The role of conceptual understanding in children's addition problem solving

The study examined the relationship between children's conceptual understanding and addition problem-solving procedures. Forty-eight 6- to 8-year-olds solved addition problems and, in a 2nd task were prompted to judge whether a puppet could use the arithmetic properties of one problem to solve the next problem. Relational properties between consecutive problems were manipulated to reflect aspects of additive composition, commutativity, and associativity principles. Conceptual understanding was assessed by the ability to spontaneously use such relational properties in problem solving (Task I) and to recognize and explain them when prompted (Task 2). Results revealed that conceptual understanding was related to using order-indifferent, decomposition, and retrieval strategies and speed and accuracy in solving unrelated problems. The importance of conceptual understanding for addition development is discussed.