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Teaching PhilosophyObservations and FeedbackWhat is Active Learning?Diversity and Inclusivity

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.

Reading Resources

Examples of Observation Protocols and Approaches

Brief, Easy Supplements for Lectures

  • The Pause Procedure – pause for two minutes every 12-18 minutes, encouraging students to discuss and rework notes in pairs.
  • Retrieval Practice – pause for two or three minutes every 15 minutes, writing everything they can remember from preceeding class segment.
  • Think-pair-share – ask students a question that requires higher order thinking; ask them to think and write their answer for a minute, then turn to their peer and discuss their responses for two minutes.

Brame, C.”Active learning.” Vanderbilt Centre for Teaching, ND(2016).

Prince, Michael. “Does active learning work? A review of the research.” Journal of engineering education 93.3 (2004): 223-231.

Encouraging a Mastery Orientation vs Performance Orientation

  •  Incorporate an element of choice and control over one’s learning;
  • Reduce the cost of failure;
  • Give assignments where the focus is on learning and making progress rather than on being correct;
  • Minimize competition and reward collaboration;
  • Make sure the value of the task is obvious;

Svinicki, Marilla. “Student goal orientation, motivation, and learning.” Idea Paper 41 (2005).

Group Work

Finnegan, Margaret. “It’s Good Till It’s Not.” Inside Higher Ed.

“First, if group projects are to be considered important outputs, then training students to work in teams needs to be an important and measurable learning objective. The process of learning to function in a group has to be as important as the product. And that means students need to learn how to identify and delegate team roles, how to set short- and long-term goals, how to plan backward, and — most importantly — how to communicate.”


Vignette on Inclusive Teaching

When teaching small classes, I often ask students to come to the board and present their solution to a problem they might have been discussing in small groups beforehand. I have found that setting norms about a classroom culture of active participation as early in the semester as possible is important. It was within the first week of class a couple of semesters ago, in my Analysis I class, when I asked one of my students, Adam, to come to the front of the classroom and share his solution with the rest of the class. He was somewhat reluctant, but I was enthusiastic, explaining that mistakes are good and help us all learn and we would all help him along. Adam froze at the board. I was asking him questions and suggesting ways to proceed, but things were not going well. After a minute or so of confusion, he went back to his seat and I solved the problem on the board. At the end of the class, one of the students in Adam’s group approached me and said: “Dr. Sendova, I just wanted to make you aware that Adam cannot hear with his right ear and the way you were standing, on his right side, he could not hear any of your suggestions.”

Since then I have become much more sensitive about conditions which might make students feel beyond uncomfortable to be at the front of the classroom, participate in the class discussion out loud, or work in groups. On the first day of the semester, I try to describe common activities that students should expect throughout the semester, including group work, presenting problems on the board, peer editing, etc., and I make a point to invite students to come talk to me if they feel like they need to avoid any of those.

Reading Resources