Units Coordination in Composing and Decomposing Whole-Number Composite Units

Students’ ability to operate with increasingly more complex units has been shown to be a key factor in their conceptual development. These abilities have been characterized as stages of units coordination. This article focuses on the domain of composing and decomposing composite units. Using data from a teaching experiment with a third-grade student, I distinguish among instances of her reasoning to postulate three levels of units coordination in this domain as well as developmental steps within each level: the ability to compose composite units but not decompose them; the ability to decompose composite units into single units; and the ability to decompose composite units into smaller composite units.