### My Teaching Philosophy

As I begin this blogging adventure, I thought it would make sense to start by outlining my teaching philosophy. There are four basic parts to the "why" of how I teach, outlined below.

## You must do mathematics to learn mathematics.

Seems obvious, right? Yet, our default way of teaching mathematics is to talk mathematics at students, or lecture. Don't get me wrong, I've fallen into this trap. By virtue of being the teacher, we know what we are talking about, so talking about it is the easiest way to present content. However, it is also probably the most inefficient way to teach, for teaching cannot happen if learning does not happen.

Lecturing is an instructor-focused activity. Learning, however, is an internal process. Students need to be working their own brains in order to learn, not passively listening to someone else. In my classrooms, I put student thinking and exploration as the focus of class time. That is not to say that I don't ever lecture. In fact, I've gotten feedback from students consistently that they like small snippets of lectures. However, I believe it is very important to think about how this instructor-led time is intentionally incorporated in order to be of most benefit to students. In other words, the backbone of my class prep is the work I plan on having students do, and lectures are dispersed throughout as needed.

Depending on the course, I've implemented this in different ways. When I was teaching in person, I would nearly always run my courses as flipped. In this model, students would do some preparation before class such as watching videos and practicing simple examples so that most of class time could be spent on active practice and exploration, mostly in groups. When we switched online, I had a lot of difficulties in getting group work to be effective. So, I instead relied on smaller activities like think-pair-share and clicker questions.

I am also hoping to include more and more opportunities for inquiry, allowing students to explore and discover mathematical concepts rather than being told what the concepts are. This is something I have tried to implement where I can, but I am working on bringing more and more of it into my classrooms.

## Mistakes are an essential part of learning and should be valued as such.

As the old adage goes, you learn more from your failures than your successes. Don't get me wrong, we need to celebrate success, and I do work to point out good work that students do. However, I also believe that mistakes should not be viewed as negatively as they are. I want students to use their mistakes as an opportunity to learn. The mistakes that students make give me a window into what their brains are doing so that I can better support them in their learning journey.

I have tried to incorporate this philosophy into the structure of my courses, but it is an ongoing process. I do try to encourage students to go back through their graded exams to reflect on what they did right and what did not go well. Where I can, I will give them credit towards their grade for this work, either as participation points or as credit towards their exam scores. I am very interested in grading schemes where this is at the core, such as mastery-based or standards-based grading. As I am mostly teaching large, coordinated courses, experimenting with such methods comes with a lot of extra complications. Though, I do believe that even these big changes are possible in large courses, even with tight course coordination. It just may be a slower and more complicated process.

## Everyone can learn mathematics, just not on the same day or in the same way.

Everyone's minds work differently. Surely we don't disagree there. However, we often teach mathematics as a one-size-fits-all dissemination of information. Just as all instructors will explain concepts a little bit differently, different students will respond to and resonate with different ways of thinking about the material. Furthermore, students need different amounts of time for things to "click" and to understand the mathematics they are learning.

Unfortunately, I think that students who don't fit in the "all" in the "one-size-fits-all" model end up with the message that they cannot learn mathematics. That they just "aren't math people". Unsurprisingly, these are disproportionally students who have historically been purposefully excluded from mathematics, such as women, students of color, and first-generation college students.

While I deeply believe that everyone can learn mathematics given the time and variation that they need, and I see obvious places that our standard teaching methods clash with that belief, I do still struggle to implement changes in course structures and policies to address it. For example, I try to be flexible with deadlines when I can, and I build course structures that take into account growth throughout the semester.

When presenting material, I try to give students multiple ways to solve a problem, and although I will point out which one I find easier and why, I make sure they know that each method is equally as valid and that they have choices to determine what makes the most sense for their brains. By using active learning techniques, I open up the opportunity for students to forge their own paths through the problems, which also helps me to provide more ways of thinking about the material to all of my students. I do, however, want to continue to find ways to build even more flexibility into my courses so that students can find what fits for them.

## Mathematics is a human endeavor and therefore cannot be separated from the human-ness of the people doing it.

Mathematics is done by mathematicians: people. All of the biases, traumas, emotions, fears, joys, and personalities that we have don't suddenly disappear when we start doing mathematics. We as humans are social, emotional creatures. We cannot do our best work if we are not supported socially or emotionally.

Furthermore, the mathematical society as well as the larger academic society are human-built and human-run. Just as all societal structures, they are not immune from structural discrimination, bias, and oppression. In fact, many of these structures were historically built explicitly to be exclusionary. Even if that is not their stated intention today, those structures still persist and therefore so does the bias they were designed to perpetuate.

I have to admit, although I feel so deeply about this, it is the part of my teaching philosophy that I struggle with the most to turn belief into action. I have taken small steps in my classrooms to at least signal to students that they can feel safe with me, such as making inclusion statements on my syllabus and at the start of the semester, sharing my pronouns and asking students for theirs, and working to be aware of my unconscious biases and not letting them dictate my actions.

However, these steps are just not enough to combat the scale of the problem. As I write this, I am in the middle of the 2021 Joint Math Meetings. Although the virtual format just isn't the same as a JMM in the Before Times, I am so grateful for the amazing mathematicians that are speaking out about inequities and injustices in the mathematics world. In just a few days, I have learned so much and have found so many places to continue to learn more. I'm sure I will continue to write about this repeatedly going forward, and next week's post will be about one specific takeaway from just one of these presentations that I believe will help me in really acting on this aspect of my teaching philosophy.

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