Mental, physical, and mathematical models in the teaching and learning of physics

Abstract In this paper, we initially discuss the relationships among physical, mathematical, and mental models in the process of constructing and understanding physical theories. We adopt the assumption that comprehension in a particular field of physics is attained when it is possible to predict a physical phenomenon from its physical models without having to previously refer to the mathematical formalism. The physical models constitute the semantic structure of a physical theory and determine the way the classes of phenomena linked to them should be “perceived.” Within this framework, the first step in order to understand a phenomenon or a process in physics is to construct mental models that will allow the individual to understand the statements that compose the semantic structure of the theory, being necessary, at the same time, to modify the way of perceiving the phenomena by constructing mental models that will permit him to evaluate as true or false the descriptions the theory makes of them. When this double process is attained concerning a particular phenomenon, in such a way that the “results” of the constructed mental models (predictions and explanations) match those scientifically accepted, one can say that the individual has constructed an adequate mental model of the physical model of the theory. Then, in the light of this discussion, we attempt to interpret the research findings we have obtained so far with college students, regarding mental models and physics education under the framework of Johnson‐Laird's mental model theory. The difficulties faced by the students to achieve the understanding of physical theories did not seem to be all of the same level: some are linked to the constraints imposed to the construction of mental models by students' previous knowledge and others, linked to the ways individuals perceive the world, seem to be much more problematic. We argue that teaching should focus on them, at least at introductory level, considering the explicit teaching of the modelling process or at least its systematic practice as a tool that might be appropriate to facilitate this process. © 2001 John Wiley & Sons, Inc. Sci Ed 86: 106–121, 2001.