A theory is proposed for how students develop competence with the written symbols of decimal fractions. The theory views competence as the cumulative and sequential mastery of four separate cognitive processes in working with written symbols. The first two processes develop for the user the semantics of the symbol system, and the second two elaborate its syntax. Initial predictions from the theory were tested by instructing small groups of students for about 2 weeks. As predicted, (a) most students were able to acquire the first two processes, (b) these processes generated correct performance and transferred to novel tasks, and (c) it was more difficult for students to acquire the semantic-based processes once they had routinized syntactic processes. The theory and data are interpreted in the context of some persistent issues in mathematics learning.
Diana Wearne, Assistant Professor, College of Education, University of Delaware, Newark, DE 19716
James Hiebert, Professor, College of Education, University of Delaware, Newark, DE 19716