I love patterns, diagrams and pictures. Ask me to record information and it gets plastered over a page in bubbles, a mind map or random boxes. I’m not particularly artistic but I find I like to store information in this way. Even with telephone numbers – I remember the pattern the digits make, not the number itself.
The power of geometry is that it can represent abstract ideas and concepts in a completely different way. Often giving students something concrete (a diagram, model or representation) can help them understand what’s going on, increase transfer (Richland et al., 2007, p. 1129), help retention and foster connections between seemingly unrelated ideas: “By using representation students can begin to recognise that the underlying mathematical concept extends into unexpected domains” (Watson et. al, 2013 p.8).
Here’s a selection of the visual representations or demonstrations I’ve come across recently. No doubt you will recognise some of them but I hope others will be new to you. Can you explain how they represent the mathematics? Can you use them in your lessons?
KS1
Even and odd
![](data:image/png;base64,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)
KS2
Factors of 12
![](data:image/png;base64,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)
Equivalent fractions
![](data:image/png;base64,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)
http://www.bbc.co.uk/skillswise/factsheet/ma17frac-l1-f-fraction-wall
KS3
(a+b)(c+d) = ac + ad + bc + bd
![](data:image/png;base64,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)
Pythagoras’ theorem
![](data:image/png;base64,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)
KS4
(a+b)2 – 4ab = (a-b)2
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KS5
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)
References
Richland, L.E., Zur, O. and Holyoak, K.J., 2007. Cognitive supports for analogies in the mathematics classroom. Science – New York then Washington, 316(5828), p.1128.
Watson, A., Jones, K., Pratt, D., 2013. Key Ideas in Teaching Mathematics. Oxford University Press, Oxford, UK.