A theory of developing competence with written mathematical symbols

Abstract

The paper presents a theory of how competence with written mathematical symbols develops. The theory proposes a succession of cognitive processes that cumulate to yield competence: (1) connecting individual symbols with referents; (2) developing symbol manipulation procedures; (3a) elaborating procedures for symbols; (3b) routinizing the procedures for manipulating symbols; and (4) using the symbols and rules as referents for building more abstract symbol systems. Each process must be engaged, and each must be engaged in sequence. Arguments in support of the theory are drawn from the history, philosophy and psychology of mathematics. The theory has implications for the sequencing and the content of instructional activities. © 1988 Kluwer Academic Publishers.