Presentation Schedule
Teaching Students to Prove: Insights from International Textbook Comparisons in Geometry and Algebra (106199)
Session Chair: Alexander Mironychev
Thursday, 18 June 2026 17:15
Session: Session 4
Room: Room FSI 125 (1F)
Presentation Type:Oral Presentation
This study highlights the importance of mathematical proofs in secondary mathematics education. Based on practical experience and international comparison of high-school textbooks from the United States (McDougal Littell), France (Hatier), Germany (Lambacher), and Italy (Atlas), the study examines how proofs are presented, or left out, in Geometry and Algebra. The analysis focuses on two central topics: triangle congruence in Geometry and the derivation of selected formulas in Algebra.The findings reveal a common trend: contemporary textbooks increasingly emphasize applications, activities, and problem-solving, while formal proofs are often left without justification or skipped. In Geometry, key congruence criteria such as SAS, ASA, and SSS are frequently introduced without proofs or clear discussion of their logical foundations. In Algebra, important formulas are typically presented in final form, leaving students with limited understanding of their origin. As a result, many students struggle to apply formulas meaningfully or engage in deductive reasoning. In response, this content analysis suggests that proof should remain in the curriculum not as lengthy formal exposition, but as a pedagogically important, student-centered component of instruction. The study highlights brief teacher demonstrations, template-based proof construction, collaborative group work, and complementary digital resources. Examples from geometry and algebra illustrate how proofs and derivations can be integrated into active learning environments. This comparative analysis concludes with recommendations for textbook authors and instructional professionals, emphasizing proofs as meaningful tools for developing students’ mathematical reasoning.
Authors:
Andrey Koptelov, Sam Houston State University, United States
Alexander Mironychev, Union College of New Jersey, United States
About the Presenter(s)
Dr Andrey Koptelov is a University Associate Professor/Senior Lecturer at Sam Houston State University in United States
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