Math Art Project Reflection

 How did our math art project come to life?

Our group - Manveen, Caris, Krystal, and I - recreated Holly Laws's "Trefoil Knot" using clay and discussed Knot Theory as a branch of topology in our presentation. We introduced key concepts like knot invariants and tricolorability. Knot invariants remain topologically equivalent through simple transformations such as stretching, bending, twisting, or shrinking. Tricolorability, a tool for identifying these invariants, refers to the ability of a knot to be coloured with three distinct colours, where each uninterrupted chain is one colour, and each intersection has either all three or just one colour. In our model, one side demonstrated tricolorability, while the other side reflected Holly Laws’s original choice of colours and materials. Additionally, we highlighted the cultural, scientific, and everyday significance of knots, noting how knot theory models DNA replication, helping visualize and predict the complex topological structures of DNA. ​​Moreover, to pique further interest, we talked about the importance of Knot Theory in understanding the behaviours of various diseases related to protein aggregation such as Alzheimers, as well as, knots in higher dimensions.

​​As part of our activity, we provided clay and strings for classmates to create their own trefoil knots, challenging them to explore transformations that preserve topological equivalence. This hands-on approach deepened our understanding and reinforced the value of incorporating interactive activities into classroom teaching to help students grasp abstract concepts. 

How did I feel making the project?

Our group delegated tasks, and I was responsible for gathering materials for creating the trefoil knot. Initially, I didn’t anticipate that buying the materials would be challenging, assuming it was as simple as walking into a store and picking up what we needed: air-dry clay, bracelet beads, and string. Because of this, I postponed the task while focusing on other coursework. The day before our group was scheduled to meet and create the trefoil, I went to Staples, only to discover that the air-dry clay was out of stock. I quickly headed to another stationery store and found an alternative clay, though it was a different color. I then visited the Dollarama on Granville (closer to where I live) to find beads, but unfortunately, the ones I found were not aesthetically pleasing. This led me to visit the Dollarama in Gastown, where I finally found suitable beads. By the time I finished all the shopping, I was running late for my inquiry class and had to take an Uber instead of the bus. Thankfully, I managed to have everything ready for our group on time without causing any delays.

From this experience, I learned that as a teacher, no task is simple. Even something as seemingly straightforward as buying project materials took extra time, money, and added stress. Teachers have many responsibilities—class preparation, grading, providing feedback to students—all of which demand effective time management. I realized that this is a skill I need to continue developing, as time is truly of the essence for teachers.

Takeaway I can use as a teacher in my own classroom 

The biggest takeaway from this project is the importance of encouraging students to contribute their own knowledge to their environment. For our math art presentation, one of my responsibilities was to introduce knot theory. I felt confident taking on this role because I had previously taken a course on the topic at UBC (MATH 309: Introduction to Knot Theory with Professor Liam Watson). Motivated and excited to share what I had learned, I was able to compile interesting information and deliver a mini crash course to my colleagues, many of whom were encountering the concept for the first time.

Presenting is something I’ve always put a lot of effort into, sometimes finding it challenging. However, with the background knowledge I had, this time I thoroughly enjoyed creating the presentation slides and found ways to make my delivery more engaging. As an added bonus, I even deepened my understanding of knot theory!

This experience has shown me the value of "reverse teaching" in the classroom. Often, when students learn a math concept, they memorize how it works, then move on. Allowing them to teach what they've learned to their peers—through methods like peer tutoring—can enhance their understanding, activate relational learning, and improve long-term retention.