I got straight on with it today. I put the question on the board and quickly told them not to say anything once they had worked it out, but to be thinking of a ‘clue’ they could give other people to help them understand what was going on. I’ve been doing this a lot lately – seems to help stop them from calling out and give everyone a chance to think.
About 5 of them were sat there with their eyes bulging out of their heads and all ten fingers waggling at the ceiling, desperate to show me they knew. Someone came to the board and traced around the edge of the shape, a good ‘clue’ I thought. Eventually we all understood what P was. I asked them what they noticed about the shapes, what was the same and what was different. I wanted them to tell me all the shapes had 4 squares, but I forced myself to give credit to all of the things they noticed, even if they were ‘irrelevant’ to where I was heading. I thought it was important to praise them for noticing things, and forced myself to keep taking asking answers even when I’d got what I wanted. I think this was a good thing, although for some reason I found it hard.
I asked them what questions we could ask. I wasn’t hopeful - I had my own list of questions prepared. But this time I didn’t need them! Someone wanted to know what the perimeter of a 3D square was. Someone else wanted to know how many different shapes there were with 4 squares. One boy wanted to know how many right angles there were, whilst someone else asked what the smallest perimeter was that we could make!
I was so impressed with their questions that I decided to let them all investigate any question they liked. I didn’t know whether this would work and questioned it a couple of times later on, but I wanted to encourage them to keep asking questions. I gave my list of questions to those that were stuck and spent my time going round the class asking people what they were working on. I felt like there were lots of people who were time wasting – not sure what to do or just drawing shapes with no purpose. But some of them were really into it. I stopped them and discussed with them how ‘being organised’ would help us spot things and notice patterns, we put some people’s results in a table. This helped focus some of them and I was soon informed that there were 4 right angles in each square so the number of right angles always had to go up in fours. I realised I would never have asked this question because it was too obvious to me, but clearly it was not obvious to everyone I taught. A few people found the maximum perimeter was four times the number of squares and they seemed very pleased with themselves. I was too.
We ended the lesson by writing. I gave them some ideas to help structure their writing, but this seemed to confuse them more than anything. Perhaps it’s just best to allow them to write what they think the lesson was about.
I felt the lesson had 'worked', although slightly hectic since everyone was doing something different. I felt worried that some of them hadn’t really achieved anything. They hadn’t got the hang of what I meant by a question. One boy had just asked what ‘was the biggest perimeter you could find’, and kept drawing bigger and bigger shapes. I wasn’t sure how to help him understand what made a ‘good’ question.
I was more confident that we had been learning things today though. We had been using mathematical language – cubes, squares, perimeters, areas etc, and noticing patterns, making predictions and explaining ourselves. I feel that they got more out of today’s lesson than any of the traditional lessons we have done on ‘algebra’, especially in terms of enjoyment, but I still feel like I would be criticised for not having a clear learning objective on the board, and for not being able to demonstrate the ‘progress’ they had made in the lesson.
