Learning Math through Fs

Over my time as a TA, I've realized, however, that just fixing what you notice is not enough: there are always problems that can't be solved in the short term. In these cases, I've found it invaluable to document any issues I notice and trust future TAs to improve them. TAing is not only about solving problems for now; it must also involve thinking about the overall sustainability of a course, including what you can learn from those who have come before you and how you can help those who will come after. Every TA knows that there's no feeling quite like helping students understand the ideas you love; by zooming out and thinking about long-term changes, you can affect not only current students, but students for semesters to come.15-151/21-128, or simply Concepts, is one of the notor- iously challenging courses that freshmen in CS and Math take at CMU, and I've had the privilege of being a teaching assistant for the last 3 years. We teach a variety of topics in discrete math to students, with a heavy emphasis on proof writing, a topic that the large majority of students have never encountered. While the TA job description may seem like it involves only teaching and grading, I believe that we help students to a much greater extent, especially given how challenging freshman fall is. If I had to characterize my philosophy as a TA and head TA, I'd describe it through 3 Fs: fun, friends, and family. I'll spend a bit of time on each of these, followed by why I think Concepts is so important as a course.

Fun: I'm a big proponent of playing hard, even in the context of working hard. On the student-facing side, I love making jokes while teaching recitations or review sessions as a quick break, or organizing class events so that everyone can get to know each other better. On the TA side, one of my missions is to make sure we have fun TA events that cater to different personalities and interests. Having fun is one of the best ways to stay sane, especially in such a challenging and rigor- ous environment, and it's important to lean into fun as much as possible. Having fun together brings people closer, where they can more easily learn and be more vulnerable with each other. With such amazing minds at a school like CMU, I strongly believe that hanging out with peers in whatever way makes you happy will lead to long term personal and academic growth.

Friends: Every year I learn an incredible amount of new things about the course and life in general from the other amazing TAs and students. I feel like my teaching style is a combination of all the great TAs that I've been inspired by, from people like Parmita Bawankule, Chittesh Thavamani and Carmel Bharav, to Vianna Seifi, Ryan Ravitz, and many others. While taking classes, some of the material I learned best was that which multiple different people had to explain to me because I didn't understand it at first. Hearing different perspectives is instrumental to the learning process, and it's great that students get the chance to talk to a multitude of TAs through recitation, office hours, and review sessions. Whether you are trying to learn the material in Concepts, or learn how to better teach material, I always recommend talking to different people with diverse backgrounds/perspectives to get a better understanding of the content and figure out what works for you.

Family: Since my first year as a Concepts TA, the staff has been a family to me, and I'm grateful to have a staff that was willing to put up with my antics and ideas for 3 years (special shoutout to my other head TAs, AJ Lim, Vianna Seifi, Ryan Ravitz, Chittesh Thavamani, and Gabriel Chuang). Having such strong connections is one of the reasons so many TAs choose to return to Concepts year after year, making the course staff even stronger as time goes by. We produce experienced TAs that can then distill their knowledge to the younger TAs and continue the cycle of growth. Extending to the CMU SCS family and beyond, I take pride in how our TA staff serves as role models and confidants as well as teachers for the underclassmen. This makes a huge difference to students coming into college with no idea what the upperclassmen will be like at a prestigious university. I have no doubt that the TAs' strong connection and commitment to the course and each other sends a powerful message about the importance of learning and camaraderie to the students.

Why Concepts is so important: The idea of thinking mathematically is underrated in our society. When learning how to write a proof, it's exceedingly important to understand every single part of the process from a question to a solution, and how each individual step follows from the last. Whenever I interact with students, instead of trying to teach them how to solve any individual problem, my main goal is to first get them to think clearly about what knowledge they are starting with, where they need to go, and what information they have to get there. More important than any full solution is teaching a student how to continue any proof from some arbitrary step to the next. If you train this general skill, roping together different concepts learned into a single cohesive idea becomes less scary and more approachable. To me, life is constantly presenting situations that beg for mathematical thinking: trying to accomplish a long term goal can be scary, and being able to break it down into parts and think clearly about how each part can be done breaks down the task into doable steps. In another vein, it's easy to jump to conclusions, or take events that happened and draw claims that may not be true ("I got a bad grade on the exam, so I'm dumb, or x person didn't look at me when we passed in the hallway so I must have done something to them"). Reasoning soundly about how to interpret our surroundings and thinking through our thoughts step by step is a game changer, and can help us to locate a bad assumption in our thought process in the same way that a student might find a bug in their proof.

I'm extremely grateful to have worked and taught with such exceptional minds, and I'm excited for the future generations of students that get to learn, laugh and make it through concepts, freshman year, and CMU together.