Students' conceptions

an introduction to a formal characterization

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
  • Nathalie Gaudin La Prépa des INP, Grenoble INP, UGA Institut d'ingénierie et de management https://orcid.org/0000-0002-5719-1632
  • 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/10.23925/1983-3156.2022v24i1p722-769

Keywords:

Conception, Formal characterization, Students

Abstract

We investigate in this paper the complexity of modeling students knowing of mathematics under the constraints of acknowledging both their possible lack of coherency and their local efficiency. For this purpose, we propose a formalization of the notion of “conception” as a possible tool to answer the epistemological problem we identify. We apply then this approach to the study of the possible conceptions of “function”, from an historical and then an epistemic point of view. We report the result of a case study in order to illustrate the benefit we expect from this approach. The notions of “conception”, “knowing” and “concept” are then related the one to the other within the model presented.

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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

Professeur  d´Université

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.; GAUDIN, N.; ALMOULOUD, S. A.; MORETTI, M. T. Students’ conceptions: an introduction to a formal characterization. Educação Matemática Pesquisa, São Paulo, v. 24, n. 1, p. 722–769, 2022. DOI: 10.23925/1983-3156.2022v24i1p722-769. Disponível em: https://revistas.pucsp.br/index.php/emp/article/view/57659. Acesso em: 20 dec. 2024.

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

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