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# Students Don’t Need Real-World Problems to Understand Maths’ Importance and Relevance

Studying maths allows us to unlock the universe, says Dougald Tidswell – so why on earth do we pretend it’s all about painting walls and scoring goals?

“Is it going to be a fun lesson, Sir?”

“It’s maths! It’s always fun!”

It cannot have escaped your attention, assuming that all the non-maths teachers are largely skipping this section, that our subject is not always the most popular with students. That’s a massive shame, because it’s definitely one of the most important ones they’ll study.

There are the well-documented financial advantages of meeting certain arbitrary grades at GCSE and at A Level, but for me, that’s not where the significance lies. The importance is the sheer power that is contained in the study of mathematics.

We are the curators of absolute truths. Our theorems have been proved, not beyond reasonable doubt, not based on a balance of probabilities, but explicitly and concretely proved.

No one is coming along to mention to Pythagoras that his triangle idea needs some adjustments; whereas the entire process of science is to test, refine and improve on its theories.

Hugely important theories, I agree, and we need to make sure we are singing their praises, whilst also pointing out the difference of theory vs theorem.

We are the defenders of logic, identifiers of logical fallacies, contradictions and tautologies, and we can enable our students to become critical thinkers, if we can get that seed to flourish.

We are the problem solvers, we show people how to strip a complex dilemma down to its components, understand how each component interacts with each of the others, and then build up to a solution, solutions or a whole family of solutions. You don’t get that with French.

### Useless examples

So why is it, that when confronted with the kryptonite question (you know the one, the one that every teacher dreads to hear – but the maths teacher in particular), “But when am I actually going to use this?”, we so often forget to extol the virtues of logic and problem solving, and instead scrabble to find a ‘real world scenario’.

Who are we fooling with these painfully artificial constructs?

Frankly, no one. Not even ourselves.

Ronaldo is not solving quadratic equations in his head to place that free kick where he wants it. The designers of a fountain probably did check that the water wasn’t going to extend beyond the fountain’s footprint – but look at your class.

You weren’t asked to find an obscure specialist job where this would be useful (let’s face it, you could have just said maths teacher), you were asked when they were going to use it.

Each time you reach for one of these constructs you run the risk of alienating your audience.

If area is useful because it will help you not overspend on paint when you’re decorating, then why bother with parallelograms, trapeziums, circles, sectors and all the various compound shapes – my walls aren’t those shapes.

Who decided maths had to have a direct usefulness anyway? Complex numbers are now essential for design and modelling of electronics, but they started as a plaything, a diversion.

### Unique power

Which is not to say that our subject doesn’t have directly applicable skills that everyone needs to develop. Skills that will absolutely enable young people to engage with the adult world in more productive and more effective ways.

Naturally, when studying percentages I want the class to grasp how taxation, inflation, pay rises, depreciation, interest (both paid and earned) work, else I am not equipping them properly for being able to manage their personal finances.

Estimation and rounding are vital skills, as is the ability to work with values in any form and perform the basic arithmetic operations with accuracy and speed.

But, for the rest, we should be waxing lyrical about the power of problem solving, logic and efficiency that is hard wired into our subject.

“When are you going to use logic and problem solving? Every single day of your life – and this is the only subject where you learn it.”

Dougald Tidswell is subject leader for mathematics at a Buckinghamshire Upper School.