Mental models are any organized pattern (often a visual representation) consisting of both structure and process (a flow chart of sorts) that helps a student comprehend content knowledge and/or solve problems relative to the principle being taught. Advance organizers are often thought of as mental models.
Mental models (often known as advance organizers) can help teachers to plan with the end in mind: teachers must clarify the big ideas students will be exploring, identify what students already know, and develop links between the two. Additionally, mental models can help students to organize their thinking in a way that is more consistent with how expert problem solvers organize their knowledge. Students who have been taught with the use of mental models in mind, or learn on the basis of advance organizers, have demonstrate much better understanding and comprehension.
The concept map shown below (Determining the Mass of an Electron) is an example provided by Inspiration Software. This concept map would be helpful in getting students to understand relationships between various acts and actors in determining the electron mass. It is probably too complex to serve as a useful mental model as far as the heuristics of problem solving is concerned. In fact, this concept map really doesn't deal with problem solving of the type typically encountered by students. Nonetheless, its construction by students would be an excellent practice in helping to organize content and process knowledge, and more clearly elucidating the interconnections between actors and acts. Creating such a concept map would help to clarify the nature of the scientific process used to determine the mass of an electron.
Next is a simpler mental model that deals with the intellectual exercise of basic "problem solving" (end-of-chapter puzzles). It is rather simple, if not incomplete. As you might have seen in your prior PTE readings, the "Establish Relationship" box is a mystery for most novice problem solvers in physics. They have no idea of the sort of mental processes that go on inside this box and, so, cannot readily learn how to do basic puzzle solving even given a large number of examples. They need to know more explicitly what goes on "inside the box." That's where the next mental model comes into play.
Next is an "Equation Finder" that helps make clear the mental process that is going on in the black box above. While the Equation Finder is not a "visual model" per se, it makes clear the mental process of finding the right equation by explicating each of the steps shown in the above diagram. The following rules are used with the Equation Finder which is handed out to student learning to solve kinematics problems:
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Structured problem solving, the structure itself, can also be thought of as a form of mental model for solving more complex physics problems where the solution depends on more that just "finding the right equation."
