Teaching Philosophy

Meeting students where they are

At Michigan State University, I have taught a range of courses, from gateway courses to advanced ones, both in person and online, as the instructor of record and as a recitation instructor. This experience led me to develop a strategy for understanding the dynamics of each class, which I call “the spectrum of courses.” I place each course and its students along a line: at one end, students with low confidence or negative prior experiences with math; at the other, students with strong foundations. Each class falls somewhere in between. These are by no means strict divisions, just definitions that help me understand the class.

Students with low confidence or negative experiences often think mathematics has nothing to do with real life, so they give up before they even start. To prevent this, I modify my course content to include at least one real-world application for each concept. For instance, in Quantitative Literacy, I created a probability-focused assignment in which students used real U.S. wage data and Lansing rental prices to determine which apartment they could actually afford on their income. After that assignment, more students came to my office hours, and I saw them actively debating budget constraints. They learned probability along the way without even realizing it.

In contrast, students with strong foundations bring different challenges, such as rigid habits that require a customized approach. In my Introduction to Proofs class, I saw students clinging to habits without realizing it. It is instinctive to reach for what has worked in the past, but learning something new requires flexibility. As a result, their proofs started to look like either overstuffed suitcases or thin sketches that left most of the information out. To address this, I had them write step-by-step instructions for making a PB&J sandwich, then watch the famous TikTok video showing how both poorly written and overly detailed instructions lead to a mess. Afterward, their proofs grew sharper and more creative, and the exercise gave them room to slow down and think.

The first day matters

Understanding what students need begins before the first session. I start every course with a short pre-survey built around two questions: “What are your best and worst experiences with math?” and “What is your best way of learning?” This helps me adjust my teaching to fit the group. On the first day of class, I begin with a short presentation about myself, sharing that I, too, have interests beyond mathematics. This loosens the atmosphere before the icebreaker, which then gives students a chance to get to know each other. I also remind them to swap phone numbers so they can work together after class.

Because of these steps, students who came to class anxious or with negative experiences settled in more quickly, and discussion grew across the class. Students even visited my office hours in groups, a sign that swapping numbers had worked.

Building groups that work

Working in groups is one of the best ways to learn and to make mistakes. In in-person classes, large groups usually form naturally; I once watched eight students pile together in a calculus class, and it slowly became a social gathering. So now I form groups on the first day with a small activity: each student picks one of four colors, then forms a group of three or four, with the rule that no color can repeat within a group. For online classes, I do the same through a poll.

Since online students can be distracted easily, I step in and build balanced groups myself when needed. Each breakout room usually has at least one person comfortable taking the initiative, and I ask everyone to keep their cameras on and use a shared Microsoft Whiteboard to keep the energy up. I have seen introverted students take active roles, and the discussions draw everyone in. Most of the time, groups divide the work so that everyone stays engaged; even on the whiteboard, they help each other by typing out their thinking.

Small check-ins

All my classes, online or in person, end with a minute paper: “What did you learn today?”, “What needs clarifying?”, and so on. At the end of each week, I ask broader questions about recurring mistakes on quizzes and exams. I use these responses to identify where the class is and to address any confusion. My notes for the next day change every time, depending on what students ask me to revisit, and once I understand the source of their confusion, I reteach the concept from a different angle.

I also arrive fifteen minutes before class and stay until the last student has left. This habit gives me time for small conversations with my students, some completely outside mathematics. It also helps me catch quiet warning signs, such as missed classes or assignments. Once, a well-performing student began submitting incomplete quizzes; after I reached out, I learned she was a single parent juggling far more than my course.

Mistakes, made on purpose

In my classes, students can resubmit quiz and homework problems for partial credit, but only if they explain what went wrong and submit corrected work. This policy encourages them to make mistakes without worrying about grades. As a result, their work improved dramatically, because redoing it forces them to address the underlying issue.

I do the same on my end by making mistakes publicly. For instance, I deliberately tangle necessary and sufficient conditions, then untangle them out loud with “I am an animal” versus “I am a cat” until the logic is straight. I also stop halfway through a computation and ask the class to finish it, so that being unsure and being wrong feel like ordinary parts of doing mathematics, for me as much as for them. As a result, students are less anxious and join the discussion without worrying about being correct.

Looking ahead