Refutations and the Logic of Practice

• Autores: David Reid, Christine Knipping, Matthew Crosby
• Localización: PNA: Revista de investigación en didáctica de la matemática, ISSN-e 1887-3987, Vol. 6, Nº. 1, 2011, págs. 1-10
• Idioma: inglés
• DOI: 10.30827/pna.v6i1.6148
• Títulos paralelos:
  • Refutaciones y la Lógica de la Práctica
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Cuando se refutan argumentos en el aula, las maneras en que se refutan pueden revelar algo acerca del desarrollo de la lógica de la práctica en el aula, así como de la epistemología que guía la enseñanza. Presentamos cuatro ejemplos que ilustran refutaciones relacionadas con la lógica de la práctica, en los que la suficiencia y pertinencia, y no la falsedad, son los motivos de refutaci

  • English

    When arguments are refuted in mathematics classrooms, the ways in which they are refuted can reveal something about the logic of practice evolving in the classroom, as well as about the epistemology that guides the teachers' teaching. We provide four examples that illustrate refutations related to the logic of practice, in which sufficiency and relevance are grounds for refutation, as opposed to falsehood.

• Referencias bibliográficas
  • Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers, and children (pp....
  • Balacheff, N. (1991). The benefits and limits of social interaction: the case of mathematical proof. In A. Bishop, S. Mellin-Olson, &...
  • Balacheff, N. (2002). The researcher epistemology: a deadlock from educational research on proof. In F. L. Lin (Ed.), 2002 International conference...
  • Boero, P., Garuti, R., Lemut, E., & Mariotti, M. A. (1996). Challenging the traditional school approach to theorems: a hypothesis about...
  • Lakatos, I. (1976). Proofs and refutations. Princeton, NJ: Princeton University Press.
  • Reid, D. A. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, 33(1), 5-29.
  • Sekiguchi, Y. (1991). An investigation on proofs and refutations in the mathematics classroom. Dissertation Abstracts International, 77(5),...
  • Toulmin, S. (1958). The uses of argument. Cambridge, United Kingdom: Cambridge University Press.
  • Zack, V. (2002). Learning from learners: robust counterarguments in fifth graders’ talk about reasoning and proving. In A. D. Cockburn &...
  • Zack, V., & Reid, D. A. (2003). Good-enough understanding: Theorizing about the learning of complex ideas (Part 1). For the Learning of...
  • Zack, V., & Reid, D. A. (2004). Good-enough understanding: Theorizing about the learning of complex ideas (Part 2). For the Learning of...