Students' conceptions of size

CHED 1667

César Delgado, delgadoz@umich.edu, Shawn Y. Stevens, sstevens@umich.edu, and Joseph S. Krajcik, krajcik@umich.edu. School of Education, University of Michigan, 610 East University Avenue, SEB4031, Ann Arbor, MI 48109
Understanding size and scale is a key prerequisite for learning chemistry at the nano, molecular, and atomic scales. We examine students' ideas about the size of objects, the units with which to measure them, and objects too small to see. Interviews with 7-12th students reveal fractured and incomplete conceptual understanding of size. Four ways of conceptualizing size are also investigated: relative (ordering), categorical (grouping), absolute (actual size, with units), and quantitative relative (number of times bigger or smaller one object is than another.) Students' consistency between pairs of conceptions is investigated. Based on the findings, we propose a developmental path for the students understanding size and scale. The link between quantitative relative (times bigger or smaller) and absolute size is last to be formed. Establishing this relationship is essential for proportional thinking (as is used in stoichiometry) and in understanding ratios of properties that change out of proportion to one another (such as surface are to volume). Implications for classroom practice are suggested.