Students’ and Teachers’ Application of Surface Area to Volume Relationships

The National Science Education Standards emphasize teaching unifying concepts and processes such as basic functions of living organisms, the living environment, and scale (NRC 2011 ). Scale includes understanding that different characteristics, properties, or relationships within a system might change as its dimensions are increased or decreased (NRC 2011 ). One such relationship involves surface area to volume which is a pervasive concept that can be found throughout different sciences. This concept is important for students to not only understand the association of the two, but to also be able to apply this relationship in science contexts. The purpose of this study is to investigate the factors that influence the understanding surface area to volume relationships. This study examined middle school students’, high school students’, and science teachers’ logical thinking skills (including proportional reasoning), visual-spatial skills, and understandings of surface area to volume relationships. Regression results indicated that participants’ reasoning abilities and components of visual-spatial skills could be possible predictors for one’s ability to understand surface area to volume relationships. Implications for teaching scale concepts such as surface area to volume relationships in the science classroom are discussed.