ABSTRACT
It seems a prerequisite of engagement in mathematics that tasks are meaningful to students. The plan to base mathematics on the real world (discussed in Chapter 2) is one way of trying to make mathematics meaningful. In contrast, I begin with another classroom transcript that, for me, gives an image of a group of students making meaning of mathematics in a context that is game-like rather than real-world. The activity they are engaged in is called ‘Frogs’. A description of the task is below, followed by the transcript. ‘Frogs' activity
The starting challenge for this task is best done actively. Set out seven chairs in a line at the front of the classroom, facing the room. Invite three girls to come and sit on one side and three boys to sit on the other, with the spare chair in the middle, as shown in Figure 3.1. Students can slide into an empty chair or jump over one student into an empty chair. The task is for the boys and girls to swap where they are sitting.
Students will probably need several goes to do this. Rather than explain how they can move – demonstrate. At some point, introduce the challenge of swapping seats in the minimum number of moves (this challenge might come from students). You may want to get different students trying it at the front.
When you are happy that the class has figured out how the game works and have been hooked by the idea of trying to find out the minimum number of moves, students can be invited to continue working at their tables, for example using counters.
If they become convinced they have the minimum number (15), they can be invited to try to record how they do it. They are likely to suggest, themselves, trying it for more people on each side. Can they predict the total number of moves for everyone in the class? or the school?
