1 Making Use of Mental Imagery John Mason East London June 2010 The Open University Maths Dept...
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Transcript of 1 Making Use of Mental Imagery John Mason East London June 2010 The Open University Maths Dept...
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Making Use of Mental ImageryMaking Use of Mental Imagery
John MasonJohn Mason
East LondonEast London
June 2010June 2010
The Open UniversityMaths Dept University of Oxford
Dept of EducationPromoting Mathematical Thinking
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ConjecturesConjectures
Mental imagery is perhaps THE Mental imagery is perhaps THE fundamental power possessed by fundamental power possessed by humans humans – It is the basis for planning and for It is the basis for planning and for
carrying out plans; carrying out plans; – It is the root of expectation and the It is the root of expectation and the
mechanism for motivationmechanism for motivation– It is the means for directing our It is the means for directing our
energiesenergies– It is the basis for algebra and geometry It is the basis for algebra and geometry
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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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Imagine …Imagine …
A straight line …A straight line … A square …A square … A point …A point … A line segment …A line segment …
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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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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