I must have been a dreadful pupil to teach. I remember being asked to complete some exercises from a textbook in a GCSE maths lesson, and complaining about the context of the questions. "Miss, I'm not being funny, but if a hedgehog can estimate the height of a lamppost that accurately, how come he can't just estimate the width of the road? Or, at least, why can't he do the trigonometry?"
The problem is, now I'm on the other side of the textbook, I'm constantly aware of that little "Using and Applying" section tucked away inside the national curriculum folder, not to mention those boxes on the lovely, wordy new Assessing Pupil Progress sheets. To attain level 5, pupils have to be able to draw conclusions and "give an explanation of their reasoning".
I've tried that. Giving an explanation usually seems to result in statements from my pupils like "I just solved it in my head" or "I worked with my partner and then we worked it out". My own particular favourite was "I just got lucky".
I'm fine with setting word problems. And money problems: they're easy. But using and applying geometrical knowledge? Sometimes I assure myself that I could just make up my own problems, but that's when I end up in dubious hedgehog territory. I blame the real-lifers. At some point we got fixated on the idea of maths problems being linked to real life, and we've been stretching the definition of "real" ever since.
Mixing pots of paint in different ratios, trains running in opposite directions, tessellating floor tiles and sharing pizzas out equally are things that few of us deal with in "real life". But who said maths had to be real? Surely some of the most interesting things that happen with mathematics these days are pushing the boundaries of reality?
I remember from my training that all maths problem-solving falls into one of five categories labelled A-E: Actual, Believable, Curious, Dubious and Educational. Actual problems for 10-year-olds to solve are rare, and Believable ones are pretty hard to come by. The Dubious but Educational hedgehog presents his own problems, but the Curious ones are what get us interested. Thankfully, these we don't have to think of, because someone else has done all the hard work for us.
The enriching maths team at the NRICH project has created hundreds of problems for every topic and every key stage, with enough curiosity to kill a whole cattery. http:nrich.maths.org
Michael Tidd teaches Year 7 at a primary school in West Sussex
Visit the Nrich profile on TES Resources to try out the project's resources.
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