P-34 Transition to Proof and Beyond: What’s Needed for Success?

Buller Hallway

This study explores mathematicians’ views on 1) transition-to-proof courses and the 2) knowledge and skills students need in order to succeed in subsequent mathematics courses. We interviewed seven mathematicians from three U.S. universities. They agreed unanimously that a content course could be used as a transition-to-proof course under certain conditions, and they agreed on a number of topics that should be included in such courses. The mathematicians said the knowledge and skills needed for success in advanced mathematics courses include precision in thought and writing, ability to make sense of abstract concepts and use them flexibly, understanding of the nature of definitions and how to use them, ability to read and validate proofs, and skill in using proof techniques. Results from this study will be used to frame a larger study investigating students’ proof processes in their subsequent mathematics content courses and investigating how these skills can be incorporated into a transition-to-proof course.