1 (the role of) mental imagery in the teaching and learning of mathematics john mason tower hamlets...
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(The Role of) Mental Imagery(The Role of) Mental Imageryin the Teaching and Learningin the Teaching and Learning
of Mathematicsof Mathematics
John MasonJohn Mason
Tower HamletsTower Hamlets
June 08June 08
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OutlineOutline
Some tasks (paration)Some tasks (paration) Some reflection (post-Some reflection (post-
paration)paration) Some pre-parationSome pre-paration
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Backwards ArithmeticBackwards Arithmetic
When I call out a number, you When I call out a number, you must write it down from right must write it down from right to left, with the units digit on to left, with the units digit on the leftthe left
Useful Strategy:impose an unusual constraint
so as to force yourself tobring internalised procedures
to the surface
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aaa
30361635542428402863483642364232455681497254635160119905
24206478979654CopperPlate CopperPlate
CalculationsCalculations
aaa
30361635542428402863483642364232455681497254635160119905
79654242064789
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What’s Being Done?What’s Being Done?
aa
562548254795478683983983983948 79 86
Does ‘it’ always work?Does ‘it’ always work? What is the it?What is the it?
The calculation comes from an Arabic manuscript Hindu Reckoning
written by Kushyar ibn-Lebban about 1000 C.E.
(quoted in NCTM 1969 p133)
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Raise your hand when you Raise your hand when you can seecan see
Something which is 2/5 of somethingSomething which is 2/5 of something Something which is 3/5 of somethingSomething which is 3/5 of something Something which is 2/3 of somethingSomething which is 2/3 of something
– What others can you see?What others can you see? Something which is 1/3 of 3/5 of something Something which is 1/3 of 3/5 of something Something which is 3/5 of 1/3 of somethingSomething which is 3/5 of 1/3 of something Something which is 2/5 of 5/2 of somethingSomething which is 2/5 of 5/2 of something Something which is 1 ÷ 2/5 of somethingSomething which is 1 ÷ 2/5 of something
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What fractions can you What fractions can you ‘see’?‘see’?
What relationships between What relationships between fractions can you see?fractions can you see?
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Using Mental ImageryUsing Mental Imagery
When planning a lessonWhen planning a lesson When reflecting on a lessonWhen reflecting on a lesson When introducing a lesson or a taskWhen introducing a lesson or a task Getting learners to use their Getting learners to use their
imageryimagery– AnticipatingAnticipating– PredictingPredicting– Going beyond the physically possibleGoing beyond the physically possible