6 Summary

In studying this unit you have thought about how to enable your students to develop proportional reasoning by using activities that stimulate creative possibility thinking.

Possibility thinking asks students to be creative, to try things out and to make their own decisions and therefore their own mistakes. Teachers sometimes think it is their job to prevent their students making mistakes; this unit demonstrates that it is the teacher’s job to allow the students to make mistakes and to learn from them. Asking the students to ‘play with ideas’ means that they exercise their creative side, try out lots of ideas and end up really knowing and understanding ideas.

Asking your students to be creative and playful and make choices for themselves also means that they are better prepared when asked about something in an unfamiliar context, as often happens in examinations. They know that if they think around an idea and try some things out, they can solve a problem that looks difficult to begin with, just as they have done before.

Pause for thought Identify three techniques or strategies you have learned in this unit that you might use in your classroom, and two ideas that you want to explore further.