Teaching Philosophy
The secret of life, though, is to fall seven times and to get up eight times! - Paulo Coelho
Teaching is the most rewarding pursuit in my life. It is not merely a career to me but a source of deep, personal fulfilment and healing. My passion for teaching began at the age of ten when I started teaching my younger brother. Ever since, becoming a mathematics teacher has always been my dream. As someone who struggled and grew through my own learning experiences, I know how impactful it is to create a space where students can feel safe, supported, and heard even when they make mistakes. In mathematics, errors are not just inevitable, but also a crucial step in the learning process. In my classroom, I aim to build a supportive, low-pressure environment where students can stumble, reflect, and improve. Just as important, I aim to cultivate a sense of belonging for all the students, whether or not they choose to continue in Mathematics. Some aspects of my teaching philosophy, as described below, are designed to help the growth of not only my students, but also myself as a teacher, and move forward together as a learning community.
My super power - Ability to adapt my teaching methods to suit the needs of different students.
I believe my greatest teaching 'superpower' is adapting my methods to meet each student's needs. Working with my brother, who struggled with math anxiety taught me the importance of tailoring my approach to individual abilities and learning styles. This experience has shaped me and enabled me to effectively engage with a broad spectrum of learners. I adapt my teaching to two broad categories: courses for students with little prior math experience and those for students with strong foundations. These are not rigid divisions but ends of a spectrum. Each class falls somewhere in between, and I adjust my methods to fit the group’s specific dynamics. For the first category, I often notice students question the relevance of mathematics to the real world. Thus, I prioritize revising the course content and assignments to reflect real-world applicability. For instance, in Quantitative Literacy, I created a probability-focused assignment using U.S. wage data and a project analyzing rental prices across East Lansing, allowing students to compare options. These adjustments deepen understanding and demonstrate how mathematical thinking supports real-world problem solving. My goal for these students is to build confidence, reduce anxiety, and foster a genuine appreciation for the usefulness of math in everyday contexts. In contrast, for the second category, even well-prepared students can fall into memorization due to the complexity and volume of material. To counter this, I emphasize conceptual rigor and reflective thinking over memorizing isolated facts. For example, instead of memorizing derivatives, I show how to derive ln(x) from e^x, reinforcing understanding and reducing cognitive load. In transition-to-proofs courses, I have students recreate a 'peanut butter and jam sandwich' instruction manual, writing every step in detail, and showing them the famous TikTok video showing how missing steps can cause failure. This exercise illustrates the importance of precise, logical flow in proofs and encourages careful reasoning. These approaches foster critical thinking and conceptual connections rather than mechanical procedures.
Know your students
Regardless of the class modality or the category of students, I begin each course by sending out a brief pre-survey to understand students' background. One important question I always include is: "What are your best and worst experiences with mathematics?" which often provides valuable insight into how students relate to the subject, allowing me to approach the class with a more informed and empathetic mindset. On the first day of class, I begin by giving a brief presentation about myself, emphasizing that I am someone just like them, with passions outside mathematics, such as oil painting, Zumba, etc. Following this, I facilitate a brief icebreaker. This first-day approach has always helped me to be extra comfortable with my students and builds a collaborative, open environment and helps me understand preferences, such as note-taking habits or working through problems in detail, allowing me to design a balanced structure. Often, I address problems thoroughly during class and then upload supplemental PDF notes on D2L for further review and support.
The second and perhaps the most important concept, both in mathematics and in life, is embracing failure.
On the first day, I share a quote like Paulo Coelho's, "The secret of life, though, is to fall seven times and to get up eight times," to emphasize that learning is about engaging with the process, making mistakes, and growing. To reinforce this, I allow students to redo quizzes and homework by providing them the opportunity to explain their mistakes and present correct work, and earn partial credit. This practice supports both foundational understanding and deeper engagement with complex material. I also model this philosophy by openly acknowledging the mistakes I made, both as a student and during class. For example, mixing up necessary and sufficient conditions, and using phrases like 'I am an animal' and 'I am a cat' to understand logical implications. I intentionally pause mid-computation to ask students for help completing steps, promoting discussion regardless of correctness. Ultimately, I show that mathematics, like painting or music, requires consistent practice and learning through trial and error.
Continuous feedback is essential.
I collect feedback at the end of each class to monitor and adapt my instruction in real time. On most days, I use a simple 'minute paper' consisting of two or three brief questions, such as: What did you learn today? What topic needs further clarification? What would you like to see done differently in the next class? On the last day of each week, I ask a more comprehensive reflection question summarizing the key concepts learned. I also adjust prompts based on homework and quiz performance, incorporating targeted questions when I notice recurring mistakes. This allows students to reflect on their learning while giving me insight into their understanding. Reading responses helps me identify learning patterns and refine my teaching. I use the same approach in online courses, adapting the format to maintain engagement and continuity across modalities.
Encouraging peer discussions is a technique I have developed gradually, using different strategies depending on the course modality.
In person, large groups often form naturally; for example, in one calculus class, a group of eight regularly clustered together. I observed that learning in such large groups is less effective than in smaller groups of two or three. To promote balanced and productive groups, I use a simple strategy on the first day: I give each student a sheet in one of four colors and ask them to form groups of 3–4 so that each group includes members with different colors. This ensures diversity within groups while still allowing flexibility to adjust based on dynamics and student needs. When I do not use this method and notice a student struggling, I initiate a math problem discussion to help them integrate smoothly. Online, I have more control over group formation through breakout rooms. By the end of the first or second session, I typically have a strong sense of students' strengths and dynamics, which enables me to create a well-balanced group. I intentionally include at least one student in each group who is comfortable taking the initiative. To keep discussions engaging, I encourage students to keep their cameras and microphones on and make use of Microsoft Whiteboard, with a dedicated board for each group to collaborate and share their work in real time.
Continuous checkup on each student.
Regardless of the modality, I always arrive 15 minutes early to the class and stay until every student has left. This practice creates a low-pressure space and more opportunities for students, especially those who are shy or hesitant to reach out to me with questions and concerns. I continually monitor each student's progress, including any unusual behavior such as missing classes, falling behind, or failing to submit work. One time, in calculus III, I had a high-performing student submitting incomplete quiz work. After contacting the student, I learned that she is a single parent juggling multiple responsibilities. This experience reminded me of the importance of flexibility. In such situations, I prepare alternative make-up exams or supplemental projects so students still have a fair opportunity to succeed.
No one is left behind.
Mathematics is a logically demanding subject; some students want to pursue it out of passion, while some take it only because they have to. In a classroom with such a variety, my end goal is to support both groups. I always help the hesitant to see the relevance and beauty of math, and challenge the advanced to push their boundaries even further. At the end, both categories are pushing their boundaries, though they may be doing so at different levels and in various ways.