Changes in Student Proving Skills and Attitudes Following a Cooperative Learning Seminar

This dissertation details research studies designed to explore undergraduate math students’ beliefs and attitudes about mathematical proof, ability to compose valid proofs, and ability to read and validate purported proofs written by other students. In two studies, a cohort of seminar participants were assessed twice on their attitudes and beliefs about mathematical proof, their ability to compose proofs, and their ability to validate arguments. Between assessments, these participants worked on carefully crafted problem sets in a Cooperative Learning environment. In each study, a cohort of comparison participants took both assessments but did not engage in structured, cooperative work in the interim. Results from both studies showed little change in participants’ attitudes, and varied changes in validation skills. However, in both studies, most seminar participants’ composition skills improved from pre-assessment to post-assessment. The composition results are consistent with the researcher’s hypothesis that working in a Cooperative Learning environment on carefully chosen problem sets can help students develop their proof writing abilities. Additionally, because the content area of the assessments (number theory) and seminar problem sets (functions) were distinct, the demonstrated improvement of the seminar participants supports the hypothesis that some proof skills can be transferred across distinct mathematical contexts. The composition and validation results from both studies call into question how proof composition and validation skills are related, as many participants demonstrated improved proof composition skills but did not show improvement in proof validation skills.MathematicsDoctoralUniversity of New Mexico. Dept. of Mathematics and StatisticsNakamaye, MichaelUmland, KristinPereyra, CristinaFukawa-Connelly, Timoth