Charlie, the tutor, and Max, the student, are working through trigonometry. They are covering a plethora of topics – including graphing sine, cosine, and tangent functions, tweaking them with dilations and shifts. There’s also differentiation, specifically the reverse chain rule, and also integration – working towards calculating the area between two trigonometric functions.

Charlie’s able to strike a balance between being confident, whilst avoiding condescension in his teaching. He has an ability to break down what initially seems like intimidating, complex problems into a manner that’s easy to follow. They work through the problems together, and if Max happens to make a mistake – Charlie quickly catches it, pointing it out with a polite correction. The enthusiasm is clear, it’s clear Charlie hasn’t simply just memorised the content and begrudgingly relays facts; he enjoys it.

Max is clearly a hardworking kind of student who puts in the effort. He listens carefully, asks questions when something isn’t clear, and applies himself to the problems they tackle. This is what makes tutoring sessions the most beneficial for the students. He has a few questions from his holiday homework, mostly about trig identities and integrating complex functions. Charlie walks him through the steps, making sure he understands not just the “how” but the “why.”

Despite the heavy amount of work that has to be gone through, they keep a steady pace, keeping it efficient but definitely not rushed to a point where information and understanding is lost. There’s an ease to the lesson. By the end of the session, Max seems more confident, his grasp on the material stronger. Math might be challenging, but the more you learn about it the more it seems like something worth figuring out.

Oliver Fletcher