Suppose my head of department were to ask me the following question: “Is it better to teach for understanding, or to teach to the test?” I would answer, with some indignation, that – while it is not a binary choice – I would always opt for the former.
What keeps me awake at night is the knowledge that sometimes I sacrifice my principles. The exact same principles I would defend so passionately if questioned by my head of department.
I entered the teaching profession keen to share my passion for mathematics. But I lacked the necessary skills, or even an idea of what good mathematics teaching looked like, given what I had experienced as a student.
My passion for teaching was eroded
My passion was eroded until gradually, and almost without realising, I would find myself saying: “And this is not how it will look on the GCSE – it will look like this,” or “In your GCSE, make sure you write this,” or “You don’t need to know this bit, so I won’t teach it,” or worse: “We won’t look at how this develops as it’s not currently in the exam specification.”
I used to justify my approach early in my career as: “I’ll get these students a C by drilling them on methods, and at least I’m setting them up for the real world with a decent maths grade for their CV or job applications.”
Only now, in my sixth year of teaching, am I beginning to understand and visualise (but by no means master) the necessary pedagogical approaches for developing proper mathematical insight.
When planning a sequence of lessons, I always set out to achieve proper understanding of a concept. What I am faced with as a teacher is a system that constantly seeks to undermine this. The greatest obstruction to developing understanding is time. Deep understanding, achieved as a result of an intensive process, takes a great deal of time to orchestrate. Teaching 21 periods a week, along with all the admin and data requirements, seriously tests this commitment to developing understanding.
Another barrier to developing understanding manifests itself in my students’ preconceptions of mathematics: “Sir, can you just get on with it?" "What’s the minimum I need to remember?” If this (horrifying) view of mathematics has been left to fester through key stage 2 and key stage 3, how can I change it – even with all the will in the world – in four hours a week at key stage 4?
I regularly find myself having to strike an uncomfortable balance between teaching for understanding and securing nationally recognised outcomes for my students. Are the two mutually exclusive? I will spend the rest of my career as a teacher trying to find the answer.
The author is a secondary maths teacher