Representations and Apparatus

At the residential weekend probably the idea that struck me the most was the idea that all children should be supported by the use of concrete apparatus. Having taught the upper ability set of year 5 for several years now, I was definitely of the opinion that apparatus such as cubes, number squares etc were for the younger children or less able. I didn’t really have any basis for this opinion, maybe it was just received wisdom from those around me or even a throw back to my own schooling.

The comment that as the maths gets more complex then the children should have more access to apparatus and other representations rather than less seemed to be a revelation that really made sense. There has to be a reason why children’s confidence and enjoyment of maths reduces rapidly during KS1 and I wonder if our insistence that the children cope with abstract concepts without the support of concrete apparatus could be partly to blame.

Today I was introducing my class to the ideas of ratio and proportion. I have always found in the past that this is a difficult area for children to grasp and understand fully. It seems to be an area where they appear to have grasped it initially but further investigation reveals that this is very superficial.

I had always used representations in my teaching of this area, I have a lovely powerpoint of dragons to illustrate how the numbers can be scaled up but the children have always struggled to understand this properly.

I decided today that I would give the children a lot more concrete support so I sorted out cubes and counters that they could use if they wished. I also started by getting children out to the front in a ratio of 2 girls:3 boys. We discussed the idea of ratio and then I added another set of 5 children. There was a lot of discussion between the children who felt that the ratio had changed and those who saw that it hadn’t. By getting the two groups of children to stand separately, they were able to see that the ratio was still the same although the numbers had changed. 

I then used the IWB to demonstrate this with purple and turquoise ladybirds and the children seemed to have fully grasped the idea. I then gave them sample ratios for them to show as a picture in the same way that I had done on the IWB. They had either cubes or counters which they could use if they wished. They then had some simple problems to solve. Probably about half of the children chose to use the apparatus but there was no obvious split between more or less able. It was also useful for me to have the apparatus to use when I was helping the children who needed a bit of extra reinforcement

At the end of the lesson I asked the children to evaluate what they had done and how they felt about their own level of understanding. All but two of the children felt that they had succeeded with the lesson and were confident that they could move on further tomorrow.

I will definitely make more of a point of having apparatus for the children to use if they wish in future lessons as it certainly seemed to make the children a lot more confident.

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