Following the standard form: Effects of equation format on algebraic modeling

When people construct algebraic equations to represent quantitative relations, they often reverse the roles of the variables (6S = P instead of 6P = S). Results from three experiments show that a major reason for such reversal errors is people’s adherence to, and interpretation of, the Standard Form of algebraic models. College students constructed, selected, and interpreted algebraic models that either had the standard multiplication format (MF: ax = y), or the mathematically equivalent division format (DF: y/a = x). A large minority of participants constructed reversed MF models, whereas most participants who were instructed to use DF equations constructed correct models (Experiment 1). Most participants understood that MF and DF models of the same relation should be mathematically equivalent (Experiment 2), but they drew a conceptual distinction between these models (Experiment 3). The authors discuss the impact of notational conventions on people’s interpretation and use of representational tools.