Conceptual and Procedural Knowledge of Mathematics: Does One Lead to the Other?

This study examined relations between children's conceptual understanding of mathematical equivalence and their procedures for solving equivalence problems (e.g., 3 + 4 + 5 = 3 + ). Students in 4th and 5th grades completed assessments of their conceptual and procedural knowledge of equivalence, both before and after a brief lesson. The instruction focused either on the concept of equivalence or on a correct procedure for solving equivalence problems. Conceptual instruction led to increased conceptual understanding and to generation and transfer of a correct procedure. Procedural instruction led to increased conceptual understanding and to adoption, but only limited transfer, of the instructed procedure. These findings highlight the causal relations between conceptual and procedural knowledge and suggest that conceptual knowledge may have a greater influence on procedural knowledge than the reverse.