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
DOI:
https://doi.org/10.23925/1983-3156.2020v22i4p438-453Palavras-chave:
Logical concepts, anthropological theory of the didactic, necessary/sufficient conditionsResumo
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.
Metrics
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.
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Autores que publicam nesta revista concordam com os seguintes termos:- Autores mantém os direitos autorais e concedem à revista o direito de primeira publicação, com o trabalho simultaneamente licenciado sob a Licença Creative Commons Attribution que permite o compartilhamento do trabalho com reconhecimento da autoria e publicação inicial nesta revista.
- Autores têm autorização para assumir contratos adicionais separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex.: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
- Autores têm permissão e são estimulados a publicar e distribuir seu trabalho online (ex.: em repositórios institucionais ou na sua página pessoal) a qualquer ponto antes ou durante o processo editorial, já que isso pode gerar alterações produtivas, bem como aumentar o impacto e a citação do trabalho publicado (Veja O Efeito do Acesso Livre).
