This project will test an instructional strategy designed to increase the pool of minority students who are successful in their study of algebra and higher mathematics courses. Since 1979, the Comprehensive Math and Science Program at Columbia University has been developing an instructional model designed to give all entering ninth grade students the opportunity to work to their highest level of capacity in mathematics. Key features of the model are a zero-based start, which makes no assumptions on students' prior mathematics background, and a complementary curriculum, which provides a set of parallel, interlocking mathematics courses that substantially increases the rate of mathematics instruction over a four semester period. Preliminary tests of the model in New York City schools have yielded encouraging results. In the current project, the instructional materials will be completed and the model will be extensively tested in New York City and in Fulton County, Georgia. The testing will be accompanied by the development of an apprenticeship model for teacher training, which will pair new teachers with experienced teachers in the interlocking courses of the program.
Cognitive research indicates that science experts commonly use diagrams as mediational tools for reasoning visually. But in science education materials and practices, visuals are typically "aids" rather than fundamental representations. This research will examine how students learn to comprehend, use, and construct diagrams as thinking tools. It will focus on the diagram-dense field of beginning optics. The project has two interacting phases: research on how students understand static optics diagrams, and development and refinement of prototype computer- based dynamic diagrams and diagramming tools. Specific tasks are: (1) Pilot research, and analysis of diagrams in optics texts, (2) research on instructional practices with these diagrams, (3) research on student understanding and use of diagrams, (4) design and develop interactive diagrams and a dynamic diagram-construction kit, (5) carry out research with prototypes, and (6) formulate and disseminate implications for creation and use of interactive diagrams in science education. Such research on visual education in science will help guide development of new curricula and software for science education. The project team of cognitive scientists, science educators, graphics specialists, and systems developers is devoted to promoting learning and reasoning in science with new data, theory, and innovative prototypes of dynamic diagrams. These interdisciplinary activities more directly link science education research, materials development, and classroom activities. Cost sharing is provided by the Institute for Research on Learning which is contributing indirect costs and APPEL which is contributing four MacIntosh II systems.