Student understanding of "surface-area-to-volume ratio" and its relationship to property change in the nano-science engineering context

Since Feynman (1960) invited us to the "room at the bottom", nanoscience and technology has not only attracted considerable interest from scientists and engineers but also from the general public. While it has grown as a new, potentially rich field in science, substantial attention has yet to be given on research about its educational perspectives. Recent studies (Stevens, et al. 2006, Wansom et. al. in press) with scientists, engineers and learning scientists have identified the concept, "surface area to volume ratio" (SA/V) as one of the 'big ideas' or key concepts central to the understanding of nanoscale science and technology. Indeed, SA/V is a prerequisite to understanding size-dependent properties and behaviors and change that are at the core of nanoscience. Previous studies have found that students tend to have difficulty truly understanding SA/V beyond its mathematical equation (Cohen et al., 1999), and that teachers often refer to SA/V without access to students' actual understanding of the concept (Gilbert, 1982). This study explores students' understanding of "surface area to volume ratio" in the nano-science engineering context, focusing specifically on how they understand SA/V in relation to property change. Informed by Variation Theory (Marton & Booth 1997, Marton et al., 2004), this study focused on differences in the ways in which students understand a particular concept or phenomena, with particular attention paid to the aspects of variation that distinguish these different understandings.