doi.org/10.23925/1983-3156.2022v24i1p816-871

Keywords:

Control, Proof, Demonstration, ck¢ Model

Abstract

Reasoning is one of the six competencies of the Common Base of Mathematics for Cycle 4 (years 7, 8 and 9 of the compulsory French curriculum). It includes proving, arguing, demonstrating, and asserts the centrality of demonstration. The comments of the programs recognize the difficulty of this teaching. The following text questions the advances made in research on the learning and teaching of demonstration and their capacity to inform the implementation of current programs. It returns to the vocabulary, insisting on the different regimes of validation in the student's activity. It then addresses these questions within the problematic of validation in the sense of the theory of didactic situations. The main themes are the articulation between proof and knowledge by briefly evoking the ck¢ model, and the relation between demonstration and argumentation.

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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, PUC-SP

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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2022-04-22

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

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