An analysis of geometry books used on a Brazilian teaching certification program in mathematics

Abstract

This article reports the findings of an analysis of plane geometry textbooks used on a Brazilian undergraduate teaching certification program in mathematics. The investigation focused specifically on tasks involving proofs and demonstrations for quadrilaterals. Drawing on Chevallard’s Anthropological Theory of the Didactic, the books were evaluated on tasks, techniques, and theoretical-technological elements. The books were also assessed on how the authors chose to introduce the deductive method and its specific terminology, and how the study of quadrilaterals was developed through the use of definitions and demonstrations. The analysis was also guided by the typology of mathematical proofs and Duval’s Theory of Registers of Semiotic Representations. Three textbooks were the primary source of data for the analysis. In these books, quadrilaterals were addressed in a superficial manner, and the properties of these polygons were validated by means of conceptual proofs. Quadrilateral-related content was addressed similarly in all three books—i.e., presentation of concepts and properties was straightforward, devoid of resources that might encourage students to make conjectures, and limited to formalization, followed by problem resolution.