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On this page are a number of examples where we expect our students to record on the their page, in a concrete way, perhaps with boxes, function machines etc to enable the student to have 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 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?.
everyday situation when working memory isn't enough
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An abstract notion such as ratio is because it is hard to "hold on to mentally" so takes up a lot of working memory (and of course it is also hard because it involves both multiplying, dividing and finding a scale factor too) - so enabling students to have a concrete model which they can put on the page, and not need to hold in working memory is hugely beneficial. With the problem
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- ... how much more money does Francis get than Eva
- Francis gets £10 more than Eva, how much ....
- Eva gets $240 how much does Francis get
- A piece of copper pipe is divided in the ratio 3:5
- A piece of copper pipe is divided in the ratio 1:3:5
and other situations to use boxes
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