This empirical research project is developing an instrument to measure students' reasoning styles when constructing proofs and applying it to test on a large scale the hypotheses that undergraduate students are consistent in their proving style and can be successful in mathematics regardless of style. Three research questions will be answered:
1. To what extent do undergraduate mathematics majors show a consistency in their reasoning on proof production tasks?
2. What is the distribution of students according to the extent to which they employ these strategies when attempting to construct a proof of a given statement?
3. What is the relationship between undergraduates' reasoning styles and their general mathematical ability, their general thinking style, and their academic success?
The work is being performed by a research team at Rutgers University New Brunswick and Montclair State University.
The proving styles for the individual students will be identified from analysis of their responses to an instrument that calls for proofs of 18 statements from calculus and linear algebra specifically selected to distinguish proving styles. The research questions will be answered by administering the instrument along with a measure of general reasoning style to 100 undergraduate mathematics majors. Participants are videotaped and asked to think aloud when solving half of the items on the proof instrument. Regression analyses are used to study the relationship between performance on proving style, general reasoning style, and mathematics SAT scores. Cluster analyses are used to sort students by general reasoning styles and then an ANOVA is used to see if clusters vary in proving styles.
The final product from the proposed work will be a reliable and valid instrument to detect approaches to proof. Such an instrument has the potential to help broaden how teachers of mathematics at the college level view students' understanding of proof. Such a broadened perspective could lead to a change in how proof is taught and make higher mathematics more accessible to a larger group of college students.
