Open AccessTeaching 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
Author(s) -
Bruno D’Amore,
George Santi
Publication year - 2021
Publication title -
rematec/rematec. revista de matemática, ensino e cultura
Language(s) - English
Resource type - Journals
eISSN - 2675-1909
pISSN - 1980-3141
DOI - 10.37084/rematec.1980-3141.2021.n39.p119-141.id487
Subject(s) - objectification , generality , natural (archaeology) , argumentation theory , semiotics , cognition , mathematical proof , natural language , perception , psychology , cognitive science , epistemology , linguistics , geometry , mathematics , philosophy , archaeology , neuroscience , psychotherapist , history
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.