Generating the raison d’être of logical concepts in mathematical activity at secondary school: Focusing on necessary/sufficient conditions<br>Générer la raison d’être des concepts logiques dans l’activité mathématique à l’école secondaire: se concentrer sur les conditions nécessaires / suffisantes

Autores

DOI:

https://doi.org/10.23925/1983-3156.2020v22i4p438-453

Palavras-chave:

Logical concepts, anthropological theory of the didactic, necessary/sufficient conditions

Resumo

Abstract

In this paper, we focus on the absence of the raison d’être for logical concepts, especially regarding necessary conditions and sufficient conditions, in mathematics at secondary schools. We investigated the fundamental role of these concepts in the mathematical organisation of mathematicians, which is related to their protomathematical and paramathematical values. Then we designed, implemented, and analysed a study and research activity with the aim to activate their functionality.

Keywords: Logical concepts, Anthropological theory of the didactic, Necessary/sufficient conditions.

Résumé

Cet article porte sur l’absence de la raison d’être des concepts logiques, en particulier des conditions nécessaires et des conditions suffisantes, dans les mathématiques secondaires au Japon. Nous étudions le rôle fondamental de ces concepts dans l’organisation mathématique de mathématiciens, qui est lié à leurs valeurs protomathématiques et paramathématiques. Ensuite, nous concevons, mettons en place et analysons une activité d’étude et de recherche ayant pour but d'activer leur fonctionnalité.

Mots-clés: Concepts logiques, Théorie anthropologique de la didactique, Conditions nécessaires / suffisantes.

 

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Referências

Barbé, J., Bosch, M., Espinoza, L. & Gascón, J. (2005). Didactic restrictions on the teacher’s practice: the case of limits of functions in Spanish high schools. Educational Studies in Mathematics, 59(1-3), 235-268.

Barquero, B. & Bosch, M. (2015). Didactic engineering as a research methodology: From fundamental situations to study and research paths. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education (pp. 249-271). Switzerland: Springer.

Bosch, M. & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51-64.

Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic.

Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the IVth Congress of the European Society for Research in Mathematics Education (pp. 22-30). Barcelona: Fundemi IQS.

Hamanaka, H. (2016). Considering proof for discovery: teaching materials concerning geometry. (Handout document for the workshop at ICME-13, Hamburg) http://hdl.handle.net/10132/17192

MEXT (2009). Guideline for upper secondary school course of study: mathematics. [in Japanese] Retrieved from http://www.mext.go.jp/component/a_menu/education/micro_detail/__icsFiles/afieldfile/2012/06/06/1282000_5.pdf

Miyakawa, T. (2012). Proof in geometry: a comparative analysis of French and Japanese textbooks. In Tai-Yih Tso (Ed.), Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (Vol.3, pp. 225-232). Taipei, Taiwan: PME.

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Publicado

2020-09-15

Edição

v. 22 n. 4 (2020)

Seção

Finalizada - Volume 22 - 4 - Advances of the anthropological theory of the didactic

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