Teaching Statement

I believe that mathematics is a beautiful discipline, deserving of clear and concise communication. In practice, "clear and concise" means different things for different audiences depending on many factors, including prior knowledge, level of interest, and the relationship one has with the participants. With these factors in mind, I approach teaching and learning in a variety of ways depending on context. I design my lectures with the goal that students take away an appreciation for the content, the tools to competently apply it to solve problems, and the desire to learn more in the next lecture. I mentor undergraduate students interested in going beyond their coursework, and with professional development. Finally, I enjoy having informal maths discussions with students during social gatherings like Maths Club meetings.

During my time in academia, I have taught courses at a variety of levels. From basic courses like pre-calculus, to proof-based courses like discrete mathematics, to courses somewhere in between like linear algebra, I found that the best way to engage students is to turn a classroom from mere physical location into a community of learners. I do so by making the room as welcoming as I can to all students, so that everyone is comfortable enough to actively participate in the lecture. I try to make personal connections with the students, and I encourage students to work together and with me to understand the material both in lecture and on office hours.

I care a lot about conveying material and expectations to students as simply as possible. For this purpose I maintain a website to house additional information, including the syllabus, more examples, notes explaining content, practice problems, and links I think the students will find useful. I sometimes include my own short tutorial videos and GeoGebra demos to help students visualise concepts. I often use technological resources to help interested folks learn the material I have taught in more interactive and meaningful ways.

I also like to try new approaches in my teaching with the hope of reaching more students; this often includes experimentation with content delivery in the classroom. Among others, I have taught in the flipped style, where content is mostly delivered to students via short videos at home and the lecture time is reserved for practice exercises and mini-lectures. I enjoy this style of teaching, as it encourages collaborative learning and I can interact with students in small groups to assess which concepts are landing and which require more work.

In my experience, flipped teaching works well in low-level classes, but has diminishing returns in higher-level classes where concepts are subtler. For such courses, I often utilise a more traditional lecture-style approach supplemented by materials I create for the students. Teaching in the pandemic era pushed me to experiment even more with various ways to foster a community of learners while maintaining social distancing. I have also found some success by making a group chat for the course where students can collaborate and talk about the class and its materials.

I understand that students of diverse backgrounds face unique challenges in their educational careers and beyond. I am dedicated to helping mitigate this injustice however I can with my position and the resources available to me. For example, I have taught for the Binghamton Enrichment Program (BEP), a part of Binghamton University's arm of the State University of New York Educational Opportunity Program (EOP); this is an educational outreach program to help prepare students from minority and disadvantaged communities for the rigours of college. The program provides students from underprivileged backgrounds with the tools they need to succeed in their college studies, with support from EOP counsellors, by familiarising students with expectations and the college atmosphere over the course of an intensive month of preliminary coursework.

Furthermore, I constantly seek ways to improve my teaching to more effectively reach students of all backgrounds. I am conscious of the fact that my students—in all courses—may face invisible challenges. I have adapted my teaching style over the years to better serve students with disabilities and students at an economic disadvantage. For each of my recent classes, I maintained a website with open educational resources (OER) for my students to access. I am careful to keep my website as accessible as I can; for example, I carefully chose a colour scheme to make my website colour-blind friendly for students with any the three most common forms of colour-blindness. I ensure that the materials I post are laid out neatly and easily scaled for those students who have difficulty reading. I adopt free OER textbooks whenever possible, and often provide supplementary materials—many of which are written and maintained by myself—so students can take my courses without additional economic burden.

Moreover, I frequently mentor students in mathematics both officially and unofficially. I am aware women and people from the LGBTQ+ are underrepresented in mathematics and try to engage those interested in pursuing professional development in STEM fields. I have mentored numerous students from underrepresented groups, in self-study projects beyond their normal course work. One of my mentees was a maths major giving a talk in an undergraduate algebra seminar; the seminar's organiser asked me to mentor this student as she read and prepared a talk on a paper. We met weekly to discuss the mathematics—the paper was on laws satisfied by some groups—and we discussed how to use LaTeX to prepare slides, and good habits for giving a compelling mathematics talk. I later mentored another talented maths major in my multivariate calculus class who feels unchallenged by her coursework. She was new to the major and mentioned an interest in group theory during office hours; I offered to meet, and we met weekly to discuss group theory.

More recently, I mentored a trans computer science student in a self-study on graph theory and games on graphs. We met weekly to discuss a mathematical game I invented several years ago with the intention of getting students excited about graph theory research. With her wealth of programming skills, she wrote a program implementing the game. She and several of her peers have since worked with me to investigate optimal strategies and several variants of the game.

In addition to these more structured forms of teaching, I have engaged in a variety of more informal teaching opportunities. I hinted earlier that I believe that mathematics should be a community-driven affair. As such, I like to foster interactions between individuals interested in learning mathematics. Most recently, I have taken on the responsibility of running the Mathematics Club at The University of the South; I am currently advising the maths club, with the goal of making it into a university-sponsored organisation. While we wait to obtain official status and university funds, I am organising talks from faculty, advising talks given by students, and working with students active in the club to create events that the club can enjoy together in this informal setting. The response from the students has been overwhelmingly positive, and these events have given them the chance to grow and learn together.

Mathematics is a worthy discipline, and I feel an obligation to convey this to my students in my teaching and through my advice and actions. At the podium, this requires willingness to reckon with the students' perspective while also maintaining the integrity of the content to accurately represent the nuances involved therein. Outside the classroom, it requires mutual understanding and a strong sense of community surrounding my courses and mathematics in general. I believe that both my students and mathematics itself are worth this effort.