Malcolm Swan, on how to begin a lesson:
Every lesson should begin by getting [students] to articulate something about what they already understand or know about something or their initial ideas. So you try and uncover where they’re starting from and make that explicit. And then when they start working on an activity, you try to confront them with things that really make them stop.
And it might be that you can do this by sitting kids together if they’ve got opposing points of views. So you get conflict between students as well as within. So you get the conflict which comes within, when you say, “I believe this, but I get that and they don’t agree.” Or you get conflict between students when they just have fundamental disagreements, when there’s a really nice mathematical argument going on. And they really do want to know and have it resolved. And the teacher’s role is to try to build a bit of tension, if you like, to try and get them to reason their way through it.
And I find the more students reason and engage like that then they can get quite emotional. But when they get through it, they remember the stuff really well. So it’s worth it.