Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students

Rafael Ramírez-Uclés and Juan F. Ruiz-Hidalgo
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Rafael Ramírez-Uclés: Department of Didactics of Mathematics, University of Granada, 18071 Granada, Spain
Juan F. Ruiz-Hidalgo: Department of Didactics of Mathematics, University of Granada, 18071 Granada, Spain

Mathematics, 2022, vol. 10, issue 5, 1-21

Abstract: Proof, a key topic in advanced mathematics, also forms an essential part of the formal learning experience at all levels of education. The reason is that the argumentation involved calls for pondering ideas in depth, organizing knowledge, and comparing different points of view. Geometry, characterized by the interaction between the visual appearance of geometric elements and the conceptual understanding of their meaning required to generate precise explanations, is one of the foremost areas for research on proof and argumentation. In this qualitative analysis of the arguments formulated by participants in an extracurricular mathematics stimulus program, we categorized students’ replies on the grounds of reasoning styles, representations used, and levels of generality. The problems were proposed in a lesson on a quotient set based on the similarity among triangles created with Geogebra and the responses were gathered through a Google form. By means a content analysis, the results inform about the reasoning style, the scope of the argumentation, and the representation used. The findings show that neither reasoning styles nor the representations used conditioned the level of generality, although higher levels of argumentation were favored by harmonic and analytical reasoning and the use of algebraic representations.

Keywords: argumentation; mathematical talent; Geogebra; generalization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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