chapter  1
Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis
Byjames Hiebert and Patricia Lefevre
Pages 28

Conceptual and procedural knowledge of mathematics represents a distinction that has received a great deal of discussion and debate through the years. Questions of how students learn mathematics, and especially how they should be taught, turn on speculations about which type of knowledge is more important or what might be an appropriate balance between them. Additionally, discussions of conceptual and procedural knowledge extend beyond the boundaries of mathematics education. The distinction between concepts and procedures plays an important role in more general questions of knowledge acquisition. In some theories of learning and development, the distinction occupies center stage. Although the types of knowledge that are identified from theory to theory are not identical, there is much overlap. The differences are primarily in emphasis rather than kind. For example, Piaget (1978) distinguishes between conceptual understanding and successful action; Tulving (1983) distinguishes between semantic memory and episodic memory; Anderson ( 1983) distinguishes between declarative and procedural knowledge. Parallel distinctions are made in philosophical theories of knowledge. For example, Scheffler ( 1965) distinguishes between the propositional use of "knowing that" and the procedural use of "knowing how to." The distinction between conceptual and procedural knowledge that we elaborate in this chapter is not synonymous with any of these distinctions, but it draws upon all of them.