Integrating Algebra and Proof in High School

Previous studies on integrating algebra and proof are scant, nonetheless promising, in regards to students' production of algebraic proofs. In this study, a group of 9 high school students (9th and 10th graders) participated in fifteen one-hour-long lessons carried out by the author at a school in the Greater Boston area, Massachusetts, United States of America. The overarching research question of the study is: what are the consequences of an integrated approach to algebra and proof on students' mathematical knowledge while they worked on math tasks from the "Calendar Sequence"? In particular, the goal of this study is to describe students' mathematical processes. In doing so, the author describes how students modeled the mathematical tasks using multiple variables and parameters. In addition, Dr. Martinez describes how students use equivalent expressions while engaged in producing and proving conjectures. The results of the teaching experiment provide promising evidence that students produced their own conjectures and meaningfully used algebra as a tool to prove.