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On this page are a number of examples where we expect our students to record on their page, in a concrete way, perhaps with boxes, function machines etc to enable The concrete diagrams will require the student to need to hold less in working memory and so free up enough working memory to continue to solve the problem.
If we as teachers think of a way situation in which our working memory isn't sufficient and what we do about this, this will help in our teaching. At every step of problem solving we could think, what am I remembering? and would all my students be able to hold all of this in their heads, without something slipping out?.
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Giving students more concrete methods "frees up" working memory for often numeracy, so will generally to enable more available to concentrate on the rest of the maths problem (the rest of the maths problem is often the numeracy aspect). More concrete methods will generally make students more accurate.
One of the problems with giving more concrete methods is that it often goes against giving "paper saving methods", which have come to be considered to be standard methods (for more on this see the long multiplication and long division sections below).
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- simple probability - write out all the possible outcomes
- % of CALC problems - write word problem in maths
- percent CALC: 17%
- % of NC problems - start by writing 100% = ...
- percent NC: 2% of £560
- percent NC: 10% of £4.60 LESLEY record
- expand
- expand: number(outside a bracket) algebra 5(x + 3)
- expand: just a letter(outside a bracket) x(x-3) algebra
- expand: (a bracket squashed)(next to another bracket) exp&simp (m + 3)(m+2)
- BIDMAS problems, write out the problem (with more space and write out BIDMAS and then again in signs)
- discreteDataDiagram: pictograms, write the amount inside or below each picture
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