‘You are teaching a group of low-attaining Year 10 students how to solve equations with unknowns on both sides. One of them calls out, “What’s the point in doing this? I’m never going to need to solve equations.” How do you respond?’

I’ve interviewed a lot of potential maths teachers over the years and, for me, this was an important question. One answer I would always look out for was something along the lines of, ‘Because it’s on your exam’. Whilst undoubtedly true, I firmly believe that such a response does little to convince or motivate students. Moreover, it is a missed opportunity and one which betrays a belief system that runs counter to those which were being fostered in the schools I was working in at the time.

As teachers of mathematics, we should expect to hear such questions from students many times in our careers. I would always advise any trainee teachers in my department to have an immediate and convincing answer ready for any question of this type. While there could be many good answers, my own response is based on the same template whatever the mathematical topic being taught:

There are four reasons why we teach mathematics. Firstly, there is a rich history and culture behind the mathematics which has underpinned the development of modern civilisation. As a truly global endeavour it is perhaps the greatest example of what can be achieved through real inclusivity. The Babylonians gave us 360 degrees in a full turn. What we, perhaps unhelpfully, refer to as Pascal’s Triangle is a pattern first recorded in the work of Chinese mathematicians. It was Fibonacci’s travels that led to his introduction – to the western world – of the Hindu-Arabic numerals that we use today. Muhammad ibn Musa al-Khwarizmi, an Iranian mathematician based in Baghdad 1200 years ago, is known as the Father of Algebra for his development of algebraic methods, and for giving us the anglicised words algebra (al-jabr) and algorithm (al-Khwarizmi). The concept of zero first arose in the Mesopotamian civilisation 5000 years ago before a patchy placeholder history resulted in its introduction as a number in India 3600 years later. It was only comparatively recently that European mathematicians accelerated the rate of progress in mathematics with advances in calculus, coordinate geometry and probability – to name just a few. It would be wrong if this was not passed on from one generation to the next. I can accept the fact that this might not inspire you personally, but I’d like you to accept that this is an important reason for learning mathematics.

Second reason: I am not going to pretend that you will all need to solve equations* when you leave school. Not everything will need to be used by everybody, but everything will be used by somebody. We just don’t know what the future will bring, and we don’t know all of the careers that will be available to you. It is not so long ago that the roles of ‘data scientist’ and ‘vertical farmer’ were hypothetical and joked about, yet today these jobs exist. Therefore, I could be failing you if I did not teach you how to solve equations*. I can accept the fact that you might never need to solve an equation* once you leave school, but I’d like you to accept that this is a reason for learning to do so.

Thirdly, some people just like doing mathematics. In fact, quite a lot of people just like doing mathematics. Have you ever experienced that warm feeling in your stomach when you’ve solved a mathematical problem? And it’s not just those who are typically seen as ‘good at maths’ that feel this way. The sensation that results from resolving a problem, often achieving a definite and correct answer, is good for the soul and is open to all. I don’t want to take that opportunity away from anyone. OK, I can accept that this reason might not ‘do it for you’, but I’d like you to accept that there are many people who do feel that way and that it is good for them.

Finally, doing mathematics develops your brain in a unique and special way. By solving equations* you are developing your mind in a way you just can’t do in any other subject; you are becoming a logical thinker, a creative problem-solver, an analyser. It is not necessarily what you are learning that is important, it is what you are doing to your brain by learning it. No other training will increase these capabilities in the same way. This is why mathematics is a core subject, this is why the importance of mathematics is recognised around the world, this is the one reason that stands above all others in terms of its relevance to everyone. And this is why you are learning to solve equations*.

I have used this response in the classroom on countless occasions, but also with parents and with teachers from other departments when appropriate. It is no exaggeration to say that not a single person has ever pushed back on it. Mostly, people appear convinced, although I suppose some could just decide not to ask the question again once they hear how involved the answer is! For it, I have to thank my own PGCE tutor who tackled this in our very first subject session on 9th October 1996 (I still have the notes). Now that I am an ITE tutor myself I make sure that I pass it on to the next generation.

* replace with your chosen mathematical skill