CONCEPT DEVELOPMENT IN FRACTIONS AND DECIMALS :
TOWARD A THEORETICAL MODEL

This paper describes two aspects of a study of children's concept development in common and decimal fractions. Initially an overall analysis of student performance will suggest a two-part developmental sequence for each type of fraction. The first culminates in an understanding of the basic concept, either the common or decimal form of the fraction. The second cycles then start with these constructs and build, as applications of the concepts are required. Finally, it will be hypothesized that two modes of functioning may be operating simultaneously in the solution of problems involving each type of fraction. The interaction of modes within each problem type and between them may help explain the complexities associated with solving problems involving fractions and decimals. Additional understanding of how these modes operate may contribute to the development of instructional schemes to facilitate children's understanding of the topics.