Integrating Algebra and Proof in High School Students' Work with Algebraic Expressions Involving Variables When Proving - Martinez, Mara V. (Tufts Archival Research Center, 2005)
A qualifying paper submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics Education. Abstract: The overarching research question of the study described in this paper is: what are the consequences of an integrated approach to algebra and proof on students' mathematical knowledge while they work through a didactical sequence (i.e., the "Calendar Sequence")? In particular, the goal of this paper is to report on the challenges that students faced in their work with variables, and equivalent expressions while engaged in producing and proving conjectures, and how these challenges were overcome. Previous studies on algebra and proof (Barallobres, 2004; Bell, 1993) are scant nonetheless promising in regards to students' production of proofs using algebra in an integrated approach. I claim that the results presented in this paper provide promising evidence that an integrated approach towards algebra and proof, such as that implemented in the Calendar Sequence, has a positive impact on students' use of algebra as a tool to prove.