Mastery of any subject requires the core elements of experiential learning – risk, failure, reflection, and accountability. In many instances, instruction in mathematics has moved away from these goals, instead focusing on building collections of well-defined skills. As a result, students can miss the point – focusing on these skills rather than on the understanding behind them.
Our proposal addresses this for two groups of students, undergraduates in introductory and intermediate courses and graduate students in the second year of their PhD. Graduate students are associated with courses and mentor groups of undergraduates in guided but open-ended research-style problems. These research experiences, crafted jointly by the graduate students and instructors for the courses, provide experiential components for undergraduates: while guided by faculty and graduate students, the undergraduate groups must chart the course of the work, decide and implement methods of solution, and report on the results. For graduate students, designing and guiding projects forces deep, novel engagement with the material as well as manipulating the presentation and exploration of the content in response to the progress of the student teams. The latter piece will form a core component of our students’ pedagogical training.