The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks

Authors

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

Document Type

Article

Date of this Version

2014

Citation

Published in Mathematical Thinking and Learning (2014) 16: 51–79.

doi 10.1080/10986065.2014.857802

Comments

Copyright © 2014, Taylor & Francis. Used by permission.

Abstract

International calls have been made for reasoning-and-proving to permeate school mathematics. It is important that efforts to heed this call are grounded in an understanding of the opportunities to reason- and-prove that already exist, especially in secondary-level geometry where reasoning-and-proving opportunities are prevalent but not thoroughly studied. This analysis of six secondary-level geometry textbooks, like studies of other textbooks, characterizes the justifications given in the exposition and the reasoning-and-proving activities expected of students in the exercises. Furthermore, this study considers whether the mathematical statements included in the reasoning-and-proving opportunities are general or particular in nature. Findings include the fact that the majority of expository mathematical statements were general, whereas reasoning-and-proving exercises tended to involve particular mathematical statements. Although reasoning-and-proving opportunities were relatively numerous, it remained rare for the reasoning-and-proving process itself to be an explicit object of reflection. Relationships between these findings and the necessity principle of pedagogy are discussed.