View source for Otten, Gilbertson, Males, & Clark (2014)

{{Title|The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks}}
__NOTOC__
* Authors: [[Samuel Otten]], [[Nicholas Gilbertson]], [[Lorraine Males]], & [[D. Lee Clark|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
* 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
<pre>
@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}
}
</pre>

[[Category:Journal Articles]]
[[Category:Mathematical Thinking and Learning]]
[[Category:2014]]
[[Category:Geometry]]
[[Category:Reasoning and Proof]]
[[Category:Curriculum]]