“But when am I actually going to use this?”
It’s a question that teachers of any subject will hear from time to time. But if you’re a maths teacher, you’ll likely hear it a lot.
Sometimes the answer is easy. You might tell a student, for example, that being able to work out percentage decreases is helpful for when there is a sale on in a shop, or that knowing how to perform calculations with decimals will make them more confident working with money.
On other occasions, finding a real-life context to apply to the current learning is a bit more of a stretch: “Perhaps one day you’ll cut down a tree, and you’ll need to use Pythagoras’ Theorem to do it.”
The fact is that, for most of the students, a lot of the maths they learn at GCSE will not be essential in their day-to-day lives. Other than teaching these to students, I have never needed to use circle theorems, vectors or the quadratic formula.
Showing how maths fits together
That’s not to say that we shouldn’t be teaching students about vectors, but that we need to be honest with them about the scope of this learning. And this doesn’t mean simply telling them that they will need to know it for their exam. So, what should we be telling them instead?
Let us tell students that we are learning about circle theorems to improve our understanding of how mathematics fits together, and to improve our logical thinking, problem solving and systematic approaches to tasks.
Telling them this isn’t enough, though; we also need to find ways to demonstrate it.
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One option here is to plan “goal-free” tasks. For example, let’s take a maths lesson on introductory angle facts, which looks at angles on a straight line, around a point and in a triangle. Once students have been explicitly taught about angles in each of these contexts, the teacher could set them an exploratory task to find as many angles in a shape as possible, without a specific target answer in mind.
This gives students an opportunity to see how much they can work out for themselves - and demonstrates how their newly developed skills support their ability to problem solve.
Another option is to plan activities that draw together a range of topics and problems, to show students how they have developed their mathematical thinking and how it all groups together. For example, “odd one out” tasks provide opportunities for students to spend time discussing similarities and differences while seeing how their knowledge interconnects.
“Let’s stop trying to force real-life contexts into every topic”
For this to work, teachers will need to plan for student success. In order for students to appreciate how their logical thinking and problem solving is developing, they need to feel they are being successful in these tasks. It may even be worth providing them with tasks that are slightly less academically challenging initially, to make sure that the focus is on the skills they are building.
Of course, there are plenty of topics in maths that will help students in their day-to-day lives, but there is also a significant amount of content that they won’t need to survive in the “real world”.
So, let’s stop trying to force real-life contexts into every topic, such as applying Pythagoras to cutting down a tree, or talking about tessellation in relation to tiling a bathroom. To suggest that learning is only worthwhile if it has a practical everyday application misses the point of having a well-rounded education.
The next time a student asks you why you are studying a particular topic, just be honest with them. I think you’ll be surprised by their response.
Nathan Burns is a head of maths and author of Inspiring Deep Learning with Metacognition. He tweets @MrMetacognition
