College physics students' conceptual understanding of area and volume, and relationships between these concepts and students' understanding of physics concepts.

摘要

Concepts such as area and volume are foundational ideas for many concepts introduced in introductory science courses. At the college level, most instructors typically assume that incoming students have already developed an understanding of these underpinning ideas. However, doubt has surfaced in recent years about students' depth of understanding and mastery of these fundamental concepts. Because deficiencies in understanding basic concepts may relate to the learning of subsequent concepts, instructors have expressed concerns about students' understanding of fundamental ideas and if the failure to understand these ideas hinders students' subsequent progress.;This study was designed to (a) investigate the nature of college physics students' understanding of the area and volume concepts and (b) to begin to inquire into the nature of the relationship between students' understanding of the area and volume concepts and their conceptualization of pressure and density.;Four hundred and thirty-one first-semester introductory physics students at Western Michigan University participated in the study. All participants completed a paper-pencil inventory designed to evaluate a student's concepts of area and volume within a framework in which four categories of conceptual understanding were defined. Twenty-seven students participated in a follow-up clinical interview which was designed to elicit additional information about their prior understanding of area and volume. Eight of these students were interviewed a second time to determine their concepts of pressure and density and to provide insights into the link between these concepts and the students' understanding of area and volume.;Results of the analyses of the paper-pencil inventory and the area and volume interviews indicated that a majority of students entering beginning college physics courses have not developed a good conceptual understanding of area and volume and that their thinking is confined to the rote use of mathematical formulae without a supporting understanding of the concepts behind the mathematical expression. Furthermore, analysis of the pressure and density interviews provided evidence that students' understanding of area and volume, how they think and reason about these concepts, and whether they require mathematical procedures and available formulae do influence their ability to conceptualize pressure and density.