Teaching Students to Prove: An International Comparative Analysis of Geometry and Algebra Textbooks

Author Information

Andrey Koptelov, Sam Houston State University, United States
Alexander Mironychev, Union College of New Jersey, United States

Abstract

This paper presents findings from an international comparative study of secondary-school mathematics textbooks, with a particular focus on Geometry and Algebra. Given the broad scope of such a comparison, the analysis is limited to two representative topics: proofs related to triangle congruence in Geometry and proofs of selected algebraic formulas. The study examines textbooks from four countries and publishers: the United States (McDougal Littell), France (Hatier), Germany (Ernst Klett Verlag), and Italy (Atlas). The comparison identifies similarities and differences in content organization, instructional design, and pedagogical approaches, with particular emphasis on the presentation, purpose, and role of mathematical proof. In addition, the paper explores opportunities to integrate traditional printed textbooks with online lessons and other digital learning resources to enhance mathematics instruction. Based on the comparative analysis, recommendations are proposed for the development of future secondary-school mathematics textbooks and instructional materials. The study is further informed by the authors' more than twenty years of combined experience teaching secondary mathematics in the Houston Independent School District (HISD), USA, providing practical insights into the role and implementation of mathematical proofs in high-school mathematics courses.

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