Maths is to be worked out not learnt by rote

When I was six years old, Miss Creamer, my teacher, gave me a test. She quickly wrote “3 x 3 = ” on a piece of paper and gave it to me to solve. I immediately noticed that the symbol in the middle was a “times” rather than an “add”, but back then I didn’t know my times tables, so I didn’t know the answer. The cross on the paper wasn’t perfectly aligned as a multiply and I decided that the best strategy would be to assume that the “x” was actually a “+” miswritten. So I added the two 3s together and went back to Miss Creamer. To my dismay she was unimpressed with what I’d done and marked it wrong, and in doing so pointed out that the symbol in the middle was a multiply not an add, which rather quashed my ploy of misunderstanding the question. I went back to my desk and spent some more time thinking about it. To me, the shapes “3” and “3” had always combined to produce the shape “6”, what else could the answer be? So I again wrote “6” and took it back to Miss Creamer. Again she marked it wrong. Now I was stuck, so I asked her to give me help. She declined to do so, but this time as she sent me back to attempt the calculation again she told me to “Think”. Here was a revelation. Suddenly I realised that this was not something that I was expected to know, this was something that I had to work out. I sat down again and this time I tried to reason what the expression meant. I knew that it didn’t mean 3 and 3, so what else could it mean? After a while I thought, could it mean three lots of three? Well it was worth a try. I calculated three lots of three to be 9, and wrote that down on the piece of paper, and took it back to Miss Creamer. This time she marked it correct, and praised me for doing well. I went back to my seat with a feeling of great pride and achievement. I had solved a difficult problem.
This story illustrates a number of elements of teaching and learning maths. It shows the reluctance that a child has to go beyond it boundaries in which it feels safe. I was comfortable with 3 + 3, I didn’t want to face the hostile idea that it might be “x” between those two numbers. Also it shows that after 2 failed attempts at answering the question I had given up and I asked for help, expecting to be bailed out. It shows the enormous satisfaction that a young child can get when they don’t give up (in my case because I was compelled not to) and solve a puzzle on their own. It is this latter point that I remembered this incident for, for many years.
But since I started teaching I’ve realised that there is a further aspect to this story. It was at this point in my life that I learnt a much more important lesson. The lesson was that maths is not a set of facts that have to be learnt, that maths can be worked out. But more than that, I solved that problem using logical reasoning. It was on that day that I realised that maths wasn’t just about numbers and the rules that govern them, but that maths was about the use of logic. This is a message that is central to the philosophy by which Puppet Maths teaches maths. Maths is a branch of logical reasoning. Maths is the expression of logic. From our experience teaching maths in schools we know that once children realise that all they have to do is reason their way to an answer, fear of maths falls away. At Puppet Maths we want to banish fear from maths, we want children to enjoy maths.