Abstract
The "same perimeter problem" is a task that requires us to compare the area of the transformed parallelogram with the original rectangle. The problem is that the angles of the parallelograms are changed with the perimeters identical. This problem can be solved by applying an area formula, but misjudgment that areas are the same is often made. The author supposes that the origin of the misjudgment lies in the fact that the students' primitive naive conception of conservation is more active than the area formula during problem solving. This study examined whether presenting a cognitive tool which shows the change in the area of the parallelogram with the same perimeter could restrain the students' primitive naive conception, and allow them to solve the problem correctly by using the formula. As a result, the pupils who were presented with the cognitive tool solved the "same perimeter problem" correctly, but they solved the other sort of problem incorrectly. It was suggested that when they were presented with the tool, they only understood that the area became smaller when the figure changed from rectangle to parallelogram.
