In this podcast with Anne Watson and John Mason, John describes his thinking about planning:
The human activity of planning for the future is about imagining yourself as fully and completely as possible in that situation... what is really effective is imagining myself in the lesson as vividly as possible, my emotional, physical and cognitive state... and that helps you wake up in that moment, in the relevant moment, and enact whatever it is you wanted to enact...
I am planning a first lesson with upper primary using the geo-boards we made last week. Here are my imaginings:
I stand at the front, slightly apprehensive, as the children settle down. Breathe deeply from my diaphragm. I write the lesson title on the board. Sometimes I seem to make this up in the moment, today the title might be'Geo-boards'... reasonably non-committal. I usually write an aim, perhaps it will be 'play' (a bit more - we started playing with them last week), and then... what else?
I have been thinking about wanting the children to create and explore their own questions. I know this is risky, as we haven't worked on creating mathematical questions before. The quality of questions might not be great, but this is part of learning how to form questions. Do I let them explore whatever they want, regardless of whether I consider their question fruitful or less than fruitful? Today, I will. The main aim of this lesson is to create mathematical questions of their own.
So, I do not write 'play' on the board, but a more specific aim: 'creating mathematical questions of your own'. I then turn to face the class. Most of them are watching. I wait a little, and then speak: "OK, so today I thought we might play with the geo-boards you made last week, and see if you can create some interesting mathematical questions which you can then try and answer."
I look at their faces. They look non-plussed. I show them the photos I took of their play last week, and ask them what they were/are wondering about. I will keep this short, and then say: "So, I'd like to invite you to play with the boards a little more, and see if there is something you notice that would be interesting to explore, mathematically. I would like you to create one mathematical question that you'd like to explore... [pause] I'll be coming round to talk about your questions, to help you think about what might be interesting for you."
I'm aware that a few of the children might take this as a signal to not do very much. Some of them might find it difficult to cope with this level of freedom. Should I constrain things a little more? I decide that I don't want to constrain the question they work on, not this time. I want to see what they do when unconstrained, and to see if we can learn something about what makes a 'fruitful' mathematical question. I will give them the choice to work on their own question, or someone else's. Will this be time well spent?
Some question stems might be useful, perhaps: "I wonder if...", "How many...?", "Can you make...", Here are some from Andrew Blair:
I'm not sure how helpful question stems will be, we shall see. Perhaps we might draw out some useful stems after the investigations, as the proof will be in the pudding.
How am I going to collate their questions? I could write them on the board, but I prefer the idea of them writing them on a piece of paper and putting them in a hat, to be read out. "After about 10 minutes, I'll be asking you to write your question on a piece of paper and put it in this box, and then we will read them out. You will be able to choose which question you want to work on, either your own, or someone else's." I'll read each question out twice, without evaluation. I need to cut up some pieces of paper.
After they have chosen a question, how are they going to record what they are doing? I don't want to use technology today: who would collate all those photos anyway? I will give sheets of paper, and provide sheets with geo-boards printed on them. They made 9-, 12- and 18-pin boards, and Caleb made a 6-pin board. I'll tell them about this after choosing a question. Today is about initial attempts at forming and investigating questions, next week I'll shift the focus onto which questions they found more or less fruitful. They can then record what they did in more detail, by writing an account, and perhaps some children will want to show everyone else what they found out.
"OK, so come and get your boards, no more than five elastic bands so that there's enough for everyone, have a mathematical play, and I'll be coming round to talk to you about your mathematical question." I stress the word mathematical.
They come and collect their geo-boards and elastic bands.