Fourth Graders Invent Ways of Computing Averages

Children easily learn the conventional algo-rithm of averaging: to find the average of a set of numbers, such as 80, 90, 94, and 100, just add rhe four numbers and divide the total by four. However, the authors are working on an approach to mathematics based on Piaget's theory, constructivism. For reasons explained later in this article and elsewhere (Kamii 1985, 1989, 1994), our approach is to encourage children to do their own thinking and to refrain from giving rules made by someone else. The purpose of this article is to describe what fourth graders can do when they are encouraged to invent their own ways of getting the average. The article also shows the teacher's active role in constructivist teaching.