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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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What Do You See?What Do You See?

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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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J. S. MillJ. S. Mill

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GasketGasket

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TulipsTulips

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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