# Otten, Gilbertson, Males, & Clark (2014)

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

- Authors: Samuel Otten, Nicholas Gilbertson, Lorraine Males, & Lee Clark
- Journal:
*Mathematical Thinking and Learning* - Year: 2014
- Source: http://www.tandfonline.com/doi/abs/10.1080/10986065.2014.857802

## 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.

## Outline of Headings

- Background
- Research on Students' Reasoning-and-Proving
- Theoretical Perspective

- Method
- Sample
- Analytic Framework
- Characterizing Mathematical Statements
- Separating Mathematical Statements from Justification
- Separating Opportunities to Prove from Opportunities to Explain
- Codes Inherited from Thompson, Senk, and Johnson
- Codes Added Based on Pilot Analysis of Geometry Textbooks
- Statements or Exercises About Reasoning-and-Proving

- Analytic Procedures

- Results
- Reasoning-and-Proving in Textbook Exposition
- Types of Statements in Textbook Exposition
- Types of Justifications in Textbook Exposition
- Summary

- Reasoning-and-Proving in Student Exercises
- Types of Statements in Student Exercises
- Types of Reasoning-and-Proving Activities in Student Exercises
- Statement-Types of Proof-Focused Exercises
- Summary

- Comparing Textbook Exposition to Student Exercises

- Reasoning-and-Proving in Textbook Exposition
- Discussion

## Also

- APA
- Otten, S., Gilbertson, N. J., Males, L. M., & Clark, D. L. (2014). The mathematical nature of reasoning-and-proving opportunities in geometry textbooks.
*Mathematical Thinking and Learning*, 16(1), 51–79. doi:10.1080/10986065.2014.857802 - BibTeX

@article{Otten2014, 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.}, author = {Otten, Samuel and Gilbertson, Nicholas J. and Males, Lorraine M. and Clark, D. Lee}, doi = {10.1080/10986065.2014.857802}, journal = {Mathematical Thinking and Learning}, number = {1}, pages = {51--79}, title = {{The mathematical nature of reasoning-and-proving opportunities in geometry textbooks}}, url = {http://www.tandfonline.com/doi/abs/10.1080/10986065.2014.857802}, volume = {16}, year = {2014} }