This article examines the usefulness of manipulatives in light of Piaget's theory of how children acquire logicomathematical knowledge. It argues that since children construct logicomathematical knowledge through their own thinking, manipulatives are desirable when they encourage children to think (i.e., to make relationships through constructive abstraction) in problem solving. A specific object can therefore be beneficial if used in certain ways but not in others. The same object can also be useful at a certain time in the child's development but not at others. We conclude by pointing out that mathematical relationships do not exist in objects and that children do not acquire these relationships through empirical abstraction from objects. © 2001 Elsevier Science Inc.