Teaching and Learning of Geometry as a process of Objectification: conditions and obstacles to argumentation and proof. The role of natural language, specific language, and figures

Bruno D’Amore; George Santi

doi:10.37084/REMATEC.1980-3141.2021.n39.p119-141.id487

Autores

Bruno D’Amore Universidad Francisco José de Caldas https://orcid.org/0000-0002-5834-9438
George Santi University of Macerata

DOI:

10.37084/REMATEC.1980-3141.2021.n39.p119-141.id487

Palavras-chave:

Geometry task, natural language, use of figures in geometry, objectification, sensuous cognition

Resumo

This paper examines some examples (taken from research conducted over the years) that show students’ linguistic attitudes in geometry tasks. The examples are framed within the Theory of Objectification with reference to the notion of sensuous cognition, semiotic means of objectification and levels of generality. We show the struggle students live, at higher levels of generality, in intertwining natural language, specific language and the spontaneous use of geometrical figures, bound to perception and kinaesthetic activity. Within the networking paradigm, we coordinate the Theory of Objectification and Duval’s semio-cognitive approach to frame the interplay between the ideal and the material that occurs in geometrical argumentations and proofs.

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Biografia do Autor

Bruno D’Amore, Universidad Francisco José de Caldas

Ph.D. ad honorem em Ciências Sociais e Educação da Universidade de Chipre, em Nicósia. Ex-professor de educação matemática na Universidade de Bolonha

George Santi, University of Macerata

PhD in Mathematics Education, Dottorato in Storia e Didattica delle Matematiche, University of Palermo. Pesquisador com contrato a termo na Universidade de Bolzano

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