The project examines changes in cognitive processes resulting from instructional interventions and applies this information in developing a prototype instructional program. The cognitive processes of interest are those involved in constructing meaning for decimal number symbols and using the meaning to solve decimal number tasks. Previous work suggests that for many students, the lack of meaning for written symbols is the source of low performance across a range of mathematical tasks. Classroom instruction designed to promote cognitive processes that create meanings for symbols is implemented and evaluated in the context of decimal fractions. Students in grades 4 and 5 will be instructed in whole classroom settings. Written tests and a series of individual interviews will provide information on changes in key cognitive processes and on how such changes are induced by specific instructional events. The information on cognitive change and instructional effectiveness, gathered through a sequence of instructional studies, will be translated into a prototype instructional program for developing meaning for written symbols in mathematics. Moving from research to practice, from descriptions of students' performance to prescriptions of instructional programs, is a major objective of this program of research. In addition to providing new knowledge and product outcomes, the project provides a model, based on chain of inquiry notions, for translating research into practice.
