Gentner, D., & Stevens, A. (Eds.). (1983). Mental Models. Lawrence Erlbaum Associates. Retrieved from http://amzn.com/0898592429

This is an entire book, and as such, I am not going to use the same structure for this post as I have been using. Instead, I’ll have a separate section per chapter and give a brief summary for each chapter.

Chapter 1

Norman, D. (1983). Some Observations on Mental Models. 7–14.

Norman distinguishes between a few different types of models/systems:

Target system – the actual system under consideration
Conceptual model – a model of the target system as construed by an expert (e.g. an educator)
Mental model – a model of the target system as constructed mentally by individuals attempting to reason about it
Scientist’s conceptualization – a model of someone’s mental model, constructed by a scientist trying to understand the mental model

He also discusses the fact that mental models are messy, and won’t be describable by “precise, elegant models”. He gives as example the behavior people exhibit when learning to use a calculator, such as when they attempt to clear the register multiple times. I actually wonder if that type of behavior could be described by a MDP where there is some probability that when you press the clear button, it doesn’t fully clear (reflecting motor noise, for example).

Chapter 2

diSessa, A. (1983). Phenomenology and the Evolution of Intuition. 15–33.

diSessa discusses what kinds of concepts novices have, how and when they use them, and how they come to be replaced by higher-order concepts by experts. He introduces the notion of a “p-prim”, short for phenomenological primitive, which seems to be something like a core concept in a mental model which originally exists on an intuitive level and may eventually be replaced by higher-order concepts and knowledge as a student gains more expertise in a topic. P-prims are used according to two notions of priority: cuing priority and reliability priority. The cuing priority is essentially a heuristic about “how likely the idea is to be profitable”. The reliability priority is essentially a heuristic about how relevent the idea is to the current situation.

For example:

If a ball is dropped, it picks up speed and hence kinetic energy. When the ball hits the floor, however, it stops (before bouncing upward again). At that instant, there is no kinetic energy since there is no motion. Where did the energy go?

To answer this question, people will rely on p-prims such as “rigidity” and “springiness”. For an expert, “rigidity” has a lower cuing priority than “springiness”, and thus they will be less likely to rely on rigidity as an explanation, whereas a novice might use rigidity. An expert has different notions of how reliable “springiness” is to the problem (e.g. seeing a bouncing ball as springy) than a novice would.

Chapter 3

Young, R. (1983). Surrogates and Mappings: Two Kinds of Conceptual Models for Interactive Devices. 35–52.

Young discusses the “user’s conceptual model” (UCM), and how there are different types or aspects of mental models:

Strong analogy, e.g. “a video display unit is like a typewriter”
Surrogate, e.g. a runnable model of the device
Mapping models, which “mediate between the task the user is trying to perform and the actions he must take”
Coherence, i.e. making sure a set of facts fit within a particular schema
Vocabulary, i.e. how concepts in the mental model are represented (either as a new symbol entirely, or combinations of existing symbols)
Problem space
Commonality

Young describes in depth surrogate models and mapping models, and conclues that surrogate models are unrealistic because people don’t necessarily need to know how a device is implemented ot understand how it works.

Chapter 4

Forbus, K. (1983). Qualitative Reasoning about Space and Motion. 53–73.

Forbus discusses how qualitative reasoning can be used to reason about spatial and physical scenes, for example, a bouncing ball. His use of qualitative simulation is related to that discussed by Kuipers, though it is different in that Forbus explicitly does include some numerical information about the location and physical properties of the ball. There are a few components to Forbus’ system (FROB):

The space graph, which encodes geometry and locations of free space. Space is divided into non-overlapping regions which are connected if they are adjacent. The edges of the regions are also included in the space graph, and have relations to the nodes (regions) like left, right, up, down.
The action sequence is similar to the qualitative behavior of the system as described by Kuipers. It is a sequence of qualitative motion types (e.g. “fly” or “collide”) and qualitative states (e.g. the place and approximate heading) that alternate with the state of the object in between motions (which is a quantitative representation of location, speed, and heading).
The action sequence is described using “constraint language”, which includes “equations describing projectile motion to compute numerical values if numerical descriptions of the state parameters are obtained” (pg. 60). This is a departure from the qualitative simulation used by Kuipers, which does not require any precise equations—the whole point of the system described by Kuipers is to give a qualitative explanation of the behavior of the equation.

The FROB system seems to me to be a simplified form of a regular physics engine: it makes a lot of the same assumptions (e.g. rigidity, point masses) and even actuall encodes the equations of motion. The more qualitative aspects of it seem to come from the ability to ask things like “will these two objects collide”, but the constraints required to answer these questions are put in by the human user. For example, in Figure 4.8, the constraint is added that “Fred” can’t be at segment S31—but what would be cool to see is if that segment were actually a wall, that the system would still figure out that the objects can’t collide. My sense is that it would, but I think it would then require manual repartitioning of the space.