Calculus by and for Young People

“So Don Cohen gets children excited about ideas of infinity. One of the activities he does with very young children is getting them to consider what happens if you add 1/2 to a 1/4 and then add on an 1/8 and 1/16 and a 1/32 and so on to infinity. He does this by getting people to imagine a square. Picture a square in your mind and imagine shading half of it. Then shade a quarter — a half of the bit that’s unshaded. Then you shade an eighth – again, a half of what’s unshaded. And then you shade a sixteenth, again you’re shaving a half of what’s unshaded. Quite quickly, even young children can get a sense that they can carry on shading half of what they’re left with forever. They’re filling up more and more of this square, but there’s always going to be a tiny bit left over. They get a sense that there might be this infinite process.Those are extraordinary ideas, I think. On one level quite counter-intuitive, but incredibly exciting and certainly I’ve worked with children of 9,10,11 on them, and there’s no way they can’t get their head around them.” Read more...

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Alf Coles, Social Scientist