1. 1 Making Use of Mental Imagery John Mason East London June 2010 The Open University Maths Dept University of Oxford Dept of Education Promoting Mathematical Thinking

2. 2 Conjectures  Mental imagery is perhaps THE fundamental power possessed by humans –It is the basis for planning and for carrying out plans; –It is the root of expectation and the mechanism for motivation –It is the means for directing our energies –It is the basis for algebra and geometry

3. 3 Outline  Some tasks (paration)  Some reflection (post-paration)  Some pre-paration

4. 4 Imagine …  A straight line …  A square …  A point …  A line segment …

5. 5 What Do You See?

6. 6 Backwards Arithmetic  When I call out a number, you must write it down from right to left, with the units digit on the left Useful Strategy: impose an unusual constraint so as to force yourself to bring internalised procedures to the surface

7. 7 J. S. Mill

8. 8 Gasket

9. 9 Tulips

10. 10 Using Mental Imagery  When planning a lesson  When reflecting on a lesson  When introducing a lesson or a task  Getting learners to use their imagery –Anticipating –Predicting –Going beyond the physically possible