Returning to the classroom to teach maths after several years away was never going to be easy. I recall my first lesson and the first pupil I tried to help. We were using the Smile system of workcards, and he had his hand up.
"Hello," I said. "So, what's the problem?" A face older than its years looked me up and down. He introduced himself as Alex. I was the latest in a string of teachers for this group: would I be any good? "I don't know how to make this bigger," he said.
The card involved picking a centre of enlargement for a shape and drawing lines through the corners to create the enlarged figure. I was battling with a sense of vertigo and could not make head nor tail of the question. My own school maths education had been traditional fare, all Euclid and no transformation geometry, a situation that my degree had done nothing to rectify.
"Er ..." I floundered. "Maybe if I did this?" offered Alex, having found a solution. "Yes, good idea," I muttered hopefully. "And I think that if you draw this line ..."
"No, look, it's this one," he replied. "It's all right, I've got it now."
I moved on to my next pupil and, as I turned, I heard Alex say wearily to his neighbour: "That's all we need - a thick teacher."
Twenty years on, I hope if I tried to help Alex I would be able to. But the memory raises the question: what happens if the pupil is brighter than the teacher? Must the relationship break down, or can that situation be turned around with a little skill into one that works well? My A-level maths groups are a mixed bunch. Yet I find myself teaching two or three pupils who are seriously bright, whose questions are excitingly perceptive and who will probably become more effective mathematicians than I am.
There are two types of brighter-than-the-teacher pupils. One looks at your equation on the board and says: "Don't you mean one over x cubed, Jonny?" The other will put it kindly: "Jonny, I like your equation but, I wonder, could it be improved slightly?"
The brighter-than-me but humble pupil is a joy to teach, the brighter-than-me but competitive pupil is harder work. But maybe there is a message there: do not try to outdo those who would overtake you. Instead, put your ego to one side and rejoice in your pupils' brighter-than-you-ness.
Jonny Griffiths teaches at Paston College in Norfolk
Visit Craig Barton's collection of resources for working with gifted and talented pupils. He has chosen his top 10.
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