Starting Points for Teaching Mathematics in Middle and Secondary Schools

"This, for many years, was my Bible of teaching. I got to know about it through Laurinda Brown, with whom I have worked and co-researched for many years now. The third author, Dick Tahta, who is dead now, was a close friend of Laurinda’s. I knew him in the last ten years or so of his life and he influenced me hugely. It’s a very simple book on one level. It begins by talking about ways of working in the classroom and there’s a section on the role of the teacher. He asks, “What is the role of the teacher? How can he or she create the conditions in which creative and independent work can take place?” That, in a nutshell, is what I’m interested in in my work in mathematics. Most of the book is just page after page of starting points for mathematical activity, which generally have something visible or tangible or something the children can just do straight away, but from which they are able to ask questions, spot patterns, make conjectures. Dick Tahta was certainly very influenced by Gattegno in this. They are just very rich starting points for children to get into the process of thinking mathematically. As a teacher wanting to develop a more creative approach to my own teaching, it was just an invaluable resource. Time and again, these activities would end up getting kids energized and excited and engaged and asking questions. One is a game called the function game, where he imagines the teacher having some rule in mind. So with quite a young group, the rule I might have in mind is “add one.” So I might write the number three on the board and a little arrow (this is all ideally done in silence) with a four next to it. Underneath, I might write seven with an arrow and then eight. Then maybe I’d write six underneath, with an arrow, and hand the pen over to the children – or motion with my pen towards the class and try and get someone to come up to the board and fill in what they think the answer it. With older children the rule might be square the number – you can make it as complex as you like. I then give them feedback – so if a child comes up and doesn’t write seven, I draw an unhappy face. It’s the kind of activity which children can get very engaged in and can just lead in so many different directions. At the school where I used to teach our results were pretty good age 16. We had a lot of people coming through to do ‘A’ level and it was quite often the most popular ‘A’ level choice [ Editor’s note : in the UK, children after age 16 choose only three subjects for their last two years of school, at the end of which they sit ‘A’ level exams in those subjects]. We were the only school in the local area to teach Further Maths as an ‘A’ level, which at that time was a subject in major decline outside public [private] schools. Those things for me were indicators that we were successful in developing in quite a few children a sense that mathematics was something they could be engaged in and excited about. I was teaching in a school with quite a disadvantaged catchment area, and we had a couple of people getting into Oxford to read maths and quite a lot of people doing maths-related university degrees. So yes, there were some good responses from the children."