We celebrate the recent publication of Upper School Mathematics Department Brian Choi’s scholarly article “Trigonometric Ratios and Measures of Angles–A Historical, Cultural and Pedagogical Viewpoint,” published by Hong Kong’s Education Bureau, Rate, Ratio and Proportion. A recent and wonderful addition to the Upper School math team, Choi’s work explores the development of trigonometry through the lenses of historical mathematics, culture of ancient civilizations, and teaching practice. The piece, he writes, offers fresh insight into how mathematics can be taught in ways that are meaningful and relevant to students—while other articles in the booklet are written in Chinese, Choi’s article is the only one in English. Please enjoy his reflection on his latest publication and his approach to teaching mathematics—one rooted in sparking curiosity and connecting math to other academic disciplines to enrich the learning experience for all students. You may find the full publication (pages 37-49 in English) here.

by Brian Choi

From Theory to Practice

At the heart of the article is a simple but powerful question: How can understanding the historical and cultural roots of mathematics help students learn better? Instead of focusing purely on formulas and memorization, the article invites both teachers and students to engage with the why behind mathematical concepts. For instance, early civilizations developed trigonometry to solve practical problems such as measuring the distance between stars, an idea that brings the subject vividly to life in the classroom.

Coincidentally, the first unit of Precalculus at Poly is trigonometry. This alignment provided an ideal opportunity to introduce these historical perspectives to students. In class, the discussion expanded beyond textbook problems to include visual and physical demonstrations. One moment that stood out was when I asked a few students (most of whom are taller than me) to stand up and demonstrate the angle of elevation and angle of depression. Suddenly, abstract terms became real people, and we could all see the math in motion.

The exploration didn’t stop there. When a student pointed out that a diagram was missing a right angle in a building illustration, the class launched into a conversation about real-world structures. Ultimately, it led to the Leaning Tower of Pisa, a historical structure that challenges our assumptions about vertical lines. It was a perfect example of how students can connect mathematical reasoning to cultural and historical knowledge.

A Lifelong Commitment to Educational Philosophy

Prior to joining Poly, I taught in a high school in Hong Kong for over a decade and was deeply involved in teacher training and curriculum development. Encouraged by an academic advisor in college, I joined the History and Pedagogy of Mathematics study group organized by the Education Bureau in Hong Kong (equivalent to the Department of Education in New York), and have since delivered over 20 seminars and published regularly on the integration of educational philosophy with classroom practice.

I have always believed that mathematics should be more than numbers and equations. It should spark curiosity and help students connect dots across disciplines. Whether through history, art, or architecture, mathematics has always been a part of human culture. That’s a story worth telling in the classroom.

Looking Ahead

Now in my first year at Poly, I am eager to continue exploring new ways to make math meaningful and relevant for students. Poly students have an incredible thirst for knowledge, and that creates a wonderful environment to bring theory into practice. 

With more collaboration and shared learning, I hope to continue writing and contributing to the broader conversation around mathematics education, both here at Poly and beyond. In early 2026, a new article, co-written by my mentor and academic advisor Prof. Man Keung Siu and me, will be published. It is more ambitious than the present one, exploring a classical question by four different approaches, namely algebra, geometry, trigonometry, and calculus.