"Using the right type of measuring equipment could make all the difference to children's understanding of area," say Mark Allerton and Terezinha Nunes who reveal for us the results of a recent research project involving 240 4th-6th grade children.

Many teachers find that when they are trying to teach the concept of area, children frequently become confused between the terms "area" and "perimeter." To try to clear the confusion, a research project was recently set up at the University of London's Institute of Education. We decided to look at the tools that children use to measure area — and to try to find out whether these affect, in any way, their understanding of the concept. We started by choosing two different ways of measuring an area — with a ruler or with 1 cm cubed bricks — and then designed some specific problems for a group of children to solve. In all, 240 children, from grades 4, 5, and 6, took part.

We covered a range of different problems — the first involved two children who had been asked to paint two walls to earn some pocket money. The walls measured 10 x 4 cm and 8 x 5 cm — they had the same area but the perimeter was different. When the children were paid, they couldn't decide how to share the money because the wall painted by one was wider than the other — but the second wall was higher. We asked the pupils taking part in the project to work out whether the children had painted the same area and whether they should each receive the same amount of money.

They drew diagrams of the walls to scale on sheets of paper. As you can imagine, it is hard to tell who has done the most work, because the first wall is wider than the second and the second is higher than the first. The children worked in two separate groups and within these groups were asked to work in pairs. Those in the first group were given rulers to solve the problem; the others were given 1 cm cubed wooded bricks. We deliberately restricted the number of bricks to 20 because we wanted the children to consider a range of options — not just use the bricks to fill the space. They quickly realized that there were not enough bricks to cover the shape — which introduced a problem-solving element. Initially, this caused some dismay but eventually many of the children put a line of bricks along the width and another line along the height, working out their own width x height formula.