On a few separate occasions over the last couple of weeks, I have asked groups of teachers 'what does a good maths lesson look like?'

A very common response was that the kids get everything right.

This is so sad.

Mathematics is not about wading through question after question of the same old tedium – effectively repeating what some teacher has just spent 10 minutes showing on the board. Jesus.

Mathematics is about discovery. It is creative. It should take real thought.

Above all, mathematics should not be straightforward. The joy of the discipline is that it takes huge amounts of creativity and inspiration. Mathematics should be about overcoming apparently insurmountable problems. That's where the learning of mathematics happens. Through the struggle, the connections, the inventiveness.

Drill has a place. Most certainly. But they are not the good lessons.

The good lessons are the ones that make kids struggle, where they have to dredge up long forgotten knowledge and create new ways of working, new ways of seeing a situation.

The response from these teachers that kids should get things right also makes me worry about the subject knowledge of the profession. Where are all the mathematicians?

When I was a mathematical modeller, my colleagues and I would spend weeks, months, maybe years on a single problem. Struggling. Fighting. Getting within tasting distance and then having it all fall away.

It is through the rigour that complex problems demand, that mathematical learning becomes rich and lasting.

So a plea to mathematics teachers everywhere: don't design lessons for kids to get everything right, design lessons that stretch their minds and their understanding of the beautiful field of mathematics.

There are simple, practical ways in which to achieve this. Instead of demonstrating and then asking kids to repeat, ask them to prove from first principles. Instead of asking kids to remember some division facts, get them to prove it always holds. Instead of lists and lists of repetitive questions, get one meaty question and let the kids have 3-4 weeks fighting with it. The mathematics will come. Trust the nature of how mathematics arises.

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