**Getting help from the learners**

Too often we teachers think we know what is best, and if not, we know where to go to find out. We get professional development, observations and mentoring; we read books, blogs and tweets, and of course, we are the teachers, so we must know. But this week I had an opportunity to talk though an exam with a learner, after she had passed it, over a long cup of coffee far away from any learning environment, and she was able to give me a personal insight into how a different type of mind works, one that is not ‘naturally’ mathematical, which I guess mine is.

We’ve been working together to achieve the mathematical qualifications needed to become a teacher – first GCSE then the QTS test. The former was easy enough – there’s a wide enough spread on the curriculum for her visual and artistic talents to make up for some of her difficulty with number work. But the QTS test is mostly number, with a bit of statistics, and has constraints that a long GCSE paper doesn’t have. These are the mental test, with a few seconds to answer each question, and the second section which varies between the deceptively simple (‘can it really be that easy?’) type to the longer, wordy ones that may suggest a very clever question but can give any of us a feeling of ‘What!’ My approach was problem oriented, using the sample tests and similar questions I created, and we’d go through each type with regularity and diligence. Any real issues I’d return to with alternative approaches. For example, for averages I printed items of data on single cards – ‘Show me five cards with a mean of six; show me five cards with a medium of six and a range of eight’. (Averages) All ideas cheerfully copied from ideas in John Holt’s book ‘How Children Fail’, which should still be required reading for all teachers. When we struggled with fractional equivalents, including decimals and percentages, I produced visual images that included diagrams and numbers, which my learner stuck around her bedroom walls. PostersVisual Displays And I bought a set of Cuisenaire rods, which were well worth the small investment. But for things like currency conversion, and using speed/distance/time ratios, how does one do that practically in a classroom?

My normal approach with complex arithmetic problems is to work with simple cases. For average speed problems for example I encourage the learner to consider simple cases – if I drive at 40 miles per hour, how far will I go in three hours, or cycling at 8 mph, how long will it take me to travel 20 miles? For currency conversion, how many euros will I get for two pounds, three pounds, two hundred and fifty pounds? All slow and I assumed effective. But when the learner is faced with such problems in a test, does she have the time or skills to think ‘What did Colin do for that?’ or ‘Can I make it simpler?’. Certainly not in the QTS tests, when time is a premium, and I’m beginning to doubt if learners do in any exam. They have been encouraged to get down an answer, and too often this can be any answer. This week I have encountered a learner entirely happy with his own wrong methods, and almost every week I meet one who says, erroneously, ‘That’s what I’ve been taught!’ Not the mind-set that encourages thoughtful reflection in an exam, and there again, exams aren’t designed for reflection. So I keep making up questions, and saving them for future use. Conversions.

And now my aspiring teacher has given me some great tips, and ones well worth remembering. In all of the things for which instant recall of knowledge is required, the learner needs to have the ability to bring it straight to mind. Flash cards worked for us, providing drill and repetition. It hurts me to say it, but for some, if not most, learners it seems drill has an important role to play. It especially applies to number bonds. I really didn’t know my times-tables thoroughly until I became a teacher – I could go through the pattern of any table quickly enough, and correctly, to satisfy my needs. But I’m a mathematical person; is that any help to one who isn’t? Not just multiplication – learners need addition bonds, and secure ones on which they can build more complex additions, along with strategies to do that, and subtraction methods such as ‘shopkeeper’s addition’.

Finally, there is the issue of getting the brain stimulated and using as much of it as we can. Recent evidence shows the usefulness of playing a musical instrument to get those connections going. Another learner of mine is about to receive intensive help for dyslexia that includes playing with soft balls and using modelling clay. This learner practised tracing with her left hand what her right hand was doing. Don’t neglect the physical side of the brain; it all helps to get it going in top form. Perhaps a little session juggling three balls – an easy enough skill if taught properly. Use what the learner has, and encourage other things too. Often my individuals are artists, so encourage creativity and imagination. Don’t provide all the methods and solutions, let the learner come up with examples and ideas.

So I’ll be making some more flash cards, for use with individuals and whole groups. With a big group, they can play in pairs and groups – learners don’t need a teacher to direct every activity. But get things moving, and keep a kinaesthetic element in every lesson, if possible related to the topic in hand, but if not, remember that distributed practice is a hot topic of the moment, so use a topic from a different part of the syllabus if necessary. And keep testing the questions that are likely to come up, because that is the other method receiving current attention ‘Improving Students’ Learning.’

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