Conceptual and procedural knowledge of mathematics: Does one lead to the other?

Abstract

ages understand and what they struggle to learn, and examine how instruction influences children's acquisition of both concepts and procedures. The purpose of the present study was to explore the relations between conceptual and procedural knowledge in children learning the principle that the two sides of an equation represent the same quantity. Specifically, the study investigated how instruction about the concept of mathematical equivalence influences children's problem-solving procedures and how instruction about a problem-solving procedure influences children's conceptual understanding of equivalence. In addressing these issues, we also identified what aspects of equivalence fourth- and fifth-grade students understand, what aspects they do not understand but can easily learn, and what aspects they have difficulty learning.