We are excited to announce that the 2025 Certificate in University Teaching (CUT) Award has been awarded to Christine Eagles, a PhD student in Pure Mathematics studying model theory. We had an opportunity to interview Christine about her experience with the Certificate in University Teaching and her dedication to teaching.听听
What motivated you to join the Certificate in University Teaching (CUT) program during your doctoral studies?
Teaching is a really important part of any academic career, and we don鈥檛 really learn how to do that in our PhD unless you seek it out. The CUT program was a great opportunity to learn those skills.鈥 Especially in our math department, many of our TAs are purely marking-based, with little to no interaction with students. The CUT program really allowed me to gain that experience and knowledge about how to handle yourself in situations with students that I wouldn鈥檛 have had otherwise.听听
When you started the CUT program, one of your goals was to learn how to effectively use active learning in math courses, in particular peer-to-peer learning that encourages students to reflect on their solutions method. Can you expand on this? To what extent were you able to accomplish this goal?听
In my undergraduate experience, I only had math courses that were all traditional lecture-style based. So, there was essentially no active learning, it was all passive. I had some active learning in non-math courses, but the techniques didn鈥檛 seem to transfer directly onto a math course. I wanted to see what that was like. Also, my greatest understanding came from talking through problems or concepts and trying to explain them to my peers. It didn鈥檛 come from sitting in the classroom or just doing questions, it came from speaking with other people at my level. It was also a good test to see if I was understanding or just regurgitating the material.听听
There is a common misconception in math that there is only one answer but there鈥檚 usually many different correct answers. It鈥檚 just some of the ways to solve the problem are more elegant or concise than others. Many times, students will just write down the first solution that comes to mind and submit. While their solution is technically correct, it doesn鈥檛 demonstrate a mastery of the course material or a deeper understanding. In the same way you wouldn鈥檛 submit your first draft for an English essay, you shouldn鈥檛 be doing that for a math assignment. I really want to focus on how the tools that you learn in the course can give you a different way to answer a problem that you might already know the answer to.听
The way that I have been able to do that is really with using things I learned in the CUT program and the Fundamentals of University Teaching. I have been able to do a lot of Think-Pair-Shares in my class, where I鈥檒l have students work on an example and work with their neighbor and then we鈥檒l take it up on the board. That way, they can see how somebody else approaches the problem and how they think differently to answer the same thing. Then they see what we use in the course material to address the problem, so it walks them through the thinking process.听听
Can you share a story of a time when you applied something that you learned from CUT program in your teaching?听
My favorite thing that I learned from CUT is the muddiest point activity. It鈥檚 when you ask students to choose a concept, a topic, or a problem type that they find the least clear so far. It really gets them to reflect on what they know and how well they鈥檙e doing in the course. I also like to pair this activity with a midterm or final review. I鈥檒l ask them to submit a question or topic on Monday, and we鈥檒l do the review on Friday. This gives me time to prepare but it also forces students to reflect on where they feel they are in the course before the day before the exam. It鈥檚 a way to get them to reflect on their learning and gives them time to address those gaps in knowledge.听听
One of the reasons you were recognized with this award is how you are able to reflect on and refine your teaching strategies based on student needs. What does this approach involve, and why do you think it鈥檚 an important one for your students?听
The way I approach teaching is to gather feedback from the students to see how they鈥檙e doing. This doesn鈥檛 have to be formal feedback - it can be simple comprehension checks: every 10 minutes I鈥檒l pause to see if there is anything I can clarify or even do a little activity. This is just to see if they鈥檙e getting the answer right or if there are any misconceptions before we move on. At the start of every week, I like to do a little warm-up question on the board which is a multiple-choice question that reviews a key concept. It really lets me see if they have any misconceptions that are not being addressed. The way math is usually taught is to build on each section, so if those misconceptions don鈥檛 get addressed, they get carried through the whole course and can impact your understanding later. It鈥檚 important to see how the students are doing and give them the chance to say if they understood that topic or not. It鈥檚 a way to really get the students to think about how they鈥檙e progressing and how they feel about the course material. I know that when I was a student, I wasn鈥檛 always the best at that.听听
Is there an activity or technique that you would like to try in your future courses?听
There is one activity that I developed with the CUT program. I called it a 鈥減roof annotation activity.鈥 Essentially, you provide students with a reverse assignment. You provide them with the questions and the solution which will have mistakes that students commonly make and you ask them to point those mistakes out, and correct them. This gets the students to focus on how things are being presented, which I find really important. You can have them do this in groups so they can talk to each other about it and it鈥檚 a nice way to make sure they are understanding and actually doing the work themselves.听听
Anything else you would like to share about your experiences in the CUT program?听
The most valuable part of the CUT experience for me was getting feedback on my teaching, from both the experts and from my peers. Having the peer evaluation at the start of my teaching journey and then having another evaluation towards the end of my class was really beneficial. It was nice to get that feedback and see how I could improve. We can always improve, and no one is ever the best they鈥檙e ever going to be. I think that was super valuable and gave me a lot of different ways to think about what I鈥檓 doing and why I鈥檓 doing it.听听
Do you have any future plans that you can tell us about?听
I鈥檓 a graduate representative on the Women in Math Committee here at 蓝莓视频. Right now, we鈥檙e partnering with the Centre for Education in Mathematics and Computing (CEMC). We are putting on a panel about teaching as an early instructor and gender minority in math. Hoping for June, so keep an eye out for that!听听