Or noticed your child having one of those “Aha” moments?

I’d love to hear your story in the comments!

You can think of puzzles and games as the sugar that helps the medicine to down, and you’re at least a bit healthier in your approach to math. But even better than sugar and nasty medicine is food that’s delicious enough to take away our craving for sugar and nutritious enough to take away any need for medicine. In the same way, good problems can help us fall in love with math and make a delicious meal of it, sinking our teeth into tough problems, tenderized by their intrigue.
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Most people like games, so that’s an easy place to begin. At first, the games can be the sweetness that helps the math medicine go down. Over time perhaps you can find the sweetness in the math itself — in a problem that inspires you to work and struggle, until you finally get it, just for your own satisfaction.

Learning math is more like taking a meandering nature walk than like climbing a ladder of one-topic-after-another. Kids need to wander around the concepts, notice things, wonder about them, and enjoy the journey.

“When I began my college education, I still had many doubts about whether I was good enough for mathematics. Then a colleague said the decisive words to me: it is not that I am worthy to occupy myself with mathematics, but rather that mathematics is worthy for one to occupy oneself with.”

I would like to win over those who consider mathematics useful, but colourless and dry — a necessary evil…

No other field can offer, to such an extent as mathematics, the joy of discovery, which is perhaps the greatest human joy.

The schoolchildren that I have taught in the past were always attuned to this, and so I have also learned much from them.

It never would have occurred to me, for instance, to talk about the Euclidean Algorithm in a class with twelve-year-old girls, but my students led me to do it.

I would like to recount this lesson.

What we were busy with was that I would name two numbers, and the students would figure out their greatest common divisor. For small numbers this went quickly. Gradually, I named larger and larger numbers so that the students would experience difficulty and would want to have a procedure.

I thought that the procedure would be factorization into primes.

They had still easily figured out the greatest common divisor of 60 and 48: “Twelve!”

But a girl remarked: “Well, that’s just the same as the difference of 60 and 48.”

“That’s a coincidence,” I said and wanted to go on.

But they would not let me go on: “Please name us numbers where it isn’t like that.”

“Fine. 60 and 36 also have 12 as their greatest common divisor, and their difference is 24.”

Another interruption: “Here the difference is twice as big as the greatest common divisor.”

“All right, if this will satisfy all of you, it is in fact no coincidence: the difference of two numbers is always divisible by all their common divisors. And so is their sum.”

Certainly that needed to be stated in full, but having done so, I really did want to move on.

However, I still could not do that.

A girl asked: “Couldn’t they discover a procedure to find the greatest common divisor just from that?”

They certainly could! But that is precisely the basic idea behind the Euclidean Algorithm!

So I abandoned my plan and went the way that my students led me.

“In 2018, I want to change the world.
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I want to make it possible for more children to claim math as their favorite subject.
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Math is how we describe our world when words are not enough. Everyone deserves to speak math and to play math, to enjoy its beauty and its power.”

If you have some time to spend pondering big ideas, dig into Devlin’s entire series of posts about what real-world mathematics looks like and the implications for math education:

“Make no mistake about it, acquiring that modern-day mathematical skillset definitely requires spending time carrying out the various procedures. Your child or children will still spend time ‘doing math’ in the way you remember.

“But whereas the focus used to be on mastering the skills with the goal of carrying out the procedures accurately — something that, thanks to the learning capacity of the human brain, could be achieved without deep, conceptual understanding — the focus today is on that conceptual understanding.

“That is a very different goal, and quite frankly a much more difficult one to reach.”