Teaching Philosophy Statement
While reflecting on my teaching philosophy, I realized it has evolved significantly since I last wrote a teaching statement about 10 years ago. While I still believe in the importance of presenting a clear and concise argument, in the significance of being well prepared for lecture, and in the importance of assigning well-chosen homework problems, which provide ample opportunities for students to assess and deepen their understanding, I would not consider these the core tenets of my teaching today.
Student engagement. From my experience, learning rarely happens by passively watching someone else do something – in the context of a mathematics class – watching the instructor solve a complicated problem or prove an intricate theorem. (As Seymour Papert, mathematician and educator, once said “Teaching is important, but learning is much more important.”) I try to incorporate a variety of active learning strategies in the classroom, which depend on the level of the class, but often include group work and think-pair-share activities. They can also be as simple as asking students to take a minute and think how they would approach a problem before I move on to discussing the solution on the board. During portions of the class that could be described as a lecture, I try not to have more than a few sentences without a question. Why do we care about this? Why did we define this object in the way we did? What do you think we should try next? Active and engaged learning is important in the classroom, just as it is outside of it. I help facilitate the formation of learning communities among my students both online (through the use of Piazza forums) and in person – by making sure I allow some time during the very fist class of the semester for students to introduce themselves and form study groups.
Curriculum. As instructors we don’t always have control of the curriculum, but a good curriculum is at least as important for student learning, as teaching methods are. Teaching a sequence of procedural techniques for specific types of problems will likely lead to students retaining this knowledge for only a short period after the final exam. Moreover, transferring this knowledge to a different context would be difficult, if we do not provide a big picture understanding of where these problems come from, why they are important, why the techniques make sense, and how they are related and can be modified to other problems that one might encounter in mathematics, physics, or engineering. In redesigning MTH 235 (Ordinary Differential Equations), which mainly serves engineering students, we are moving away from an approach which teaches recipes for a variety of seemingly disconnected problems and towards a “modeling first” approach, which emphasizes conceptual understanding. Starting with a physical problem, students learn how to model it mathematically, study it using graphical, numerical, and analytic techniques, and finally, determine if their modeling assumptions were reasonable by comparing the model predictions to real data.
Assessment. Rather than viewing assessment as just a way to assign grades, I have gained new appreciation for the key role it plays in learning. In conversations with colleagues we often share the frustration that students are too focused on gaining procedural knowledge rather than conceptual understanding, on only completing their WebWork assignment, but not the suggested modeling problems. Students will naturally focus on learning what is being assessed. Designing clear, performance-based assessments and aligning them with learning goals is not easy, but is definitely worth trying.
I strive to create a friendly classroom, where students feel comfortable asking questions and are unafraid to make mistakes. All that said, when asked which aspects of my teaching they appreciate the most, at end-of-semester evaluations, my students most often refer to my enthusiasm for teaching mathematics and how deeply I care about them as individuals.