Focus of Investigation The project was motivated by several key questions 1. What knowledge from their mathematics learning do students transfer to the rest of their lives? 2. What is the evolution of a student's perception of the role of and need for proof? 3. What is the role fo the mathematics workshop sequence in students' understanding of proofs ahd how do students see their knowledge applied more liberally?

Selected Bibliography Alexander, P. (2003) The development of expertise: the journey from acclimation to proficiency. Educational Researcher. 32(8), 10-14. Barnes, L., Christensen, C., Hansen, A., Premises and Practices of Discussion Teaching in Teaching and the Case Method, Harvard Business School Press, Boston, 1994, 23-33. Duschl, R. (2003), Assessment of Inquiry, in Everyday Assessment, edited by J. Myron Atkin and Janet E. Coffey, NSTA Press, Arlington, 41-60. Pirie, S.E.B. and Kieren, T.E. (1989), A recursive theory of mathematical understanding, For the Learning of Mathematics, 9 (3), 7-11. Recio, A.M., and Godino, J.D. (2001). Institutional and personal meanings of proof. Educational Studies in Mathematics, 48(1), 83-99

8-Dimensional Knowledge Continuum Based on student responses to mathematical tasks, we combined the knowledge typology of R. Shavelson and the Models of Domain Learning of P. Alexander to create a knowledge continuum for mathematics

Evidence Student interviews Surveys of math majors (open-ended and Likert scale questions). Digital audio-tapes of 7 MATH 190 class days. Interviews with faculty from other disciplines (2 Education, 1 Philosophy, and 1 English). 12 Student "proof aloud" interviews. Student work from the MATH 190/191 course. Interviews with workshop students. Student focus group

Emergent Results Student knowledge progresses through major (chart) The Mathematics Workshop plays a significant role (course) Community is critical to student learning 15 minute problems play key role Student interest in explaining ideas to others plays a key role in social learning Habits of mind and writing skills transfer

Implications for Teaching Typology can be used for targeting instruction and gives language for complexity of the task. (Particularly as epistemic knowledge has factual, procedural, schematic, and strategic knowledge components) Epistemic learning is enhanced by community There is a risk of learners partitioning themselves into the "cans" and "cannots" that can be alleviated by tasks with initial (solo) time insufficient for completion. Habits of mind are skills most likely to transfer - they need to be incorporated into core classes.

Pitfalls More data collected than could be analyzed in time frame. Professors in disciplines unwilling to ascribe differences of mathematics students to their mathematical training, but education professors more willing. Rubrics we intended to use were not complex enough.