A mathematical proof can be thought of as an argument that uses accepted rules of logic to validate the claims in a mathematical statement. Becoming proficient at producing mathematically valid proofs is one of the central expectation for undergraduate mathematics majors, but has also been identified as one of the key challenges that these students face. Working toward addressing this problem, this project, "Promoting Reasoning In Undergraduate Mathematics (PRIUM)", will implement a cycle of assessing student knowledge, planning and implementing instructional responses to those findings, assessing learning, followed by reflection on assessment outcomes and further course revision. More specifically, the project will employ results from a strong body of research in undergraduate mathematics education (RUME) about student learning and understanding of mathematical proving in order to inform instructional and assessment decisions in upper-division undergraduate mathematics courses that focus on mathematical proofs. Key to this project is the collaboration between mathematics educators who are experts in the research about student learning and research mathematicians who are the instructors of the courses. Also key to this project is the emphasis on connecting education research and classroom practice.
In this project, investigators from Georgia State University (GSU) and North Dakota State University (NDSU) will support research mathematicians in the implementation of education-research-based methods for teaching and assessing learning of proof at two large state universities. Using interviews, surveys, artifacts (e.g., annual department assessment reports), and discussions/presentations at mini-conferences, the proposed project will address the following research questions: (1) How do mathematicians make use of a RUME-based model for assessing proof in their instruction? (2) What impact does this approach have on student understanding of proof made evident by the extent to which students demonstrate a qualitative understanding of the local and global concepts of proofs? (3) How does this collaboration between mathematicians and mathematics educators impact professors' attitudes toward implementing research-based methods of mathematics teaching and assessment? (4) What changes, if any, have the participating mathematics departments instituted as a result of this project over a three-year period?
