Children’s notions of commutativity: Do we need more than “turn-arounds”?

The author describes a study in which videotaped interviews from the NEMP project were analysed to see how children explained their answers to questions involving the commutative (“changing the order”) properties of addition, subtraction and multiplication. Many of the children, having grasped that “turn-arounds” worked in addition, incorrectly applied that same reasoning to subtraction. Asking students to explain their understanding of why number properties such as commutativity “hold good” helps them to apply those concepts appropriately in a variety of contexts.