When I got married my mother gave me a case of woodworking tools. This was a bit of a surprise. No-one in the family did any woodworking and I’d done only a token amount at school. So the tools sat in the spare room gathering dust until after a year or two I felt sufficiently guilty to sign up for an evening class.
I turned up expecting to be told how to saw straight and perhaps make a few mortices and tenons. Instead the teacher gave me a cup of tea and sat me in an armchair. He gave me a pile of woodworking magazines and asked me what I wanted to make. By the end of the evening I was committed to making a rocking chair.
It took two years, but more than 45 years later the rocking chair still sits in our dining room and every day reminds me to reflect upon his teaching. I’d expected laboriously to master a hundred different skills and finally be allowed to make something interesting. His approach was exactly the opposite: I’d start on something I wanted to make and whenever I needed a skill he’d teach me the technique.
What a wonderful learning experience that was. I saw myself as being the woodworking equivalent of innumerate; he believed everyone was capable of producing work fit to grace a living room. (And what a shame I never went to an evening class to learn the saxophone!)
It took me a shamefully long time to recognise the contrast between the way he taught woodwork and the way my colleagues and I taught mathematics. Rather than start from “What useful and interesting things can we do with mathematics?” we took the approach that only when children had adequately mastered a vast number of skills and routines might they at some vague time in the future get around to doing something useful with their mathematics. Of course, the vast proportion of pupils leave school long before that point is reached, most of them never to touch the subject willingly again.
(This piece first appeared on NRICH, and an expanded version can be found at http://nrich.maths.org/7094)