Refutations and the logic of practice

Autores

  • David Reid Acadia University, Canadá
  • Christine Knipping Acadia University, Canadá
  • Matthew Crosby Acadia University, Canadá

DOI:

https://doi.org/10.30827/pna.v6i1.6148

Palavras-chave:

Enseñanza, Epistemología, Lógica de la práctica, Pertinencia, Pruebas, Refutación, Suficiencia

Resumo

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.

Refutaciones y la lógica de la práctica

Cuando los argumentos son refutados en las aulas de matemáticas, las maneras en que estos son refutados 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 refutación.

Handle: http://hdl.handle.net/10481/16011

Downloads

Biografia Autor

David Reid, Acadia University, Canadá

Referências

Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers, and children (pp. 316-230). London: Hodder and Stoughton.

Balacheff, N. (1991). The benefits and limits of social interaction: the case of mathematical proof. In A. Bishop, S. Mellin-Olson, & J. Van Doormolen (Eds.), Mathematical knowledge: its growth through teaching (pp. 175-192). Boston, MA: Kluwer Academic.

Balacheff, N. (2002). The researcher epistemology: a deadlock from educational research on proof. In F. L. Lin (Ed.), 2002 International conference on mathematics-understanding proving and proving to understand (pp. 23-44). Taipei, Taiwan: NSC and NTNU.

Boero, P., Garuti, R., Lemut, E., & Mariotti, M. A. (1996). Challenging the traditional school approach to theorems: a hypothesis about the cognitive unity of theorems. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 113-120). Valencia, Spain: Departament de Didàctica de la Matemàtica, Universitat de València.

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), 835A-836A.

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 & E. Nardi (Eds.), Proceedings of the 26th International Conference for the Psychology of Mathematics Education (Vol. 4, pp. 433-441). Norwich, UK: PME.

Zack, V., & Reid, D. A. (2003). Good-enough understanding: Theorizing about the learning of complex ideas (Part 1). For the Learning of Mathematics, 23(3), 43-50.

Zack, V., & Reid, D. A. (2004). Good-enough understanding: Theorizing about the learning of complex ideas (Part 2). For the Learning of Mathematics, 24(1), 25-28.

Downloads

Publicado

2011-09-01

Edição

Secção

Artículos