The Introduction of Proof in Secondary Geometry Textbooks

Authors

Samuel Otten, University of MissouriFollow
Lorraine Males, University of Nebraska‐LincolnFollow
Nicholas J. Gilbertson, Michigan State UniversityFollow

Document Type

Article

Date of this Version

2013

Citation

Published in International Journal of Educational Research 64 (2014), pp 107–118.

doi 10.1016/j.ijer.2013.08.006

Comments

Copyright © 2013 Elsevier Ltd. Used by permission.

Abstract

Explicit reasoning-and-proving opportunities in the United States are often relegated to a single secondary geometry course. This study analyzed the reasoning-and-proving opportunities in six U.S. geometry textbooks, giving particular attention to the chapter that introduced proof. Analysis focused on the types of reasoning-and-proving activities expected of students and the type of mathematical statement around which the reasoning-and-proving took place, be it general or particular. Results include the fact that reasoning-and-proving opportunities in student exercises were predominantly of the particular type, whereas textbook exposition most commonly had general statements. Within the chapters introducing proof, opportunities for students to develop proofs were less common than exercises involving conjectures and statements or exercises about the reasoning-and-proving process. Opportunities to reflect on the reasoning-and-proving process were prevalent in the introduction chapters, though rare in the remainder of the books.