Every student learns maths differently. Some students find it easier to have questions broken down step by step in a formulaic way, while others grasp concepts better through patterns and intuition. In a recent tutoring session, I was reminded of just how important it is to adapt to a student’s learning style.
My student was struggling with trigonometry, particularly understanding sine and cosine beyond just plugging numbers into equations. At first, I explained the unit circle in a structured way, defining angles, coordinates, and key values. However, even as my student said that they understood, I noticed that when trying to apply the knowledge to new problems on their own, they were not able to use the concepts.
So, I shifted my approach. Instead of numbers and formulas, I took a different approach. By explaining, it as a wave in a more graphical form, my student quickly was able to grasp the new concepts and after some practice, was able to apply it to new problems.
Furthermore, once he visualized the concept, the equations made more sense. We then graphed sine and cosine together, reinforcing the connection. By the end of the session, he wasn’t just solving problems—he was predicting patterns before even using his calculator.
This session was a reminder that maths isn’t just about numbers; it’s about seeing connections. Some students need real-world analogies, others need visual aids, and some learn best in a purely formulaic way. No one way is incorrect, they are all paths to the same solution. A good tutor doesn’t just teach a topic—they find the right language for each student’s mind.
In the end, the best teaching isn’t about making students memorize facts. It’s about making them see maths in a way that feels natural to them. Once that happens, the numbers start to make sense on their own.

Samuel Lotter