Archive: October 13th, 2008

Gentner and Stevens: Mental Models

[Readings] (10.13.08, 4:12 pm)


This collection was released in 1983, the same year as Jonson-Laird’s publishing of a book with the same name. While Johnson-Laird is concerned with developing a linguistic theory of mental models grounded in computational theory, Gentner and Stevens present a collection of papers on how mental models are used in numerous applications. There is a strong theme of using models in science, especially science education and expert reasoning.

My concern with mental models is twofold: I want to understand how to model characters within simulation, and I also want to understand how users will form models after interacting with a simulation. I am not as concerned with the instruction and dissemination of a specific model, but rather, I want to find ways of provoking introspection and criticism of models.

In these essays, individuals have and use models, often conflicting models. With so many conflicting models it seems almost a wonder that people can think at all. Model use is often ingrained and automatic, but only when the model appears to be inconsistent with the subject to which the model is applied, does the model become suddenly a conscious jumble of ideas and rules. My reading of Gentner and Stevens is going to primarily be oriented towards examining these areas of model formation, use, and critique.


Mental models, as argued here, are how we understand the world. Research on them is about furthering and deepening self understanding. Applied use of mental models is pedagogical, teaching better models, and teaching models better, for applied use. Mental models research tends to have three dimensions. These are good guidelines for considering models of fictional domains.

  1. Domains. In mental models research, the problem domains should be something tractable, where it is possible to discern an expert from a novice. Thus, a domain such as fluid dynamics is more tractable than interpersonal dynamics. It is easier to distinguish an expert in a scientific domain than a humanistic one.
  2. Theoretical Approach. The research should have a formal representation of the models to be used. Representations are usually made with computational semantics. I would argue that not all domains will have the same representations, but some formalization is necessary.
  3. Methodology. The methodologies used are highly varied and eclectic. This can be anything from protocol analysis, to psychological experiments, to simulation and comparison with experts.

This is priceless: “From what we have said so far, it is clear that the ideal mental-models researcher would be a combination of cognitive psychologist, artificial intelligence researcher, anthropologist, linguist, and philosopher, and certainly a knowledgable practitioner of the domain being studied.” The suite of skills is very reminiscent of the artist/programmer and theorist/practitioner interdisciplinary hybrids.

Donald Norman: Some Observations on Mental Models

Norman’s paper is to essentially extend the introduction and explain a little bit more about what mental models are and what sort of properties they have. Norman explains that his goal is to partly belabour the obvious. He gives a few useful bullet points about how he sees mental models (p. 8):

  1. Mental models are incomplete.
  2. People’s abilities to “run” their models are severely limited.
  3. Mental models are unstable: People forget the details of the system they are using, especially when those details (or the whole system) have not been used for some period.
  4. Mental models do not have firm boundaries: similar devices and operations get confused with one another.
  5. Mental models are “unscientific”: people maintain “superstitious” behavior patterns even when they know they are unneeded because they cost little in physical effort and save mental effort.
  6. Mental models are parsimonious: Often people do extra physical operations rather than the mental planning that would allow them to avoid those actions; they are willing to trade-off extra physical action for reduced mental complexity. This is especially ture where the extra actions allow one simplified rule to apply to a variety of devices, thus minimizing the chances for confusion.

Norman also explains some formalizations of models. A system is t, the conceptualization is C, and the model M. The conceptualization, as defined, is the scientific or expert model of the system. Four elements may be observed: t, the system itself. C(t), the expert model of the system. M(t), the user’s model of the system. Finally, C(M(t)) is the researcher’s understanding of the user’s mental model. There are three issues related to understanding models: beliefs, observability, and predictive power.

The formulation of conceptual models is as tools for teaching a system. This phrasing privleges it to other kinds of models. It suggests thtat ideally, M(t) = C(t). This is the notion of classic authorship, privleging the author’s interpretation, precisely the sort of thing that Barthes rebelled against. The idea is necessarily that the expert’s understanding is the ideal way, and that a user’s model is wrong if it does not line up. This makes sense when the subject matter is something like a Nuclear reactor, where it is important for users have a strong and correct model that reflects the system itself, but it is less explicable when dealing with everyday artifacts that may be used toward a variety of ends, as opposed to original stated goals.

Jill Larkin: The Role of Problem Representation in Physics

The problem here is the relationship between ordinary human prediction with formal physics. A naive representation or model uses objects in the real world, but an expert will construct a special model in addition, that replaces objects with physical objects (that have special properties), and also includes fictitious entities, such as forces and moments.

Physicists use several schemas for producing physical representations. The schemas are the “forces schema” and the “work-energy schema.” Both of these have internally consistent sets of rules and operations. They are consistent with each other, but require very different understandings of the underlying problems. Representations have rules for construction and extension, and these are very different between the two schemas.

Larkin examines how several users of varying proficiency apply these schemas in problem solving, from easy problems, to hard, and then very hard problems. Harder problems require the solver to make use of multiple schemas and translate between them. In the very hard problem, the subjects will form a model with a schema, attempt to work with it, and then discard it if it is inconsistent. The very hard problem can be solved using one of the schemas, but the translation from the given information in the problem cannot be filled in directly. Expert subjects quickly select a schema and then spend time constructing the model itself.

Novice problem solvers, specifically students, quickly match problems to quantitative models, without constructing a physical representation. This seems to be done via pattern matching, identifying elements in the problem that fit into to learned formulas.

Williams, Hollan, Stevens: Human Reasoning About a Simple Physical System

The goal here is to understand reasoning with mental models. A model is a tool used in reasoning. Understanding a model and how it is used informs understanding of human mistakes and reasoning. The authors give an extremely useful formalization of models. A model is runnable, with autonomous objects with some internal topology. An autonomous object has an explicit state, relations, parameters, and rules. The model is a collection of autonomous objects. (p. 133-134)

The concept of an autonomous object is extremely important to the author’s formalization of models here. It further strongly resembles the way to construct a system for simulation. If objects are autonomous, the model can simply be run by gathering the objects together and applying the rules of the system over time. According to the description given, autonomous objects are generally opaque, but may themselves be deconstructed into models themselves. Generally, they will only have 3 to 4 ports with which to interact with other objects.

The rest of the chapter explores the applications of this theory of mental models to subjects understanding of a heat exchanger. The exchanger is the simple physical system, and the authors examine the models that subjects form while trying to answer questions about the system. There are about three models used, which are inconsistent with each other and thus exclusive. The way subjects form the models is analyzed according to inference diagrams. Models are shifted rapidly, and subjects uses multiple models to answer questions. New models are only created when some form of inconsistency occurs.

Each of the models also appear to be grounded in some sort of metaphorical analogy. For example, the pipes in the exchanger are containers: they contain heat. Thus, the subject reasons about the pipes as they would reason about containers.

Michael McCloskey: Naive Theories of Motion

This section is concerned with understanding students naive theories of motion. Many students make very similar mistakes regarding the motion of objects. What is startling is that the naive theoriy of motion is internally conistent, and shared very consistently among the observed subjects. That means that most incorrect responses are of the same inherent type, and stem from a single misconception about objects.

The naive theory of physics is essentially “impetus” theory, which has roots in pre-Newtonian science. The idea with impetus theory is an object that is moving has some internal force that keeps it going. Without extra effort spent pushing the object, the impetus will eventually subside and the object will stop. This is fascinating because it relates back to emobodiment and self-analogy: Young learners will understand objects as they understand themselves: “I have to expend effort to keep moving, so other objects moving must do that as well.” This model is pervasive, and even knowledgable subjects who understand the principles of energy and momentum will explain those concepts in terms of impetus.

There is a brief discussion on education. We should think here about exploring more complex models (that do not have a necessarily correct solution to every problem). What is revealing is that for dispersal of impetus theory, it is not enough to simulate the real models, but rather deconstruct the faulty ones. This is important in situations where models are ambiguous or complicated. There is an emphasis here on exposure. It is of utmost importance to expose the internal workings of flawed or faulty models.

Reading Info:
Author/EditorGentner, Dedre and Stevens, Albert
TitleMental Models
Tagsspecials, mental models
LookupGoogle Scholar, Google Books, Amazon