When all is said and done - as I have made clear in this Blog, maths is more a game of writing, than counting. Write it in way that tallies with your eyes, and your expectations, and it is clear and easy - but if you do not you have not got a hope.
Yesterday's lessons were a classic example.
Yesterday's three separate sessions (with maniac drives between in the devon-county dark, with famers harvesting, and forcing me and the transit to reverse half a mile, in the dark....But that aside), illustrate this point very well.
Each of the pupils I saw I taught caught a different aspect of this problem. The first, who was sitting an exam for a second time, in the hope of firming up a C into a B, is in an exam where one needs to experiment greatly with numbers- and hates it. For him maths is all about getting the answer done (a reasonable proposition - unfortunately one not shared by AQA linker maths GCSE). For AQA numbers are about play and experimentation. The Examiners want you to pull out formulas which you have never seen, and things you do not know from the maths you do know. To do this one simply has to write down the formulas, and then pull them around, again and again until one gets the answer. It takes a lot of trust, but also a lot of confidence in the fact that one is writing it down right and well. If one does not have either the show cannot get going. The problem for this pupil is, as is so often the case, he does most of this maths on My Maths and no one has ever (well apart from me), really worried him about the writing down of equation (I have always thought he has been taught them by his school in a way to make them easy at the simple level, but so much harder at the level he is now on). The result is that he will not even start to play. He sees what I have done, but cannot get going himself. What I will do is attempt of the weeks to persuade to starting on the pretext that he 'might get a method mark if he always does this...' - only once we have got going do I think he will turn round and suddenly get it!
The second pupil (three tractor reverses away), is younger and had another version of the same problem. For her it is all about narratives. She understands (although does not belief she understands) the individual calculation quite well. But what she cannot do is tell a story with the figures - and unfortunately she is in an exam (Linear Edxcel GCSE ) which loves its stories. One does not therefore only need to count, but also describe in figures, and keep the narrative going. In teaching her therefore I am still very much trying to explain to her what she cannot do - because she does not really know. What she thinks is that she cannot DO MATHS, what I think though, is that she cannot make maths tell stories.... Once this become clearer to her (and we will need to do a little more method work I think to make it so), then I am optimistic she will be fine, if I can get her through the collywobbles that far.
My final lesson (another long drive to the coast though back lanes away), same problem, but again in another setting. This one was a pupil half way through a foundation GCSE exam. She had done one exam yesterday (and was very confident), but had others to do. What she lacks, again is the basic ability to know where to being in any question if it is at all complex. She can do perfectly well short questions, but does not want to try longer ones. My break though with her (she is a dancer) was to persuade her that maths is just another performance (which it is). To understand the kind of wordy questions she is having to do in her GCSE exam one needs to role play! That is one needs to pretend the numbers make sense and are about ones own life, and not merely a faceless set of nothings. It was this basic move that made the difference I think for her. It made the numbers feel like something, and do so even when they do not make sense (and actually her mental maths is a little weak). Once she gets the part, she understands the problem, and how to write it down.
Three very different pupils, three different solutions, and yet one real problem, Modern GCSE is a game of reading and writing in a weird way - and one needs to be endless creativity to teach that oddity.
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