Refutations and the logic of practice
DOI:
https://doi.org/10.30827/pna.v6i1.6148Palabras clave:
Enseñanza, Epistemología, Lógica de la práctica, Pertinencia, Pruebas, Refutación, SuficienciaResumen
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
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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.