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. Gentner, D. (2002). Mental models, of. In N. J. Smelser & P. B. Bates (Eds.), International Encyclopedia of the Social and Behavioral Sciences (pp. 9683-9687). Amsterdam: Elsevier Science.

Mental Models, Psychology of

configural description or a mixture of the two, and the study of mental models. One approach seeks rarely any other kind. to characterize the and processes that These questions are not just an issue of academic support and reasoning in knowledge- interest. We have all often had frustrating experience rich domains. The other approach focuses on mental trying to understand verbal directions abut how to models as working- constructs that support get somewhere or trying to grasp the layout of an area logical reasoning (see Reasoning with Mental Models). by means of a map. Virtual is currently This article focuses chiefly on the knowledge-based proposed as having great potential for training people, approach. e.g., soldiers, for tasks in new environments. However, Mental models are used in everyday reasoning. For with the present state-of-the-art it is difficult to build a example, if a glass of water is spilled on the table, good sense of the layout (a good mental map) of a people can rapidly mentally simulate the ensuing virtual world one is moving through. How to use these events, tracing the water through its course of falling media most effectively to enable the most desirable downward and spreading across the table, and in- mental map is a goal for research. ferring with reasonable accuracy whether the water will go over the table’s edge onto the floor. People’s ability to infer and predict events goes well beyond their direct experience. For example, if asked ‘which Bibliography can you throw further, a potato or a potato chip?’ Bloom P, Peterson M A, Nadel L, Garrett M F (eds.) 1996 most people can give an answer immediately (the Language and Space. MIT Press, Cambridge, MA potato) even if they have never actually tossed either Gallistel C R 1990 The Organization of . MIT Press, item. Cambridge, MA However, mental models are not always accurate. Gladwin T 1970 East is a Big Bird. Harvard University Press, Mental models researchers aim to capture human Cambridge, MA knowledge, including incorrect beliefs. The study of Hazen N L, Lockman J J, Pick H L Jr 1978 The development of children’s representations of large-scale environments. Cltild incorrect models is important for two . First, Deuelopment 49: 623-36 the errors that a learner makes can help reveal what Hutchins E 1995 in the Wild. MIT Press, Cambridge, the learning processes must be.. Second, if typical MA incorrect models are understood, then instructors Hutchins E, Hinton G E 1984 Why the islands move. and designers can create materials that minimize the 13629-32 changes of triggering errors. Lewis D 1978 The Voyaging Stars: Secrets of the Pacific Island A striking example of an incorrect Nauigators. Norton, New York is the curdinear momentum error (Clement 1983, Loomis JM, Klatzky RL, Golledge RG, CicineIli JG, McCloskey 1983). When college students are asked: ‘If Pellegrino J W, Fry P A 1993 Nonvisual navigation by blind a ball a string is spun in a circle and then let go, and sighted: Assessment of path inkgrationability. Joumul of on : General 122: 73-91 what path will it take?’, many of them correctly say that Rieser J J, Guth D A, Hi11 E W 1988 Sensitivity to perspective the ball will travel at a tangent to the circle. However, structure while waking without vision. Perception 15 173-88 a fair proportion states that the ball will move in a Thorndyke P W, Hayes-Roth B 1982 Difierences in spatia1 curved path, retaining some of the curvilinear mo- knowledge acquired from maps and navigation. Cognitive mentum gained from being spun in a circle. The usual Psychology 14 56&89 is that the ball will gradually lose this ‘curvi- Tversky B 1996 Spatial perspective in descriptions. In: Bloom P, linear momentum’, so that the path will straighten Peterson MA, Nadel L, Garrett M F (eds.) Language and out over . This erroneous intuition is fairly Space. MIT Press, Cambridge, MA pp. 463-91 Tolman EC 1948 Cognitive maps in rats and men. Psycho- general; for example, the same error turns up when logical Review 56: 144-55 people are asked about the path of a ball blown Uttal DH 2001 Seeing the big picture: Map use and the through a circular tube. Further, the error does not development of spatial cognition. Developmental Science 3 yield immediately to training; it is found even in 247-86 students with a few years of . However, it does diminish with increasing expertise. H.L. Pick Jr. Another striking error is seen when people are asked what trajectory a ball will follow if it rolls off the edge of a table (McCloskey 1983). Instead of the correct answer, that the ball will fall in a parabolic path (Fig. la), many people believe the ball will continue traveling straight, and begin falling (either Mental Models, Psychology of straight down or in a curved path) only when its forward momentum begins to flag (Fig. IC and lb). A mental model is a representation of some domain People seem to believe that sufficient forward momen- or situation that supports understanding, reasoning, tum will overcome the tendency to fall. This error and prediction. There are two main approaches to is sometimes called ‘Roadrunner physics’ because it 9683 Mental Models, Psychology of

**** ....I...... * ** ...... *....., *** %* ****’.= . .: 8 . . W . i O a Figure 1 Responses to the question ‘What path will the ball take after it rolls off the table? (adapted from McCloskey 1983) resembles the event in which a cartoon character runs chiefly linear temporal order, with limited inferential off a cliff but does not fall until some distance over flexibility. Nufve theories or folk theories are global the edge. However, McCloskey noted that the same systems of , typically encompassing larger error occurs in the writings of Jean Buridan and domains such as biOl9gY. The terms mental models and other fourteenth-century Aristotelian philosophers. It naibe or folk theories overlap in their application, appears that cartoon events were created to match a though mental models are typically more specific than mental model that arises naturally from experience, theories. possibly by overgeneralizing from experiences with linear momentum. Mental models can facilitate learning, particularly I, Characteristics of Mental Models when the structure of the new learning is consistent with the model, For example, Kieras and Bovair Mental models reasoning relies on quulitatwe relations, (1984) showed that subjects could operate a simulated rather than on quantitative relations. People can device more accurately and could diagnose malfunc- well about the that one quantity is less tions better when they had a causal mental model of its than another without invoking the precise values of functioning, rather than a merely procedural grasp of the quantities. This forms the basis for quali- how to operate it. Similarly, Gentner and Schumacher tative process theory, discussed below (Forbus 1984). (1986) showed that subjectswere better able to transfer Mental models often permit mental simulation: the an operating procedure from one device to another sense of being able to run a mental model internally, so when they had a causal mental model of the operation that one can observe how it will behave and what the of the first device, rather than just a of procedures. outcome of the process will be. The processes that The degree of facilitation depended greatly on the underlie mental simulation are still under study. match between the original model and the new However, there is good that people are able, material. within limits, to mentally simulate the of a Mental models are used to explain human reasoning device, even if they are simply shown a static display about physical systems: devices and mechanisms (de (Hegarty and Just 1993). There is an apparent tradeoff Kleer and Brown 1983, Hegarty and Just 1993, Kieras between online simulation and retrieval of stored and Bovair 1984, Williams et al. 1983); electricity outcomes (Schwartz and Black 1996). As people (Gentner and Gentner 1983); the interactionsof people become familiar with a system, they no longer carry with computers and other devices (Norman 1988), and out full simulations of behavior in all cases, but knowledge of home heating systems (Kempton 1986). instead simply access their stored knowledge of the They have also been applied to spatial representation outcome. and navigation (Forbus 1995, Hutchins 1983, Tversky Another finding of mental models research is that 1991); ecology (Kempton et al. 1995), human popula- people are capable of holding two or more inconsistent tion growth (Gentner and Whitley 1997), and the models within the same domain, a pattern referred to development of astronomical knowledge (Vosniadou as pastiche models (Collins and Gentner 1987) or and Brewer 1992). knowledge in pikes (disessa 1982). For example, Mental models are related to several other kinds of Collins and Gentner (1987) found that many novice representational structures (see Markman 1999 for subjects had ‘pastiche’ models of evaporation. A a comprehensive discussion). Schemas (or schemata) novice learner may give one of what are general belief structures. Scripts are schemas causes a towel to dry in the sun and a completely summarizing event sequences, characterized by a different explanation of what causes a puddle of water 9684 Mental Models, Psychology of h to evaporate, failing to see any connection between the 3. Analogies and Mental Models two phenomena. Novices often use locally coherent but globally inconsistent accounts, often quite closely Mental models are often based on implicit or explicit tied to the details of the particular example. This analogies with other knowledge. The incorrect valve pattern emphasizes the tendency of novices to learn models used by Kempton’s informants, discussed conservatively, with knowledge cached in highly above, were apparently drawn from experiential specific, context-bound categories. So long as each analogies. However, analogical models can also be a model is narrowly accessed in contexts specific to it, useful way to extend knowledge from well-under- the inconsistencies may never come to the learner’s stood domains to less familiar domains. For example, . Gentner and Gentner (1983) identified two common mental models of electricity, the$owing water model and the moving crowd model. In the flowing water model, current flows through a wire the way water 2. Mental Models in Everyday Life flows through a pipe, and a resistor is a narrow pipe. Kempton et al. (1995) note that mental models ‘give an In the moving crowd model, current is viewed as the underlying structure to environmental beliefs and a rate of movement of a crowd through a hall, and a critical underpinning to environmental values.’ For resistor as a gate through to the next hall. Although example, Kempton (1986) proposed on the basis of both analogies can account for many simple interviews that people used two distinct models of about d.c. circuits, they each have drawbacks. Voltagq home heating systems. In the (incorrect) valve model, is easy to map in the flowing water model (the number the thermostat is to regulate the rate at which of batteries corresponds to the number of pumps the furnace produces heat; setting hi&er makes the pushing the water forward), but it is awkward to map furnace work harder. In the threshold model, the in the moving crowd model (unless perhaps to a loud thermostat is viewed as setting the goal temperature, noise impelling the crowd forward). In contrast, the but not as controlling the rate of heating; the furnace behavior of resistors is easier to predict if they are runs at a constant rate. (This is the correct model for seen as gates (as in the moving crowd model) than if most current household systems.) they are seen as constrictions (as in the flowing water Having derived these two models from interviews, model). Thus, if these analogical models are really Kempton asked whether these models could explain used in reasoning, people with the water model people’s real behavior in running their household should reason more accurately about combinations of furnaces. He examined thermostat records collected batteries than people with the crowd model, and the by Socolow (1978) from real households and found reverse for resistors. Indeed, that was what was found. that the patterns of thermostat settings fitted nicely When people filled out a questionnaire about their with the two models he had found. In particular, some mental model of electricity, and then made simple simply set their thermostat twice a day-low predictions about combination circuits, people who at night, higher by day, consistent with the threshold held the flowing water model were more accurate model-while others constantly adjusted their ther- about combinations of batteries, and those with the mostats and used a range from extremely high to much moving crowd model were more accurate about lower temperatures. This is an extremely expensive combinations of resistors. strategy, in terms of fuel consumption, but it follows from the valve model. In this model, the thermostat setting controls how hard the furnace works, so the higher the setting, the faster the house 4. Methods of Studying Mental Models will warm up. This reasoning can be seen in the The initial elicitation of mental models is often done analogies produced by Kempton’s interviewees. Those by the direct method of interviews or questionnaires with the valve model often compared the furnace to that explicitly ask people about their beliefs (for other valve devices, such as a gas pedal or a faucet and example, Collins and Gentner 1987, Kempton 1986) suggested that you need to ‘turn ’er up high’ to make or by analyzing think-aloud protocols collected during the house warm up quickly. Thus, there is evidence reasoning (Ericksson and Simon 1984) (see Protocol that mental models can influence real-life environ- Analysis in Psychology). However, directly asking mental decision making. people about their mental models is not enough, for Three significant generalizationscan be made so far. people are often unable to fully articulate their First, people use mental models to reason with; they knowledge. Therefore, many researchers follow this are not merely a convenient way of talking. Second, direct interview with other methods of validating the mental models can facilitate and proposed mental models. Once the mental models in a reasoningin$ domain. Third, mental models can yield domain are roughly known or guessed, materials can incorrect results as well as correct ones. The next issues be designed to bear down on the details. For example, are where mental models come from and how they are problems are designed such that subjects’ mental used in learning and instruction. models can be inferred from patterns of correct and

9685 Mental Models, Psychology of d incorrect answers, response , eye movements, or 6. Implications for Instruction and Design particular errors made (Gentner and Gentner 1983, Mental models developed from experience can be Hegarty and Just 1993, Schwartz and Black 1996) or resistant to instruction. In the case of curvilinear patterns of retention for new materials in the domain momentum cited above, even students who had (Bostrom et al. 1994). learned Newton’s in physics classes often main- tained their belief in curvilinear momentum. One technique that has been used to induce model revision 5. Representing Mental Models is that of bridging analogies (Clement 1991). Learners Mental models research often includes an explicit are given a series of analogs. The first analog is a close representation of the knowledge. For example, in match to the learner’s existing model (and therefore Patrick Hayes’ (1 985) classic paper on the naïve physics easy to map). The hlstep exemplifies the desired of liquids, roughly 80 are used to represent the new model. The progression of analogs in small steps knowledge involved in understanding the possible helps the learner to move gradually to another way of states a liquid can take and the possible transitions conceptualizing the domain. that can occur between states. These axioms capture Mental models have been used in intelligent learning knowledge about when a liquid will flow, stand still, or environments (see Intelligent Tutoring Systems). For spread into a thin sheet on a surface. example, White and Frederiksen’s (1990) system for A useful formalism for representing mental models teaching physical reasoning begins with a simple is qualitative process (QP) theory (Forbus 1984). This mental model and gradually builds up a more complex theory, originating in artificial , aims to causal model. Early in learning, they suggest, learners capture the representations and reasoning that under- may have only rudimentary knowledge, such as lie human reasoning about physical processes in a whether a particular quantity is present or absent at a manner sufficiently precise to permit computer simu- particular location. By adding knowledge of how lation. A central intuition is that human reasoning changes in one quantity affect others, and then relies on qualitative relations, such as whether one progressing to more complex relationships among quantity is greater or less than another, rather than on quantities, learners can acquire a robust model. quantitative relations. For example, in QP theory, a Another implication of mental models research is mental model is represented in terms of (a) the entities that the pervasiveness and persistence of mental in the domain-cg., water in a pan; (b) qualitative models needs to be taken into account in designing relations between quantities in the domain--e.g., that systems for human use. Norman (1988) argues that the temperature of water is above freezing and below designers’ ignorance of human mental models leads to boiling; (c) the processes that create change-e.g., heat design errors that plague their intended users. Some- flow or liquid flow; and (d) the preconditions that must times these are merely annoying--e.g., a door that hold for processes to operate. An important feature of looks as though it should be pulled, but that needs to be QP theory is that it uses ordinal relationships between pushed instead. However, failure to take mental quantities, such as that one quantity is greater than modeks into account can lead to serious costs. another, rather than representing quantities as nu- An example of such a failure of mental models merical values. The is to match human patterns of occurred in the Three-mile Island nuclear disaster, reliance on qualitative relations rather than on exact Early in the events that led to the melt-down, operators values. A second important feature is that instead of noted that the reactor’s coolant water was registering using exact equations, QP theory uses a qualitative at a high pressure level. They interpreted this to mean mathematics to provide a causal language that ex- that there was too much coolant and accordingly they presses partial knowledge about relationships between pumped offlarge amounts of coolant. In fact, the level quantities. For instance, qualitative proportionalitks was dangerously low, so much so that the coolant was express simple causal relations between two quantities. turning into steam-which, of course, led to a sharp The idea is that people may know, for example, that increase in pressure. Had this alternate model been at greater force leads to greater acceleration, without hand, the operators might have taken different action. knowing the exact numerical of the function (linear, exponential, etc.). An interesting aspect of QP theory is that, in addition to representing novice: 7. Mental Models as Temporary Aids to Logical models, it can also capture an important aspect of Reasoning expert knowledge: namely, that experts typically parse a situation into qualitatively distinct subsystems be- Another approach to mental models is taken by fore applying more exact equations. QP theory allows Johnson-Laird (1 983) and his colleagues (see Reason- researchers to describe people’s knowledge about what ing with Mental Models). This approach differs from is happening in a situation at a particular time, how the research cited in the remainder of this article in the system is changing, and what further changes will that it views mental models as temporary working- occur. memory sketches set up for the purposes of immediate 9686 of Persons, Psychology of a reasoning tasks such as propositional inference vironmental Valuation and Degradation. New Lexington Press, (Johnson-Laird 1983). The focus on immediate San Francisco, CA, pp. 209-33 working-memory tasks in this approach has led to a Hayes P J 1985 Naive physics I: for liquids. In: Hobbs J R, Moore R C (eds.) Formal Theories of the Commonsense relative lack of emphasis on long-term knowledge and World. Ablex Publishing Corporation, Norwood, NJ causal relations. However, there may be in Hegarty M, Just MA 1993 Constmting mental models of bringing together the working-memory approach with machines from text and diagrams. Journal of Memory and the knowledge-intensive approach. There is evidence Language 32 7 17-42 that long-term causal mental models can influence the Hutchins E 1983 Understanding micronesian navigation. In: working-memory representations that are set up in Gentner D, Stevens AL (4s.) Mental Models. Erlbaum, speeded tasks (Hegarty and Just 1993, Schwartz and Hillsdale, NJ, pp- 191-225 Black 1996). Johnson-Laird P N 1983 Mental Models: Towards a of Language, Inference. and . Harvard See also: Informal Reasoning, Psychology of; Mental University Press, Cambridge, MA Imagery, Psychology of; Problem Solving and Reason- Kempton W 1986 Two theories of home heat control. Cognitive ing: Case-based; Problem Solving and Reasoning, Science 10 75-90 Kempton W,Boster J S, Hartley J 1995 Environmental Valuesin Psychology of; Problem Solving: Deduction, Induc- American . MIT Press, Cambridge, MA tion, and Analogical Reasoning; Reasoning with Kieras D E, Bovair S 1984 The role of a mental model in learning Mental Models; Scientific Reasoning and Discovery, to operate a device. Cognitwe Science 8: 255-73 of Markman A B 1999 Knowledge Representation. Erlbaum, Mahwah, NI McCloskey M 1983 Intuitive physics. Scientific American 248(4): Bibliography 122-30 Norman D A 1988 The Psychology of Every&y Tltings. Basic Bostrom A, Atman C J, Fischhoff B, Morgan MG 1994 Books, New York Evaluating risk communications: Completing and correcting Schwartz D L, Black J B 1996 Analog imagery in mental model mental models of hazardous processes. Part II. Risk Analysis reasoning: Depictive models. Cognitive Psychology 30: 154- 14(5): 789-98 219 Clement J 1983 A discussed by Galileo and Socolow R H (ed.)1978 Saving Energy in the Home: Princeton’s used intuitively by physics students. In: Gentner D, Stevens Experiments at Twin Rlvers. Ballinger, Cambridge, MA A L (eds.) Mental Models. Erlbaum, Hillsdale, NJ, pp. 325-40 Stevens A, Collins A 1980 Multiple conceptual models of a Clement J 1991 Nonformal reasoning in experts and in science complex system. In: Snow R, Federico P, Montague W (eds.) students: The use of analogies, extreme cases, and physical Aptitude, Learning and Instruction: Cognitive Process Analysis. intuition. In: Voss J, Perkins D, Siegal J (eds.) Informal Erlbaum, Hillsdale, NJ, Vol. 2, pp. 177-97 Reasoning and . Erlbaum, Hillsdale, NJ, pp. 345-62 Tversky B 1991 Distortions in memory for visual displays. In: Collins A, Gentner D 1987 How people construct mental models. Ellis R, Kaiser Grunewald A (eds.) Spatial Instruments In: Holland Quinn N (eds.) Cultural Models in Language S M, D, and Spatial Displu-vs. Erlbaum, Hillsdale, NJ, pp. 61-75 and Thought. Cambridge University Press, Cambridge, UK, Vosniadou S, Brewer W F 1992 Mental models of the Earth: A pp. 243-65 study of conceptual change in childhood. Cognitive Psy- de Kleer J, Brown J S 1983 Assumptions and ambiguities in chology 24(4): 535-85 mechanistic mental models. In: Gentner D, Stevens A L (eds.) Williams M D, Hollan J D, Stevens A L 1983 Human reasoning Mental Models. Erlbaum, Hillsdale, NJ, pp. 155-90 about a simple physical system. In: Gentner D, Stevens A diSessa A A 1982 Unlearning Aristotelian physics: A study of L (+S.) Mental Models. Erlbaum, Hillsdale, NJ, pp. 131-53 knowledge-based learning. Cognitive Science 6 37-75 WteB Y, Fredricksen J R 1990 Causal model progressions as Ericksson K A, Simon H A 1984 Protocol Analysis. MIT Press, a foundation for intelligent learning environments. Artificial Cambridge, MA Intelligence 42( 1): 99-1 57 Forbus K D 1984 Qualitative process theory. Journal ofArrificial Intelligence 2A: 85-168 Forbus K 1995 Qualitative spatial reasoning: Framework and D. Gentner frontiers. In: Glasgow J, Narayanan N, Chandrasekaran B (eds.) : Cognitive and Computational Perspectives. MIT Press, Cambridge, MA, pp. 183-202 Gentner D, Gentner DR 1983 Flowing waters or teeming Mental Representation of Persons, crowds: Mental models of electricity. In: Gentner D, Stevens A L (eds.) Mental Models. Erlbaum, Hillsdale, NJ, pp. 99-129 Psychology of Gentner D, Schumacher R M 1986 Use of structure-mapping theory for complex systems. In: Proceedings of the IEEE Within , a major research focus is the International Conference on Systems, Man, and Cybernetics, processes by which perceivers form impressions of pp. 252-8 Gentner D, Stevens A L (4s.) 1983 Mental Models. Erlbaum, other persons, and the nature of the mental represen- Hillsdale, NJ tations that they construct as a result. Mental repre- Gentner D, Whitley E W 1997 Mental models of population sentations or impressions of persons are organized growth: A preliminary investigation. In: Bazerman M, configurations including many types of , Messick D M, Tenbrunsel A E, Wade-Benzoni K (eds.) such as physical appearance, personality characteri- Environment. , and Behavior: The Psychology of En- stics, and group memberships, as well as the perceiver’s

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Copyright O 2001 Elsevier Science Ltd. All reserved. International Encyclopedia of the Social & Behavioral Sciences ISBN: 0-08-043076-7