Comparing perimeters and areas. Children's pre-conceptions and spontaneous procedures

In this paper we present research carried out into the concepts of perimeter and area among fourth and fifth year Primary school pupils. The paper focuses on children’s pre-conceptions and spontaneous procedures. Researches show that the conflict perimeter-area is an epistemological obstacle causing difficulties in the comprehension of these important geometrical concepts. In fact it is only by recognising and understanding these that we can identify teaching strategies for overcoming the ‘perimeter-area conflict’. We present and discuss two worksheets aimed at revealing pupils’ reasoning and behaviour, especially unpredicted. We make a detailed analysis of how children completed the worksheets, and of subsequent individual interviews with them.