Proof Processes of Novice Mathematics Proof Writers
Previous studies have shown that a large portion of undergraduate mathematics students have difficulties constructing, understanding, and validating proofs (Martin and Harel, 1989; Coe and Ruthven, 1994; Moore, 1994; Baker, 1996; Mingus and Grassl, 1999; Knuth, 2002; Weber, 2001, 2003). However, proofs are the foundation of mathematics; it is therefore essential that every university mathematics student be able to step through the proof writing process. Research has sought to describe the strategies involved in the process of mathematical problem solving (Baker, 1996; Bell, 1979; Carlson and Bloom, 2005; McGivney and DeFranco, 1995; Pape and Wang, 2003; Polya, 1973; Pugalee, 2001; Schoenfeld, 1985; Yerushalmy, 2000).
This study was designed to describe the detailed processes and strategies used during the proof-writing process in order to more completely understand this process.
Specifically, this study was designed to answer the questions:
What are the proof-writing strategies of novice mathematics proof writers?
What strategies are in use during a successful proof writing attempt?
In what specific ways do novice mathematics proof writers use heuristics or strategies when working through a proof, which go beyond the application of standard problem-solving heuristics?
Do the strategies used by individuals remain static across multiple questions or do questions have an effect on the choice of strategies?
In this study, 18 novice mathematics proof writers engaged in individual task-based interviews, in which each was asked to think aloud while proving results which were unfamiliar to him or her. Results indicate that each participant had his or her own set of strategies that remained, for the most part, static across all questions. In particular, three categories of strategies emerged in frequent use, but with mixed levels of success. These categories were use of examples, use of equations, and use of other visualizations. A fourth category, the use of self-regulation strategies, was found to be overall successful, when in use with proper content knowledge and without computational errors.
Advisor:Bharath Sriraman; David Patterson; James Hirstein; Daved Erickson; Libby Knott
School:The University of Montana
School Location:USA - Montana
Source Type:Master's Thesis
Date of Publication:10/01/2008