On the connection between basic mental models and the understanding of equations

Basic mental models (BMMs) of equations have been proposed as structures describing conceptual understanding of equations. Two of these BMMs are those of equations as relations and equations as objects. We are interested in the relation between these BMMs and special errors associated with working with equations. In this study we concentrate on very basic equations in the form of a ∙ x = b and a + x = b. We are interested in obstacles, errors and misunderstandings concerning these prototypes of equations. An empirical investigation shows that two types of errors, the reversal error and the attribute error, are statistically related to the BMMs students have established