Teaching Statement — Debanjana Kundu
I consider myself fortunate to have learnt mathematics from some of the best teachers. One of the main
reasons I wish to pursue a career in academia is so that I can share the under-appreciated beauty of mathematics with others. I have been a part of two education systems, with significantly different philosophies,
and I believe this valuable experience will help me adapt to any teaching environment.
A major obstacle in teaching mathematics stems from the fact that most people believe mathematics is asubject meant only for those who are “born with it”. The Telegraph published an article1 in 2011, wherethe opening lines were “Being good at mathematics may be entirely pre-destined—you either have it or
you don’t”. The article cites a paper from the psychology journal Developmental Science based on a study
conducted at Johns Hopkins University. The idea that math ability is mostly genetic is one dark facetof a larger fallacy that intelligence is mostly genetic. Mathematical skills are increasingly important forgetting good jobs these days — so believing you can not learn math is especially self-destructive. As amathematician, and as a teacher, my primary goal is to help students move past this mindset.
In my experience, the traditional lecture style often reinforces students’ beliefs about needing an innate
ability to understand mathematics. They watch an experienced problem solver tackle questions withease, often without making mistakes, as they arrive at their solutions. Students expect they should have asimilar experience while attempting problems. When this does not happen, they quickly become frustrated.
I constantly remind my students that everybody struggles with mathematics, including me. But the only
way around is by practising. In the words of W. E. Hickson “if at first you don’t succeed, try, try again”.
Tutorials are crucial to an undergraduate level mathematics course. They reinforce key concepts, provide
new perspectives, and create opportunities to work on problems with guidance. The environment tends tobe more relaxed as there are fewer students and the tutors themselves are (graduate) students. Students canuse this welcoming environment to explore new ideas and to test their understanding of lecture material.
As I look back at my undergraduate years, I realize that I learnt those subjects better where I would get“stuck” often and would discuss the material with my peers. I believe that an interactive style of teachingis the most effective one in smaller classes. When asked a question in class or during office hours, I prefer
not to give away the answer immediately. I engage other students in the discussion and try to make themwork out the answer to the question. During the early years of graduate school, I ran several tutorials. In
recent years, I have carried my philosophy from these tutorials into my position as an instructor. After
introducing a concept, I give a few examples and then give time in-class to work on a harder problem, often
in small groups. During this time, I walk around to give ideas and/or hints and to make sure that they areon the right path. To encourage peer learning, I ask for volunteers to present their solutions. Often, thestudents are shy about presenting their work so I read through their solutions making sure it is correct.
Once they know they have the right answer, they are more confident while presenting. This entire process
is time consuming, but in my opinion they gain greater knowledge from solving problems with guidance.
Whether it is a first year linear algebra course or an upper year advanced number theory course, I think
my students go back home knowing that they can tackle hard problems.
Over the years, I have taught Linear Algebra, Calculus, and Multivariable Calculus to non-math majors.
Unfortunately, most students need to register for these introductory courses because of university mandate
and not out of an interest in mathematics. In such courses, I am willing to sacrifice a bit of rigour tomake sure they remain enthusiastic till the end. Teaching my first Calculus II course in Winter 2018 wasparticularly challenging as this was my first experience of teaching a flipped classroom; it was also thefirst time I was teaching a class of 200 students. The biggest challenge in teaching large classes is thatsome students find the material too easy whereas some others find it too hard. It is difficult to hit the“Goldilock zone”. I took regular (anonymous) feedback from students to make sure that majority of thestudents were comfortable. I encouraged those who continued to find the material difficult to come to myoffice hours. At the end of every lecture, we spent 15 minutes solving problems on Top Hat2 ; the focus
12https://www.telegraph.co.uk/education/educationnews/8693105/People-are-born-bad-at-maths.html
http://www.tophat.com

was often on the subtle points. This application allowed me to post objective-type questions which thestudents could answer. I could see how many students got the correct answer and if a significant numberof students answered incorrectly, I would encourage them to discuss the problem with fellow students andgive them an opportunity to answer the question again. Almost always, this discussion with classmates
proved helpful and majority of the students got the correct answer. Knowing which concepts students werestruggling with, helped me prepare for the next lecture. Even though as a student I was never exposed tothis style of lecturing, I have come to appreciate this relatively recent learner-centred model of instruction.
Just when I started feeling comfortable teaching large classes, we were hit by COVID-19 and teaching wentonline, literally overnight. This was a challenge for me, just as it was for everyone else. I coordinated a(multi-section) course on Multi Variable Calculus in Summer 2020. Our goals were modest; we wanted tobe adequate. With trial and error, I realized that it is hard for students to stare and concentrate at a screen
for long intervals of time; so I started teaching in 20-minute bursts followed by a short break. I shared myOneNote notebook with students to create a blackboard-like effect. This allowed students to look back at
definitions, examples, or notations. I used Breakout Rooms on Zoom, Piazza, virtual study rooms, etc. toencourage students to continue discussing mathematics with their classmates. Even though we have once
again returned to in-person classes, I continue to incorporate some of these features, like teaching in shortbursts and maintaining a OneNote notebook for lecture notes and recording my lectures.
At my current institution (UTRGV), class sizes are small – e.g., my honours Algebra course had 15students. Now, there are new challenges. Almost all our students are first generation and work part-time
or full-time, in addition to taking 5 courses per semester. I needed to redesign my courses to support
learning. For example, I no longer enforce homework deadlines students can submit their assignments till
the day before the final exam. I continue to be (pleasantly) surprised by the number of students whocomplete their pending homework before the final exam and do well on the test. Every few weeks, I bringin-class worksheets which allows for group discussions. Even when students are unable to complete their
homework, this approach allows them to practice a few problems and clarify misconceptions. I assign peer
learning assignments where students grade a peer’s solution to a problem following my rubric – this gives
them an idea of how much details are necessary for an answer to be complete and how to present an answer.
In every endeavour, I make it clear to my students and peers that they are welcome to ask questions, thatmaking mistakes is how you learn, and that developing good problem solving skills takes time and effort.
Over the years, I have organized semester-long learning seminars involving undergraduate students, graduate students, post-docs and faculty members. The goal has been to establish a sense of community, improve
communication skills, and also learn about different areas of math not necessarily related to my research.
As a part of the University of Toronto Outreach Program3 , I mentored three high school students between
2018 and 2020. Students came from varied backgrounds; some were interested in competitive mathematicswhereas some found high school mathematics boring and wanted to do “fun” math. It was a wonderfulexperience to work with such students as it allowed me to design projects geared towards their interests.
Since 2021, I have regularly mentored undergraduate students. I was a mentor for Adithya Chakravarthy’sbachelors thesis at the University of Toronto which resulted in a single-author publication. In my current
job, I have offered independent reading courses to students outside of regular class hours. I am currently
mentoring two (final year) bachelors projects and one masters project. In addition, I am also running anintroductory elliptic curves seminar course geared towards undergraduates during Fall 2024.
I am eager to design a course on computational Number Theory with emphasis on working through examples using SAGE. I intend to bring the courses I teach closer to my area of research and whenever possible
introduce students to undergraduate research. In addition to my teaching experience, I have given talks
at conferences and seminars about my research. Although these talks are on completely different subjects
than what I teach my students, they give me the necessary experience of addressing a large audience. Istrive to become a better educator who is knowledgeable, competent, and respectful to my students.
3

https://www.mathematics.utoronto.ca/outreach/current-programs/grades-9-12-programs/math-mentorshipMentorship Activities
Below is a table of high school, undergraduate, and graduate students I have mentored since 2018.
Name
Anna Krokhine
Maya Bozo-Ray
Jennifer Wang
Adithya Chakravarthy
Vitthal Yelambalse
Shubhrojyoti DharaLéonie Chipot
Samyak Jha
Raul Marquez
Gourab Mukhopadhyay
Nandini Parkhi
Aniruddha Mandal
Raul Marquez
Alejandro Delgado
Ama Quansah

Institution
High School
High School
High School
UofT
BITS Goa, India
ISI B, India
UOttawa
IIT B, India
UTRGV
UTRGV
IISER Bhopal, India
IISER Mohali, India
UTRGV
UTRGV
UTRGV

CourseMentorship
Mentorship
Mentorship
Bachelors Thesis
Bachelors Thesis
Summer Project
Summer Project
Reading Project
Reading Project
Research Project
Summer Project
Summer Project
Bachelors Thesis
Reading Project
Masters ProjectYear
2018
2019
2020
2021–23
2022
2023
2023
2023
2023–24
2024
2024
2024
2024–present
2024–present
2024–present

Topic
Graph Theory
Benford’s Law
Number TheoryIwasawa Theory
Cyclotomic Fields
Elliptic Curves
Proof Writing
p-adic L-functions
Elliptic Curves
Fibonacci Numbers
p-adic Numbers
p-adic Numbers
Elliptic Curves
Group Theory
Fibonacci Numbers

Feedback from students (Courses)
In 2021, I was nominated for the UBC Mathematics Department’s Postdoctoral Teaching Prize4 . I include
here some of the comments I have received in the mid semester or end of semester surveys over the years:
1. “I thought Dr. Kundu was very organized this semester in terms of her notes and providing uswith information regarding assignments, midterms, and the final. She was always open to answering
student’s questions. I think it was a great idea to include bonus marks for students and I think
this should be continued in future terms as it gives students a chance to practice while potentiallyboosting their grade.” – MAT105 (Calculus) UBC
2. “Dr. Kundu explained the concept well by using quite a few practice questions during class. In
addition, she provided us with extra practice questions which were pretty helpful.” – MAT105 UBC
3. “I enjoyed attending Professor Kundu’s class. She communicated the material really well and she
made math more fun. I found the weekly practice problems helpful as I always did them as extra
practice and it allowed for me to brush up on topics that I had difficulties on.” – MAT105 UBC
4. “Very respectful, dilligent, and dedicated teacher. Always made time to make sure students understood if they still had questions.” – MAT105 UBC
5. “I loved Professor Kundu’s style of lectures. She would take the notes with us and do a lot of practicequestions and made sure that we had a full understanding before she moved forward. Not only is shea very effective teacher she also showed that she cared for our well being and is a very welcomingperson.” – MAT105 UBC
6. “Deb always made an effort to answer my emails and my questions in a timely manner and was verykind and respectful to me when I spoke with her. . . . Deb is a lovely person who cares about her
students, and made lots of effort to connect with us which was greatly appreciated.” – MAT105 UBC
4Nominations are from students or supervisors.

7. “Very effective that she asked about what she can do to change and improve the course.” – MAT105
UBC
8. “The professor is really good at asking for/answering questions and the pace if the lectures wasgood.” – MAT152 (Linear Systems) UBC
9. “Material presented in such way that inspired learning and made it interesting. The instruction wasclear and easy to understand.” – MAT152 UBC
10. “The practice midterms are very useful and applicable.” – MAT152 UBC
11. “Instructor was very available and willing to help with explanations. Enjoyed PLA (Peer LearningAssignment) especially the one we graded eachothers to see how others work. Instructor encouraged
us to work together as you learn best from speaking with others. ” – MATH2413 (Linear Algebra)
UTRGV
12. “This professor is one of the best math teachers I’ve ever had!” – MATH2413 UTRGV
13. “You are an amazing mathematics teacher! It was a pleasure learning from you this semester.” –MATH2413 UTRGV
14. “She was always very helpful, understanding, and gave clear instructions.” – MATH2413 UTRGV
15. “Definitely enjoyed many of the aspects of the course, but wished there could’ve been more groupassignments and work. Enjoyed the pacing and structure” – MATH3363 (Algebra I) UTRGV
16. “Please continue to provide recorded lectures and notes. I struggled to keep up with the material so
this was very helpful to have. I also liked that you were available outside of office hours. And when
I went you were very kind and understanding of my situation. You seem to genuinely care about
wanting your students to learn. UTRGV could use more professors like you so I hope you’re here fora long time. Thanks again for all the help” – MATH3363 UTRGV
17. “The professor was helpful, and the homework and review problems were useful for preparing forquizzes/midterms.” – MATH3363 UTRGV
18. “Very understandable and cognizant of students’ situations. Provided opportunities and then some.”–
MATH3363 UTRGV