Last week, I talked about the great importance of building conceptual understanding in teaching maths and how fluency should build on this understanding rather than be based on teaching procedures without understanding. One of the most powerful ways of doing this is by using concrete materials and representations and there are a wealth of these available to us. When I was in school (admittedly rather a long time ago now), the only concrete materials I can remember are some shells and counters we used to help us do ‘sums’. There was very little in the way of representation either – possibly shapes and fractions might be illustrated by diagrams, but otherwise little comes to mind. Admittedly, I did manage to learn maths despite this, but even with the benefit of a maths degree, I found that some mathematical concepts became much clearer when I started teaching them and discovered representations that would support me in this.
This week, I have been reading a very helpful book by Tandi Clausen-May. Teaching Mathematics Visually and Actively introduces a whole range of concrete and visual material to support teaching maths in different areas. Clausen-May argues that visual and practical approaches are vital in teaching children who may have struggled to learn maths in a more abstract way and the book is aimed mainly at teachers of these groups. However, I believe that these approaches are actually beneficial for children of all abilities. I want to be upfront and admit to being sent a copy of the book by the publishers for possible review, but I have no hesitation in recommending it. The book is divided into chapters for several different areas of maths and for each introduces some key ways of using visual and practical approaches. I am always keen to use this sort of approach in my own teaching, but I found here some useful reminders of approaches I was already familiar with, together with some that were new to me. As well as key representations and materials for each area, there are also practical ideas about how to use these in the classroom and suggestions for further reading. Information is also given about online tools and information, or in the case of concrete materials, guidance as to where these can be obtained. As a bonus, a CD is included with the book, on which can be found useful printable materials and powerpoints.
In schools today, lots of visual and active approaches to teaching mathematical ideas can often be seen in Early Years setting and in KS1, but much less in KS2 and beyond. Where representations and concrete materials are used it is often with less able children. Children can then become reluctant to use these because they see them as ‘babyish’. We need to use these approaches much more routinely, so that this sort of stigma is not be attached to them. Admittedly, some of the concrete materials will need to be bought, but arguably this is a much better use of our budget than buying text books or photocopying worksheets. Many can be fairly simply made or printed off and in many cases there are interactive versions available (although caution needs to be taken that these don’t completely replace the ‘hands on’ experience of manipulating objects which is so important in the early stages of learning a new concept).
I have started a pinterest board which includes some of my favourite concrete and representational resources and I hope to be adding to this regularly as I remember and come across others.