Saturday dawned bright and sunny, well it would be a lovely day wouldn’t it? A very filling breakfast was followed by a brisk walk around Northampton town centre just so I got to go outside at least once during the day. Then it was down to work. We had 4 two hour sessions timetabled with a break between 4.30 and 6.00 so it promised to be a very intensive day. We were divided into groups of approx 20 and did the first 3 sessions on rotation basis. Each session was based on one of the big mathematical ideas, mathematical thinking was Friday eve and we started Sat with a session on Representation.
This was probably the session that got me thinking the most over the weekend. We looked at how all maths is abstract and we need representations to help us to make sense of it. We considered the use of different resources such as number lines and number squares and whether using both could be confusing to children. It was felt that children should be given access to a wide variety of resources and representations to help them make sense of things. A point that struck home strongly was the idea that some teachers and a lot of children feel that they out grow the use of apparatus such as number squares or cubes. Often children who still need the support of apparatus are seen as less able by themselves and others.
The point was made that as the maths gets more complex then children should have more access rather than less to representations and apparatus. KS2 classes in particular often don’t use enough images, representations and apparatus to allow children to fully understand new concepts. Could this be a reason why children find maths harder in KS2 than in KS1? Would they retain their confidence if apparatus were more readily available and more images used?
There should also be a greater emphasis on the value of children’s own representations and jottings. That is certainly an issue at school where some children are reluctant to spoil their nice page with jottings or working out, even asking if they can rub it out! They need to made to see that it is an important part of their work. Maybe this could be helped by doing more jottings and working out myself for them to see as well as getting them to demonstrate their images etc on the IWB.
Lots of ideas about different ways of using representations as well as lots of reading to do around the subject. We also have a directed task to do before our next session on representation. This involves either developing your use of an existing representation such as a number line or arrays and with a colleague developing it further, or to use an alternative resource that represents a mathematical concept and be prepared to explain how you have used it to develop understanding of the concept.
After 2 hours it was definitely time for a cup of coffee!