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(The Role of) Mental Imagery in the Teaching and Learning of Mathematics

(The Role of) Mental Imagery in the Teaching and Learning of Mathematics. John Mason Tower Hamlets June 08. Outline. Some tasks (paration) Some reflection (post-paration) Some pre-paration. Backwards Arithmetic.

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(The Role of) Mental Imagery in the Teaching and Learning of Mathematics

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  1. (The Role of) Mental Imageryin the Teaching and Learningof Mathematics John Mason Tower Hamlets June 08

  2. Outline • Some tasks (paration) • Some reflection (post-paration) • Some pre-paration

  3. 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 constraintso as to force yourself tobring internalised proceduresto the surface

  4. Tulips

  5. Kites

  6. CopperPlate Calculations

  7. What’s Being Done? • Does ‘it’ always work? • What is the it? The calculation comes from an Arabic manuscript Hindu Reckoningwritten by Kushyar ibn-Lebban about 1000 C.E. (quoted in NCTM 1969 p133)

  8. Construction

  9. Construction

  10. Raise your hand when you can see • Something which is 2/5 of something • Something which is 3/5 of something • Something which is 2/3 of something • What others can you see? • Something which is 1/3 of 3/5 of something • Something which is 3/5 of 1/3 of something • Something which is 2/5 of 5/2 of something • Something which is 1 ÷ 2/5 of something

  11. What fractions can you ‘see’? • What relationships between fractions can you see?

  12. 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

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