The authors provide a framework for investigating proof-related reasoning in high school algebra and precalculus textbooks and suggest ways to increase students' opportunity to learn proof-related reasoning.
Gwendolyn J. Johnson, Denisse R. Thompson and Sharon L. Senk
Denisse R. Thompson, Sharon L. Senk and Gwendolyn J. Johnson
This article addresses the nature and extent of reasoning and proof in the written (i.e., intended) curriculum of 20 contemporary high school mathematics textbooks. Both the narrative and exercise sets in lessons dealing with the topics of exponents, logarithms, and polynomials were examined. The extent of proof-related reasoning varied by topic and textbook. Overall, about 50% of the identified properties in the 3 topic areas were justified, with about 30% of the addressed properties justified with a general argument and about 20% justified with an argument about a specific case. However, less than 6% of the exercises in the homework sets involved proof-related reasoning, with developing an argument and investigating a conjecture as the most frequently occurring types of proof-related reasoning.