Last week, I posted an innocuous-looking question on Twitter:

Maths teachers! Which topics in the curriculum do you find are most likely to get a response “when am I ever going to need to know this?”

— Alison Kiddle (@ajk_44) October 25, 2018

And a fascinating conversation followed, with loads of suggestions, as well as a meta-discussion about why this question gets asked. This seemed like a good opportunity to dust off my blog again, to gather together the ideas and add a few thoughts of my own.

Firstly then, the most straightforward answers were from teachers who actually did what I asked, and told me curriculum topics! This is particularly useful, because both in my work for NRICH and also my wider engagement with maths outreach, it’s good to reflect on what teenagers perceive as relevant and worth learning. Many people mentioned geometry, and particularly circle theorems. Other topics mentioned included trigonometry, surds, algebra, quadratic equations, Pythagoras’s Theorem, inequalities …

The general theme that emerged, which was picked up on by a couple of commentators, was that anything which was difficult and where it was not immediately obvious why it might be important prompted the “When am I gonna need to know this, Miss?” cry. (Or “Sir”, or a gender-neutral term of your choice.) Some people connected it with student attitude, others with level of confidence. Distracting Teacher by making them justify the choice of lesson material is a technique as old as the hills for a student who is unwilling or unable to engage with the topic at hand.

Another interesting type of response is illustrated nicely by Colin’s post:

Analysing the themes of Measure For Measure. Being able to identify a minor third. Knowledge of mediaeval agriculture systems. Names of parts of a cell. The départements of Ile-de-France and their numbers. Or is it just maths that’s supposed to have everyday use?

— Colin Beveridge (@icecolbeveridge) October 25, 2018

As I have never had the good fortune to teach anything other than Maths, I can only assume that teachers of other subjects DO hear the same plaintive cry. Certainly I know my head is still full of half-remembered facts from humanities lessons that I rarely use in my day-to-day life unless I’m solving a general knowledge crossword or entering a pub quiz.

This brings us nicely on to the question of why we teach, why we choose to include certain topics into the curriculum. At least some of the role of education is to turn out well-rounded young people with a decent grasp of the world around them and their place in it. As far as the maths curriculum is concerned, I want students to have a sense of what mathematics is all about, the way in which different mathematical topics link together, the way in which mathematical knowledge and proof is different from the way things are done in other academic subjects, and yet the way in which it fits into and supports other disciplines, particularly science, technology and engineering.

This comment sums up one of the real challenges that faces us as maths teachers:

The problem isn’t the content per se in my opinion but the schizophrenic nature of the GCSE. It is both the entry to further study for some who question all this boring numeracy and others who are ending their mathematics here who question the need for all the abstract algebra.

— theperfectlanguage (@theperfectlang1) October 26, 2018

At least some of the “When am I ever going to need to know it” content is there because some students WILL need to know it someday. And there’s no way of telling at age 11, or 14, or even 16, which students are which. Sure, you get people like me who knew from upper primary school that I probably wanted to do a maths degree someday, but you also get the kid who isn’t bothered about maths until they suddenly find the spark, the part that brings it alive for them, because of their hobby or their dream job or something that requires them to use trigonometry, or statistical analysis, or circle theorems…

I don’t really have any answers for teachers who want a ready reckoner of places where maths is used in the Real World so they can give a glib response every time this question comes up. What I would recommend is for all of us to encourage engagement with maths for its own sake, the beauty of number patterns, the elegance of geometrical reasoning, the stories of people who find maths a joyful experience, so that even if students aren’t ready yet to feel that joy for themselves, they are aware of it as a possibility. When am I ever going to need to know this miss? Well maybe you won’t NEED it, but you might WANT to know it, you might ENJOY learning it. And you might surprise yourself and find that you are actually better at it than you thought.

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