Proportional Reasoning Ability and Concepts of Scale: Surface Area to Volume Relationships in Science

The "National Science Education Standards" emphasise teaching unifying concepts and processes such as basic functions of living organisms, the living environment, and scale. Scale influences science processes and phenomena across the domains. One of the big ideas of scale is that of surface area to volume. This study explored whether or not there is a correlation between proportional reasoning ability and a student's ability to understand surface area to volume relationships. Students' knowledge of surface area to volume relationships was assessed pre and post to a one-week instructional intervention involving investigations about surface area to volume as a limiting factor in biological and physical systems. Results showed that proportional reasoning scores of middle school students were correlated to pre-test and post-test assessment scores, and a paired-sample t-test found significant differences from pre-test to post-test for the surface area to volume assessment. Relationships between proportional reasoning, visualisation abilities and success in solving surface to volume problems are discussed. The implications of the results of this study for learning concepts such as magnitudes of things, limits to size, and properties of systems that change depending on volume and surface are explored. (Contains 2 tables.)