4 Making up own questions to develop geometric imagery

Activity 2 and Case Study 2 illustrate how school geometry can be learned by working on the intuitive knowledge that students have. Mrs Chakrakodi described how he reinforced the link between what was learned outside and inside the classroom through discussions. By studying geometry using sticks and asking students to ‘enact’ the movement, time and time again, images are formed in their minds. These images are important for developing the geometric intuition described earlier in this unit. It is also important to become aware that not all people will ‘see’ the same image when given a description.

A good way to ask students to engage with a geometrical image is to ask them what questions could be posed.

Activity 3: Asking good questions

This task works well for students working both individually and in pairs, followed by a whole-class discussion or a brainstorm, followed by more individual/paired work, and so on.

Ask the students to look at Figure 5 and come up with possible questions about it.

Figure 5 What is the question?

Some of the questions could be:

  • What is the centre of the circle?
  • What is the point P?
  • Why is the angle OTP a right angle?
  • What is the line t?
  • How is the line t related to the line t’?

Pause for thought

  • How did it go with your class? Were they able to think of questions? How did this help you to evaluate their understanding of circles?
  • Did you feel you had to intervene at any point?
  • What points did you feel you had to reinforce?

Guiding students to ask good questions is a technique that you can use in many different topics. It is an excellent technique for helping you to assess students’ understanding of the topic. When students have generated their questions, you can ask pairs to swap questions and try to answer each other’s questions. Then return the answers to be marked. When students are doing this type of activity it is important to walk round the room and listen to what they are saying – if students are not participating, you should encourage them. In the next lesson you might want to move students to work with different partners so that they can help each other.

3 Developing geometric intuition