5 Summary

This unit has discussed some ideas associated with trigonometry, but its chief focus has been on creativity and allowing the students to think ‘What happens if …?’, or to engage in ‘possibility’ thinking. Possibility thinking asks students to be creative, to try things out and make their own decisions – and therefore their own mistakes.

Teachers sometimes think it is their job to prevent their students from 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 so, end up really knowing and understanding what they have learned.

Asking your students to be creative and playful, and to make choices for themselves, also means that they are better placed 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 ideas that you have used in this unit that would work when teaching other topics. Make a note now of two topics you have to teach soon where those ideas can be used with some small adjustments.