Generating the raison d’être of logical concepts in mathematical activity at secondary school: Focusing on necessary/sufficient conditions
Tipo de documento
Autores
Lista de autores
Hamanaka, Hiroaki y Otaki, Koji
Resumen
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.
Fecha
2020
Tipo de fecha
Estado publicación
Términos clave
Construcciones geométricas | Gestión de aula | Lógica matemática | Unidimensional
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Referencias
Barbé, J., Bosch, M., Espinoza, L. & Gascón, J. Didactic restrictions on the teacher’s practice: the case of limits of functions in Spanish high schools. Educational Studies in Mathematics, 59(1-3), p. 235-268, 2005. Barquero, B. & Bosch, M. Didactic engineering as a research methodology: From fundamental situations to study and research paths. In: Task design in mathematics education, Switzerland: Springer, p. 249-271, 2015. Bosch, M. & Gascón, J. Twenty-five years of the didactic transposition. ICMI Bulletin, 58, p. 51-64, 2006. Brousseau, G. Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic, 1997. Chevallard, Y. Steps towards a new epistemology in mathematics education. In: Proceedings of the IVth Congress of the European Society for Research in Mathematics Education, Barcelona: Fundemi IQS, p. 22-30, 2006. Hamanaka, H. Considering proof for discovery: teaching materials concerning geometry. Handout document for the workshop at ICME-13, Hamburg, 2016 http://hdl.handle.net/10132/17192 Mext (2009). Guideline for upper secondary school course of study: mathematics. [in Japanese] http://www.mext.go.jp/component/a_menu/education/micro_detail/__icsFiles/afieldfile/2012/06/06/1282000_5.pdf Miyakawa, T. Proof in geometry: a comparative analysis of French and Japanese textbooks. In: Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education, Vol.3, Taipei, Taiwan: PME, p. 225-232, 2012.