Mathematical Immersion Unit for Pre-Service Teachers
Assistant Professor of Mathematics and Director of Mathematics Education, St. Olaf College
MCTM VP for Mathematics
For those working with pre-service secondary mathematics teachers, I’ve developed a two-week mathematics immersion unit as part of my secondary methods course. I start the methods course with this immersion experience as a kind of learning touchstone that we can go back to later when we are thinking about teaching. The goal of the materials is to provide students with a low-threshold, high-ceiling “experience first” approach to unfamiliar mathematics (number theory).
In this unit, students learn mathematics by getting hands-on experience of grappling with mathematics—creating own examples, looking for patterns and underlying structure, formulating generalizations, and arguing over solutions—all before they see any formal presentation of those ideas. Such an experience leads the development of mathematical habits of mind (MHoM). This is especially important for pre-service teachers, because of their role in shaping the experiences of their future students.
The MHoM perspective to learning and teaching has significant overlap with recent educational policy and standards. NCTM’s Principles to Actions (2014), for example, encourages teachers to support students’ productive struggle in learning mathematics. If teachers are expected to teach with such a focus, then they must first develop these mathematical habits for themselves.
But perhaps more importantly, the MHoM perspective will equip these teachers with the tools necessary to become lifelong learners of mathematics and pedagogy. With an ever-growing knowledge base about how students learn mathematics, the expectations and demands for our teachers will continue to evolve and change. We cannot possibly give them all the knowledge they will need to teach mathematics—and, in fact, research suggests that is the wrong point of view. Instead, we must equip them with the know-how to seek and acquire new knowledge on their own. Using MHoM as the basis for teacher preparation means they will be ready with the skill set and confidence to handle whatever standards and mathematical demands they will encounter in their profession.
There are problem sets and homework for pre-service teachers, facilitator guides for faculty, and there will be solutions soon. If anyone is interested, I’ll send you a web link to the materials and a password. Please let me know (firstname.lastname@example.org).