What Are Models and Why Do We Need Them?

Educators and philosophers tout the virtues of the `new' view of theories. Unfortunately, there is no agreed-on name for the new view, but a recently a favored term has been `model based'. I address what a model might be in the context of science education. I am concerned about when and why we need to make the transition from implicit mental models to explicit external models.I explore two theories/models in physics. One draws on misunderstandings of rotating objects. The second concerns concerning density and flotation.I offer two morals:`Models' in physics are often mathematical, and more attention needs to be devoted to integrating mathematics and scienceModels are required in physics when we need an equation in which two variables occur and which is not linearly additive.