### My First Teaching Experience

As I mentioned before, this past summer I taught my first course. The Pure Math Department at the University of Waterloo offered me such an opportunity last January to which I accepted. I was very pleased because I had been waiting for such an opportunity since it’s usually the case that pure math PhD students at Waterloo are offered such an opportunity before completing their degrees. I had done well so far in the CUT (Certificate of University Teaching) program that the university offers to its PhD students and have explained my positive experience in this program in Learning How to Teach (I have since completed it). I had done two guest lectures for a couple of courses where one of my PhD supervisors was the actual instructor and they had gone well. I was also pleased that that the course they offered me was a third year pure math course in Elementary Number Theory, which is my research speciality and one of my favourite mathematical subjects.

The course was set to begin in May and run through August where I would be lecturing three hours per week for about 12 weeks. I did prepare a lot beforehand though and spent a lot of time preparing a course outline and lecture notes. I managed to get a lot of resources from another PhD student who was teaching the course that winter, including various lecture notes and sample midterms and exams from him and various professors. I also got a textbook on Elementary Number Theory out of the university library that I was familiar with and that I liked and that contained almost all of the material I need to cover. I ended up basing most of my lecture notes out of the material in this book, the rest out of the sample lecture notes. By the time it had come to actually teach the course I had done up all of the lecture notes and had put together a first assignment. I felt pretty prepared.

As I taught the course, I used my lecture notes in a bit of a unique way. As the weeks went by, I would post the relevent lecture notes up on LEARN. LEARN is a website that a lot of professors and instructors at Waterloo use to organise their courses and upload course materials such as course outlines and assignments. My own lecture notes consisted of all of the material that I would cover, but with a lot of blank spaces. For example, a short proof of a minor result I would leave blank and for longer proofs I would write down a few steps of the proof and leave the class to fill in the details. The idea here was that before each class the students would print off the lecture notes, take them to class, and fill in the rest as I went through my lectures. As a student and instructor, I felt that such a strategy minimizes the amount of writing students need to do during the lecture, while maximizing the amount of listening and participating they do to help them get a stronger grasp of the material. As a student, I was in a class before where the professor used exactly this strategy and found tht it really helped me follow along, which was why I decided to try it out. I was pretty pleased when this strategy seemed to work and that a few students even printed them off to follow along. In my course evaluations, some students even praised this strategy. I will therefore continue to use this strategy for future courses I teach.

The first day I lectured, I was pretty nervous. It did, however, go very well and I looked forward to the next one afterwards. After each subsequent lecture teaching came more and more naturally to me. I also used various other strategies in my lectures that I learned from being in the CUT program. For example, I used the teaching method think-pair-share to give students a chance to apply what they have learned without having it be formally graded. Think-pair-share is a strategy where the instructor poses a problem that can be solved in a couple of minutes to the class. The class tries to solve the problem, and then spend another minute conversing with a partner on their answer to the problem. Also, one time earlier on in the course, I used the one minute paper method, which is a strategy where the instructor hands out sheets of blank paper to the students, giving them a prompt relevant to the material covered in that particular lecture. The students’ answers are not graded. Rather, the instructor collects them and picks the three to comment on without revealing the authors. Here I used the prompt of asking them about the most confusing part of the lecture. I then looked over their answers and spent the first few minutes of the next lecture answering three of their questions thoroughly.

Overall, my first teaching experience was a real success and I look forward to doing it again.