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

Discover the power of mental imagery in teaching mathematics with practical tasks, reflections, and pre-paration strategies. Explore backward arithmetic, historical calculations, fraction constructions, and innovative approaches to engage learners' visualization skills.

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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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