Learning: Analogical Reasoning

LEARNING: ANALOGICAL REASONING 1421

LEARNING sponding objects in the base and target need not re- semble each other; what is important is that they ANALOGICAL REASONING hold like roles in the matching relational structures. Dedre Gentner Thus, analogy provides a way to focus on relational Jeffrey Loewenstein commonalities independently of the objects in CAUSAL REASONING which those relations are embedded. Joseph P. Magliano Bradford H. Pillow In explanatory analogy, a well-understood base CONCEPTUAL CHANGE or source situation is mapped to a target situation Carol L. Smith that is less familiar and/or less concrete. Once the KNOWLEDGE ACQUISITION, REPRESENTATION, AND two situations are aligned—that is, once the learner ORGANIZATION Danielle S. McNamara has established correspondences between them— Tenaha O’Reilly then new inferences are derived by importing con- NEUROLOGICAL FOUNDATION nected information from the base to the target. For Howard Eichenbaum example, in the analogy between blood circulation PERCEPTUAL PROCESSES and plumbing, students might first align the known John J. Rieser facts that the pump causes water to flow through the PROBLEM SOLVING pipes with the fact that the heart causes blood to flow Richard E. Mayer through the veins. Given this alignment of structure, REASONING Thomas D. Griffin the learner can carry over additional inferences: for TRANSFER OF LEARNING example, that plaque in the veins forces the heart to Daniel L. Schwartz work harder, just as narrow pipes require a pump to Na’ilah Nasir work harder. Gentner and Phillip Wolff in 2000 set forth four ANALOGICAL REASONING ways in which comparing two analogs fosters learning. First, it can highlight common relations. For ex- Analogy plays an important role in learning and in- ample, in processing the circulation/plumbing struction. As John Bransford, Jeffrey Franks, Nancy analogy, the focus is on the dynamics of circulation, Vye, and Robert Sherwood noted in 1989, analogies and other normally salient knowledge—such as the can help students make connections between differ- red color of arteries and the blue color of veins—is ent concepts and transfer knowledge from a well- suppressed. Second, it can lead to new inferences, as understood domain to one that is unfamiliar or not noted above. Third, comparing two analogs can re- directly perceptual. For example, the circulatory sys- veal meaningful differences. For example, the circu- tem is often explained as being like a plumbing sys- lation/plumbing analogy can bring out the tem, with the heart as pump. difference that veins are flexible whereas pipes are rigid. In teaching by analogy, it is important to bring The Analogical Reasoning Process out such differences; otherwise students may miss them, leading them to make inappropriate infer- Analogical reasoning involves several sub-processes: ences. Fourth, comparing two analogs can lead (1) retrieval of one case given another; (2) mapping learners to form abstractions, as amplified below. between two cases in working memory; (3) evaluating the analogy and its inferences; and, sometimes, (4) abstracting the common structure. The core pro- What Makes a Good Analogy cess in analogical reasoning is mapping. According As Gentner suggested in 1982, to facilitate making to structure-mapping theory, developed by Dedre clear alignments and reasonable inferences, an anal- Gentner in 1982, an analogy is a mapping of knowl- ogy must be structurally consistent—that is, it edge from one domain (the base or source) into an- should have one-to-one correspondences, and the other (the target) such that a system of relations that relations in the two domains should have a parallel holds among the base objects also holds among the structure. For example, in the circulation/plumbing target objects. In interpreting an analogy, people system analogy, the pump cannot correspond to seek to put the objects of the base in one-to-one cor- both the veins and the heart. Another factor influ- respondence with the objects of the target so as to encing the quality of an analogy is systematicity: obtain the maximal structural match. The corre- Analogies that convey an interconnected system of

1422 LEARNING: ANALOGICAL REASONING relations, such as the circulation/pumping analogy, tionnaire or interview to elicit the person’s own ana- are more useful than those that convey only a single logical models. For example, Willet Kempton in isolated fact, such as ‘‘The brain looks like a walnut.’’ 1986 used interviews to uncover two common ana- Further, as Keith Holyoak and Paul Thagard argued logical models of home heating systems. In the (in- in 1995, an analogy should be goal-relevant in the correct) valve model, the thermostat is like a faucet: current context. It controls the rate at which the furnace produces In addition to the above general qualities, sever- heat. In the (correct) threshold model, the thermo- al further factors influence the success of an ex- stat is like an oven: It simply controls the goal tem- planatory analogy, including base specificity, trans- perature, and the furnace runs at a constant rate. parency, and scope. Base specificity is the degree to Kempton then examined household thermostat re- which the structure of the base domain is clearly un- cords and found patterns of thermostat settings cor- derstood. Transparency is the ease with which the responding to the two analogies. Some families correspondences can be seen. Transparency is in- constantly adjusted their thermostats from high to creased by similarities between corresponding ob- low temperatures, an expensive strategy that follows jects and is decreased by similarities between from the valve model. Others simply set their ther- noncorresponding objects. For example, in 1986 mostat twice a day—low at night, higher by day, Gentner and Cecile Toupin found that four- to six- consistent with the threshold model. year-old children succeeded in transferring a story to new characters when similar characters occupied Analogy in Children → → similar roles (e.g., squirrel chipmunk; trout Research on the development of analogy shows a re- salmon), but they failed when the match was cross- lational shift in focus from object commonalities to mapped, with similar characters in different roles relational commonalities. This shift appears to result → → (e.g., squirrel salmon; trout chipmunk). The from gains in domain knowledge, as Gentner and same pattern has been found with adults. Transpar- Mary Jo Rattermann suggested in 1991, and perhaps ency also applies to relations. In 2001 Miriam Bassok from gains in processing capacity as suggested by found that students more easily aligned instances of Graeme Halford in 1993. In 1989 Ann Brown ‘‘increase’’ when both were continuous (e.g., speed showed that young children’s success in analogical of a car and growth of a population) than when one transfer tasks increased when the domains were fa- was discrete (e.g., attendance at an annual event). Fi- miliar to them and they were given training in the nally, scope refers to how widely applicable the anal- relevant relations. For example, three-year-olds can ogy is. transfer solutions across simple tasks involving familiar relations such as stacking and pulling, and six- Methods Used to Investigate Analogical Learning year-olds can transfer more complex solutions. In Much research on analogy in learning has been de- 1987 Kayoko Inagaki and Giyoo Hatano studied voted to the effects of analogies on domain under- spontaneous analogies in five- to six-year-old chil- standing. For example, in 1987 Brian Ross found dren by asking questions such as whether they could that giving learners analogical examples to illustrate keep a baby rabbit small and cute forever. The chil- a probability principle facilitated their later use of dren often made analogies to humans, such as ‘‘We the probability formula to solve other problems. In cannot keep the baby the same size forever because classroom studies from 1998, Daniel Schwartz and he takes food. If he eats, he will become bigger and John Bransford found that generating distinctions bigger and be an adult.’’ Children were more often between contrasting cases improved students’ subse- correct when they used these personification analo- quent learning. As reported in 1993, John Clement gies than when they did not. This suggests that chil- used a technique of bridging analogies to induce re- dren were using humans—a familiar, well- vision of faulty mental models. Learners were given understood domain—as a base domain for a series of analogs, beginning with a very close match reasoning about similar creatures. and moving gradually to a situation that exemplified the desired new model. Retrieval of Analogs: The Inert Knowledge Another line of inquiry focuses on the sponta- Problem neous analogies people use as mental models of the Learning from cases is often easier than learning world. This research generally begins with a ques- principles directly. Despite its usefulness, however,

LEARNING: ANALOGICAL REASONING 1423 training with examples and cases often fails to lead transferring knowledge from a known domain, and to transfer, because people fail to retrieve potentially they promote noticing and abstracting principles useful analogs. For example, Mary Gick and across domains. Analogies are most successful, how- Holyoak found in 1980 that participants given an in- ever, if their pitfalls are understood. In analogical sight problem typically failed to solve it, even when mapping, it is important to ensure that the base do- they had just read a story with an analogous solu- main is understood well, that the correspondences tion. Yet, when they were told to use the prior exam- are clear, and that differences and potentially incor- ple, they were able to do so. This shows that the prior rect inferences are clearly flagged. When teaching for knowledge was not lost from memory; this failure to transfer, it is important to recognize that learners access prior structurally similar cases is, rather, an tend to rely on surface features. One solution is to instance of ‘‘inert knowledge’’—knowledge that is minimize surface features by using simple objects. not accessed when needed. Another is to induce analogical encoding by asking One explanation for this failure of transfer is learners to explicitly compare cases. The better edu- that people often encode cases in a situation-specific cators understand analogical processes, the better manner, so that later remindings occur only for they can harness them for education. highly similar cases. For example, in 1984 Ross gave See also: Learning, subentry on Transfer of people mathematical problems to study and later Learning; Learning Theory, subentry on Histor- gave them new problems. Most of their later re- ical Overview. mindings were to examples that were similar only on the surface, irrespective of whether the principles matched. Experts in a domain are more likely than BIBLIOGRAPHY novices to retrieve structurally similar examples, but Bassok, Miriam. 2001. ‘‘Semantic Alignments in even experts retrieve some examples that are similar Mathematical Word Problems.’’ In The Analogi- only on the surface. However, as demonstrated by cal Mind: Perspectives from Cognitive Science, ed. Laura Novick in 1988, experts reject spurious re- Dedre Gentner, Keith J. Holyoak, and Biocho N. mindings more quickly than do novices. Thus, espe- Kokinov. Cambridge, MA: MIT Press. cially for novices, there is an unfortunate Bransford, John D.; Franks, Jeffrey J.; Vye, dissociation: While accuracy of transfer depends Nancy J.; and Sherwood, Robert D. 1989. critically on the degree of structural match, memory ‘‘New Approaches to Instruction: Because Wis- retrieval depends largely on surface similarity be- dom Can’t Be Told.’’ In Similarity and Analogi- tween objects and contexts. cal Reasoning, ed. Stella Vosniadou and Andrew Ortony. New York: Cambridge University Press. Analogical Encoding in Learning Brown, Ann L. 1989. ‘‘Analogical Learning and In the late twentieth century, researchers began ex- Transfer: What Develops?’’ In Similarity and ploring a new technique, called analogical encoding, Analogical Reasoning, ed. Stella Vosniadou and that can help overcome the inert knowledge prob- Andrew Ortony. New York: Cambridge Univer- lem. Instead of studying cases separately, learners are sity Press. asked to compare analogous cases and describe their Brown, Ann L., and Kane, Mary Jo. 1988. ‘‘Pre- similarities. This fosters the formation of a common school Children Can Learn to Transfer: Learn- schema, which in turn facilitates transfer to a further ing to Learn and Learning from Example.’’ problem. For example, in 1999 Jeffrey Loewenstein, Cognitive Psychology 20:493–523. Leigh Thompson, and Gentner found that graduate Chen, Zhe, and Daehler, Marvin W. 1989. ‘‘Posi- management students who compared two analogical tive and Negative Transfer in Analogical Prob- cases were nearly three times more likely to transfer lem Solving by Six-Year-Old Children.’’ the common strategy into a subsequent negotiation Cognitive Development 4:327–344. task than were students who analyzed the same two Clement, John. 1993. ‘‘Using Bridging Analogies cases separately. and Anchoring Intuitions to Deal with Students’ Preconceptions in Physics.’’ Journal of Research Implications for Education in Science Teaching 30:1241–1257. Analogies can be of immense educational value. Gentner, Dedre. 1982. ‘‘Are Scientific Analogies They permit rapid learning of a new domain by Metaphors?’’ In Metaphor: Problems and Per-

1424 LEARNING: ANALOGICAL REASONING

spectives, ed. David S. Miall. Brighton, Eng.: Loewenstein, Jeffrey; Thompson, Leigh; and Harvester Press. Gentner, Dedre. 1999. ‘‘Analogical Encoding Gentner, Dedre. 1983. ‘‘Structure-Mapping: A Facilitates Knowledge Transfer in Negotiation.’’ Theoretical Framework for Analogy.’’ Cognitive Psychonomic Bulletin and Review 6:586–597. Science 7:155–170. Markman, Arthur B., and Gentner, Dedre. Gentner, Dedre, and Rattermann, Mary Jo. 2000. ‘‘Structure Mapping in the Comparison 1991. ‘‘Language and the Career of Similarity.’’ Process.’’ American Journal of Psychology In Perspectives on Thought and Language: Inter- 113:501–538. relations in Development, ed. Susan A. Gelman Novick, Laura R. 1988. ‘‘Analogical Transfer, and James P. Brynes. London: Cambridge Uni- Problem Similarity, and Expertise.’’ Journal of versity Press. Experimental Psychology: Learning, Memory, and Gentner, Dedre; Rattermann, Mary Jo; and Cognition 14:510–520. Forbus, Kenneth D. 1993. ‘‘The Roles of Simi- Perfetto, Greg A.; Bransford, John D.; and larity in Transfer: Separating Retrievability from Franks, Jeffrey J. 1983. ‘‘Constraints on Ac- Inferential Soundness.’’ Cognitive Psychology cess in a Problem Solving Context.’’ Memory 25:524–575. and Cognition 11:24–31. Gentner, Dedre, and Toupin, Cecile. 1986. ‘‘Sys- Reed, Steve K. 1987. ‘‘A Structure-Mapping Model tematicity and Surface Similarity in the Devel- for Word Problems.’’ Journal of Experimental opment of Analogy.’’ Cognitive Science 10:277– Psychology: Learning, Memory, and Cognition 300. 13:124–139. Gentner, Dedre, and Wolff, Phillip. 2000. Ross, Brian H. 1984. ‘‘Remindings and Their Ef- ‘‘Metaphor and Knowledge Change.’’ In Cogni- fects in Learning a Cognitive Skill.’’ Cognitive tive Dynamics: Conceptual Change in Humans Psychology 16:371–416. and Machines, ed. Eric Dietrich and Arthur B. 1987. ‘‘This Is Like That: The Use Markman. Mahwah, NJ: Erlbaum. Ross, Brian H. of Earlier Problems and the Separation of Simi- Gick, Mary L., and Holyoak, Keith J. 1980. ‘‘Ana- larity Effects.’’ Journal of Experimental Psycholo- logical Problem Solving.’’ Cognitive Psychology gy: Learning, Memory, and Cognition 13:629– 12:306–355. 639. Gick, Mary L., and Holyoak, Keith J. 1983. Ross, Brian H. 1989. ‘‘Distinguishing Types of Su- ‘‘Schema Induction and Analogical Transfer.’’ perficial Similarities: Different Effects on the Cognitive Psychology 15:1–38. Access and Use of Earlier Problems.’’ Journal of Goswami, Usha. 1992. Analogical Reasoning in Experimental Psychology: Learning, Memory, and Children. Hillsdale, NJ: Erlbaum. Cognition 15:456–468. Halford, Graeme S. 1993. Children’s Understand- Schank, Roger C.; Kass, Alex; and Riesbeck, ing: The Development of Mental Models. Hills- Christopher K., eds. 1994. Inside Case-Based dale, NJ: Erlbaum. Explanation. Hillsdale, NJ: Erlbaum. Holyoak, Keith J., and Koh, K. 1987. ‘‘Surface and Schwartz, Daniel L., and Bransford, John D. Structural Similarity in Analogical Transfer.’’ 1998. ‘‘A Time for Telling.’’ Cognition and In- Memory and Cognition 15:332–340. struction 16:475–522. Holyoak, Keith J., and Thagard, Paul R. 1995. Spiro, Rand J.; Feltovich, Paul J.; Coulson, Mental Leaps: Analogy in Creative Thought. and 1989. Cambridge, MA: MIT Press. Richard L.; Anderson, Daniel K. ‘‘Multiple Analogies for Complex Concepts: Inagaki, Kayoko, and Hatano, Giyoo. 1987. Antidotes for Analogy-Induced Misconception ‘‘Young Children’s Spontaneous Personification in Advanced Knowledge Acquisition.’’ In Simi- as Analogy.’’ Child Development 58:1013–1020. larity and Analogical Reasoning, ed. Stella Vos- Kempton, Willet. 1986. ‘‘Two Theories of Home niadou and Andrew Ortony. New York: Heat Control.’’ Cognitive Science 10:75–90. Cambridge University Press. Kolodner, Janet L. 1997. ‘‘Educational Implica- tions of Analogy: A View from Case-Based Rea- Dedre Gentner soning.’’ American Psychologist 52:(1)57–66. Jeffrey Loewenstein

LEARNING: CAUSAL REASONING 1425

CAUSAL REASONING on an assessment of criteria of necessity and suffi- ciency in these circumstances. A necessary cause is A doorbell rings. A dog runs through a room. A seat- one that must be present for the effect to occur. ed man rises to his feet. A vase falls from a table and Event A is necessary for event B if event B will not breaks. Why did the vase break? To answer this ques- occur without event A. For example, the vase would tion, one must perceive and infer the causal relation- not have broken if the dog had not hit the table. A ships between the breaking of the vase and other cause is sufficient if its occurrence can by itself bring events. Sometimes, the event most directly causally about the effect (i.e., whenever event A occurs, event related to an effect is not immediately apparent (e.g., B always follows). Often, more than one causal fac- the dog hit the table), and conscious and effortful tor is present. In the case of multiple necessary thought may be required to identify it. People rou- causes, a set of causal factors taken together jointly tinely make such efforts because detecting causal produces an effect. In the case of multiple sufficient connections among events helps them to make sense causes, multiple factors are present, any one of of the constantly changing flow of events. Causal which by itself is sufficient to produce an effect. reasoning enables people to find meaningful order in events that might otherwise appear random and chaotic, and causal understanding helps people to The Development of Causal Perception and plan and predict the future. Thus, in 1980 the phi- Causal Reasoning Skills losopher John Mackie described causal reasoning as Causal perception appears to begin during infancy. ‘‘the cement of the universe.’’ How, then, does one Between three and six months of age, infants re- decide which events are causally related? When does spond differently to temporally and spatially contig- one engage in causal reasoning? How does the ability uous events (e.g., one billiard ball contacting a to think about cause–effect relations originate and second that begins to roll immediately) compared to develop during infancy and childhood? How can events that lack contiguity (e.g., the second ball be- causal reasoning skills be promoted in educational gins to roll without collision or does not start to settings, and does this promote learning? These move until half a second after collision). Thus, the questions represent important issues in research on psychologist Alan Leslie proposed in 1986 that in- causal reasoning fants begin life with an innate perceptual mechanism specialized to automatically detect cause–effect rela- Causal Perceptions and Causal Reasoning tions based on contiguity. However, psychologists An important distinction exists between causal per- Leslie Cohen and Lisa Oakes reported in 1993 that ceptions and causal reasoning. Causal perceptions familiarity with role of a particular object in a causal refer to one’s ability to sense a causal relationship sequence influence ten-month-old infants’ percep- without conscious and effortful thought. According tion of causality. Therefore, they suggest that infants to the philosopher David Hume (1711–1776), per- do not automatically perceive a causal connection ceptual information regarding contiguity, prece- when viewing contiguous events. The question of dence, and covariation underlies the understanding whether infants begin with an innate ability to auto- of causality. First, events that are temporally and matically detect causality, or instead gradually devel- spatially contiguous are perceived as causally related. op casual perception through general learning Second, the causal precedes the effect. Third, events processes remains a central controversy concerning that regularly co-occur are seen as causally related. the origins of causal thought. In contrast, causal reasoning requires a person to Although infants perceive causal relationships, reason through a chain of events to infer the cause complex causal reasoning emerges during early of that event. People most often engage in causal rea- childhood and grows in sophistication thereafter. soning when they experience an event that is out of Thus, information about precedence influences the ordinary. Thus, in some situations a person may causal reasoning during childhood. When asked to not know the cause of an unusual event and must determine what caused an event to occur, three- search for it, and in other situations must evaluate year-olds often choose an event that preceded it, whether one known event was the cause of another. rather than one that came later, but understanding The first situation may present difficulty because the of precedence becomes more consistent and general causal event may not be immediately apparent. Phi- beginning at five years of age. Unlike contiguity and losophers have argued that causal reasoning is based precedence, information about covariation is not

1426 LEARNING: CAUSAL REASONING available from a single casual sequence, but requires both children and adults often have difficulty identi- repeated experience with the co-occurrence of a fying multiple necessary or sufficient causes. cause and effect. Children do not begin to use covariation information consistently in their casual Teaching Causal Reasoning Skills thinking before eight years of age. Because the various types of information relevant to causality do not The psychologist Diane Halpern argued in 1998 that always suggest the same causal relation, children and critical thinking skills should be taught in primary, adults must decide which type of information is secondary, and higher educational settings. Casual most important in a particular situation. reasoning is an important part of critical thinking because it enables one to explain and predict events, In addition to the perceptual cues identified by and thus potentially to control one’s environment Hume, knowledge of specific causal mechanisms and achieve desired outcomes. plays a central role in causal reasoning. By three years of age, children expect there to be some mech- Three approaches to teaching causal reasoning anism of transmission between cause and effect, and skills may be efficacious. First, causal reasoning skills knowledge of possible mechanisms influences both can be promoted by teaching students logical deduc- children’s and adults’ interpretation of perceptual tion. For example, teaching students to use counter- cues. For instance, when a possible causal mecha- factual reasoning may help them assess whether nism requires time to produce an effect (e.g., a mar- there is a necessary relationship between a potential ble rolling down a lengthy tube before contacting cause and an effect. Counterfactual reasoning re- another object), or transmits quickly across a dis- quires student to imagine that a potential cause did tance (e.g., electrical wiring), children as young as not occur and to infer whether the effect would have five years of age are more likely to select causes that occurred in its absence. If it would occur, then there lack temporal spatial contiguity than would other- is no causal relationship between the two events. wise be the case. Because causal mechanisms differ Second, causal reasoning skills can be promoted for physical, social, and biological events, children by teaching students to generate informal explana- must acquire distinct conceptual knowledge to un- tions for anomalous events or difficult material. For derstand causality in each of these domains. By three instance, learning from scientific texts can be partic- to four years of age, children recognize that whereas ularly challenging to students, and often students physical effects are caused by physical transmission, have the misconception that they do not have ade- human action is motivated internally by mental quate knowledge to understand texts. The psycholo- states such as desires, beliefs, and intentions, and gist Michelene Chi demonstrated in 1989 that they begin to understand some properties of biologi- students who use their general world knowledge to cal processes such as growth and heredity. Further- engage in causal, explanatory reasoning while read- more, conceptual understanding of specific causal ing difficult physics texts understand what they read mechanisms may vary across cultures and may be considerably better than do students who do not learned through social discourse as well as through draw upon general knowledge in this way. Further- direct experience. more, in 1999 the psychologist Danielle McNamara developed a reading training intervention that pro- A fundamental understanding of causality is motes explanatory reasoning during reading. In this present during early childhood; however, prior to program, students were taught a number of strate- adolescence children have difficulty searching for gies to help them to use both information in the text causal relations through systematic scientific experi- and general knowledge to generate explanations for mentation. Preadolescents may generate a single difficult material. Training improved both compre- causal hypothesis and seek confirmatory evidence, hension of scientific texts and overall class perfor- misinterpret contradictory evidence, or design ex- mance, and was particularly beneficial to at-risk perimental tests that do not provide informative evi- students. dence. In contrast, adolescents and adults may generate several alternative hypotheses and test them Third, the psychologist Leona Schauble demon- by systematically controlling variables and seeking strated in 1990 that causal reasoning skills can be both disconfirmatory and confirmatory evidence. promoted by teaching students the principles of sci- Nevertheless, even adults often have difficulty de- entific experimentation. A primary goal of experi- signing valid scientific experiments. More generally, mentation is to determine causal relationships

LEARNING: CONCEPTUAL CHANGE 1427 among a set of events. Students may be taught to McNamara, Danielle S., and Scott, Jeremy L. identify a potential cause of an effect, manipulate the 1999. Training Reading Strategies. Hillsdale, NJ: presence of the cause in a controlled setting, and as- Erlbaum. sesses whether or not the effect occurs. Thus, stu- Schauble, Leona. 1990. ‘‘Belief Revision in Chil- dents learn to use the scientific method to determine dren: The Role of Prior Knowledge and Strate- whether there are necessary and sufficient relation- gies for Generating Evidence.’’ Journal of ships between a potential cause and an effect. Be- Experimental Child Psychology 49:31–57. cause the principles of science are often difficult for Sedlak, Andrea J., and Kurtz, Susan T. 1981. ‘‘A students to grasp, teaching these principles would Review of Children’s Use of Causal Inference provide students with formal procedures for evalu- Principles.’’ Child Development 52:759–784. ating causal relationships in the world around them. Wellman, Henry M., and Gelman, Susan A. 1998. See also: Learning, subentry on Reasoning; ‘‘Knowledge Acquisition in Foundational Do- Learning Theory, subentry on Historical Over- mains.’’ In Handbook of Child Psychology: Cog- view; Literacy, subentry on Narrative Compre- nition, Perception, and Language, 5th edition, ed. hension and Production; Reading, subentries on Deanna Kuhn and Robert Siegler. New York: Comprehension, Content Areas. Wiley. White, Peter A. 1988. ‘‘Causal Processing: Origins and Development.’’ Psychological Bulletin BIBLIOGRAPHY 104:36–52. Bullock, Merry; Gelman, Rochel; and Baillar- geon, Renee. 1982. ‘‘The Development of Joseph P. Magliano Causal Reasoning.’’ In The Developmental Psy- Bradford H. Pillow chology of Time, ed. William J. Friedman. New York: Academic Press. Chi, Michelene T. H., et al. 1989. ‘‘Self- CONCEPTUAL CHANGE Explanation: How Students Study and Use Ex- The term conceptual change refers to the develop- amples in Learning to Solve Problems.’’ Cogni- ment of fundamentally new concepts, through re- tive Science 13:145–182. structuring elements of existing concepts, in the Cohen, Leslie B., and Oakes, Lisa M. 1993. ‘‘How course of knowledge acquisition. Conceptual change Infants Perceive a Simple Causal Event.’’ Devel- is a particularly profound kind of learning—it goes opmental Psychology 29:421–433. beyond revising one’s specific beliefs and involves restructuring the very concepts used to formulate Epstein, Richard L. 2002. Critical Thinking, 2nd those beliefs. Explaining how this kind of learning edition. Belmont, CA: Wadsworth. occurs is central to understanding the tremendous Halpern, Diane F. 1998. ‘‘Teaching Critical Think- power and creativity of human thought. ing for Transfer across Domains.’’ American The emergence of fundamentally new ideas is Psychologist 53:449–455. striking in the history of human thought, particular- Hume, David. 1960. A Treatise on Human Nature ly in science and mathematics. Examples include the (1739). Oxford: Clarendon Press. emergence of Darwin’s concept of evolution by natural selection, Newton’s concepts of gravity and in- Kuhn, D.; Amsel, Eric; and O’Loughlin, Mi- ertia, and the mathematical concepts of zero, chael. 1988. The Development of Scientific negative, and rational numbers. One of the chal- Thinking Skills. San Diego, CA: Academic Press. lenges of education is how to transmit these complex Leslie, Alan M. 1986. ‘‘Getting Development off products of human intellectual history to the next the Ground: Modularity and the Infant’s Per- generation of students. ception of Causality.’’ In Theory Building in De- Although there are many unresolved issues velopmental Psychology, ed. Paul Van Geert. about how concepts are mentally represented, con- Amsterdam: North-Holland. ceptual-change researchers generally assume that ex- Mackie, John L. 1980. The Cement of the Universe. planatory concepts are defined and articulated Oxford: Clarendon Press. within theory-like structures, and that conceptual

1428 LEARNING: CONCEPTUAL CHANGE change requires coordinated changes in multiple and projectile motions under a new category, accel- concepts within these structures. New concepts that erated motion. Similarly, children initially see plants have arisen in the history of science are clearly part and animals as fundamentally different: animals are of larger, explicit theories. Making an analogy be- behaving beings that engage in self-generated move- tween the organization of concepts in scientists and ment, while plants are not. Later they come to see children, researchers have proposed that children them as two forms of ‘‘living things’’ that share im- may have ‘‘commonsense’’ theories in which their portant biological properties. Conceptual coales- everyday explanatory concepts are embedded and cence is not the same as simply adding a more play a role. These theories, although not self- general category by abstracting properties common consciously held, are assumed to be like scientific to more specific categories. In conceptual coales- theories in that they consist of a set of interrelated cence the initial concepts are thought to be funda- concepts that resist change and that support infer- mentally different, and the properties that will be ence making, problem solving, belief formation, and central to defining the new category are not repre- explanation in a given domain. The power and use- sented as essential properties of the initial concepts. fulness of this analogy is being explored in the early Different forms of conceptual change mutually twenty-first century. support each other. For example, conceptual coales- A challenge for conceptual-change researchers is cences (such as uniting free-fall and projectile mo- to provide a typology of important forms of conception in a new concept of accelerated motion, or tual change. For example, conceptual differentiation plants and animals in a new concept of living things) is a form of conceptual change in which a newer (de- are accompanied by conceptual differentiations scendant) theory uses two distinct concepts where (such as distinguishing uniform from accelerated the initial (parent) theory used only one, and the un- motion, or distinguishing dead from inanimate). differentiated parent concept unites elements that These changes are also supported by additional will subsequently be kept distinct. Examples of con- forms of conceptual change, such as re-analysis of ceptual differentiation include: Galileo’s differentia- the core properties or underlying structure of the tion of average and instantaneous velocity in his concept, as well as the acquisition of new specific be- theory of motion, Black’s differentiation of heat and liefs about the relations among concepts. temperature in his theory of thermal phenomena, and children’s differentiation of weight and density Mechanisms of Conceptual Change in their matter theory. Conceptual differentiation is not the same as adding new subcategories to an ex- One reason for distinguishing conceptual change isting category, which involves the elaboration of a from belief revision and conceptual elaboration is conceptual structure rather than its transformation. that different learning mechanisms may be required. In that case, the new subcategories fit into an exist- Everyday learning involves knowledge enrichment ing structure, and the initial general category is still and rests on an assumed set of concepts. For exam- maintained. In differentiation, the parent concept is ple, people use existing concepts to represent new seen as incoherent from the perspective of the subse- facts, formulate new beliefs, make inductive or de- quent theory and plays no role in it. For example, an ductive inferences, and solve problems. undifferentiated weight/density concept that unites What makes conceptual change so challenging the elements heavy and heavy-for-size combines two to understand is that it cannot occur in this way. The fundamentally different kinds of quantities: an ex- concepts of a new theory are ultimately organized tensive (total amount) quantity and an intensive (re- and stated in terms of each other, rather than the lationally defined) quantity. concepts of the old theory, and there is no simple one-to-one correspondence between some concepts Another form of conceptual change is coales- of the old and new theories. By what learning mech- cence, in which the descendant theory introduces a anisms, then, can scientists invent, and students new concept that unites concepts previously seen to comprehend, a genuinely new set of concepts and be of fundamentally different types in the parent come to prefer them to their initial set of concepts? theory. For example, Aristotle saw circular planetary and free-fall motions as natural motions that were Most theorists agree that one step in conceptual fundamentally different from violent projectile mo- change for both students and scientists is experienc- tions. Newton coalesced circular, planetary, free-fall, ing some form of cognitive dissonance—an internal

LEARNING: CONCEPTUAL CHANGE 1429 state of tension that arises when an existing concep- period of time and include intermediate, bridging tual system fails to handle important data and prob- constructions. For example, Darwin’s starting idea lems in a satisfactory manner. Such dissonance can of evolution via directed, adaptative variation initial- be created by a series of unexpected results that can- ly prevented his making an analogy between this not be explained by an existing theory, by the press process and artificial selection. He transformed his to solve a problem that is beyond the scope of one’s understanding of this process using multiple analo- current theory, or by the detection of internal incon- gies (first with wedging and Malthusian population sistencies in one’s thinking. This dissonance can sig- pressure, and later with artificial selection), imagistic nal the need to step outside the normal mode of reasoning (e.g., visualizing the jostling effects of applying one’s conceptual framework to a more 100,000 wedges being driven into the same spot of meta-conceptual mode of questioning, examining, ground to understand the tremendous power of the and evaluating one’s conceptual framework. unseen force in nature and its ability to produce spe- Although experiencing dissonance can signal cies change in a mechanistic manner), and thought that there is a conceptual problem to be solved, it experiments (e.g., imagining how many small effects does not solve that problem. Another step involves might build up over multiple generations to yield a active attempts to invent or construct an under- larger effect). Each contributed different elements to standing of alternative conceptual systems by using his final concept of natural selection, with his initial a variety of heuristic procedures and symbolic tools. analogies leading to the bridging idea of selection Heuristic procedures, such as analogical reasoning, acting in concert with the process of directed adap- imagistic reasoning, and thought experiments, may tive variation, rather than supplanting it. be particularly important because they allow both Constructing a new conceptual system is also students and scientists to creatively extend, combine, accompanied by a process of evaluating its adequacy and modify existing conceptual resources via the against known alternatives using some set of criteria. construction of new models. Symbolic tools, such as These criteria can include: the new system’s ability natural language, the algebraic and graphical repre- to explain the core problematic phenomena as well sentations of mathematics, and other invented nota- as other known phenomena in the domain, its inter- tional systems, allow the explicit representation of nal consistency and fit with other relevant knowl- key relations in the new system of concepts. edge, the extent to which it meets certain In analogical reasoning, knowledge of concep- explanatory ideals, and its capacity to suggest new tual relations in better-understood domains are fruitful lines of research. powerful sources of new ideas about the less- Finally, researchers have examined the personal, understood domain. Analogical reasoning is often motivational, and social processes that support con- supported by imagistic reasoning, wherein one ceptual change. Personal factors include courage, creates visual depictions of core ideas using visual confidence in one’s abilities, openness to alterna- analogs with the same underlying relational struc- tives, willingness to take risks, and deep commit- ture. These depictions allow the visualization of un- ment to an intellectual problem. Social factors seen theoretical entities, connect the problem to the include working in groups that combine different well-developed human visual-spatial inferencing kinds of expertise and that encourage consideration system, and, because much mathematical informa- of inconsistencies in data and relevant analogies. In- tion is implicit in such depictions, facilitate the con- deed, many science educators believe a key to pro- struction of appropriate mathematical descriptions moting conceptual change in the classroom is of a given domain. Thought experiments use initial through creating a more reflective classroom dis- knowledge of a domain to run simulations of what course. Such discourse probes for alternative student should happen in various idealized situations, in- views, encourages the clarification, negotiation, and cluding imagining what happens as the effects of a elaboration of meanings, the detection of inconsis- given variable are entirely eliminated, thus facilitat- tencies, and the use of evidence and argument in de- ing the identification of basic principles not self- ciding among or integrating alternative views. evident from everyday observation. Case studies of conceptual change in the history Educational Implications of science and science education reveal that new in- Conceptual change is difficult under any circum- tellectual constructions develop over an extended stances, as it requires breaking out of the self-

1430 LEARNING: CONCEPTUAL CHANGE perpetuating circle of theory-based reasoning, mak- See also: Categorization and Concept Learn- ing coordinated changes in a number of concepts, ing; Learning, subentry on Knowledge Acquisi- and actively constructing an understanding of new tion, Representation, and Organization. (more abstract) conceptual systems. Students need signals that conceptual change is needed, as well as BIBLIOGRAPHY good reasons to change their current conceptions, Carey, Susan. 1999. ‘‘Sources of Conceptual guidance about how to integrate existing conceptual Change.’’ In Conceptual Development: Piaget’s resources in order to construct new conceptions, Legacy, ed. Ellin K. Scholnick, Katherine Nelson, and the motivation and time needed to make those Susan A. Gelman, and Patricia H. Miller. Mah- constructions. Traditional education practice often wah, NJ: Erlbaum. fails to provide students with the appropriate signals, Chi, Micheline. 1992. ‘‘Conceptual Change within guidance, motivation, and time. and across Ontological Categories: Examples Conceptual change is a protracted process call- from Learning and Discovery in Science.’’ In ing for a number of coordinated changes in instruc- Cognitive Models of Science, ed. Ronald N. Giere. tional practice. First, instruction needs to be Minnesota Studies in the Philosophy of Science, grounded in the consideration of important phe- Vol. 15. Minneapolis: University of Minnesota nomena or problems that are central to the experts’ Press. framework—and that challenge students’ initial Chinn, Clark A., and Brewer, William F. 1993. commonsense framework. These phenomena not ‘‘The Role of Anomalous Data in Knowledge only motivate conceptual change, but also constrain Acquisition: A Theoretical Framework and Im- the search for, and evaluation of, viable alternatives. plications for Science Instruction.’’ Review of Second, instruction needs to guide students in the Educational Research 63(1):1–49. construction of new systems of concepts for under- Clement, John. 1993. ‘‘Using Bridging Analogies standing these phenomena. Teachers must know and Anchoring Intuitions to Deal with Students’ what heuristic techniques, representational tools, Preconceptions in Physics.’’ Journal of Research and conceptual resources to draw upon to make new in Science Teaching 30(10):1241–1257. concepts intelligible to students, and also how to Dunbar, Kenneth. 1995. ‘‘How Scientists Really build these constructions in a sequenced manner. Reason: Scientific Reasoning in Real-World Laboratories.’’ In The Nature of Insight, ed. Rob- Third, instruction needs to be supported by a ert J. Sternberg and Janet E. Davidson. Cam- classroom discourse that encourages students to bridge, MA: MIT Press. identify, represent, contrast, and debate the adequacy of competing explanatory frameworks in terms of Gentner, Dedre; Brem, Sarah; Ferguson, Ron- emerging classroom epistemological standards. Such ald; Markman, Arthur; Levidow, Bjorn; Wolff, Phillip; and Forbus, Kenneth. 1997. discourse supports many aspects of the conceptual- ‘‘Analogical Reasoning and Conceptual Change: change process, including making students aware of A Case Study of Johannes Kepler.’’ Journal of the their initial conceptions, helping students construct Learning Sciences 6(1):3–40. an understanding of alternative frameworks, moti- vating students to examine their conceptions more Laurence, Stephen, and Margolis, Eric. 1999. critically (in part through awareness of alternatives), ‘‘Concepts and Cognitive Science.’’ In Concepts: Core Readings, ed. Eric Margolis and Stephen and promoting their ability to evaluate, and at times Laurence. Cambridge, MA: MIT Press. integrate, competing frameworks. Lehrer, Richard; Schauble, Leona; Carpenter, Finally, instruction needs to provide students Susan; and Penner, David. 2000. ‘‘The Inter- with extended opportunities for applying new sys- related Development of Inscriptions and Con- tems of concepts to a wide variety of problems. Re- ceptual Understanding.’’ In Symbolizing and peated applications develop students’ skill at Communicating in Mathematics Classrooms: Per- applying a new framework, refine their understand- spectives on Discourse, Tools, and Instructional ing of the framework, and help students appreciate Design, ed. Paul Cobb, Erna Yackel, and Kay its greater power and scope. McClain. Mahwah, NJ: Erlbaum.

LEARNING: KNOWLEDGE ACQUISITION, REPRESENTATION, AND ORGANIZATION 1431

Millman, Arthur B., and Smith, Carol L. 1997. KNOWLEDGE ACQUISITION, ‘‘Darwin’s Use of Analogical Reasoning in The- REPRESENTATION, AND ory Construction.’’ Metaphor and Symbol ORGANIZATION 12(3):159–187. Knowledge acquisition is the process of absorbing Nercessian, Nancy J. 1992. ‘‘How Do Scientists and storing new information in memory, the success Think? Capturing the Dynamics of Conceptual of which is often gauged by how well the informa- Change in Science.’’ In Cognitive Models of Sci- tion can later be remembered (retrieved from mem- ence, ed. Ronald N. Giere. Minnesota Studies in ory). The process of storing and retrieving the Philosophy of Science, Vol. 15. Minneapolis: information depends heavily on the representation and organization of the information. Moreover, the University of Minnesota Press. utility of knowledge can also be influenced by how Pintrich, Paul R.; Marx, Ronald W.; and Boyle, the information is structured. For example, a bus Robert A. 1993. ‘‘Beyond Cold Conceptual schedule can be represented in the form of a map or Change: The Role of Motivational Beliefs and a timetable. On the one hand, a timetable provides Classroom Contextual Factors in the Process of quick and easy access to the arrival time for each bus, Conceptual Change.’’ Review of Educational Re- but does little for finding where a particular stop is search 63(2):167–199. situated. On the other hand, a map provides a detailed picture of each bus stop’s location, but cannot Posner, Gerald; Strike, Kenneth; Hewson, efficiently communicate bus schedules. Both forms Peter; and Gertzog, W. A. 1982. ‘‘Accommo- of representation are useful, but it is important to se- dation of a Scientific Conception: Toward a lect the representation most appropriate for the task Theory of Conceptual Change.’’ Science Educa- at hand. Similarly, knowledge acquisition can be im- tion 66:211–227. proved by considering the purpose and function of the desired information. Smith, Carol; Maclin, Deborah; Grosslight, Lorraine; and Davis, Helen. 1997. ‘‘Teaching Knowledge Representation and Organization for Understanding: A Study of Students’ Pre- instruction Theories of Matter and a Compari- There are numerous theories of how knowledge is son of the Effectiveness of Two Approaches to represented and organized in the mind, including Teaching about Matter and Density.’’ Cognition rule-based production models, distributed networks, and propositional models. However, these and Instruction 15(3):317–393. theories are all fundamentally based on the concept van Zee, Emily, and Minstrell, Jim. 1997. ‘‘Using of semantic networks. A semantic network is a meth- Questioning to Guide Student Thinking.’’ Jour- od of representing knowledge as a system of connec- nal of the Learning Sciences 6:227–269. tions between concepts in memory. Vosniadou, Stella, and Brewer, William F. 1987. ‘‘Theories of Knowledge Restructuring in Semantic Networks Development.’’ Review of Educational Research According to semantic network models, knowledge 57:51–67. is organized based on meaning, such that semantically related concepts are interconnected. Knowl- White, Barbara. 1993. ‘‘ThinkerTools: Causal edge networks are typically represented as diagrams Models, Conceptual Change, and Science In- of nodes (i.e., concepts) and links (i.e., relations). struction.’’ Cognition and Instruction 10:1–100. The nodes and links are given numerical weights to Wiser, Marianne, and Amin, Tamir. 2001. ‘‘‘Is represent their strengths in memory. In Figure 1, the Heat Hot?’ Inducing Conceptual Change by In- node representing DOCTOR is strongly related to SCALPEL, whereas NURSE is weakly related to tegrating Everyday and Scientific Perspectives SCALPEL. These link strengths are represented here on Thermal Phenomena.’’ Learning and Instruc- in terms of line width. Similarly, some nodes in Fig- tion 11(4–5):331–355. ure 1 are printed in bold type to represent their strength in memory. Concepts such as DOCTOR Carol L. Smith and BREAD are more memorable because they are

1432 LEARNING: KNOWLEDGE ACQUISITION, REPRESENTATION, AND ORGANIZATION

FIGURE 1

more frequently encountered than concepts such as Types of Knowledge SCALPEL and CRUST. There are numerous types of knowledge, but the Mental excitation, or activation, spreads auto- most important distinction is between declarative and procedural knowledge. Declarative knowledge matically from one concept to another related con- refers to one’s memory for concepts, facts, or epi- cept. For example, thinking of BREAD spreads sodes, whereas procedural knowledge refers to the activation to related concepts, such as BUTTER and ability to perform various tasks. Knowledge of how CRUST. These concepts are primed, and thus more to drive a car, solve a multiplication problem, or easily recognized or retrieved from memory. For ex- throw a football are all forms of procedural knowl- ample, in David Meyer and Roger Schvaneveldt’s edge, called procedures or productions. Procedural 1976 study (a typical semantic priming study), a se- knowledge may begin as declarative knowledge, but ries of words (e.g., BUTTER) and nonwords (e.g., is proceduralized with practice. For example, when BOTTOR) are presented, and participants deter- first learning to drive a car, you may be told to ‘‘put the key in the ignition to start the car,’’ which is a mine whether each item is a word. A word is more declarative statement. However, after starting the car quickly recognized if it follows a semantically related numerous times, this act becomes automatic and is word. For example, BUTTER is more quickly recog- completed with little thought. Indeed, procedural nized as a word if BREAD precedes it, rather than knowledge tends to be accessed automatically and NURSE. This result supports the assumption that se- require little attention. It also tends to be more dura- mantically related concepts are more strongly con- ble (less susceptible to forgetting) than declarative nected than unrelated concepts. knowledge. Network models represent more than simple as- Knowledge Acquisition sociations. They must represent the ideas and com- Listed below are five guidelines for knowledge acqui- plex relationships that comprise knowledge and sition that emerge from how knowledge is represent- comprehension. For example, the idea ‘‘The doctor ed and organized. uses a scalpel’’ can be represented as the proposition Process the material semantically. Knowledge is or- USE (DOCTOR, SCALPEL), which consists of the ganized semantically; therefore, knowledge acquisi- nodes DOCTOR and SCALPEL and the link USE tion is optimized when the learner focuses on the (see Figure 2). Educators have successfully used sim- meaning of the new material. Fergus Craik and ilar diagrams, called concept maps, to communicate Endel Tulving were among the first to provide evi- important relations and attributes among the key dence for the importance of semantic processing. In concepts of a lesson. their studies, participants answered questions con-

LEARNING: KNOWLEDGE ACQUISITION, REPRESENTATION, AND ORGANIZATION 1433

FIGURE 2

cerning target words that varied according to the with breaks, or on different days. In contrast, repeat- depth of processing involved. For example, semantic ing information numerous times sequentially in- questions (e.g., Which word, friend or tree, fits ap- volves only a single retrieval from long-term propriately in the following sentence: ‘‘He met a memory, which does little to improve memory for ____ on the street’’?) involve a greater depth of pro- the information. cessing than phonemic questions (e.g., Which word, Learning and retrieval conditions should be simi- crate or tree, rhymes with the word late?), which in lar. How knowledge is represented is determined by turn have a greater depth than questions concerning the conditions and context (internal and external) in the structure of a word (e.g., Which word is in capi- which it is learned, and this in turn determines how tal letters: TREE or tree?). Craik and colleagues found that words processed semantically were better it is retrieved: Information is best retrieved when the learned than words processed phonemically or conditions of learning and retrieval are the same. structurally. Further studies have confirmed that This principle has been referred to as encoding speci- learning benefits from greater semantic processing ficity. For example, in one experiment, participants of the material. were shown sentences with an adjective and a noun printed in capital letters (e.g. The CHIP DIP tasted Process and retrieve information frequently. A delicious.) and told that their memory for the nouns second learning principle is to test and retrieve the would be tested afterward. In the recognition test, information numerous times. Retrieving, or self- participants were shown the noun either with the producing, information can be contrasted with sim- original adjective (CHIP DIP), with a different ad- ply reading or copying it. Decades of research on a jective (SKINNY DIP), or without an adjective phenomenon called the generation effect have shown (DIP). Noun recognition was better when the origi- that passively studying items by copying or reading nal adjective (CHIP) was presented than when no them does little for memory in comparison to self- adjective was presented. Moreover, presenting a dif- producing, or generating, an item. Moreover, learn- ferent adjective (SKINNY) yielded the lowest recog- ing improves as a function of the number of times nition. This finding underscores the importance of information is retrieved. Within an academic situa- matching learning and testing conditions. tion, this principle points to the need for frequent practice tests, worksheets, or quizzes. In terms of Encoding specificity is also important in terms studying, it is also important to break up, or distrib- of the questions used to test memory or comprehen- ute retrieval attempts. Distributed retrieval can in- sion. Different types of questions tap into different clude studying or testing items in a random order, levels of understanding. For example, recalling in-

1434 LEARNING: KNOWLEDGE ACQUISITION, REPRESENTATION, AND ORGANIZATION formation involves a different level of understand- dures when learning information. Procedures can ing, and different mental processes, than recognizing include shortcuts for completing a task (e.g., using information. Likewise, essay and open-ended ques- fast 10s to solve multiplication problems), as well as tions assess a different level of understanding than memory strategies that increase the distinctive multiple-choice questions. Essay and open-ended meaning of information. Cognitive research has re- questions generally tap into a conceptual or situa- peatedly demonstrated the benefits of memory strat- tional understanding of the material, which results egies, or mnemonics, for enhancing the recall of from an integration of text-based information and information. There are numerous types of mnemon- the reader’s prior knowledge. In contrast, multiple- ics, but one well-known mnemonic is the method of choice questions involve recognition processes, and loci. This technique was invented originally for the typically assess a shallow or text-based understand- purpose of memorizing long speeches in the times ing. A text-based representation can be impover- before luxuries such as paper and pencil were readily ished and incomplete because it consists only of available. The first task is to imagine and memorize concepts and relations within the text. This level of a series of distinct locations along a familiar route, understanding, likely developed by a student prepar- such as a pathway from one campus building to an- ing for a multiple-choice exam, would be inappro- other. Each topic of a speech (or word in a word list) priate preparation for an exam with open-ended or can then be pictured in a location along the route. essay questions. Thus, students should benefit by ad- When it comes time to recall the speech or word list, justing their study practices according to the expect- the items are simply found by mentally traveling the ed type of questions. pathway. Alternatively, students may benefit from review- Mnemonics are generally effective because they ing the material in many different ways, such as rec- increase semantic processing of the words (or ognizing the information, recalling the information, phrases) and render them more meaningful by link- and interpreting the information. These latter pro- ing them to familiar concepts in memory. Mnemon- cesses improve understanding and maximize the ics also provide ready-made, effective cues for probability that the various ways the material is retrieving information. Another important aspect of studied will match the way it is tested. From a teach- mnemonics is that mental imaging is often involved. er’s point of view, including different types of ques- Images not only render information more meaning- tions on worksheets or exams ensures that each ful, but they provide an additional route for finding student will have an opportunity to convey their un- information in memory. As mentioned earlier, in- derstanding of the material. creasing the number of meaningful links to informa- Connect new information to prior knowledge. tion in memory increases the likelihood it can be Knowledge is interconnected; therefore, new materi- retrieved. al that is linked to prior knowledge will be better re- Strategies are also an important component of tained. A driving factor in text and discourse meta-cognition, which is the ability to think about, comprehension is prior knowledge. Skilled readers understand, and manage one’s learning. First, one actively use their prior knowledge during compre- must develop an awareness of one’s own thought hension. Prior knowledge helps the reader to fill in processes. Simply being aware of thought processes contextual gaps within the text and develop a better increases the likelihood of more effective knowledge global understanding or situation model of the text. construction. Second, the learner must be aware of Given that texts rarely (if ever) spell out everything whether or not comprehension has been successful. needed for successful comprehension, using prior Realizing when comprehension has failed is crucial knowledge to understand text and discourse is criti- to learning. The final, and most important stage of cal. Moreover, thinking about what one already meta-cognitive processing is fixing the comprehen- knows about a topic provides connections in memo- sion problem. The individual must be aware of, and ry to the new information—the more connections use, strategies to remedy comprehension and learn- that are formed, the more likely the information will ing difficulties. For successful knowledge acquisition be retrievable from memory. to occur, all three of these processes must occur. Create cognitive procedures. Procedural knowledge Without thinking or worrying about learning, the is better retained and more easily accessed. There- student cannot realize whether the concepts have fore, one should develop and use cognitive proce- been successfully grasped. Without realizing that in-

LEARNING: KNOWLEDGE ACQUISITION, REPRESENTATION, AND ORGANIZATION 1435 formation has not been understood, the student Low-Achieving Inner-City Seventh Graders.’’ cannot engage in strategies to remedy the situation. RASE: Remedial and Special Education 21:356– If nothing is done about a comprehension failure, 365. awareness is futile. Hacker, Douglas J.; Dunlosky, John; and Gr- aesser, Arthur C. 1998. Metacognition in Edu- Conclusion cational Theory and Practice. Mahwah, NJ: Knowledge acquisition is integrally tied to how the Lawrence Erlbaum. mind organizes and represents information. Learn- Jensen, Mary Beth, and Healy, Alice F. 1998. ing can be enhanced by considering the fundamental ‘‘Retention of Procedural and Declarative Infor- properties of human knowledge, as well as by the ul- mation from the Colorado Drivers’ Manual.’’ In timate function of the desired information. The Memory Distortions and their Prevention, ed. most important property of knowledge is that it is Margaret Jean Intons-Peterson and Deborah L. organized semantically; therefore, learning methods Best. Mahwah, NJ: Lawrence Erlbaum. should enhance meaningful study of new informa- Kintsch, Walter. 1998. Comprehension: A Para- tion. Learners should also create as many links to the digm for Cognition. Cambridge, Eng.: Cam- information as possible. In addition, learning meth- bridge University Press. ods should be matched to the desired outcome. Just Light, Leah L., and Carter-Sobell, Linda. 1970. as using a bus timetable to find a bus-stop location ‘‘Effects of Changed Semantic Context on Rec- is ineffective, learning to recognize information will ognition Memory.’’ Journal of Verbal Learning do little good on an essay exam. and Verbal Behavior 9:1–11. See also: Learning, subentry on Conceptual McNamara, Danielle S., and Kintsch, Walter. Change; Reading, subentry on Content Areas. 1996. ‘‘Learning from Text: Effects of Prior Knowledge and Text Coherence.’’ Discourse Processes 22:247–287. BIBLIOGRAPHY Melton, Arthur W. 1967. ‘‘Repetition and Re- Anderson, John R. 1982. ‘‘Acquisition of a Cogni- trieval from Memory.’’ Science 158:532. tive Skill.’’ Psychological Review 89:369–406. Meyer, David E., and Schvaneveldt, Roger W. Anderson, John R., and Lebière, Christian. 1998. 1976. ‘‘Meaning, Memory Structure, and Men- The Atomic Components of Thought. Mahwah, tal Processes.’’ Science 192:27–33. NJ: Erlbaum. Paivio, Allen. 1990. Mental Representations: A Bransford, John, and Johnson, Marcia K. 1972. Dual Coding Approach. New York: Oxford Uni- ‘‘Contextual Prerequisites for Understanding versity Press. Some Investigations of Comprehension and Re- Rumelhart, David E., and McClelland, James L. call.’’ Journal of Verbal Learning and Verbal Be- 1986. Parallel Distributed Processing: Explora- havior 11:717–726. tions in the Microstructure of Cognition, Vol. 1: Craik, Fergus I. M., and Tulving, Endel. 1975. Foundations. Cambridge, MA: MIT Press. ‘‘Depth of Processing and the Retention of Slamecka, Norman J., and Graf, Peter. 1978. Words in Episodic Memory.’’ Journal of Experi- ‘‘The Generation Effect: Delineation of a Phe- 194:268–294. mental Psychology: General. nomenon.’’ Journal of Experimental Psychology: Crovitz, Herbert F. 1971. ‘‘The Capacity of Mem- Human Learning and Memory 4:592–604. ory Loci in Artificial Memory.’’ Psychonomic Tulving, Endel, and Thompson, Donald M. Science 24:187–188. 1973. ‘‘Encoding Specificity and Retrieval Pro- Glenberg, Arthur M. 1979. ‘‘Component-Levels cesses in Episodic Memory.’’ Psychological Re- Theory of the Effects of Spacing of Repetitions view 80:352–373. on Recall and Recognition.’’ Memory and Cog- Yates, Francis A. 1966. The Art of Memory. Chica- nition 7:95–112. go: University of Chicago Press. Guastello, Francine; Beasley, Mark; and Sinatra, Richard. 2000. ‘‘Concept Mapping Danielle S. McNamara Effects on Science Content Comprehension of Tenaha O’Reilly

1436 LEARNING: NEUROLOGICAL FOUNDATION

NEUROLOGICAL FOUNDATION procedural memory, the capacity to acquire habitual behavioral routines that can be performed without Learning is mediated by multiple memory systems conscious control. This system involves cortical in- in the brain, each of which involves a distinct ana- puts to the striatum as a nodal stage in the associa- tomical pathway and supports a particular form of tion of sensory and motor cortical information with memory representation. The major aim of research voluntary responses via the brainstem motor system. on memory systems is to identify and distinguish the An additional, parallel pathway that mediates differ- different contributions of specific brain structures ent aspects of sensori-motor adaptations involves and pathways, usually by contrasting the effects of sensory and motor systems pathways through the selective damage to specific brain areas. Another cerebellum. major strategy focuses on localizing brain areas that are activated, that is, whose neurons are activated The Declarative Memory System during particular aspects of memory processing. Some of these studies use newly developed function- Declarative memory is the ‘‘everyday’’ form of mem- al imaging techniques to view activation of brain ory that most consider when they think of memory. Therefore, the remainder of this discussion will areas in humans performing memory tests. Another focus on the declarative memory system. Declarative approach seeks to characterize the cellular code for memory is defined as a composite of episodic mem- memory within the activity patterns of single nerve ory, the ability to recollect personal experiences, and cells in animals, by asking how information is repre- semantic memory, the synthesis of the many episod- sented by the activity patterns within the circuits of ic memories into the knowledge about the world. In different structures in the relevant brain systems. addition, declarative memory supports the capacity Each of the brain’s memory systems begins in for conscious recall and the flexible expression of the vast expanse of the cerebral cortex, specifically in memories, one’s ability to search networks of epi- the so-called cortical association areas (see Figure 1). sodic and semantic memories and to use this capaci- These parts of the cerebral cortex provide major in- ty to solve many problems. puts to each of three main pathways of processing Each of the major components of the declarative in subcortical areas related to distinct memory func- memory system contributes differently to declarative tions. One system mediates declarative memory, the memory, although interactions between these areas memory for facts and events that can be brought to are also essential. Initially, perceptual information as conscious recollection and can be expressed in a va- well as information about one’s behavior is pro- riety of ways outside the context of learning. This cessed in many dedicated neocortical areas. While system involves connections from the cortical asso- the entire cerebral cortex is involved in memory pro- ciation areas to the hippocampus via the parahippo- cessing, the chief brain area that controls this pro- campal region. The main output of hippocampal cessing is the prefrontal cortex. The processing and parahippocampal processing is back to the same accomplished by the prefrontal cortex includes the cortical areas that provided inputs to the hippocam- acquisition of complex cognitive rules and concepts pus, and are viewed as the long-term repository of and working memory, the capacity to store informa- declarative memories. tion briefly while manipulating or rehearsing the in- The other two main pathways involve cortical formation under conscious control. In addition, the inputs to specific subcortical targets that send direct areas of the cortex also contribute critically to mem- outputs that control behavior. One of these systems ory processing. Association areas in the prefrontal, mediates emotional memory, the attachment of affili- temporal, and parietal cortex play a central role in ations and aversions towards otherwise arbitrary cognition and in both the perception of sensory in- stimuli and modulation of the strength of memories formation and in maintenance of short-term traces that involve emotional arousal. This system involves of recently perceived stimuli. Furthermore, the orga- cortical (as well as subcortical) inputs to the amyg- nization of perceptual representations in cerebral dala as the nodal stage in the association of sensory cortical areas, and connections among these areas, inputs to emotional outputs effected via the hypo- are permanently modified by learning experiences, thalamic-pituitary axis and autonomic nervous sys- constituting the long term repository of memories. tem, as well as emotional influences over widespread The parahippocampal region, which receives brain areas. The second of these systems mediates convergent inputs from the neocortical association

LEARNING: PERCEPTUAL PROCESSES 1437 areas and sends return projections to all of these FIGURE 1 areas, appears to mediate the extended persistence of these cortical representations. Through interactions between these areas, processing within the cortex can take advantage of lasting parahippocampal representations, and so come to reflect complex associa- tions between events that are processed separately in different cortical regions or occur sequentially in the same or different areas. These individual contributions and their interactions are not conceived as sufficient to link representations of events to form episodic memories or to form generalizations across memories to create a semantic memory network. Such an organization requires the capacity to rapidly encode a sequence of events that make up an episodic memory, to retrieve that memory by re-experiencing one facet of the event, and to link the ongoing experience to stored episodic representations, forming the semantic network. The neuronal elements of the hippocampus contain the fundamental coding properties that can support this kind of organization. However, interactions among the components of the system are undoubtedly critical. It is unlikely that the hippocampus has the storage capacity to contain all of one’s episodic memories and the hip- Schacter, Daniel L., and Tulving, Endel, eds. pocampus is not the final storage site. Therefore, it 1994. Memory Systems 1994. Cambridge, MA: seems likely that the hippocampal neurons are in- MIT Press. volved in mediating the reestablishment of detailed Squire, Larry R., and Kandel, Eric R. 1999. Mem- cortical representations, rather than storing the de- ory: From Mind to Molecules. New York: Scien- tails themselves. Repetitive interactions between the tific American Library. cortex and hippocampus, with the parahippocampal Squire, Larry R.; Knowlton, Barbara; and region as intermediary, serve to sufficiently coacti- Musen, Gail. 1993. ‘‘The Structure and Orga- vate widespread cortical areas so that they eventually nization of Memory.’’ Annual Review of Psychol- develop linkages between detailed memories without ogy 44:453–495. hippocampal mediation. In this way, the networking provided by the hippocampus underlies its role in Howard Eichenbaum the organization of the permanent memory networks in the cerebral cortex. PERCEPTUAL PROCESSES See also: Brain-Based Education. As Eleanor Gibson wrote in her classic text Principles of Perceptual Learning and Development, perceptual learning results in changes in the pickup of informa- BIBLIOGRAPHY tion as a result of practice or experience. Perception Eichenbaum, Howard. 2000. ‘‘A Cortical- and action are a cycle: People act in order to learn Hippocampal System for Declarative Memory.’’ about their surroundings, and they use what they Nature Reviews Neuroscience 1:41–50. learn to guide their actions. From this perspective, Eichenbaum, Howard, and Cohen, Neal J. 2001. the critical defining features of perception include From Conditioning to Conscious Recollection: the exploratory actions of the perceiver and the Memory Systems of the Brain. Upper Saddle knowledge of the events, animate and inanimate ob- River, NJ: Oxford University Press. jects, and surrounding environment gained while

1438 LEARNING: PERCEPTUAL PROCESSES engaged in looking, listening, touching, walking, and sions, learning to identify different people and other forms of direct observation. Perception often understand their facial expressions, learning to dif- results in learning information that is directly rele- ferentiate the different elements of speech when vant to the goals at hand, but sometimes it results learning a second language, and learning to differen- in learning that is incidental to one’s immediate tiate efficient routes to important destinations when goals. faced with new surroundings. Perception becomes more skillful with practice In ‘‘nonacademic’’ subjects within the realm of and experience, and perceptual learning can be academic pursuits, important examples involve thought of as the education of attention. Perceivers music, art, and sports. For example, music students come to notice the features of situations that are rel- learn to differentiate the notes, chords, and instru- evant to their goals and not to notice the irrelevant mental voices in a piece, and they learn to identify features. Three general principles of perceptual pieces by period and composer. Art students learn learning seem particularly relevant. First, unskillful to differentiate different strokes, textures, and styles, perceiving requires much concentrated attention, and they learn to classify paintings by period and whereas skillful perceiving requires less attention artist. Athletes learn to differentiate the different de- and is more easily combined with other tasks. Sec- grees of freedom that need to be controlled to pro- ond, unskillful perceiving involves noticing both the duce a winning ‘‘play’’ and to anticipate what actions relevant and irrelevant features of sensory stimula- need to be taken when on a playing field. tion without understanding their meaning or rele- Finally, perceptual learning plays an equally vance to one’s goals, whereas skillful perceiving broad role in classically academic subjects. For ex- involves narrowing one’s focus to relevant features ample, mathematics students gain expertise at per- and understanding the situations they specify. And ceiving graphs, classifying the shapes of curves, and third, unskillful perceiving often involves attention knowing what equations might fit a given curve. Sci- to the proximal stimulus (that is, the patterns of ence students gain expertise at perceiving laboratory light or acoustic or pressure information on the reti- setups. These range widely across grade levels and nas, cochleae, and skin, respectively), whereas skill- domains, including the critical features of hydrolyz- ful perceiving involves attention to the distal event ing water in a primary school general science setting, that is specified by the proximal stimulus. molecular structures in organic chemistry and ge- netics, frog dissections in biology, the functional re- Different Domains lation of the frequency of waves and diffraction in different media in physics, and the critical features Perceptual learning refers to relatively durable gains of maps in geology. in perception that occur across widely different domains. For example, at one extreme are studies dem- The borders separating perceptual learning onstrating that with practice adults can gain from conceiving and reasoning often become exquisite sensitivity to vernier discriminations, that blurred. And indeed, people perceive in order to un- is, the ability to resolve gaps in lines that approach derstand, and their understanding leads to more and the size of a single retinal receptor. At the opposite more efficient perception. For example, Herbert A. extreme, perceptual learning plays a central role in Simon elaborated on this in 2001 in his discussion gaining expertise in the many different content areas of the visual thinking involved in having an expert of work, everyday life, and academic pursuits. understanding of the dynamics of a piston in an internal combustion engine. When experts look at a In the realm of work, classic examples include piston or a diagram of a piston or a graph represent- farmers learning to differentiate the sex of chickens, ing the dynamics of a piston, they ‘‘see’’ the higher restaurateurs learning to differentiate different di- order, relevant variables, for example, that more mensions of fine wine, airplane pilots misperceiving work is performed when the combustion explosion their position relative to the ground, and machinists moves the piston away from the cylinder’s base than and architects learning to ‘‘see’’ the three- when the piston returns toward the base. The ability dimensional shape of a solid object or house from to ‘‘see’’ such higher-order relations is not just a the top, side, and front views. question of good visual acuity, but it instead de- In the realm of everyday life, important exam- pends on content knowledge (about energy, pres- ples include learning to perceive emotional expres- sure, and work) and on an understanding of how

LEARNING: PERCEPTUAL PROCESSES 1439 energy acts in the context of an internal combustion ing, there is evidence that the timing of the engine. In a 2001 article, Daniel Schwartz and John experience can be critical to whether, and to what Bransford emphasized that experience with con- degree, it is learned effectively. trasting cases helps students differentiate the critical The ‘‘constancy’’ of perception is a remarkable features when they are working to understand statistics and other academic domains. In a 1993 article, feat of perceptual development. The issue is that the J. Littlefield and John Rieser demonstrated the skill energy that gives rise to the perception of a particu- of middle school students at differentiating relevant lar object or situation varies widely when the per- from irrelevant information when attempting to ceiver or object moves, the lighting changes, and so solve story problems in mathematics. forth. Given the flux in the sensory input, how is it that people manage to perceive that the objects and Classical Issues in Perceptual Learning and situations remain (more or less) the same? Research Perceptual Development about perceptual constancies has reemerged as an important topic as computer scientists work to de- Perceptual development involves normative age- sign artificial systems that can ‘‘learn to see.’’ related changes in basic sensory sensitivities and in perceptual learning. Some of these changes are con- Intersensory coordination is a major feature of strained by the biology of development in well- perception and perceptual development. How is it, defined ways. For example, the growth in auditory for example, that infants can imitate adult models frequency during the first year of life is mediated in who open their mouths wide or stick out their part by changes in the middle ear and inner ear. tongues? How is it that infants can identify objects Growth in visual acuity during the first two years is by looking at them or by touching them and can rec- mediated in several ways: by changes in the migra- ognize people by seeing them or listening to them? tion of retinal cells into a fovea, through increasing control of convergence eye movements so that the The increasing control of actions with age is a two eyes fixate the same object, and through increas- major result of perceptual learning, as infants being control of the accommodate state of the lens so come more skillful at perceiving steps and other fea- that fixated objects are in focus. The role of physical tures of the ground and learn to control their changes in the development of other perceptual balance when walking up and down slopes. skills, for example, perceiving different cues for In 1955 James Gibson and Eleanor Gibson depth, is less clear. wrote an important paper titled ‘‘Perceptual Learn- Nativism and empiricism are central to the ing: Differentiation or Enrichment?’’ By differentia- study of perception and perceptual development. tion they meant skill at distinguishing smaller and Stemming from philosophy’s interest in epistemolo- smaller differences among objects of a given kind. By gy, early nativists (such as seventeenth-century enrichment they meant knowledge of the ways that French mathematician and philosopher René Des- objects and events tend to be associated with other cartes and eighteenth-century German philosopher objects and events. Their paper was in part a reaction Immanuel Kant) argued that the basic capacities of to the predominant view of learning at the time: that the human mind were innate, whereas empiricists learning was the ‘‘enrichment’’ of responses through argued that they were learned, primarily through as- their association with largely arbitrary stimulus con- sociations. This issue has long been hotly debated in ditions. The authors provided a sharp counterpoint the field of perceptual learning and development. to this view. Instead of conceiving of the world as How is it that the mind and brain come to perceive constructed by add-on processes of association, they three-dimensional shapes from two-dimensional viewed perceivers as actively searching for the stimu- retinal projections; perceive distance; segment the speech stream; represent objects that become cov- li they needed to guide their actions and decisions, ered from view? The debate is very lively in the early and in this way coming to differentiate the relevant twenty-first century, with some arguing that percep- features situated in a given set of circumstances from tion of some basic properties of the world is innate, the irrelevant ones. and others arguing that it is learned, reflecting the statistical regularities in experience. Given that expe- See also: Attention; Learning Theory, subentry rience plays a role in some forms of perceptual learn- on Historical Overview.

1440 LEARNING: PERCEPTUAL PROCESSES

BIBLIOGRAPHY Gibson, Eleanor J. 1969. Principles of Perceptual Acredolo, Linda P.; Pick, Herb L.; and Olsen, M. Learning and Development. Englewood Cliffs, 1975. ‘‘Environmental Differentiation and Fa- NJ: Prentice-Hall. miliarity as Determinants of Children’s Memory Gibson, Eleanor J., and Pick, Anne D. 2000. An for Spatial Location.’’ Developmental Psychology Ecological Approach to Perceptual Learning and 11:495–501. Development. New York: Oxford University Adolph, Karen E. 1997. Learning in the Develop- Press. ment of Infant Locomotion. Chicago: University Gibson, Eleanor J., and Walk, Richard D. 1961. of Chicago Press. ‘‘The ‘Visual Cliff.’’’ Scientific American 202:64– Arnheim, Rudolph. 1974. Art and Visual Percep- 71. tion: A Psychology of the Creative Eye. Berkeley: Gibson, James J., and Gibson, Eleanor J. 1955. University of California Press. ‘‘Perceptual Learning: Differentiation or En- Aslin, Richard N. 1998. ‘‘Speech and Auditory richment?’’ Psychological Review 62:32–41. Processing during Infancy: Constraints on and Goldstone, Robert L. 1998. ‘‘Perceptual Learn- Precursors to Language.’’ In Handbook of Child ing.’’ Annual Review of Psychology 49:585–612. Psychology, 5th edition, ed. William Damon, Goodnow, Jacqueline J. 1978. ‘‘Visible Thinking: Vol. 2: Cognition, Perception, and Language, ed. Cognitive Aspects of Change in Drawings.’’ Deanna Kuhn and Robert S. Siegler. New York: Child Development 49:637–641. Wiley. Granrud, Carl E. 1993. Visual Perception and Cog- Bahrick, Lorraine E., and Lickliter, Robert. nition in Infancy. Hillsdale, NJ: Erlbaum. 2000. ‘‘Intersensory Redundancy Guides Atten- tional Selectivity and Perceptual Learning in In- Haber, Ralph N. 1987. ‘‘Why Low-Flying Fighter fancy.’’ Developmental Psychology 36:190–201. Planes Crash: Perceptual and Attentional Fac- tors in Collisions with the Ground.’’ Human Baillargeon, Renee. 1994. ‘‘How Do Infants Learn Factors 29:519–532. about the Physical World?’’ Current Directions in Psychological Science 3:133–140. Johnson, Jacqueline S., and Newport, Elissa L. 1989. ‘‘Critical Period Effects in Second Lan- Barsalou, Lawrence W. 1999. ‘‘Perceptual Symbol guage Learning: The Influence of Maturational Systems.’’ Behavior and Brain Sciences 22:577– State on the Acquisition of English as a Second 660. Language.’’ Cognitive Psychology 21:60–99. Bransford, John D., and Schwartz, Daniel L. 2000. ‘‘Rethinking Transfer: A Simple Proposal Johnson, Mark. 1998. ‘‘The Neural Basis of Cogni- tive Development.’’ In with Multiple Implications.’’ Review of Research Handbook of Child Psy- 5th edition, ed. William Damon, Vol. 2: in Education 24:61–100. chology, Cognition, Perception, and Language, ed. Deanna Bryant, Peter, and Somerville, S. 1986. ‘‘The Kuhn and Robert S. Siegler. New York: Wiley. Spatial Demands of Graphs.’’ British Journal of Psychology 77:187–197. Jusczyk, Peter W. 2002. ‘‘How Infants Adapt Speech-Processing Capacities to Native Lan- Dodwell, Peter C., ed. 1970. Perceptual Learning guage Structure.’’ Current Directions in Psycho- and Adaptation: Selected Readings. Harmonds- logical Science 11:15–18. worth, Eng.: Penguin. Kellman, Philip, and Banks, Martin S. 1998. ‘‘In- Dowling, W. Jay., and Harwood, Dane L. 1986. fant Visual Perception.’’ In Handbook of Child Music Cognition. New York: Academic Press. Psychology, 5th edition, ed. William Damon, Epstein, William. 1967. Varieties of Perceptual Vol. 2: Cognition, Perception, and Language, ed. Learning. New York: McGraw-Hill. Deanna Kuhn and Robert S. Siegler. New York: Fahle, Manfred, and Poggio, Tomaso, eds. 2000. Wiley. Perceptual Learning. Cambridge, MA: MIT Littlefield, J., and Rieser, John J. 1993. ‘‘Seman- Press. tic Features of Similarity and Children’s Strate- Garling, Tommy, and Evans, Gary W. 1991. Envi- gies for Identifying Relevant Information in ronment, Cognition, and Action: An Integrated Mathematical Story Problems.’’ Cognition and Approach. New York: Oxford University Press. Instruction 11:133–188.

LEARNING: PROBLEM SOLVING 1441

McLeod, Peter; Reed, Nick; and Diences, Zol- Walk, Richard D. 1966. ‘‘Perceptual Learning and tan. 2001. ‘‘Toward a Unified Fielder Theory: the Discrimination of Wines.’’ Psychonomic Sci- What We Do Not Yet Know about How People ence 5:57–58. Run to Catch a Ball.’’ Journal of Experimental Walker-Andrews, Arlene, and Bahrick, Lor- Psychology: Human Perception and Performance raine E. 2001. ‘‘Perceiving the Real World: In- 27:1347–1355. fants’ Detection of and Memory for Social Postman, Leo. 1955. ‘‘Association Theory and Per- Information.’’ Infancy 2:469–481. ceptual Learning.’’ Psychological Review 62:438– Welch, Robert B. 1978. Perceptual Modification: 446. Adapting to Altered Sensory Environments. New Quinn, Paul C.; Palmer, Vanessa; and Slater, York: Academic Press. Alan M. 1999. ‘‘Identification of Gender in Do- mestic Cat Faces with and without Training: John J. Rieser Perceptual Learning of a Natural Categorization Task.’’ Perception 28:749–763. PROBLEM SOLVING Rieser, John J.; Pick, Herb L.; Ashmead, Daniel H.; and Garing, A. E. 1995. ‘‘Calibration of Cognitive processing aimed at figuring out how to Human Locomotion and Models of Perceptual- achieve a goal is called problem solving. In problem Motor Organization.’’ Journal of Experimental solving, the problem solver seeks to devise a method Psychology: Human Perception and Performance for transforming a problem from its current state 21:480–497. into a desired state when a solution is not immedi- Saarni, Carolyn. 1998. ‘‘Emotional Development: ately obvious to the problem solver. Thus, the hall- Action, Communication, and Understanding.’’ mark of problem solving is the invention of a new In Handbook of Child Psychology, 5th edition, method for addressing a problem. This definition ed. William Damon, Vol. 3: Social, Emotional, has three parts: (1) problem solving is cognitive— and Personality Development, ed. Nancy Eisen- that is, it occurs internally in the mind (or cognitive berg. New York: Wiley. system) and must be inferred indirectly from behavior; (2) problem solving is a process—it involves the Saffran, Jenny R.; Aslin, R. N.; and Newport, E. manipulation of knowledge representations (or car- L. 1996. ‘‘Statistical Learning by Eight-Month- rying out mental computations); and (3) problem Old Infants.’’ Science 274:1926–1928. solving is directed—it is guided by the goals of the Saffran, Jenny R., and Griepentrog, G. J. 2001. problem solver. ‘‘Absolute Pitch in Infant Auditory Learning: The definition of problem solving covers a Evidence for Developmental Reorganization.’’ broad range of human cognitive activities, including Developmental Psychology 37:74–85. educationally relevant cognition—figuring out how Schwartz, Daniel L., and Bransford, John D. to manage one’s time, writing an essay on a selected 2001. ‘‘A Time for Telling.’’ Cognition and In- topic, summarizing the main point of a textbook struction 16:475–522. section, solving an arithmetic word problem, or de- termining whether a scientific theory is valid by con- 2001. ‘‘Observations on the Sci- Simon, Herbert A. ducting experiments. ences of Science Learning.’’ Journal of Applied Developmental Psychology 21:115–121. A problem occurs when a problem solver has a goal but initially does not know how to achieve the Tighe, L. S., and Tighe, T. J. 1966. ‘‘Discrimination goal. This definition has three parts: (1) the current Learning: Two Views in Historical Perspective.’’ state—the problem begins in a given state; (2) the Psychological Bulletin 66:353–370. goal state—the problem solver wants the problem to von Hofsten, Claes. 1994. ‘‘Planning and Perceiv- be in a different state, and problem solving is re- ing What Is Going to Happen Next.’’ In The De- quired to transform the problem from the current velopment of Future-Oriented Processes, ed. (or given) state into the goal state, and (3) obsta- Marshall M. Haith, Janette B. Benson, and cles—the problem solver does not know the correct Ralph J. Roberts. Chicago: University of Chica- solution and an effective solution method is not ob- go Press. vious to the problem solver.

1442 LEARNING: PROBLEM SOLVING

According to this definition a problem is per- jars of size 21, 127, and 3 units and an unlimited sonal, so that a situation that is a problem for one supply of water, how can you obtain exactly 100 person might not be a problem for another person. units of water?’’ This is a well-defined problem be- For example, ‘‘3 + 5 = ___’’ might be a problem for cause the given state is clearly specified (you have a six-year-old child who reasons, ‘‘Let’s see. I can empty jars of size 21, 127, and 3), the goal state is take one from the 5 and give it to the 3. That makes clearly specified (you want to get 100 units of water 4 plus 4, and I know that 4 plus 4 is 8.’’ However, in one of the jars), and the allowable operators are this equation is not a problem for an adult who clearly specified (you can fill and pour according to knows the correct answer. specific procedures). Well-defined problems may be either routine or nonroutine; if you do not have pre- Types of Problems vious experience with water jar problems, then finding the solution (i.e., fill the 127, pour out 21 once, Routine and nonroutine problems. It is customary and pour out 3 twice) is a nonroutine problem. to distinguish between routine and nonroutine problems. In a routine problem, the problem solver In an ill-defined problem, the given state, goal knows a solution method and only needs to carry it state, and/or operations are not clearly specified. For out. For example, for most adults the problem ‘‘589 example, in the problem, ‘‘Write a persuasive essay x 45 = ___’’ is a routine problem if they know the in favor of year-round schools,’’ the goal state is not procedure for multicolumn multiplication. Routine clear because the criteria for what constitutes a ‘‘per- problems are sometimes called exercises, and techni- suasive essay’’ are vague and the allowable operators, cally do not fit the definition of problem stated such as how to access sources of information, are not above. When the goal of an educational activity is to clear. Only the given state is clear—a blank piece of promote all the aspects of problem solving (includ- paper. Ill-defined problems can be routine or non- ing devising a solution plan), then nonroutine prob- routine; if one has extensive experience in writing lems (or exercises) are appropriate. then writing a short essay like this one is a routine problem. In a nonroutine problem, the problem solver does not initially know a method for solving the problem. For example, the following problem (re- Processes in Problem Solving ported by Robert Sternberg and Janet Davidson) is The process of problem solving can be broken down nonroutine for most people: ‘‘Water lilies double in into two major phases: problem representation, in area every twenty-four hours. At the beginning of which the problem solver builds a coherent mental the summer, there is one water lily on the lake. It representation of the problem, and problem solution, takes sixty days for the lake to be completely covered in which the problem solver devises and carries out with water lilies. On what day is the lake half cov- a solution plan. Problem representation can be bro- ered?’’ In this problem, the problem solver must in- ken down further into problem translation, in which vent a solution method based on working backwards the problem solver translates each sentence (or pic- from the last day. Based on this method, the prob- ture) into an internal mental representation, and lem solver can ask what the lake would look like on problem integration, in which the problem solver in- the day before the last day, and conclude that the tegrates the information into a coherent mental rep- lake is half covered on the fifty-ninth day. resentation of the problem (i.e., a mental model of Well-defined and ill-defined problems. It is also the situation described in the problem). Problem so- customary to distinguish between well-defined and lution can be broken down further into solution ill-defined problems. In a well-defined problem, the planning, in which the problem solver devises a plan given state of the problem, the goal state of the prob- for how to solve the problem, and solution execution, lem, and the allowable operators (or moves) are each in which the problem solver carries out the plan by clearly specified. For example, the following water- engaging in solution behaviors. Although the four jar problem (adapted from Abrahama Luchins) is an processes of problem solving are listed sequentially, example of a well defined problem: ‘‘I will give you they may occur in many different orderings and with three empty water jars; you can fill any jar with water many iterations in the course of solving a problem. and pour water from one jar into another (until the For example, consider the butter problem de- second jar is full or the first one is empty); you can scribed by Mary Hegarty, Richard Mayer, and Chris- fill and pour as many times as you like. Given water topher Monk: ‘‘At Lucky, butter costs 65 cents per

LEARNING: PROBLEM SOLVING 1443 stick. This is two cents less per stick than butter at a cardboard parallelogram and attaching it to the Vons. If you need to buy 4 sticks of butter, how other end to form a rectangle. Once students have much will you pay at Vons?’’ In the problem transla- the insight that a parallelogram is just a rectangle in tion phase, the problem solver may mentally repre- disguise, they can compute the area because they al- sent the first sentence as ‘‘Lucky = 0.65,’’ the second ready know the procedure for finding the area of a sentence as ‘‘Lucky = Vons − 0.02,’’ and the third rectangle. Students taught by the insight method sentence as ‘‘4 x Vons = ___.’’ In problem integra- perform well on both retention and transfer prob- tion, the problem solver may construct a mental lems. Wertheimer used the term productive thinking number line with Lucky at 0.65 and Vons to the right to refer to problem solving in which one invents a of Lucky (at 0.67); or the problem solver may men- new approach to solving a novel problem. tally integrate the equations as ‘‘4 x (Lucky + 0.02) = ____.’’ A key insight in problem integration is to Educationally Relevant Advances in Problem recognize the proper relation between the cost of Solving butter at Lucky and the cost of butter at Vons, name- ly that butter costs more at Vons (even though the Recent advances in educational psychology point to keyword in the problem is ‘‘less’’). In solution plan- the role of domain-specific knowledge in problem ning, the problem solver may break the problem solving—such as knowledge of specific strategies or into parts, such as: ‘‘First add 0.02 to 0.65, then mul- problem types that apply to a particular field. Three tiply the result by 4.’’ In solution executing, the important advances have been: (1) the teaching of problem solver carries out the plan: 0.02 + 0.65 = problem-solving processes, (2) the nature of expert 0.67, 0.67 x 4 = 2.68. In addition, the problem solver problem solving, and (3) new conceptions of indi- must monitor the problem-solving process and vidual differences in problem-solving ability. make adjustments as needed. Teaching of problem-solving processes. An important advance in educational psychology is cognitive Teaching for Problem Solving strategy instruction, which includes the teaching of problem-solving processes. For example, in Project A challenge for educators is to teach in ways that fos- Intelligence, elementary school children successfully ter meaningful learning rather than rote learning. learned the cognitive processes needed for solving Rote instructional methods promote retention (the problems similar to those found on intelligence tests. ability to solve problems that are identical or highly In Instrumental Enrichment, students who had been similar to those presented in instruction), but not classified as mentally retarded learned cognitive pro- problem solving transfer (the ability to apply what cesses that allowed them to show substantial im- was learned to novel problems). For example, in provements on intelligence tests. 1929, Alfred Whitehead used the term inert knowledge to refer to learning that cannot be used to solve Expert problem solving. Another important ad- novel problems. In contrast, meaningful instructional vance in educational psychology concerns differ- methods promote both retention and transfer. ences between what experts and novices know in given fields, such as medicine, physics, and comput- In a classic example of the distinction between er programming. For example, expert physicists tend rote and meaningful learning, the psychologist Max to store their knowledge in large integrated chunks, Wertheimer (1959) described two ways of teaching whereas novices tend to store their knowledge as iso- students to compute the area of a parallelogram. In lated fragments; expert physicists tend to focus on the rote method, students learn to measure the base, the underlying structural characteristics of physics measure the height, and then multiply base times word problems, whereas novices focus on the sur- height. Students taught by the A = b x h method are face features; and expert physicists tend to work for- able to find the area of parallelograms shaped like ward from the givens to the goal, whereas novices the ones given in instruction (a retention problem) work backwards from the goal to the givens. Re- but not unusual parallelograms or other shapes (a search on expertise has implications for professional transfer problem). Wertheimer used the term repro- education because it pinpoints the kinds of domain- ductive thinking to refer to problem solving in which specific knowledge that experts need to learn. one blindly carries out a previously learned procedure. In contrast, in the meaningful method, stu- Individual differences in problem-solving ability. dents learn by cutting the triangle from one end of This third advance concerns new conceptions of in-

1444 LEARNING: REASONING tellectual ability based on differences in the way peo- Pressley, Michael J., and Woloshyn, Vera. 1995. ple process information. For example, people may Cognitive Strategy Instruction that Really Im- differ in cognitive style—such as their preferences proves Children’s Academic Performance. Cam- for visual versus verbal representations, or for im- bridge, MA: Brookline Books. pulsive versus reflective approaches to problem solv- Sternberg, Robert J., and Davidson, Janet E. ing. Alternatively, people may differ in the speed and 1982. ‘‘The Mind of the Puzzler.’’ Psychology efficiency with which they carry out specific cogni- Today 16:37–44. tive processes, such as making a mental comparison Sternberg, Robert J., and Zhang, Li-Fang, eds. or retrieving a piece of information from memory. 2001. Perspectives on Thinking, Learning, and Instead of characterizing intellectual ability as a sin- Cognitive Styles. Mahwah, NJ: Erlbaum. gle, monolithic ability, recent conceptions of intellectual ability focus on the role of multiple Wertheimer, Max. 1959. Productive Thinking. New differences in information processing. York: Harper and Row. Whitehead, Alfred North. 1929. The Aims of Ed- See also: Creativity; Learning, subentry on Ana- ucation. New York: Macmillan. logical Reasoning; Mathematics Learning, subentry on Complex Problem Solving. Richard E. Mayer

BIBLIOGRAPHY REASONING Chi, Michelene T. H.; Glaser, Robert; and Farr, Marshall J., eds. 1988. The Nature of Expertise. Reasoning is the generation or evaluation of claims Hillsdale, NJ: Erlbaum. in relation to their supporting arguments and evidence. The ability to reason has a fundamental im- Dunker, Karl. 1945. On Problem Solving. Washing- pact on one’s ability to learn from new information ton, DC: American Psychological Association. and experiences because reasoning skills determine Feuerstein, Reuven. 1980. Instrumental Enrich- how people comprehend, evaluate, and accept ment. Baltimore: University Park Press. claims and arguments. Reasoning skills are also cru- Hegarty, Mary; Mayer, Richard E.; and Monk, cial for being able to generate and maintain view- Christopher A. 1995. ‘‘Comprehension of points or beliefs that are coherent with, and justified Arithmetic Word Problems: Evidence from Stu- by, relevant knowledge. There are two general kinds dents’ Eye Fixations.’’ Journal of Educational of reasoning that involve claims and evidence: for- Psychology 84:76–84. mal and informal. Hunt, Earl; Lunneborg, Cliff; and Lewis, J. 1975. ‘‘What Does It Mean to Be High Verbal?’’ Formal Reasoning Cognitive Psychology 7:194–227. Formal reasoning is used to evaluate the form of an Larkin, Jill H.; McDermott, John; Simon, Doro- argument, and to examine the logical relationships thea P.; and Simon, Herbert A. 1980. ‘‘Expert between conclusions and their supporting asser- and Novice Performance in Solving Physics tions. Arguments are determined to be either valid Problems.’’ Science 208:1335–1342. or invalid based solely on whether their conclusions Luchins, Abrahama S. 1942. Mechanization in necessarily follow from their explicitly stated prem- Problem Solving: The Effect of Einstellung. Evans- ises or assertions. That is, if the supporting assertions ton, IL: American Psychological Association. are true, must the conclusion also be true? If so, then the argument is considered valid and the truth of the Mayer, Richard E. 1992. Thinking, Problem Solv- conclusion can be directly determined by establishing, Cognition, 2nd edition. New York: Freeman. ing the truth of the supporting assertions. If not, Mayer, Richard E. 1999. The Promise of Education- then the argument is considered invalid, and the al Psychology. Upper Saddle River, NJ: Prentice- truth of the assertions is insufficient (or even irrele- Hall. vant) for establishing the truth of the conclusion. Nickerson, Raymond S. 1995. ‘‘Project Intelli- Formal reasoning is often studied in the context of gence.’’ In Encyclopedia of Human Intelligence, categorical syllogisms or ‘‘if-then’’ conditional proofs. ed. Robert J. Sternberg. New York: Macmillan. Syllogisms contain two assertions and a conclusion.

LEARNING: REASONING 1445

An example of a logically valid syllogism is: All dogs generally poor, but can be better or worse depending are animals; all poodles are dogs; therefore poodles are upon the particular aspects of the task. People per- animals. A slight change to one of the premises will form worse on problems that require more cognitive create the invalid syllogism: All dogs are animals; work, due to excessive demands placed on their lim- some dogs are poodles; therefore all poodles are ani- ited processing capacity or working memory. The re- mals. This argument form is invalid because it can- quired cognitive work can be increased simply by not be determined with certainty that the conclusion having more information, or by the linguistic form is true, even if the premises are true. The second of the argument. Some linguistic forms can affect premise does not require that all poodles are dogs. performance because they violate conventional dis- Thus, there may be some poodles who are not dogs and, by extension, some poodles who are not ani- course or must be mentally rephrased in order to be mals. This argument is invalid despite the fact that integrated with other information. an accurate knowledge of dogs, poodles, and animals In addition, people’s existing knowledge about confirms that both the premises and the conclusion the concepts contained in the problem can affect are true statements. This validity-truth incongru- performance. People have great difficulty evaluating ence highlights the important point that the concep- the logical validity of an argument independent of tual content of an argument or the real-world truth their real-world knowledge. They insert their knowl- of the premises and conclusion are irrelevant to the edge as additional premises, which leads them to logic of the argument form. make more inferences than is warranted. Prior Discussions of formal reasoning may sometimes knowledge can also lead people to misinterpret the refer to the rules of logic. It is common for formal meaning of premises. Another common source of reasoning to be described as a set of abstract and pre- error is belief bias, where people judge an argument’s scriptive rules that people must learn and apply in validity based on whether the conclusion is consis- order to determine the validity of an argument. This is the oldest perspective on formal reasoning. Some tent with their beliefs rather than its logical relation- claim that the term formal reasoning refers directly ship to the given premises. to the application of these formal rules. The systematic errors that have been observed However, many theorists consider this perspec- provide some insights about what skills a person tive misguided. Describing formal reasoning as the might develop to improve performance. Making stu- evaluation of argument forms conveys a more inclu- dents explicitly aware of the likely intrusion of their sive and accurate account of the various perspectives prior knowledge could facilitate their ability to con- in this field. There are at least four competing theo- trol or correct such intrusions. Students may also ries about how people determine whether a conclu- benefit from a detailed and explicit discussion of sion necessarily follows from the premises. These what logical validity refers to, how it differs from theories are commonly referred to as rule-based per- real-world truth or personal agreement, and how spectives, mental models, heuristics, and domain- easy it is to confuse the two. Regardless of whether sensitive theories. People outside the rule-based per- or not people commonly employ formal rules of spective view the rules of logic as descriptive rules logic, an understanding and explicit knowledge of that simply give labels to common argument forms and to common errors or fallacies in logical reason- these rules should facilitate efforts to search for vio- ing. These theories are too complex to be detailed lations of logical validity. Theorists of informal rea- here, and there is currently no consensus as to which soning such as James Voss and Mary Means have theory best accounts for how people actually reason. made a similar argument for the importance of ex- A number of books and review articles provide com- plicit knowledge about the rules of good reasoning. prehensive discussions of these theories and their Errors attributed to limited cognitive resources can relative merits; one example is Human Reasoning: be addressed by increasing reasoning skill, and prac- The Psychology of Deduction by Jonathan Evans, Ste- tice on formal reasoning tasks should increase profi- phen Newstead, and Ruth Byrne. ciency and reduce the amount of cognitive effort There is a consensus that human reasoning per- required. Also, working memory load should be re- formance is poor and prone to several systematic er- duced by external representation techniques, such as rors. Performance on formal reasoning tasks is Venn diagrams.

1446 LEARNING: REASONING

Informal Reasoning Successful reasoning requires the understanding Informal reasoning refers to attempts to determine that evidence must provide information that is inde- what information is relevant to a question, what pendent of the claim or theory, and that evidence conclusions are plausible, and what degree of sup- must do more than simply rephrase and highlight the assumptions of the theory. For example, the as- port the relevant information provides for these var- sertion ‘‘Some people have extrasensory perception’’ ious conclusions. In most circumstances, people does not provide any evidence about the claim ‘‘ESP must evaluate the justification for a claim in a con- is real.’’ These are simply ways of restating the same text where the information is ambiguous and in- information. Evidence must be an assertion that is complete and the criteria for evaluation are complex independent of the claim, but that still provides in- and poorly specified. Most of what is commonly re- formation about the probable truth of the claim. An ferred to as ‘‘thinking’’ involves informal reasoning, example of potential evidence for the claim that including making predictions of future events or try- ‘‘ESP is real’’ would be ‘‘Some people know informa- ing to explain past events. These cognitive processes tion that they could not have known through any of are involved in answering questions as mundane as the normal senses.’’ In other words, evidence consti- ‘‘How much food should I prepare for this party?’’ tutes assertions whose truth has implications for, but and as profound as ‘‘Did human beings evolve from is not synonymous with, the truth of the claim being simple one-celled organisms?’’ Informal reasoning supported. has a pervasive influence on both the everyday and the monumental decisions that people make, and on Without an understanding of evidence and counterevidence and how they relate to theories, the ideas that people come to accept or reject. people would be ineffective at identifying informa- Informal and formal reasoning both involve at- tion that could be used to determine whether a claim tempts to determine whether a claim has been suffi- is justified. Also, lack of a clear distinction between ciently justified by the supporting assertions, but evidence and theory will lead to the assimilation of these types of reasoning differ in many respects. The evidence and the distortion of its meaning and logi- vast majority of arguments are invalid according to cal implications. This eliminates the potential to formal logic, but informal reasoning must be em- consider alternative claims that could better account ployed to determine what degree of justification the for the evidence. People will also fail to use coun- supporting assertions provide. Also, the supporting terevidence to make appropriate decreases in the de- assertions themselves must be evaluated as to their gree of justification for a claim. validity and accuracy. Formal reasoning involves Discussions of informal reasoning, argumenta- making a binary decision based only on the given in- tion, and critical thinking commonly acknowledge formation. Informal reasoning involves making an that a prerequisite for effective reasoning is a belief uncertain judgment about the degree of justification in the utility of reasoning. The cognitive skills de- for a claim relative to competing claims—and basing scribed above are necessary, but not sufficient, to this evaluation on an ill-defined set of assertions produce quality reasoning. The use of these skills is whose truth values are uncertain. clearly effortful; thus, people must believe in the Based on the above characterization of informal importance and utility of reasoning in order to con- reasoning, a number of cognitive skills would be ex- sistently put forth the required effort. The episte- pected to affect the quality of such reasoning. The mology that promotes the use of reasoning skills is first is the ability to fully comprehend the meaning the view that knowledge can never be absolutely cer- of the claim being made. Understanding the concep- tain and that valid and useful claims are the product tual content is crucial to being able to consider what of contemplating possible alternative claims and other information might bear on the truth or false- weighing the evidence and counterevidence. Put hood of a claim. Other cognitive processes involved simply, people use their reasoning skills consistently in reasoning include the retrieval of relevant knowl- when they acknowledge the possibility that a claim edge from long-term memory, seeking out new rele- may be incorrect and also believe that standards of vant information, evaluating the validity and utility good reasoning produce more accurate ideas about of that information, generating alternatives to the the world. claim in question, and evaluating the competing Inconsistent, selective, and biased application of claims in light of the relevant information. reasoning skills provides little or no benefits for

LEARNING: REASONING 1447 learning. Greater reasoning skills are assumed to aid tion of reasoning skills is not random, but is selective in the ability to acquire new knowledge and revise and biased such that prior beliefs are protected from one’s existing ideas accordingly. However, if one scrutiny. This systematic inconsistency cannot be ac- contemplates evidence and theory only when it can counted for by underdeveloped skills, but can be ac- be used to justify one’s prior commitments, then counted for by assuming a biased motivation to use only supportive information will be learned and ex- these skills selectively. Regardless of whether or not isting ideas will remain entrenched and unaffected. people have the capacity for sound reasoning, they The development of reasoning skills will confer very have no philosophical basis that could provide the little intellectual benefit in the absence of an episte- motivation to override the selective and biased use mological commitment to employ those skills con- of these skills. sistently. Development of Reasoning Skills General Reasoning Performance There is only preliminary data about how and when Reports from the National Assessment of Education- informal reasoning skills develop. There is prelimi- al Progress and the National Academy of Sciences nary support that the development of reasoning consistently show poor performance on a wide array takes a leap forward during the preadolescent years. of tasks that require informal reasoning. These tasks These findings are consistent with Piagetian assump- span all of the core curriculum areas of reading, tions about the development of concrete operational writing, mathematics, science, and history. thinking, in other words, thinking that involves the mental manipulation (e.g., combination, transfor- Some smaller-scale studies have attempted to mation) of objects represented in memory. Howev- paint a more detailed picture of what people are er, younger children are capable of some key aspects doing, or failing to do, when asked to reason. People of reasoning. Thus, the improvement during early demonstrate some use of informal reasoning skills, adolescence could result from improvements in but these skills are underdeveloped and applied in- other subsidiary skills of information processing, consistently. Children and adults have a poor under- from meta-cognitive awareness, or from an increase standing of evidence and its relationship to theories in relevant knowledge. or claims. Only a small minority of people attempt A somewhat striking finding is the lack of devel- to justify their claims by providing supporting evi- opment in informal reasoning that occurs from early dence. When explicitly asked for supporting evi- adolescence through adulthood. Some evidence sug- dence, most people simply restate the claim itself or gests that college can improve reasoning, but the describe in more detail what the claim means. It is overall relationship between the amount of postse- especially rare for people to generate possible count- condary education and reasoning skill is weak at er-evidence or to even consider possible alternative best. The weak and inconsistent relationship that claims. does exist between level of education and reasoning The inconsistent application of informal rea- is likely due to indirect effects. Students are rarely re- soning skills could have multiple causes. Some theo- quired to engage in complex reasoning tasks. How- rists suggest that reasoning skills are domain specific ever, the spontaneous disagreements that arise in the and depend heavily on the amount of domain classroom could expose them to the practice of justi- knowledge a person possesses. Alternatively, under- fying one’s claim. Also, engagement in inquiry activ- developed or unpracticed skills could lead to their ities, such as classroom experiments, could provide haphazard use. A third possibility is that people’s implicit exposure to the principles of scientific rea- lack of explicit knowledge about what good reason- soning. ing entails prevents them from exercising conscious There are relatively few programs aimed at de- control over their implicit skills. veloping informal reasoning skills; hence, there is Inconsistent use of informal reasoning skills little information about effective pedagogical strate- may also arise because people lack a principled belief gies. Where they do exist, curricula are often aimed in the utility of reasoning that would foster a consis- at developing general reasoning skills. Yet, many be- tent application of sound reasoning. People have ex- lieve that effective reasoning skills are domain- or treme levels of certainty in their ideas, and they take discipline-specific. Nevertheless, given the pervasive this certainty for granted. In addition, the applica- impact of reasoning skills on learning in general, it

1448 LEARNING: REASONING is clear that more systematic efforts are needed to Baron, Jonathan. 1988. Thinking and Deciding. foster reasoning skills at even the earliest grade le- Cambridge, Eng.: Cambridge University Press. vels. Of the approaches that have been attempted, Boyer, Ernest L. 1983. High School: A Report on there is some evidence for the success of scaffolding, Secondary Education in America. New York: which involves a teacher interacting with a student Harper and Row. who is attempting to reason, and prompting the student to develop more adequate arguments. Another Cary, Susan. 1985. ‘‘Are Children Fundamentally approach is to explicitly teach what good reasoning Different Thinkers and Learners Than Adults?’’ means, what evidence is, and how evidence relates to In Thinking and Learning Skills: Current Re- theories. This approach could be especially effective search and Open Questions, Vol. 2, ed. Susan if classroom experiments are conducted within the Chipman, Judith Segal, and Robert Glaser. Hil- context of explicit discussions about the principles lsdale, NJ: Erlbaum. of scientific reasoning. Also, if reasoning skills are Evans, Jonathan St. B. T.; Newstead, Stephen discussed in conjunction with the content of the core E.; and Byrne, Ruth M. J. 1993. Human Rea- subject areas, then students may develop an appreci- soning: The Psychology of Deduction. Hillsdale, ation for the pervasive utility and importance of rea- NJ: Erlbaum. soning for the progress of ideas. Johnson-Laird, Philip N., and Byrne, Ruth M. J. A number of theorists have suggested that de- 1991. Deduction. Hillsdale, NJ: Erlbaum. bate between students with opposing views could foster the basic skills needed for informal reasoning. Kuhn, Deanna. 1991. The Skills of Argument. Cam- Debates could give students practice in having to bridge, Eng.: Cambridge University Press. consider opposing viewpoints and having to coordi- Means, Mary L., and Voss, James F. 1996. ‘‘Who nate evidence and counterevidence in support of a Reasons Well? Two Studies of Informal Reason- claim. Also, providing justification for one’s posi- ing Among Children of Different Grade, Ability, tions requires some cognitive effort, and the norms and Knowledge Levels.’’ Cognition and Instruc- of social dialogue could provide the needed motivation 14:139–178. tion. However, interpersonal debates are most commonly construed as situations in which individuals Nickerson, Raymond S. 1991. ‘‘Modes and Models are committed to a position ahead of time, and in of Informal Reasoning: A Commentary.’’ In In- which their goal is to frame the issue and any evi- formal Reasoning and Education, ed. James F. dence in a manner that will persuade their opponent Voss, David N. Perkins, and Judith W. Segal. or the audience that their own position is correct. Hillsdale, NJ: Erlbaum. Students’ reasoning is already greatly impaired by Perloms, David N. 1985. ‘‘Postprimary Education their tendency to adopt a biased, defensive, or non- Has Little Impact on Informal Reasoning.’’ contemplative stance. Debate activities that reinforce Journal of Educational Psychology 77:562–571. this stance and blur the difference between defend- Stein, Nancy L., and Miller, Christopher A. ing a claim and contemplating a claim’s justification 1991. ‘‘I Win–You Lose: The Development of may do more harm than good. To date, there is no Argumentative Thinking.’’ In Informal Reason- empirical data that compare the relative costs and ing and Education, ed. James F. Voss, David N. benefits of using interpersonal debate exercises to Perkins, and Judith W. Segal. Hillsdale, NJ: Erl- foster critical reasoning skills. baum.

See also: Learning, subentry on Causal Reason- Voss, James F., and Means, Mary L. 1991. ‘‘Learn- ing; Learning Theory, subentry on Historical ing to Reason via Instruction and Argumenta- Overview. tion.’’ Learning and Instruction 1:337–350. Vygotsky, Lev S. 1978. Mind in Society: The Devel- opment of Higher Psychological Processes, ed. Mi- BIBLIOGRAPHY chael Cole. Cambridge, MA: Harvard University Baron, Jonathan. 1985. Rationality and Intelli- Press. gence. Cambridge, Eng.: Cambridge University Press. Thomas D. Griffin

LEARNING: TRANSFER OF LEARNING 1449

TRANSFER OF LEARNING there are a number of contextual features she might also learn. There are incidental features—it is Imagine that every time that people entered a new Christmas; there are surface features—the candy is environment they had to learn how to behave with- small and striped; and there are deep features—the out the guidance of prior experiences. Slightly novel candy cane is rigid and hooked. Instruction for tasks, like shopping online, would be disorienting transfer must help the child discern the deep fea- and dependant on trial-and-error tactics. Fortunate- tures. This way the child might subsequently use an ly, people use aspects of their prior experiences, such umbrella handle to gather a stuffed animal instead as the selection of goods and subsequent payment, of trying a candy-striped rope. to guide their behavior in new settings. The ability to use learning gained in one situation to help with When people learn, they not only encode the another is called transfer. target idea, they also encode the context in which it Transfer has a direct bearing on education. Edu- occurs, even if that context is incidental. For a study cators hope that students transfer what they learn published in 1975, Gooden and Baddeley asked from one class to another—and to the outside adults to learn a list of words on land or underwater world. Educators also hope students transfer experi- (while scuba diving). Afterwards, the adults were ences from home to help make sense of lessons at subdivided; half tried to remember the words under- school. There are two major approaches to the study water and half on land. Those people who learned of transfer. One approach characterizes the knowl- the words underwater remembered them better un- edge and conditions of acquisition that optimize the derwater than on land, and those people who chances of transfer. The other approach inquires learned the words on land remembered them better into the nature of individuals and the cultural con- on land than underwater. This result reveals the contexts that transform them into more adaptive partic- text dependency of memory. Context dependency is ipants. useful because it constrains ideas to appear in appropriate contexts, rather than cluttering people’s Knowledge-Based Approaches to Transfer thoughts at odd times. But context dependency can be a problem for transfer, because transfer, by defi- There are several knowledge-based approaches to nition, has to occur when the original context of transfer. learning is not reinstated—when one is no longer in Transferring out from instruction. Ideally, the school, for example. knowledge students learn in school will be applied outside of school. For some topics, it is possible to Surface features, which are readily apparent to train students for the specific situations they will the learner, differ from incidental features, because subsequently encounter, such as typing at a key- surface features are attached to the idea rather than board. For other topics, educators cannot anticipate the context in which the idea occurs. Surface features all the out-of-school applications. When school- can be useful. A child might learn that fish have fins based lessons do not have a direct mapping to and lay eggs. When he sees a new creature with fins, out-of-school contexts, memorization without un- he may decide it is a fish and infer that it too lays derstanding can lead to inert knowledge. Inert eggs. Surface features, however, can be imperfect knowledge occurs when people acquire an idea with- cues. People may overgeneralize and exhibit negative out also learning the conditions of its subsequent ap- transfer. For example, the child may have seen a dol- plication, and thus they fail to apply that idea phin instead of a fish. People may also undergeneral- appropriately. Memorizing the Pythagorean formu- ize and fail to transfer. A child might see an eel and la, for example, does not guarantee students know assume it does not lay eggs. Good instruction helps to use the formula to find the distance of a shortcut. students see beneath the surface to find the deep features of an idea. Knowing when to use an idea depends on knowing the contexts in which the idea is useful. The ideas Deep features are based on structures integral to that people learn are always parts of a larger context, an idea, which may not be readily apparent. To a and people must determine which aspects of that physicist, an inclined plane and scissors share the context are relevant. Imagine, for example, a young same deep structure of leverage, but novices cannot child who is learning to use the hook of a candy cane see this similarity and they fail to use a formula to pull a toy closer. As the child learns the action, learned for inclined planes to reason about scissors.

1450 LEARNING: TRANSFER OF LEARNING

Analogies are built on deep features. For exam- Otherwise, the lesson simply involves pushing alge- ple, color is to picture as sound is to song. On the braic symbols. surface, color and sound differ, as do pictures and Unlike transfer to out-of-school settings, which song. Nonetheless, the relation of used to create depends on the spontaneous retrieval of relevant makes it possible to compare the common structure prior knowledge, transfer to in-school settings can between the two. Analogy is an important way peo- be directly supported by teachers. A common ap- ple discover deep features. In the 1990s, Kevin Dun- proach to help students recruit prior knowledge uses bar studied the laboratory meetings of cell biologists. cover stories that help students see the relevance of He found that the scientists often used analogies to what they are about to learn. A teacher might discuss understand a new discovery. They typically made the challenge of finding the distance of the moon transfers of near analogies rather than far ones. A far from the earth to motivate a lesson on trigonometry. analogy transfers an idea from a remote body of This example includes two ways that transferring in knowledge that shares few surface features, as might prior knowledge can support learning. Prior knowl- be the case when using the structure of the solar sys- edge helps students understand the problems that a tem to explain the structure of an atom. A near anal- particular body of knowledge is intended to solve— ogy draws on a structure that comes from a similar in this case, problems about distance. Prior knowl- body of knowledge. The scientists in Dunbar’s study edge also enables learners to construct a mental used near analogies from biology because they had model of the situation that helps them understand precise knowledge of biology, which made for a what the components of the trigonometric formulas more productive transfer. refer to. Instruction can help students determine deep Sometimes students cannot transfer knowledge features by using analogous examples rather than to school settings because they do not have the rele- single examples. In a 1983 study, Mary Gick and vant knowledge. One way to help overcome a lack Keith Holyoak asked students how to kill a tumor of prior knowledge is to use contrasting cases. with a burst of radiation, given that a strong burst Whereas pairs of analogies help students abstract kills nearby tissue and a weak burst does not kill the deep features from surface features, pairs of con- tumor. Students learned that the solution uses mul- trasting cases help students notice deep features in tiple weak radiation beams that converge on the the first place. Contrasting cases juxtapose examples tumor. Sometime later, the students tried to solve that only differ by one or two features. For example, the problem of how a general could attack a fortress: a teacher might ask students to compare examples If the general brought enough troops to attack the of acute, right, and obtuse triangles. Given the con- fortress, they would collapse the main bridge. Stu- trasts, students can notice what makes a right triangle distinctive, which in turn, helps them construct dents did not propose that the general could split his precise mental models to understand a lesson on the forces over multiple bridges and then converge on Pythagorean theorem. the fortress. The students’ knowledge of the convergence solution was inert, because it was only associated with the radiation problem. Gick and Holyoak Person-Based Approaches to Transfer found they could improve transfer by providing two The second approach to transfer asks whether per- analogous examples instead of one. For example, son-level variables affect transfer. For example, do students worked with the radiation problem and an IQ tests or persistence predict the ability to transfer? analogous traffic congestion problem. This helped Person-based research relevant to instruction asks students abstract the convergence schema from the whether some experiences can transform people in radiation context, and they were able to transfer general ways. their knowledge to the fortress problem. Transferring out from instruction. An enduring Transferring in to instruction. In school, transfer issue has been whether instruction can transform can help students learn. If students can transfer in people into better thinkers. People often believe that prior knowledge, it will help them understand the mastering a formal discipline, like Latin or program- content of a new lesson. A lesson on the Pythagorean ming, improves the rigor of thought. Research has theorem becomes more comprehensible if students shown that it is very difficult to improve people’s can transfer in prior knowledge of right triangles. reasoning, with instruction in logical reasoning

LEARNING: TRANSFER OF LEARNING 1451 being notoriously difficult. Although people may their linguistic practice of signifying. These children learn to reason appropriately for one situation, they brought their cultural heritage to bear on school do not necessarily apply that reasoning to novel situ- subjects, and this fostered a school-based identity in ations. More protracted experiences, however, may which students viewed themselves as competent and broadly transform individuals to the extent that they engaged in school. apply a certain method of reasoning in general, regardless of situational context. For example, the cul- Conclusion tural experiences of American and Chinese adults lead them to approach contradictions differently. The frequent disconnect between in-school and out- of-school contexts has led some researchers to argue There have also been attempts to improve learn- that transfer is unimportant. In 1988, Jean Lave ing abilities by improving people’s ability to transfer. compared how people solved school math problems Ann Brown and Mary Jo Kane showed young chil- and best-buy shopping problems. The adults rarely dren how to use a sample solution to help solve an used their school algorithms when shopping. Be- analogous problem. After several lessons on trans- cause they were competent shoppers and viewed ferring knowledge from samples to problems, the themselves as such, one might conclude that school- children spontaneously began to transfer knowledge based learning does not need to transfer. This con- from one example to another. Whether this type of clusion, however, is predicated on a narrow view of instruction has broad effects—for example, when transfer that is limited to identical uses of what one the child leaves the psychologist’s laboratory— has learned or to identical expressions of identity. remains an open question. Most likely, it is the From an educational perspective, the primary accumulation of many experiences, not isolated, function of transfer should be to prepare people to short-term lessons, that has broad implications for learn something new. So, even though shoppers did personal development. not use the exact algorithms they had learned in Transferring in to instruction. When children enter school, the school-based instruction prepared them school, they come with identities and dispositions to learn to solve best-buy problems when they did that have been informed by the practices and roles not have paper and pencil at hand. This is the central available in their homes and neighborhoods. Schools relevance of transfer for education. Educators can- also have practices and roles, but these can seem for- not create experts who spontaneously transfer their eign and inhospitable to out-of-school identities. knowledge or identities to handle every problem or Na’ilah Nasir, for example, found that students did context that might arise. Instead, educators can only not transfer their basketball ‘‘street statistics’’ to put students on a trajectory to expertise by preparing make sense of statistics lessons in their classrooms them to transfer for future learning. (nor did they use school-learned procedures to solve statistics problems in basketball). From a knowledge See also: Learning, subentries on Analogical Rea- approach to transfer, one might argue that the soning, Causal Reasoning, Conceptual school and basketball statistics were analogous, and Change. that the children failed to see the common deep features. From a person approach to transfer, the cultural contexts of the two settings were so different BIBLIOGRAPHY that they supported different identities, roles, and Boaler, Jo, and Greeno, James G. 2000. ‘‘Identity, interpretations of social demands. People can view Agency, and Knowing in Mathematical and express themselves quite differently in school Worlds.’’ In Multiple Perspectives on Mathemat- and nonschool contexts, and there will therefore be ics Teaching and Learning, ed. Jo Boaler. West- little transfer. port, CT: Ablex. One way to bridge home and school is to alter Bransford, John D.; Franks, Jeffrey J.; Vye, instructional contexts so children can build identi- Nancy J.; and Sherwood, Robert D. 1989. ties and practices that are consistent with their out- ‘‘New Approaches to Instruction: Because Wis- of-school personae. Educators, for example, can dom Can’t Be Told.’’ In Similarity and Analogi- bring elements of surrounding cultures into the cal Reasoning, ed. Stella Vosniadou and Andrew classroom. In one intervention, African-American Ortony. Cambridge, Eng.: Cambridge Universi- students learned literary analysis by building on ty Press.

1452 LEARNING COMMUNITIES AND THE UNDERGRADUATE CURRICULUM

Bransford, John D., and Schwartz, Daniel L. Novick, Laura R. ‘‘Analogical Transfer, Problem 1999. ‘‘Rethinking Transfer: A Simple Proposal Similarity, and Expertise.’’ Journal of Experi- with Multiple Implications.’’ In Review of Re- mental Psychology: Learning, Memory, and Cog- search in Education, ed. Asghar Iran-Nejad and nition 14(3):510–520. P. David Pearson. Washington, DC: American Peng, Kaiping, and Nisbett, Richard E. 1999. Educational Research Association. ‘‘Culture, Dialectics, and Reasoning about Con- Brown, Ann L., and Kane, Mary Jo. 1988. ‘‘Pre- tradiction.’’ American Psychologist 54(9):741– school Children Can Learn to Transfer: Learn- 754. ing to Learn and Learning from Example.’’ Schwartz, Daniel L., and Bransford, John D. Cognitive Psychology 3(4):275–293. 1998. ‘‘A Time for Telling.’’ Cognition and In- Ceci, Stephen J., and Ruiz, Ana. 1993. ‘‘Transfer, struction 16(4):475–522. Abstractness, and Intelligence.’’ In Transfer on Trial, ed. Douglas K. Detterman and Robert J. Daniel L. Schwartz Sternberg. Stamford, CT: Ablex. Na’ilah Nasir Chi, Michelene T.; Glaser, Robert; and Farr, Marshall J. 1988. The Nature of Expertise. Hil- lsdale, NJ: Erlbaum. Dunbar, Kevin. 1997. ‘‘How Scientists Think: On- LEARNING COMMUNITIES AND line Creativity and Conceptual Change in Sci- THE UNDERGRADUATE ence.’’ In Creative Thought, ed. Thomas B. CURRICULUM Ward, Stephen M. Smith, and Jyotsna Vaid. Washington DC: APA. Educational observers have long argued that student Gentner, Dedre. 1989. ‘‘The Mechanisms of Ana- involvement is important to student education. In- logical Reasoning.’’ In Similarity and Analogical deed a wide range of studies, in a variety of settings Reasoning, ed. Stella Vosniadou and Andrew and of a range of students, have confirmed that aca- Ortony. Cambridge, Eng.: Cambridge Universi- demic and social involvement, sometimes referred to ty Press. as academic and social integration, enhances student Gick, Mary L., and Holyoak, Keith J. 1983. development, improves student learning, and in- ‘‘Schema Induction and Analogical Transfer.’’ creases student persistence. Simply put, involvement Cognitive Psychology 15(1):1–38. matters. But getting students involved can be difficult. This is especially true for the majority of college Godden, D. R., and Baddeley, A. D. 1975. ‘‘Con- students who commute to college, who work while text-Dependent Memory in Two Natural Envi- in college, or have substantial family responsibilities ronments: On Land and Under Water.’’ British beyond college. Unlike students who reside on cam- Journal of Psychology 66(3):325–331. pus, these students have few, if any, opportunities to Lave, Jean. 1988. Cognition in Practice. Cambridge, engage others beyond the classroom. Eng.: Cambridge University Press. For that reason an increasing number of univer- Lee, Carol. 1995. ‘‘A Culturally Based Cognitive sities and colleges, both two- and four-year, have Apprenticeship: Teaching African-American turned their attention to the classroom—the one High School Students Skills of Literary Interpre- place, perhaps the only place, where students meet tation.’’ Reading Research Quarterly 30(4):608– each other and the faculty. Researchers have asked 630. how that setting can be altered to better promote Moll, Luis C., and Greenberg, James B. 1990. student involvement and in turn improve student ‘‘Creating Zones of Possibilities: Combining So- education. In response, schools have begun to insti- cial Contexts for Instructions.’’ In Vygotsky and tute a variety of curricular and pedagogical reforms Education, ed. Luis C. Moll. Cambridge, Eng.: ranging from the use of cooperative and problem- Cambridge University Press. based learning to the inclusion of service learning in Nisbett, Richard E.; Fong, Geoffrey T.; Leh- the college curriculum. One reform that is gaining man, Darrin R.; and Cheng, Patricia W. attention, that addresses both the need for student 1987. ‘‘Teaching Reasoning.’’ Science involvement and the demands for curricular coher- 238(4827):625–631. ence, is the use of learning communities.