Measuring and Modeling: Towards a Conceptual Understanding of Science and Mathematics

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This project will examine the learning of both science and mathematics concepts by 9th and 10th grade students. The investigators intend to conduct a series of teaching experiments designed to study how measuring and modeling activities with real science situations influence student learning of basic notions of calculus (rates of change, level of accumulation-formally called derivative and integral). The students will conduct experiments with sample dynamic systems involving the variation of physical variables over time (falling objects, flowing water, heating substances, etc.); the experimental apparatus will include Microcomputer-based Laboratory probes to measure and represent the relevant physical quantities. The symbol system will be implemented using a computer program with the software environment that will be provided, students will be able to construct models and represent whatever is predicated by a particular model. RESEARCH QUESTIONS The central research question is, "What is the effect of measuring and modeling activities upon students' understanding of science experiments and the underlying calculus concepts of rate of change and integration?" Two additional, related research questions are: (1) How do students use different representations (graphs, numerical data, iconic networks, etc.), as they work to understand an experiment and a model? (2) Which symbol systems are most effective for student learning, and to what extent may the optimal symbol system vary with the domain? OUTCOMES A product of the research will be an analysis of the cognitive models that are stimulated in students by measuring and modeling activities. This analysis will be used to formulate: (1) Guidelines for educational applications: Instructional strategies that enrich students' understanding of science situations combining activities of measuring and modeling. (2) Guidelines for software designers: Criteria for the design of symbol systems and user interfaces that will facilitate the construction of models by the students.