Educational implications of some of wittgenstein’s remarks on mathematics: proposition, inference and proof
Palavras-chave:
Meaning, Rationality, Teaching, New School, Linguistic Turn, WittgensteinResumo
Inspired by Rousseau’s ideas, the different tendencies of the new school have emphasised educational practices centred on the pupil’s activity, presupposing in the learning process a natural rationality being developed as much as possible through observation and experimentation, and not by means of verbal instructions. The goal in this paper is to point out some misleading practices which arise from these empiric directives, by using some of Wittgenstein’s remarks on the nature of mathematics, particularly those published in Philosophical Remarks (PR). As one of the major representatives of the linguistic turn, the Austrian philosopher presents a new conception of language where the senses are not developed from cognitive structures or abstracted from some extra linguistic reality; but rather they are formed within language, which has a multiplicity of functions. In particular, the mathematical propositions perform a normative function, very similar to rules, as they allow inferences and determine what makes sense and what does not make sense. From this perspective, we defend that learning mathematics involves essentially a training, process in which the student forms an accepted rationality, among many other effective and possible ones.
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Referências
Bartley III, W. W. (1978). Wittgenstein, une vie. Bruxelas: Editions Complexe.
Gerrard, S. (1987) Wittgenstein in Transition: The Philosophy of Mathematics. Dissertation of Philosophy at the University of Chicago.
Gottschalk, C. M. C. (2002). Uma reflexão sobre a matemática nos PCN. Unpublished doctoral dissertation, São Paulo State University at São Paulo, Brazil.
Gottschalk, C. M. C. (2006) Ver e ver como na construção do conhecimento matemático. Colóquio Wittgenstein. Fortaleza: Edições UFC, 73-93.
Gottschalk, C. M. C. (2012). O conceito de compreensão – a mudança de perspectiva de Wittgenstein após uma experiência docente. International Studies on Law and Education, nº 12, 49-56.
Gottschalk, C. M. C. (2013). Natureza, Gramática e Aquisição de Conceitos. Coleção CLE – Wittgenstein e a Epistemologia. Campinas: Unicamp, Centro de Lógica, Epistemologia e História da Ciência, vol. 63, 109-127.
Moreno, A. R. (2003). Wittgenstein – os labirintos da linguagem. Ed. Moderna/Unicamp.
Moreno, A. R. (2011). Introduction à une épistemologie de l’usage. Paris : L’Harmattan.
Piaget, J. (1998). Sobre a Pedagogia - textos inéditos. Orgs.: Parrat, S. e Tryphon, A. São Paulo: Casa do Psicólogo.
Rousseau, J-J (1999). EmÃlio – ou Da Educação. São Paulo: Martins Fontes.
Stern, D. (1991). Heraclitu’s and Wittgenstein’s River Images: Stepping Twice in the Same River. The Monist 74, 579-604.
Stickney, J. (2008). Wittgenstein’s ‘Relativity’: Training in language-games and agreement in Forms of Life. Educational Philosophy and Theory, vol.40, nº5, 621-637.
Wittgenstein, L. (1967) Zettel. Ed. By G.E.M. Anscomb and G. H. Wright. Oxford: Basil Blackwell.
Wittgenstein, L. (1979). On Certainty. Oxford: Basil Blackwell.
Wittgenstein, L. (1989a). Philosophische Bemerkungen/Philosophical Remarks. Org. Rush Rhees. Frankfurt am Main: Suhrkamp.
Wittgenstein, L. (1989b). Bemerkungen über die Grundlagen der Mathematik. Frankfurt am Main: Suhrkamp.
Wittgenstein, L. (1997) Philosophical Investigations. Trad. G. E. M. Anscombe. Oxford: Blackwell Publishers.
Wittgenstein, L. (1998). Wittgenstein’s Lectures on the Foundations of Mathematics Cambridge 1939. Edited by Cora Diamond. Chicago: The University of Chicago Press.
Wright, C. (1980). Wittgenstein on the Foundations of Mathematics. London: Duckworth.
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