Maths - Knowledge snowballs

11th May 2012 at 01:00
Working it out for themselves - an avalanche of enlightenment

"Man gave names to all the animals," Bob Dylan once sang - a reference to Adam's creativity in Genesis. Naming was one of the first skills he required, coming in a whisker after listening and gardening. And in the classroom, we maths teachers need to be able to name phenomena.

I came across the wonderful word "lubbing" the other day, short for "looking up in the back of the book". In a maths classroom especially, this is an activity that deserves a name. "Lubbing" for me carries connotations of "lubrication", which judicious use of the answers can certainly provide. The word also contains a touch of "landlubber" - someone too cautious, perhaps, to set out alone on their own mathematical ocean.

Words can suggest extended metaphors, can become resonant labels that we share with others, and can be gathering points for discussion.

In my classroom, I'm fond of the "avalanche". Let me explain. A pupil calls me over, and I think I can see a key weakness in their argument. Often (preferably), it needs no word from me, just a subtle indication. Then comes the "Aaahh!" moment.

Should the teacher stay and help in the reconstruction that must follow? Surely it is better to let the pupil reconstruct for themselves, while the teacher heads off to the next raised arm.

I call the "Aaahh!" moment "an avalanche" - an overwhelming influx, my dictionary says. "Avalanche" comes from avaler - Old French for "to descend" - and that fits, too. The solution has somehow "got above itself". "Avalanche" can also be a verb - the teacher "avalanches" the problem for the pupil to produce that precious "Aaahh!"

What else does my dictionary tell me? An "avalanche" is a shower of particles produced after a high-energy particle meets matter - the result of an impact produced by something tiny, but extremely intense. So the teacher who wants to avalanche effectively must aim their "particle" carefully; the greater the precision and focus, the wider the shower produced.

Is my naming here fanciful, trite - grandiose, even? Is the phenomenon it notices so quotidian as to be unworthy of the honour? Maybe if we noticed the everyday more and accorded it greater respect, we would reap surprising rewards. We should all, perhaps, aspire to follow the physiologist Albert Szent-Gyorgyi, who said: "Discovery consists of seeing what everybody has seen, and thinking what nobody has thought."

Jonny Griffiths teaches maths at a sixth-form college

In the forums

In the TES Maths forum there's an interesting debate on GCSE pass marks and whether or not they're fair. Why not join the discussion?

And if you want to make the most of iPads in the classroom, check out the thread on their practical uses.

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