Mental Models

Dedre Gentner, Albert L. Stevens, Dedre Gentner, Albert L. Stevens

• Publisher: Psychology Press
• Year: 2014
• Print ISBN: 9780898592429
• eBook ISBN: 9781317769392
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

This classic volume compiles and describes interdisciplinary research on the formal nature of human knowledge about the world. Three key dimensions that characterize mental models research are examined: the nature of the domain studied, the nature of the theoretical approach, and the nature of the methodology.

1 Some Observations on Mental Models

Donald A. Norman
University of California, San Diego

One function of this chapter is to belabor the obvious; people's views of the world, of themselves, of their own capabilities, and of the tasks that they are asked to perform, or topics they are asked to learn, depend heavily on the conceptualizations that they bring to the task. In interacting with the environment, with others, and with the artifacts of technology, people form internal, mental models of themselves and of the things with which they are interacting. These models provide predictive and explanatory power for understanding the interaction. These statements hardly need be said, for they are consistent with all that we have learned about cognitive processes and, within this book, represent the major underlying conceptual theme. Nonetheless, it does not hurt to repeat them and amplify them, for the scope of the implications of this view is larger than one might think.

In the consideration of mental models we need really consider four different things: the target system, the conceputal model of that target system, the user's mental model of the target system, and the scientist's conceptualization of that mental model. The system that the person is learning or using is, by definition, the target system. A conceptual model is invented to provide an appropriate representation of the target system, appropriate in the sense of being accurate, consistent, and complete. Conceptual models are invented by teachers, designers, scientists, and engineers.

Mental models are naturally evolving models. That is, through interaction with a target system, people formulate mental models of that system. These models need not be technically accurate (and usually are not), but they must be functional. A person, through interaction with the system, will continue to modify the mental model in order to get to a workable result. Mental models will be constrained by such things as the user's technical background, previous experiences with similar systems, and the structure of the human information processing system. The Scientist's conceptualization of a mental model is, obviously, a model of a model.

Some Observations on Mental Models

My observations on a variety of tasks, with a wide variety of people, lead me to a few general observations about mental models:

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 true where the extra actions allow one simplified rule to apply to a variety of devices, thus minimizing the chances for confusions.

Let me now expand upon these remarks. In my studies of human error and human-machine interaction, I have made reasonably extensive observation of people's interactions with a number of technological devices. The situations that I have studied are quite diverse, including such tasks as the use of calculators, computers, computer text editors, digital watches and cameras, video cameras and recorders, and the piloting of aircraft. Some of these have been studied extensively (the computer text editor), others only in informal observation. I conclude that most people's understanding of the devices they interact with is surprisingly meager, imprecisely specified, and full of inconsistencies, gaps, and idiosyncratic quirks. The models that people bring to bear on a task are not the precise, elegant models discussed so well in this book. Rather, they contain only partial descriptions of operations and huge areas of uncertainties. Moreover, people often feel uncertain of their own knowledge—even when it is in fact complete and correct—and their mental models include statements about the degree of certainty they feel for different aspects of their knowledge. Thus, a person's mental model can include knowledge or beliefs that are thought to be of doubtful validity. Some of this is characterized as "superstitious"—rules that "seem to work," even if they make no sense. These doubts and superstitions govern behavior and enforce extra caution when performing operations. This is especially apt to be the case when a person has experience with a number of different systems, all very similar, but each with some slightly different set of operating principles.

Observations of Calculator Usage

Let me briefly review some of my observations on people's use of calculating machines. I observed people using hand-held versions of four-function, algebraic, and stack calculators while they were solving a series of arithmetic problems. They were asked to "think aloud" as they did the problems and I watched and recorded their words and actions. When all problems were complete, I questioned them about the methods they had used and about their understanding of the calculator.¹ Although the people I observed were all reasonably experienced with the machines on which I tested them, they seemed to have a distrust of the calculator or in their understanding of the details of calculator mechanics. As a result, they would take extra steps or decline to take advantage of some calculator features, even when they were fully aware of their existence. Most of the people I studied had experience with several different calculators, and as a result they mixed up the features. They were often unsure which feature applied to which calculator, and had various superstitions about the operations of the calculator. Finally, their estimation of the amount of mental workload required by various strategies often determined their actions; they would perform extra operations in order to reduce the amount of mental effort. Let me provide some examples.

One of the subjects I studied (on a four-function calculator) was quite cautious. Her mental model seemed to contain information about her own limitations and the classes of errors that she could make. She commented: "I always take extra steps. I never take short cuts." She was always careful to clear the calculator before starting each problem, hitting the clear button several times. She wrote down partial results even where they could have been stored in the machine memory. In a problem involving "constant sums," she would not use the calculator's memory because:

I would not have done that because often when you play with the memory and the clear button, if you are not really clear about what it actually clears you can clear out the memory and it—it—I'm too cautious for that. I would be afraid that I'd mess up the memory.

All the people I observed had particular beliefs about their machines and about their own limitations, and as a result had developed behavior patterns that made them feel more secure in their actions, even if they knew what they were doing was not always necessary. A major pattern that seemed to apply to all my calculator studies was the need for clearing the registers and displays. The four-function calculator did need to be cleared before starting new problems, but the stack and algebraic calculators did not. Yet, these people always cleared their calculators, regardless of the type. Moreover, they would hit the clear button several times saying such things as "you never know—sometimes it doesn't register," or, explaining that "there are several registers that have to be cleared and sometimes the second and third clears do these other registers." (The four-function calculator that I studied does require two depressions of the CLEAR button to clear all registers.)

In an interesting complement to the excessive depressing of CLEAR to ensure that everything got cleared, during a problem with the four-function calculator where it became necessary to clear the display during the solution of a problem, one person balked at doing so, uncertain whether this would also clear the registers. All the people I observed expressed doubts about exactly what did and did not get cleared with each of the button presses or clear keys (one of the algebraic calculators has 3 different clear keys). They tended toward caution: excessively clearing when they wanted the calculator to be restarted, and exhibiting reluctance to use CLEAR during a problem for fear of clearing too much.

A similar pattern applied to the use of the ENTER button on the stack calculator. They would push it too much, often while commenting that they knew this to be excessive, but that is what they had learned to do. They explained their actions by saying such things as "It doesn't hurt to hit it extra" or "I always hit it twice when I have to enter a new phrase—its just a superstition, but it makes me feel more comfortable."

These behaviors seem to reflect some of the properties of mental models, especially the ease of generating rules that have great precision and of keeping separate the rules for a number of very similar, but different devices. The rule to hit the CLEAR button excessively allows the user to avoid keeping an accurate count of the operation. Moreover, it provides a rule that is functional on all calculators, regardless of design, and that also makes the user resistant to slips of action caused by forgetting or interference from other activities. All in all, it seems a sensible simplification that eases and generalizes what would otherwise be a more complex, machine specific set of knowledge.

When people attribute their actions to superstition they appear to be making direct statements about limitations in their own mental models. The statement implies uncertainty as to mechanism, but experience with the actions and outcomes. Thus, in this context, superstitious behavior indicates that the person has encountered difficulties and believes that a particular sequence of actions will reduce or eliminate the difficulty.

Finally, there seemed to be a difference in the trade-off between calculator operations and mental operations that the people I studied were willing to employ. For problems of the sort that I was studying, the four-function machine was the most difficult to use. Considerable planning was necessary to ensure that the partial answers from the subparts of the problem could be stored in the machine memory (most four-function calculators only have one memory register). As a result, the users seemed to prefer to write down partial sums and to do simple computations in their heads rather than with the machine. With the stack machine, however, the situation is reversed. Although the machine is difficult to learn, once it is learned, expert users feel confident that they can do any problem without planning: They look at the problem and immediately start keying in the digits.

On Modeling a Mental Model

Consider the problem of modeling some particular person's mental model of some particular target system. Let the particular target system be called t. Before we can understand how a person interacts with a target system, we need to have a good conceptualization of that system. In other words, we need a conceptual model of the system: call the conceptual model of t, C(t). And now let the user's mental model of that target system be called M(t).

We must distinguish between our conceptualization of a mental model, C(M(t)), and the actual mental model that we think a particular person might have, M(t). To figure out what models users actually have requires one to go to the users, to do psychological experimentation and observation.²

In order to effectively carry out such observation and experimentation, we need to consider both representational and functional issues. Let me discuss three of the necessary properties: belief systems, observability, and predictive power. These three functional factors apply to both the mental model and our conceptualization of the model, to both M(t) and C(M(t)). They can be summarized in this way:

Belief System. A person's mental model reflects his or her beliefs about the physical system, acquired either through observation, instruction, or inference. The conceptual model of the mental model C(M(t)), should contain a model of the relevant parts of the person's belief system.

Observability. There should be a correspondence between the parameters and states of the mental model that are accessible to the person and the aspects and states of the physical system that the person can observe. In the conceptual model of the mental model, this means that there should be a correspondence between parameters and observable states of C(M(t)) and the observable aspects and states of t.

Predictive Power. The purpose of a mental model is to allow the person to understand and to anticipate the behavior of a physical system. This means that the model must have predictive power, either by applying rules of inference or by procedural derivation (in whatever manner these properties may be realized in a person); in other words, it should be possible for people to "run" their models mentally. This means that the conceptual mental model must also include a model of the relevant human information processing and knowledge structures that make it possible for the person to use a mental model to predict and understand the physical system.

On the Relationship between Conceptual and Mental Models

Conceptual models are devised as tools for the understanding or teaching of physical systems. Mental models are what people really have in their heads and what guides their use of things. Ideally, there ought to be a direct and simple relationship between the conceptual and the mental model. All too often, however, this is not the case.

That a mental model reflects the user's beliefs about the physical system seems obvious and has already been discussed. What is not so obvious is the correspondence that should hold between the mental model and a conceptual model of the physical system, that is, between M(t) and C(t).

In the literature on mathematical learning models, Greeno and Steiner (1964) introduced the notion of "identifiability." That is, they pointed out that a useful model will have a correspondence between the parameters and states of the model and the operation of the target system. I find that these remarks apply equally well to the problems of mental models. It is important that there be a correspondence between the parameters and states of one's model and the things...

Table of contents

• Cover Page
• Half Title page
• Series Page
• Title Page
• Copyright Page
• Contents
• Introduction
• 1 Some Observations on Mental Models
• 2 Phenomenology and the Evolution of Intuition
• 3 Surrogates and Mappings: Two Kinds of Conceptual Models for Interactive Devices
• 4 Qualitative Reasoning About Space and Motion
• 5 The Role of Problem Representation in Physics
• 6 Flowing Waters or Teeming Crowds: Mental Models of Electricity
• 7 Human Reasoning About a Simple Physical System
• 8 Assumptions and Ambiguities in Mechanistic Mental Models
• 9 Understanding Micronesian Navigation
• 10 Conceptual Entities
• 11 Using the Method of Fibres in Mecho to Calculate Radii of Gyration
• 12 When Heat and Temperature Were One
• 13 Naive Theories of Motion
• 14 A Conceptual Model Discussed by Galileo and Used Intuitively by Physics Students
• Appendix I
• Author Index
• Subject Index