Monthly Archives: June 2012

How to teach mathematics

There are a few rules to being a teacher, and most of them involve trying to avoid being the centre of attention; rules like never answering a question, and never doing anything yourself if one or more of your learners can do it for you, perhaps not so well as you think you can, but nevertheless, learn to let go.  Some of the difficult rules involve feedback; don’t tell the learner what they should have done, but lead them to a solution by asking questions – never forget Socrates, and if you have to be critical, as I do when giving formative feedback to budding teachers, suggest what they need to do to improve the assignment or write-up.  So when I find myself awfully critical of fellow professionals I find myself at the point of wanting to tell them what is wrong, and accepting I need to say what I might have done, or what I do do, which I think might be better.  Today is my first attempt at that, and I hope to continue with suggestions for teaching mathematics and the topics of the National Curriculum.

So what got me grumpy in the first place?  A number of posts on the TES twitter feed have led me to ‘superb’ resources that I found to be mind-numbingly boring.  The first time I replied, and got a nice response accepting my point, but I was told that young, new teachers loved ready-made materials that engaged learners in the classroom, and kept them busy and happy.  All very well, but has it anything to do with learning?  The latest one was described as ‘A very high quality substitution code breaker activity to help with algebra.’  No it isn’t.  A code breaker suggests some thought needed to break the code, not a set of simple calculations using letter substitution to reveal some ‘hidden’ message.  If you want the learner to break a code, make them do some work, make them think, not simple swapping of letters for numbers to find new letters to make a catch-phrase.

We need to go back and ask ourselves what we understand by algebra.  Or more appropriately, what does the National Curriculum understand by algebra?  I well remember the NC and the need for all children of all ages to ‘do’ algebra.  It was a complete disaster because primary school teachers, by and large, had no grasp of algebra themselves, and hence no idea how to teach it.  So in 1992 a task group was set up to review algebra teaching and I recall being part of that discussion.  Algebra, at all key stages, is about moving from the concrete to the abstract, for learners to make generalisations and to use symbols other than numerals to define mathematical relationships; to look for patterns, to describe and define those patterns, to tabulate patterns and to turn them into pictures using Cartesian co-ordinates, and to arrive at generalisations using symbols, usually letters.

If I get encouraged by the realisation that someone is reading this, and I hope someone does, I hope to continue and explain how I introduce adult learners to algebra.  I teach in FE, and have to cover the National Curriculum mathematics in less than eleven months, and nothing like the eleven years that school teachers have to develop the subject, so I don’t have time for mind-numbing tedium.  But I do have grown-ups who can be trusted to stay on task, and to bring their own experiences. So I’ll start with one simple example, and if it flies, I’ll develop it over the next few months.  My example is teaching a sculptor, a learner who needs to gain a GCSE in mathematics in order to commence a PGCE.  In a crash course in the month before her exam she asked me to explain a formula question on a past paper.  ‘What do you understand by a formula?’ I innocently asked.  She thought for a moment and replied  ‘Like A+B?’.  ‘No!’ I’m screaming inside, but keep that inside.  I looked around her studio (we were working at her place) and saw the model she is working on for the Wedgewood company.  ‘How do you price a sculpture?’.  The answers started to flow: ‘Materials, labour…’, which we were able to break down to a simple linear relationship, being M + T x R, where T and R represented Time and Rate of pay.  Simple, and so common a relationship in so many exam questions: electricity bills, phone bills, taxi costs, anything of the form y=mx + c, which is pretty much all that is required to pass the hurdle of gaining a ‘C’ in mathematics.  I was able to draw on the knowledge and experience of the learner, but then kids have enthusiasm and intelligence and a desire to learn, which makes teaching such an easy and enjoyable job.  So don’t make formulas to be mindless repetition of sums, but make them abstract representations of real-life, or imagined, situations.

Next I could explain what I did this week with a packet of 1000 ‘matches’, which cost me £1.99 and worth every penny, and provided a lovely photographic record of patterns in number, and how I will use the hand-shaking lemma in September when the next cohort arrives.  Will I be tempted to produce some easy repetitive worksheets?  Who knows, it might depend on the classes I get!  All I need is some feedback.