A difficulty for those who want to understand or to appraise mental models is that their proponents seem to have

somewhat different views.

Rips (1986, p. 259)

Although the phrase "mental models" is ubiquitous in

the literature, there are surprisingly few explicit defini-

tions of them.

Rouse and Morris (1986, p. 349)

The concept of "mental models" has been vitally important to the field of system dynamics since its inception. Information about the structure and relationships in dynamic systems gleaned from mental models, for example, are what allow system dynamic computer models to be constructed in the absence of written and numerical data. System dynamics researchers have in fact devoted a substantial portion of their research effort to developing a wide variety of techniques and procedures for eliciting, representing, and mapping mental models to aid model building (see Hall et al., 1994; Vennix, 1996). And, the stated goal of most educational interventions based on systems thinking, management flight simulators, or system dynamics model building is to change or improve mental models in order to, in turn, improve the quality of the dynamic decisions based upon them.

Mental models are thus the stock in trade of research and practice in system dynamics: they are the "product" that modelers take from students and clients, disassemble, reconfigure, add to, subtract from, and return with value added. An understanding of exactly what mental models are, what properties and characteristics they have, and how they influence and are influenced by learning and decision making is clearly essential for such an enterprise to succeed. Given their importance to the field, one might expect mental models to be a concept that is as clearly defined and universally understood as such other centrally important system dynamics concepts as stocks, flows, and feedback. But as we will show, this is clearly not the case: explicit definitions of mental models in the system dynamics literature are in fact quite rare. Those definitions that are available are usually general and vague, and the definitions offered by different authors often markedly disagree.

The ambiguity and confusion resulting from the lack of a clear, specific, and mutually agreed upon conceptual definition of the term "mental models" has several important consequences for the field. In the absence of a clear consensus, different researchers and practitioners develop and apply idiosyncratic conceptions of mental models and techniques for mapping them to their own work. The dizzying array of different ideas that result from this process hinders communication between researchers, as marked differences of opinion hidden under the same generic name go unnoticed and unexamined. Since each research group employs, to some degree, a different technique for eliciting and mapping mental models based on their unique definitions of them, it is also difficult for research results to cumulate across research programs. In addition, the various definitions of mental models used in the field of system dynamics diverge from the way in which these same terms are used outside the field, interfering with the ability of system dynamicists to share their insights, techniques, and research results with researchers from other disciplines. Finally, the field's apparent willingness to accept the current level of ambiguity has likely discouraged researchers from developing more sophisticated definitions and descriptions of mental models and their impacts on dynamic systems, which in turn makes the process of incorporating mental models into computer simulation models less reliable.

The primary goals of the present paper are (a) to reduce the amount of confusion in the literature about the nature of mental models by "unbundling" the mental models concept into a set of more specific interrelated concepts currently used in system dynamics and cognitive science and (b) initiate a dialogue within the field of system dynamics that will hopefully lead to a clearer, more sophisticated, and ultimately shared understanding of the concept of mental models. Toward these ends, we will review, compare, and analyze existing definitions of mental models within the system dynamics literature; compare these definitions with those employed by other fields interested in the study of mental models, such as cognitive psychology, cognition and instruction, human-computer interaction, and risk perception and communication; identify the shortcomings of existing definitions; and, following established criteria, propose a new, more comprehensive conceptual definition of "mental models" for use in system dynamics. The present work will not attempt to provide a comprehensive theory of the role of mental models in dynamic decision making [see Richardson et al. (1994) for a recent example of such an effort] but will instead focus on clarifying definitions and providing explanations that can serve as the basis of future theory-building, research, and applications.

Defining Mental Models: A Review of the Literature

The literature that touches on the concept of mental models, both within and particularly outside the field of system dynamics, is truly vast, making it impractical to review every article or book that mentions mental models or related concepts. We have therefore focused the following review on sources for which mental models serve as the main focus of the work and sources which, in the course of addressing other topics, explicitly attempt to define mental models or describe their characteristics. In addition, attention is restricted to literatures in which the term "mental model," rather than related terms such as "cognitive map" or "schema," is commonly and widely used.

System Dynamics

In system dynamics the mental model concept dates back to Industrial Dynamics, where Forrester (1961) offers the following introduction to mental models:

A mental image or a verbal description in English can form

a model of corporate organization and its processes. The

manager deals continuously with these mental and verbal

models of the corporation. They are not the real corporation. They are not necessarily correct. They are models to substitute

in our thinking for the real system that is represented (p. 49).

Forrester (1971) elaborates on these ideas, providing the following description of mental models:

The mental image of the world around us that we carry

in our heads is a model. One does not have a city or a

government, or a country in his head. He has only selected

concepts and relationships, which he uses to represent

the real system. (p. 213)

He goes on to describe some of the characteristics of mental models:

The mental model is fuzzy. It is incomplete. It is

imprecisely stated. Furthermore, within one individual,

a mental model changes with time and even during the flow

of a single conversation. (p. 213)

The main shortcoming of mental models, in Forrester's opinion, is

that their dynamic consequences cannot be simulated mentally, providing the primary rationale for the need to use system dynamics modeling to support dynamic decision making.

Several system dynamics researchers have subsequently added to this list of characteristics of mental models. Richardson and Pugh (1981), for example, describe mental models as "fuzzy and implicit," containing "rich, intuitive detail," highly adaptable, and "unable to handle complexity." Meadows et al. (1992) suggest that mental models are "extremely simple compared to reality" and "mostly wrong."

According to Vazquez et al. (1996), mental models are "not fixed," "not simple," and "contain rich information." Sterman (1994) describes mental models of systems as being "vastly simplified compared to the complexity of the systems themselves" and "dynamically deficient" in the following ways:

. . . people generally adopt an event-based, open-loop view

of causality, ignore feedback processes, fail to appreciate

time delays between action and response and in the reporting

of information, and are insensitive to nonlinearities that may

alter the strengths of different feedback loops as a system

evolves . . .

Many of the above-described limitations of mental models have been confirmed by controlled experimental research (see, e.g., Dörner, 1980; Sterman, 1989a, 1989b; Brehmer, 1992; Kleinmutz, 1993).

Thus, system dynamics researchers generally agree about the primary shortcomings of mental models. However, there is much less agreement on precisely what mental models are. In fact few system dynamics authors attempt to provide an explicit definition of what they mean by the term "mental models." The following are some representative examples of available definitions and descriptions:

Each person carries in his head a mental model, an abstraction

of all his perceptions and experiences in the world, which he

uses to guide his decisions about future actions. . . .[mental

models are] intuitive generalizations from observations of

real-world events. (Meadows et al., 1974, pp. 4-5)

. . . a "mental model" . . . is an understanding of the operation of the real world. (Randers, 1980, p. 119)

mental models . . . contain the ideas, opinions, assump-

tions, etc. with respect to a policy problem and related

issues (Vennix, 1990, p. 16)

"Mental models" are deeply ingrained assumptions, generalizations, or even pictures or images that influence

how we understand the world and how we take action.

Very often, we are not consciously aware of our mental

models or the effects they have on our behavior (Senge,

1990, p. 8)

What we carry in our heads are images, assumptions, and

stories . . . Mental models can be simple generalizations . . .

or they can be complex theories . . .(Senge, 1990, p. 175)

The term mental model means the conceptual model that

each member of the management team carries in his or her

head to explain the way the business (or more generally, the outside world) operates. . . . So it is useful to think of mental models as a dynamic pattern of connections comprising a core network of "familiar" facts and concepts, and a vast matrix of

potential connections that are stimulated by thinking and by

the flow of conversation. (Morecroft, 1994, p. 7)

Mental models are the images, assumptions, and stories

which we carry in our minds of ourselves, other people, institutions, and every aspect of the world. (Senge et al.,

1994, p. 235)

. . . mental models are multifaceted, including distinguish-

able submodels focused on ends (goals), means (strategies,

tactics, policy levers) and connections between them (the means/end model). (Richardson et al., 1994)

In system dynamics, the term mental model stresses the

implicit causal maps of a system we hold, our beliefs about the network of causes and effects that describe how a system operates, the boundary of the model (the exogenous variables) and the time horizon we consider relevant -- our framing or articulation of a problem. (Sterman, 1994, p. 294)

. . . mental models are some sort of psychological construction

with an intended representational content. Mental models

lead to certain descriptions of reality that are usually expressed

by a set of sentences in ordinary language, describing both the

interactions among the elements within the system and their

external influences. (Vazquez et al., 1996, p. 25)

These statements and others available in the literature show evidence of substantial disagreement on some centrally important questions about how the term "mental models" should be used. For example, are mental models deeply ingrained and relatively stable (Senge, 1990) or fleeting and unstable (Forrester, 1971)? Are they "extremely simple" (Meadows et al., 1992), "not simple" (Vazquez et al., 1996), or "ranging from simple . . . to complex" (Senge, 1990)? Are they "images" (Forrester, 1971; Senge, 1990), "facts and concepts" (Morecroft, 1994), or "beliefs about . . . causes and effects" (Sterman, 1994)? Should a single belief be considered a mental model (Schley and Laur, 1996) or should the term instead refer to "sets of interacting beliefs" (Ford et al., 1993)? Are mental models an "abstraction of all . . . perceptions and experiences in the world" (Meadows et al., 1974) or some subset of these abstractions that are applied to a particular problem (Vennix, 1990)? Should the term "mental models" refer to one particular type of cognitive structure [e.g., "dynamic patterns of connections" (Morecroft, 1994)] or to a set of different types of cognitive structures (Richardson et al., 1994)?

Although the contents of these definitions vary widely, their character, with a few exceptions, generally does not. First, all of the definitions lack coverage of issues critical for defining mental models:

although some of the definitions answer some of the above-stated questions, none answer all or even most of them. Second, the majority of the available definitions are brief, simple, and somewhat vague. Brevity and simplicity, of course, are not necessarily bad, particularly given how much is still unknown about the structure, content, and function of mental models: conceptual definitions should not be more specific than can be supported by current research. Vagueness, on the other hand, should be avoided: definitions that describe mental models using terms that are equally as ill-defined (e.g., images, assumptions, generalizations, perceptions) hinder the process of achieving consensus. Third, in most of the definitions the term "mental models" is used very generally to indicate any among a wide variety of quite different and distinct mental constructs. Very general terms, of course, can be quite useful if they serve to organize a set of more specific, subordinate terms. However, that is not the case here: of the references reviewed for this paper, for example, only Richardson et al. (1994) attempt to build a richer, more sophisticated glossary of terms and concepts for describing mental models.

Finally, references to cognitive psychology and other fields with long histories of research on mental models and other cognitive structures and processes are relatively rare. Although some authors refer briefly to this literature, only Sterman (1994) and Richardson et al. (1994) appear to have reviewed substantial portions of it with a critical eye in order to propose definitions of mental models

that are particularly useful for research and practice in system dynamics.

In short, in system dynamics the term "mental models" is currently ill-defined and means too many different things to different people to be useful in research and practice. To inform the development of an improved definition, we turn now to a brief review of the long and varied history of the mental models concept in psychology and several related applied fields.

Psychology, Cognitive Science, and Related Fields

In psychology the mental model concept can be traced back to

Craik's (1943) book The Nature of Explanation. In that work, written when psychology was still dominated by Behaviorism, Craik proposed that people construct internal symbolic representations or models of external events. Craik defined the term "model" as:

. . . any physical or chemical system which has a similar

relation-structure to that of the process it imitates . . . it is a physical working model which works in the same way as the process it parallels (p. 51)

Thus for Craik human reasoning involves mental simulation of dynamic internal representations of the external world.

Over time, the view that human judgment, reasoning, and problem solving is based on the manipulation of complex mental representations that intervene between stimuli and behavioral responses has, of course, become the dominant view in psychology and is the very foundation of the disciplines of cognitive psychology and cognitive science (Gardner, 1985; Hunt, 1989). However, although virtually all psychologists now agree that human cognition and behavior cannot be understood without

postulating some form of mental representation of external events,

the study of mental models of systems of the sort described by Craik and of interest to system dynamics researchers has, for a variety of reasons, not been a major focus of research in psychology. For example:

1. A substantial portion of the research effort in cognitive psychology has been devoted to developing and testing alternate theories of how knowledge is represented in the mind in long-term memory (Atkinson and Shiffrin, 1968). The cognitive structures proposed, for example, conceptual networks (Collins and Loftus, 1975), propositional networks (Anderson, 1983), and connectionist networks (McClelland and Rumelhart, 1986), are general, very large, and universal, and their form does not model the structure of the external world. This view is quite different from the mental models approach, which supposes the existence of different, specialized cognitive structures in long-term memory for different tasks and situations.

2. Other researchers in cognitive psychology have proposed and studied a large number of specialized cognitive structures that differ widely in size, form, function, and character. They also vary in duration: some are thought to be stored permanently in long-term memory, whereas others are thought to be constructed and stored only temporarily in short-term or working memory (Baddeley, 1986) or even more briefly in sensory memory (see Baddeley, 1990). According to this view, people have different cognitive structures that serve different purposes: e.g., scripts (Schank and Abelson, 1977; Bower and Morrow, 1990) for understanding routine activities, situation models for understanding text (Van Dijk and Kintsch, 1983), causal scenarios (Read, 1987; Tversky and Kahneman, 1973; Kahneman and Tversky, 1982) or stories (Pennington and Hastie, 1991) to aid in making causal attributions or judging likelihood, scenarios (Jungermann and Thuring, 1987) to enable judgmental forecasting, schemas (Fiske and Taylor, 1991) for perceiving and remembering information about people, imagery (Kosslyn, 1990) that allows objects not physically present to be scanned and mentally manipulated, and problem representations (Greeno, 1977) to help structure and manipulate information during problem solving. From this perspective mental models of systems are just one among a large family of cognitive structures, and thus they are not considered to be so centrally important to human cognition as they are described in the system dynamics literature.

3. Psychologists generally view the detailed study of mental models

as a difficult and complex, if not impossible, task. According to this view, mental models are continually changing and efforts to elicit, measure, or map them can themselves induce changes in mental models. When people are asked to report their mental models, they may fail to report them accurately for any of several reasons: e.g., they may simply not be aware of the contents of their mental models; they may feel compelled to invent explanations and answers on the spot that did not exist until the question was asked; or they may deliberately or unconsciously change their answers to correspond to the answers they think the researchers want to hear (Norman, 1983). The methodologies that cognitive psychologists believe are necessary to address these problems and to minimize measurement error [see, e.g., Doyle et al. (1997)] are labor-intensive, time-consuming, and expensive, and are therefore only rarely applied.

4. The theoretical basis and empirical evidence for mental models has a large following in the cognitive psychology literature, but the topic still generates controversy. For example, Johnson-Laird's (1983) widely cited work on mental models in conditional reasoning [and his subsequent extension of the mental models approach to explain probabilistic thinking (Johnson-Laird, 1994)] has been challenged by other researchers who suggest that human ability to reason deductively and inductively is best explained by supposing that people use abstract reasoning rules or principles either in place of (Rips, 1986; 1990; O'Brien et al., 1994) or at least in addition to (Roberts, 1993) constructing and manipulating mental models. Galotti et al. (1986) have suggested that the extent to which people use mental models versus abstract rules varies with experience, with experts relying more on abstract rules than novices. Conflicting evidence for and against mental model theories also exists in other domains, e.g., in the study of text comprehension [compare, e.g., Bower and Morrow (1990) and Wilson et al. (1993)]. Thus, in contrast to the field of system dynamics, in cognitive psychology the jury is still out on whether or not human reasoning is primarily based on the manipulation of mental models.

5. System dynamics researchers have examined the evidence suggesting that people cannot "run" or mentally simulate any but the simplest of mental models without error and have responded by developing computer simulation software and other cognitive decision aids designed to improve people's ability to determine the dynamic implications of their mental models. Cognitive psychologists have drawn the same conclusions from the evidence, but have generally responded in a quite different way -- by assuming that manipulation of mental models is not a plausible explanation for human judgment and problem solving in complex environments and developing descriptive models of what people do instead. This has led researchers to focus less on cognitive structures and more on the cognitive processes, particularly simplifying heuristic rules (Newell and Simon, 1972; Kahneman et al., 1982), through which information is mentally reduced and transformed in the face of complex decisions and problems.

For these reasons the mental models concept and the term "mental models" has historically been (and is currently still) widely used in only a handful of distinct research domains in and related to cognitive psychology and cognitive science. The theory behind the mental models approach in cognitive science has in fact not progressed very far beyond the ideas offered by Johnson-Laird (1983) and the authors collected in Gentner and Stevens (1983) that inspired most of the subsequent research on mental models. Much of the research on mental models has therefore taken place in interdisciplinary fields on the fringes of cognitive science and has been applied rather than theoretical in nature.

Most prominent among the fields related to cognitive science that emphasize mental models are deductive reasoning, human-machine and human-computer interaction, cognition and instruction, and risk perception and communication, so it is these fields which have been reviewed for statements related to defining and characterizing mental models. Virtually all of these fields agree with each other and with the system dynamics literature that the most noteworthy characteristics of mental models are various deficiencies that arise from bounded rationality (Simon, 1956) and the limitations of experience. Johnson-Laird's (1983) mental models theory was in fact proposed in order to explain the errors people typically make when trying to answer even fairly simple logical syllogisms. These errors are thought to arise from difficulties in constructing mental models due to cognitive limitations; in fact, the main empirical support for the theory is the observation that the more different mental models that must be constructed to reason about a syllogism, the more difficult it is for people to solve (Johnson-Laird et al., 1989).

In the human-machine interaction field, Norman (1983) has described mental models as "incomplete," "unstable," and "unscientific." Like Forrester, Norman believes that people's ability to mentally simulate their mental models is "severely limited." Norman goes on to 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. (p. 8)

Other authors in the field of human-machine interaction have similarly observed that mental models of mechanical devices are typically oversimplified, inaccurate, and incomplete (see, e.g., Borgman, 1986; Moray, 1987; Williams et al., 1983).

Not surprisingly, since researchers in the areas of cognition and instruction generally study novices (and sometimes children) attempting to understand technical and scientific subjects, they also report finding a wide variety of errors and omissions in people's mental models. Studies of mental models in the domain of physics have found, for example, that most people hold incorrect, "pre-Newtonian" mental models concerning the laws of motion (McCloskey, 1983a, 1983b) and draw incorrect analogies between how water flows in a river and how electricity flows in a wire when forming mental models of electrical circuits (Gentner and Gentner, 1983). Similarly, studies of novices learning to program and use computer software (see, e.g., Bayman and Mayer, 1983; Staggers and Norcio, 1993; and Janosky et al., 1986) have documented serious flaws in people's mental models of how computers work that hinder learning.

In the field of risk perception and communication, problems with mental models are, if anything, worse than in the other fields described, since the topics under investigation are typically very complex social/ technological problems. Studies in this field have shown, for example, that people's mental models of global warming tend to confuse ozone depletion with the greenhouse effect and weather with climate (Kempton, 1991; Bostrom et al., 1994; Read et al., 1994); their mental models of radon risk often include health effects that have no basis in fact and mistakenly assume radon contamination is permanent (Bostrom et al., 1993); their mental models of toxicology are typically insensitive to dose (Kraus et al., 1992); and their mental models of the risks associated with electric fields generally reflect a failure to differentiate between electric and magnetic fields and to take into account how quickly the strength of fields decreases over distance

(Morgan et al., 1990)

Thus, as in the system dynamics literature, almost all of the researchers who study mental models in cognitive science and related fields agree on what the shortcomings of mental models are. However, again in parallel with the situation in system dynamics, explicit definitions are rare, and a review of representative definitions uncovers very little agreement either within or between literatures when it comes to describing mental models.

Johnson-Laird's work on the role of mental models in deductive reasoning is probably the most widely cited work on mental models in any field, and is therefore an appropriate place to begin a review of how mental models are defined in cognitive science and related fields. According to Johnson-Laird (1989),

a mental model can be defined as a representation of a body of knowledge -- either long-term or short-term that meets the following conditions: 1. its structure corresponds to the

structure of the situation that it represents. 2. It can consist

of elements corresponding only to perceptible [capable of being perceived by the senses] entities, in which case it may be

realized as an image, perceptual or imaginary. 3. Unlike other proposed forms of representation, it does not contain variables

. . . In place of a variable . . . a model employs tokens [symbols that are fixed rather than capable of assuming alternate values

or states] (p. 488).

Thus, for Johnson-Laird, a mental model is a sort of "mental diagram" that contains "mental images" which are similar to the images formed during perception and are spatially arrayed in a manner corresponding to their real-life counterparts. During deductive reasoning, Johnson-Laird postulates that inferences are made by "reading" information from the mental diagram that was not stated in the original premises used to construct the diagram.

In the field of human-computer interaction, mental models have been variously described as "knowledge about the system, external influences, and control strategies" (Veldhuyzen and Stassen, 1977), special types of "schema" (Jagacinski and Miller, 1978), "mental representations of a system" (Young, 1983), knowledge about "how a device works in terms of its internal structures and processes" (Kieras and Bovair, 1984, p. 255), "organized structures consisting of objects and their relationships" (Staggers and Norcio, 1993, p. 590), and "abstract concepts that are used by people to organize and guide decision making behavior and represent a person's knowledge of a decision problem" (Coury et al., 1992, p. 673). In summarizing this literature more than a decade ago, Rouse and Morris (1986) stated that

definitions within the cognitive science community range

from broad and intentionally amorphous generalizations to specific and occasionally esoteric constructs. (p. 350)

In response to this problem, they demurred from developing a conceptual definition and offered the following "functional definition" instead:

Mental models are the mechanisms whereby humans are

able to generate descriptions of system purpose and form, explanations of system functioning and observed system

states, and predictions of future system states. (Rouse and

Morris, 1986, p. 351)

Available definitions in the field of cognition and instruction are also often functional definitions that largely avoid details. For example, Halford (1993) defines mental models as "representations that are active while solving a particular problem and that provide the workspace for inference and mental operations." Shih and Alessi (1993, p. 157) state that "by a mental model we mean a person's understanding of the environment. It can represent different states of the problem and the causal relationships among states." Vosniadou and Brewer (1994, p. 125) get somewhat more specific when they explain that they

use the term mental model to denote a particular kind of

mental representation which has the following characteristics:

(a) its structure is an analog to the states of the world that it represents; (b) it can be manipulated mentally, or "run in the mind's eye," to make predictions about the outcomes of

causal states in the world; and (c) it provides explanations

of physical phenomena.

However, perhaps because many researchers in this field are new to the study of mental models, the definitions that are proffered are typically more like Wild's (1996, p. 10) general statement that "a mental model is a mediating intervention between perception and action."

Because it is a relatively new field of study, the definitions of mental models found in the literature on risk perception tend to be simple statements that are largely borrowed from other literatures and are often indistinguishable from the concept of knowledge in general. According to Fischhoff et al. (1993), for example, "The term mental model is often applied to intuitive theories that are elaborated well enough to generate predictions in diverse circumstances." Maharik and Fischhoff (1992) define mental models as "people's collection of beliefs (both true and false) about a certain topic, on the basis of which they intuit how it works." Jungermann et al. (1988) suggest that "a mental model is a mapping from a domain into a mental representation that contains the main characteristics of the domain." Occasionally, the shortcomings of mental models of risks become entangled with their definition, as, for example, when Atman et al. (1994) refer to mental models as "the pattern of knowledge gaps, overly general understandings, and outright misconceptions that can frustrate learning."

In characterizing the definitions of mental models offered in the above (and similar) examples in the field of cognitive science, it is clear that they suffer from the same problems as the definitions available in system dynamics. With few exceptions, the definitions are brief, simple, and vague. No single definition addresses more than a small subset of the important issues raised by the entire set of definitions. There is surprisingly little referencing of mental models research outside of disciplinary boundaries (in particular, none of the literature reviewed in cognitive science displayed an awareness of the history or current usage of the term mental models in the field of system dynamics).

There is one important point on which virtually all of the definitions offered in cognitive science fields agree, namely, the idea that the structure of mental models "mirrors" the perceived structure of the external system being modeled. Johnson-Laird (1983) refers to this feature of mental models as "the principle of structural identity." However, apart from agreement on this basic principle, disagreements on the nature of central, basic features of mental models are, as in system dynamics, easy to find. For example, are mental models composed of picture-like images (e.g., Johnson-Laird, 1983; Rouse and Morris, 1986; Jih and Reeves, 1992), declarative knowledge (e.g., Veldhuyzen and Stassen, 1977), concepts (Coury et al., 1992), or intuitive theories (Fischhoff et al., 1993)? Are they stable and held in memory for long periods of time (Seel, 1995), or are they fleeting, being constructed and discarded as needed to solve problems (Johnson-Laird, 1983; Vosniadou and Brewer, 1992)? Do mental models include only information about a system (Young, 1983) or do they also include information about external influences and decision strategies (Veldhuyzen and Stassen, 1977)? Are mental models accessible (i.e., are people aware of their mental models and able to report on their contents) as most researchers assume, or are they outside of conscious awareness and inaccessible as Van Heusden (1980), Whitfield and Jackson (1982), and Rouse and Morris (1986) have suggested? Do people have a single mental model of a system as assumed, for example, by researchers in risk perception, or can they have multiple alternate mental models of the same system as suggested by McCloskey (1983a), Clement (1983), DeKleer and Brown (1983), Williams et al. (1983) and Moray (1987)?

In short, as in system dynamics, progress in these literatures has been limited by an inability to achieve consensus on a specific, unambiguous definition of mental models. System dynamics researchers looking to the cognitive science literature for answers on precisely what mental models are are likely to come away with more questions instead. However, only by addressing and carefully considering these questions, and assessing the attitude of the system dynamics community toward their answers, can a more specific and useful definition of mental models for system dynamics be constructed.

Towards a Shared Definition of "Mental Models"

in System Dynamics

Like other research disciplines that have adopted the mental models concept, the field of system dynamics has developed its own definitions and methodologies largely in isolation from past or current work on mental models in other disciplines. Important distinctions described by other literatures have been largely ignored, resulting in definitions of mental models that are so general they serve to replace such overarching concepts as "psychology" or "cognition." At the same time, the shortcomings of these other literatures have also been ignored, and when they are cited, they are too often described as authoritative sources when they do not in actuality contain ideas about mental models that are more specific or detailed than those found in the system dynamics literature. Furthermore, each author tends to cite a different subset of the large and widely diverse literature on mental models. Thus, the problem is not that existing definitions in system dynamics are wrong; the problem is that, due to their generality and selective attention to other literatures, they are all partly right and at the same time they are all different.

We believe that in order to improve upon existing definitions, the mental models concept must be "unbundled," that is, its distinct, separable components must be identified and given separate names. The term "mental model" should be used more specifically to refer to only a small subset of the wide variety of mental phenomena to which it is currently associated. Which cognitive structures are given the name "mental model" and which are given alternate names is not critically important at this point; what is important is that a more precise and useful glossary of mental models concepts be developed and shared so that it is amenable to future review and revision by the system dynamics research community.

To begin this process, we propose that system dynamics researchers are primarily interested in specialized cognitive structures that are best described as "mental models of dynamic systems" (MMODS). We suggest that the term "mental model" in system dynamics should be understood to be an abbreviation of this longer term, and that the term "mental representations" (Gardner, 1985) rather than "mental models" should be used to indicate the variegated set of all types of proposed cognitive structures. In the following section of the paper, we propose a definition of mental models of dynamic systems, annotated to clarify definitional choices and to suggest terms for other cognitive structures not covered by the definition of MMODS.

The definition offered below is a conceptual definition, that is, a definition that describes a concept using other concepts. In constructing this definition, we have been mindful of the following features that improve the ability of a conceptual definition to enhance communication (Frankfort-Nachmias and Nachmias, 1992, p. 31):

1. A definition must point out the unique attributes or

qualities of whatever is defined. It must be inclusive

of all cases it covers and exclusive of all cases not

covered.

2. A definition should not be circular; that is, it must not

contain any part of the thing being defined.

3. A definition should be stated positively.

4. A definition should use clear terms [on whose meaning

different people agree].

Our goal is not to attempt to impose a new definition on the system dynamics community, but to create a definition that, insofar as possible, corresponds with how the term is most typically used at present in system dynamics. For example, the reliance in system dynamics on stock-flow diagrams, causal loop diagrams, and other conceptually based representations to describe and communicate mental models makes clear the preference in the field for thinking of mental models as concept-based rather than image-based, and this preference is preserved in our proposed definition. Similarly, the central role assigned to mental models in system dynamics descriptions of dynamic decision making suggests that the majority of researchers in the field conceive of mental models as relatively enduring structures rather than temporary structures created only during problem solving, and this preference is also reflected in the definition below.

We have attempted to create a definition that is as specific as possible, but not more: issues which have not yet been addressed by the research literature are omitted or are treated more generally than issues which have been more thoroughly studied. For example, we do not attempt to specify the role of mental models in dynamic decision making since much of the empirical work necessary to confirm this role (e.g., controlled studies that demonstrate that mental models are recalled from memory and used during dynamic decision making and that different mental models lead to different decisions) has yet to be conducted. Nor do we attempt to render judgment on the issue of whether people have a single mental model or (potentially) multiple mental models of a system. The preference in the system dynamics literature is clearly on the side of unitary models, but the alternative has not yet been considered by most researchers.

Finally, since the literature is crowded with too many alternate terms already, we have whenever possible suggested the use of existing terms rather than creating new ones.

Mental Models of Dynamic Systems: An Annotated Definition

A mental model of a dynamic system . . .

Although some authors prefer to use "theory" in place of "model," we believe that the term "theory" suggests a degree of completeness and coherence that is often lacking in mental models. "Theory" might more appropriately be used to describe only the subset of mental models that have these additional properties.

The terms "beliefs," "set of beliefs," or "belief system" are also often used in place of "mental model." However, we agree with Norman (1983) that mental models can include "knowledge or beliefs that are thought to be of doubtful validity." From this perspective, the term "belief," which implies a fairly high a degree of confidence in one's knowledge, describes some but not all mental models.

. . . is a relatively enduring . . .

The stability of mental models is a difficult question to answer. Parts of mental models may be altered, deleted, or added on a time scale of minutes or seconds. Yet, a mental model considered as a whole,

while continually changing in detail, may endure in memory in some form for years or decades. The phrase "relatively enduring" means that the term "mental model" should be reserved for cognitive structures that are stored in a potentially permanent state in long-term memory (Atkinson and Shiffrin, 1968) rather than structures that are stored only temporarily (on the order of seconds or minutes) in short-term or working memory (Baddeley, 1986). It also implies that mental models are structures that are "precompiled," that is, they are stored as a unit in long-term memory rather than being constructed from smaller components during decision making.

Reserving the term "mental models" for relatively enduring structures by no means implies that less enduring structures are unimportant: in fact, recent research suggests that constructive processes play an important role in human decision making (Payne et al., 1992). For cognitive structures that are actively constructed (from existing mental representations in combination with new information) during decision making and held only temporarily in working memory, we suggest the term "dynamic problem representation," after Greeno (1977).

. . . and accessible, . . .

Virtually all psychological theorists acknowledge that conscious thought is supported by a tremendous amount of mental information and activity that takes place "unconsciously" and cannot be described by people with any degree of reliability. In some cases unconscious mental representations and processes can have a significant effect on people's judgments without their being aware of it (see, e.g., Nisbett and Wilson, 1977; Begg et al., 1992). We suggest the term "implicit model" (see Rouse and Morris, 1986) for mental model-like structures that are outside conscious awareness, reserving the term "mental models" for cognitive structures that are relatively available to conscious introspection.

. . . but limited, . . .

We believe the term "mental model" should not be used to refer to knowledge in general or even to all knowledge that can be recalled from memory about a given system, but, as stated above, to a "precompiled" subunit of information held in memory. Such a mental model can vary significantly in size and complexity, just as a real system may vary in size and complexity. However, it is possible to specify upper and lower limits to this variation.

We propose that the upper limit on the size and complexity of a mental model is determined by limits on "bounded rationality" (Simon, 1956). To aid decision making, a mental model must be small enough to be implemented in short term memory, the capacity of which is generally considered to be seven plus or minus two "chunks" of information (Miller, 1956; Simon, 1974). This limit is flexible in the sense that the amount of information that can be organized meaningfully into a chunk can increase with experience and expertise; the maximum number of different chunks, however, is unalterable.

A reasonable lower bound on the size of a mental model is the minimum requirement for a "closed" system, that is, two variables and two causal relationships. Thus a single causal assertion such as "an increase in X causes an increase in Y" is not sufficiently complex to be called a "model" and should instead be referred to as an "assumption" or "belief," depending on the degree of confidence that is associated with it.

. . . internal . . .

The term "internal" implies that a mental model is a cognitive phenomenon, that is, something that exists only in the mind. The products of efforts to "surface," "elicit," or "map" mental models, which are typically causal-loop or stock-flow diagrams on paper or in a computer program, should not be confused with the mental model itself due to the strong likelihood of measurement error and the possibility of bias [as discussed by Norman (1983), these externalized models are really the researcher's conceptualization of a subjects' mental model, and may be influenced by the researcher's own mental models of human cognition and behavior]. To refer to external representations of mental models, we suggest the commonly used term "cognitive map" (see Axelrod, 1976; Eden, 1994).

. . . conceptual . . .

By conceptual we mean that mental models are based on concepts, ideas, or other language-like components. Of course, there is substantial evidence for the existence and use of mental imagery (see Finke, 1989; Kosslyn, 1990), and such imagery may be associated in memory with conceptual models. However, we suggest that the term "mental image," not "mental model," be used to refer to these picture-like represen-tations.

. . . representation . . .

The term "representation" means that mental models are cognitive structures, which should be distinguished from cognitive processes. Cognitive structures store information; cognitive processes are the mental operations that transform, elaborate, and reduce this information during decision making or problem solving.

. . . of an external group of interrelated stocks and flows

(i.e., a system) . . .

This phrase suggests that for a mental representation to be called a mental model, it must have an external referent. Thus, we are proposing that such mental constructs as attitudes (Eagly and Chaiken, 1993), prototypes (Rosch, 1973), and goals (Schank and Abelson, 1977), which do not have external analogues, should not be included in the term "mental model."

It should be noted that it is possible to have a mental model of one's own internal cognitive structures. We suggest that this exception to the requirement for an external referent be referred to as a "metamodel," after the cognitive psychology term "metacognition" (see Nelson, 1992).

. . . whose structure and relationships . . .

The words "structure and relationships" imply that mental models

include not merely knowledge but detailed information about how this knowledge is organized and interconnected. We suggest that the term "knowledge" should be used in place of "mental model" when no assumptions concerning how information is organized are implied.

It is clear that mental models contain internal analogues of external stocks and flows, but the precise nature of the conceptual nodes and links that form a mental model of a dynamic system has yet to be confirmed by empirical research. For example, are the nodes highly abstract concepts that summarize many experiences, or are they more concrete tokens that represent specific examples of systems? Is there only one type of link or are there several types of links? Do the links vary in strength or are they uniform? It is in fact likely that the nature of the nodes and links in a mental model is variable and changes as people gain experience and develop expertise in a certain field. Several authors, for example, have suggested that the degree to which mental models are abstract versus representational varies with expertise (see, e.g., Larkin, 1983; DiSessa, 1983; Greeno, 1983; De Jong and Ferguson-Hessler, 1986).

. . . maintain the perceived structure and relationships of that system.

The word "perceived" is clearly very important. The evidence collected in a variety of research disciplines that people's mental models are prone to errors and omissions is overwhelming. Mental models attempt to preserve the structure and relationships in the external system, but only rarely succeed.

Conclusion

A review of existing descriptions and definitions of "mental models" in a variety of literatures, including system dynamics

and several research disciplines associated with cognitive science,

has uncovered a common set of problems: available definitions

are overly simple, general, and vague, and different authors offer

definitions that markedly disagree on centrally important features of mental models. We believe that the lack of a clearly specified, comprehensive, and agreed upon definition of mental models has hindered communication between researchers and dramatically slowed the progress of research aimed at describing, understanding, and improving mental models of dynamic systems.

As a step toward the resolution of this problem, we have suggested that the term "mental models" should be used much more

narrowly than it is at present, and have offered the following conceptual definition of "mental models of dynamic systems:"

A mental model of a dynamic system is a relatively enduring

and accessible, but limited, internal conceptual representation

of an external group of interrelated stocks and flows (i.e., a

system) whose structure and relationships maintain the

perceived structure and relationships of that system.

We have also provided an extended annotated version of this

definition to clarify its meaning and to suggest a glossary of terms

to refer to cognitive structures that have been excluded from our

definition of mental models.

We make no claim that this conceptual definition is correct or complete, only that it is more detailed and explicit than any previously existing definition, and thus can serve as a useful starting point for further review and debate. According to Frankfort-Nachmias and Nachmias (1992, p. 31),

Conceptual definitions are neither true nor false . . . Concep-

tual definitions are either useful for communication and

research, or they are not.

Thus the true test of this definition will be if the system dynamics

community finds it to be useful for conducting and disseminating its

research.

We also believe that it would be premature to make claims

of correctness or completeness for any definition of mental models

at this time. The majority of research on mental models in all of the disciplines that employ the concept has been applied, and surprisingly little attention has been paid to theoretical concerns or to basic research that would yield answers to general definitional questions about the structure and characteristics of mental models of dynamic systems that would provide a firmer foundation for applied research. In particular, basic research is needed to establish the stability of mental models and how they interact with less enduring cognitive structures, the limitations to people's access to their own mental models, the precise nature of the conceptual nodes and links which form mental models, how the nature and role of mental models changes with experience and expertise, and the extent to which mental models are employed naturally and spontaneously in dynamic decision making. Theoretical work that places mental models in the context of a more elaborate cognitive system, such as that described by Richardson et al. (1994), should be encouraged and followed up by empirical research that puts assumptions to the test. Collaboration between system dynamics researchers, who have developed appropriate tools and techniques for examining and describing complexity, and cognitive psychologists, who have developed a large body of knowledge relating to human cognition and established rigorous empirical techniques for studying the mind, may be particularly important for such a research effort to succeed (see Doyle, 1997).

Conducting the basic and theoretical research necessary to further define mental models will not be easy. Describing mental models is inherently difficult, since mental models are not directly observable and can change during procedures designed to assess them. Compounding matters is the sheer complexity of the human mind and brain, which has been described as "the most complex structure in the known universe" (Staff, 1992). However, we believe that this difficult work is necessary for the field of system dynamics to fulfill its goals of improving mental models and the quality of the dynamic decisions based upon them. The system dynamics community must achieve the same level of sophistication in how it thinks and talks about human cognitive systems that it has reached in its research into a wide variety of other complex systems.

Biographical Information

James K. Doyle is an assistant professor of psychology at Worcester Polytechnic Institute. Address: Department of Social Science and Policy Studies, Worcester Polytechnic Institute, 100 Institute Rd., Worcester, MA 01609. E-mail: doyle@wpi.edu. Web: http://www.tiac.net/ users/sustsol.

David N. Ford is an associate professor at the University of Bergen. Address: Department of Information Science, University of Bergen, N-5020 Bergen, Norway. E-mail: david.ford@ifi.uib.no.

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