Interpretation of Scientific or Mathematical Concepts: Cognitive Issues and Instructional Implications.
Technical rept. Aug 83-Feb 86,
CALIFORNIA UNIV BERKELEY SCHOOL OF EDUCATION
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Scientific and mathematical concepts are significantly different from everyday concepts and are notoriously difficult to learn. It is shown that particular instances of such concepts can be identified or generated by different possible modes of concept interpretation. Some of these modes use formally explicit knowledge and though processes, others rely on various kinds of compiled knowledge. Each mode has distinctive consequences in terms of attainable precision, likely errors, and ease of use. A combination of such modes can be exploited to formulate a ideal model for interpreting scientific concepts so as to achieve both reliable scientific effectiveness and cognitive processing efficiency. This model can be compared with the actual concept interpretations of expert scientists or novice students. All the preceding remarks are illustrated in the specific case of the physics concept acceleration. The discussion elucidates both cognitive and metacognitive reasons why the learning of scientific or mathematical concepts is difficult. It also suggests instructional methods for teaching such concepts more effectively.