Place Value: An Explanation of Its Difficulty and Educational Implications for the Primary Grades

Abstract Recent research has shown that place value remains difficult in third and fourth grade, in spite of the fact that it is taught repeatedly in every primary grade. This study was conducted to understand the cognitive processes underlying this difficulty. A counting task was devised, based on Piaget's theory of number, to find out if children in grades 1–5 are constructing a system of tens on a system of ones. Only some children in grades 2–5 evidenced this construction. The implications of the findings for place value instruction are discussed, with observations from second grade classrooms in which children are encouraged to invent their own ways of doing double-column addition.