“Almost every class period, we were active in the development of concepts. Many, many concrete examples were made which made it feel a lot more like an investigation into ideas rather than a simple passing on of information through lecturing.” (From anonymous student evaluation.)
An important goal in my teaching is that my students not only learn the content, but also develop the mathematical habits of mind needed to think critically, to reason concretely and abstractly, and to apply their knowledge to a variety of problem-solving situations. In my classrooms, I try to implement the “Experience First” approach to teaching and learning. Students conduct experiments, look for patterns, make conjectures, and uncover underlying structures and connections—all before the formal definitions, formulas, and theorems are introduced. Such an environment allows students to learn and make sense of mathematics through their own doing of mathematics. Of course, I try to instill the same approach to teaching in my pre-service teachers.