5 Summary

This unit has discussed geometric ideas, particularly focusing on circles. The ideas are not complex in themselves, but you have been asked to think about some complex pedagogical ideas. First you were asked to think about asking the students to use circle vocabulary themselves in describing what they were enacting, rather than just to learn new words by rote. Students who use vocabulary themselves – especially to describe something they or their peers are doing – internalise the words naturally and remember them. Think now about another area of mathematics where it may help the students to remember better if they used and enacted the words themselves.

The other important pedagogical idea in this unit is the use of variance and invariance. Asking what is the same and what is different directs the students’ attention to important mathematical ideas. They can make connections or understand and generalise for themselves – something else that helps students make the ideas their own and easy to draw on, control and use in unfamiliar contexts.

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.

4 Making up own questions to develop geometric imagery