Idea Transcript
Reviewof EducationalResearch Spring1989, Vol.59, No. 1, pp. 43-64
Models for Understanding Richard E. Mayer University of California, Santa Barbara Whatcan be done to empowerstudentsto be creativewhen they are faced with problems?One promising instructionaltechniquefor improvingstudents'understanding of scientificexplanationsis the use of conceptualmodels. This review examinesthreepredictionsconcerningthe effectsof conceptualmodelson students' understandingof scientificprose: that models improverecall of conceptualinformation, decreaseverbatimretention,and increasecreativesolutions on transfer problems.In a reviewof 20 studies involving31 separatetests, resultsconsistently indicatedthatmodelscan helploweraptitudelearnersto thinksystematicallyabout the scientificmaterialtheystudy.
Whyis it thatsomepeople,whentheyarefacedwithproblems, getcleverideas, makeinventions anddiscoveries? Whathappens? Whataretheprocesses thatlead Whatcanbe doneto helppeopleto be creativewhen peopleto suchsolutions? & Luchins,1970,p. 1) (Luchins theyarefacedwithproblems? Whenthe greatGestaltpsychologist,Max Wertheimer,proposedthesequestions to his seminarstudentsin 1936, no one responded.Indeed,in Wertheimer'sday there was not a sufficientresearchbase to provide the illuminatinganswersthat these challengingquestions deserved.In the half century that has elapsed, and particularlyin the last decade,however,cognitivetheoriesof learningand transfer have emergedthat may be able to shed more light (Ausubel, 1968; Cormier& Hagman, 1987;Gentner& Stevens, 1983;Mayer, 1987a;West & Pines, 1985). The goal of this review is to examine one promising technique for helping studentsto learn new materialin ways that allow them to be creativewhen faced with problems. In particular,this review examines the usefulness of providing conceptualmodelsas aidsto students'understandingof scientificexplanations.For purposesof this review,a conceptualmodel is defined as wordsand/or diagrams that are intendedto help learnersbuild mentalmodels of the systembeing studied; a conceptualmodel highlightsthe majorobjectsand actionsin a systemas well as the causalrelationsamongthem.' For purposesof this review,understandingrefers to a student's ability to creativelyuse presentedinformation to solve transfer problems. For example,supposethatwe askedsome studentsto reada passageaboutradar. What can we do to help studentslearn about radarin ways that will enable them to use what they have learnedto generatecreativesolutionsto transferproblems? In short,we want our studentsto be able to answerquestionsthat were not partof One the lesson,such as, "Howcan you increasethe areaunderradarsurveillance?" relatively modest instructionalmanipulation that might help is to provide a diagram,such as in Figure1, that spellsout the majorobjects(such as transmitter, receiver, pulse, remote object, etc.) and major actions (such as transmission, reflection,reception,etc.) in a radarsystem and that shows the causal relations amongactions. 43
RichardE. Mayer 1. TRANSMISSION:A pulse travels from an antenna.
O 2.
0 3.
04 4.
REFLECTION:The pulse bounces off a remote object.
RECEPTION: The pulse returns to the receiver.
MEASUREMENT: The difference between the time out and the time back tells the total time traveled.
LOUT
5.
BACKj
CONVERSION: The time can be converted to a measure of distance because the pulse travels at a constant speed. =
miles I how radarworks FIGURE 1. Modelfor understanding
I seconds
A Model of MeaningfulLearning In orderto conductthis reviewon models for understanding,it is firstnecessary to outline the relevantcomponentsin the teaching/learningprocess:learnercharacteristics,learning material,instructionalmethod, learning processes,learning outcome,and performance.These componentsare summarizedin Figure2. Learnercharacteristics.Novices. Learnercharacteristicsreferto the preexisting knowledgeand capacitiesthat the learnerbringsto the learningsituation.For the purposesof this review,I focus on novices ratherthan experts,that is, on students who lack prerequisiteknowledgeand capacitiesfor the subjectdomain. These less skilledstudentsaremost likelyto benefitfromdirectinstructionin how to construct a conceptualmodel for the to-be-learnedmaterial,whereasmore skilledstudents arelikelyto alreadypossessand spontaneouslyuse sophisticatedconceptualmodels that may conflictwith modelspresentedduringinstruction. To-be-learned material:Systems.The to-be-learnedmaterialis the subject-matter content that is presentedfor the studentto acquire.For purposesof this review,I focus on explanativematerial (Mayer, 1985, 1987b), that is, on material that explainshow some system works.A system is a coherentcollection of partsthat interact (Simon, 1969). Examples include technologicaldevices such as radar 44
Modelsfor Understanding
FIGURE 2. Componentsin the teaching/learning process systems, cameras, and braking systems; scientific explanations such as the nitrogen cycle, Ohm's law, or the concept of density; and programming languages such as BASIC or data management systems. Explanative material allows students to think systematically, that is, to build and use models that explain the information. I have focused this review on explanative material because meaningful methods of instruction can only have an effect for learning of material that is potentially meaningful. Unfortunately, much of the material in science textbooks does not meet this criterion (White & Mayer, 1980). The left column of Table 1 lists the topics that were taught in the studies included in this review. Instructional method: Models. Instructional method refers to the way in which the material is presented to the student. For purposes of this review, I focus on one promising technique for fostering meaning learning of the material, namely, the use of conceptual models that spell out the major parts, states, and actions in TABLE 1 Some topics,models,and measuresof scientificexplanation Model
Topic Radar
Figure1
Ohm'slaw
Figure5
Density
Figure6
Data base
Figure7
BASIC Nitrogencycle
Figures8 & 12 Figure9
Camera
Figure10
Brakes
Figure11
Exampletransferproblem How can you increasethe areaunderradar surveillance? How is resistancelike pushinga wheelbarrow up a ramp? If heat appliedto an objectincreasesits volume,what happensto the densityof that same objectwhen it is heated? Tell the problemthat is solvedby a given program. Tell whattask is accomplishedby a given program. If you used only naturalmeans,how could you makethe soil richerin nitrogenfor use by plants? How wouldyou set a camerato take a pictureof a pole vaulteron a cloudy day? Whatcould be done to improvethe reliability of brakes? 45
RichardE. Mayer ORGANIZING
FIGURE 3. An informationprocessingmodel
systems.In reviewingresearch,I include studiesthat comparestudentswho learn with the aid of a conceptualmodel (model group) with studentswho learn the same materialwithout a model (control group). I focus on conceptual models because recent theoriesof analogicaltransferhave pointed to the crucial role of models in enablingtransfer(Curtis& Reigeluth, 1984; deKleer & Brown, 1981, 1983; Gentner, 1983; Hayes & Henk, 1986; Royer & Cable, 1976). The second column of Table 1 describesmodels used in the studiesincludedin this review.In each case, the model is a text and pictorial representationof the explanative informationin the passage;it highlightsthe key conceptsfromthe text and suggests relationshipsamong them. Learningprocesses.'Selecting, organizing,and integrating.Learningprocesses referto the way in which studentsencode to-be-learnedinformation.The mode of instructionis intendedto affectthe way that studentsselect,organize,and integrate information(Mayer, 1984). In this review, I focus on three specific processes: models are expectedto guide students'selectiveattention towardthe conceptual informationin the lesson(i.e., the majorobjects,states,and actions,and the causal relationsamong them), to organizethe informationaroundcoherentexplanations (i.e., build internalconnections),and to integratethe informationwith existing relevant knowledge(i.e., build external connections). Appendix A summarizes definitions and examples from the radar passage of these types of cognitive processes,and AppendixB elaborateson the examples. Figure 3 shows an information processingmodel for describingmeaningful learningprocesses.The boxes in the model referto short-term(or working)and long-termmemory stores;the arrowsreferto processes,includingselectinginformationto pay attentionto (i.e., arrowfrom input to short-termmemory),organizing incoming information in short-termmemory (i.e., arrow from short-term memory to short-termmemory), integratingprior knowledge from long-term 46
Modelsfor Understanding memorywith incominginformation(i.e., arrowfrom long-termmemoryto shortterm memory),and encodingthe resultantlearningoutcome in long-termmemory (i.e., arrowfrom short-termmemoryto long-termmemory). The outcomeof learningrefersto the knowlLearningoutcomes:Understanding. edge that the studentacquiresas a resultof the learningprocesses.Studentsgiven model instructionmay be more likely to build mental models of the systemsthey are studying and to use these models to generatecreative solutions to transfer problems. In short, these students may be better able to engage in systematic thinking.In each studyreviewedin this paper,the transfertest involvesanswering questionsthat go beyondboth the passageand the model. Figure4 summarizesthe conditionsfor buildingmeaningfullearningoutcomes. As can be seen, meaningful learning requiresthat students attend to relevant information,buildinternalconnectionsamongthe piecesof information,and build externalconnections between the informationand relevantexisting knowledge. For example,in the radarexample,the relevantinformationinvolves the partssuch as transmitter,receiver,remote object, and pulse-and processes-such as transmission,reflection,and reception.(Examplesof internaland externalconnections for the radarlesson are listedin AppendixB.) Performance:Systematicthinking.Performancerefersto what the student can do as a result of learning.In this review, I focus on three specific performance indicatorsof systematicthinking:recallof conceptualinformation,retentionof the informationin nonverbatimformat,and generationof creativeproblemsolutions. The rightportionof Table 1 lists some creativetransferquestionsused to evaluate systematicthinking. Researchon text illustrationshas providedsome empiricalevidencethat students retain more informationfrom expositorytext passagesthat include illustrations than from text without illustrations(Alesandrini,1984; Anglin & Stevens, 1986; Curtis, 1988;Curtis& Reigeluth, 1984; Dean & Enomoth, 1983; Levie & Lentz, 1982; Levin & Berry, 1980; Levin & Lesgold, 1978; Readence & Moore, 1981; Reid & Beveridge,1986;Reid, Briggs,& Beveridge,1983;Rusted, 1984;Rusted& Coltheart,1979a,1979b;Rusted& Hodgson,1985;Saroyan& Geis, 1988;Schallert, 1980). Research on text illustrations,however, generally has not focused on cognitive analyses of students'learning and thinking processesas measuredby dependentmeasuresthat go beyondoverallamountretained,exceptin studiesthat measurestudents'inferences(e.g., Holmes, 1987). Correspondingly,researchon mental models has provided some theoreticalcontributionsconcerning how a person'sknowledgemay affect their problem-solvingperformancebut generally has not focused on empirical work related to instructionalissues (Gentner & Stevens, 1983;Michalski,Carbonell,& Mitchell, 1986). Consequently,this review requiresbridgingthe gap between the educationalrelevanceof researchon text illustrationsand the theoreticalrelevanceof researchon mental models. In summary,this review examines publishedresearchstudies-all conducted over the past 15 yearsin my laboratory-that meet four criteria.First,the learners must be novices ratherthan experts.Second, the to-be-learnedmaterialmust be explanativeratherthan descriptiveor narrative.Third, the major independent variablemust be whetherconceptualmodelsareusedas aidsto instruction.Fourth, the majordependentmeasuresmust be recallof conceptualinformation,retention of materialin verbatimformat,and/or creativeproblem-solvingtransferperform47
LEARNING MATERIAL NON-EXPLANATIVE
HIGHLY SKILLED LEARNERCHARACTERISTICS
LEARNING PROCESS UNSELECTIVE
UNORGANIZED LEARNING PROCESS
UNINTEGRATED LEARNING PROCESS
NO EVIDENCEOF MEANINGFUL LEARNING
OFMEANINGFUL EVIDENCE LEARNING DUETOMODELS
FIGURE 4. Conditionsformeaningfullearning
48
Modelsfor Understanding ance ratherthan the more traditionalmeasuresof overallamount recalledand/or overallperformanceon comprehensiontests. Finally, this review examines three specific predictionsbased on the foregoing analysisof learningprocessesand outcomes. First, model students should recall more conceptualinformationthan control students.This predictionfollows from the idea that models guide students'selection of materialfor learning.Second, model students should be less likely to retain the materialin verbatimform as comparedto control students.This predictionfollows from the idea that models encouragestudentsto reorganizeand integratethe acquiredinformation.Third, model studentsshouldgeneratemore creativesolutionsto transferproblemsthan controlstudents.This predictionfollowsfromthe ideathat studentswho havebuilt useful mental models will be better able to make novel inferencesby "running" (deKleer& Brown, 1981)their models. Researchon Models for Understanding Model Beforethe Lesson Thissectionreviewsa seriesof studiesin whicha conceptualmodelwaspresented priorto a lesson, as summarizedin the top portionof Table 2. Radar. In a recent study (Mayer, 1983, Experiment1), studentslistened to a 640-wordlectureon how radarworks,adaptedfrom The Encyclopediaof How It Works(Clarke,1977). Priorto hearingthe lecture,some studentshad 1 minute to examine a model sheet, as shown in Figure 1, whereasother students did not. Althoughthe informationin the model was redundantwith informationin the lecture,the model servedto highlightand organizethe main stepsand elementsin radarprocessingas had been determinedin previousanalyses (Mayer& Cook, 1980). For example, the model used a set of five concretediagramsto represent the five majorsteps in radarprocessing:transmission,reflection,reception,measurement,and conversion.In addition,the model concretizedthe majorelements in the system:the radarpulse, the remote object,the transmitter,the receiver,the clock,and the converter.Consistentwith our predictionsthat modeltrainingwould elicit systematicthinking,the model studentsrecalled57%more of the conceptual information,scored 14%lower in verbatimretention,and generated83% more correctanswerson problem-solvingtransferas comparedto controlstudents. Ohm'slaw. In a similarstudy (Mayer,1983, Experiment2), studentslistenedto a 390-word lecture on Ohm's law taken from a high school physics textbook (Herron,Palmer,& Joslin, 1972).Priorto hearingthe lecture,some studentswere given 1 minute to examine a model sheet, as shown in Figure 5, whereasother studentswere not. The model consistedof four labeleddiagramsthat emphasized the majorelements and states in electricalflow as identifiedin previousanalyses of the majorconceptsunderlyingOhm'slaw (White& Mayer,1980).In particular, the diagramsprovidedmodelsfor concretizingthe conceptsof circuit(i.e., a battery, a bulb, and connectingwiresallow continuouselectricalflow), potentialdifference (i.e., a batteryproducesnegativeand positiveparticles),current(i.e., electronsflow througha wire), and resistance(i.e., obstaclesin a wire slow electricalflow). The model is similarto some aspectsof the flowing waterand teemingcrowdanalogies used by Gentnerand Gentner(1983) to help studentsunderstandthe concept of electrical flow. As predicted, the model students recalled 120% more of the conceptualinformationthan the controlstudents. 49
Richard E. Mayer TABLE 2 Summaryof researchon modelsfor understanding Type of test (%)
Topic Radar Ohm'slaw Density Database BASIC
Nitrogencycle Camera Brakes BASIC
Source
Conceptual Verbatim recall retention
Modelbeforethe lesson +57 (Mayer,1983, Exp. 1) +120 (Mayer,1983, Exp.2) +144 (Mayer,Dyck, & Cook, 1984, Exp. 1) (Mayer,1980, Exp. 1) (Mayer,1980,Exp.4) +26 (Mayer,1980,Exp. 5) +43 (Mayer& Bromage, 1980,Exp. 1) +44 (Mayer& Bromage, 1980,Exp. 2a) +30 (Mayer& Bromage, 1980,Exp. 2b) (Mayer,1976, Exp. la) (Mayer,1976, Exp.2a) (Mayer,1976, Exp. 2b) Modelwithinthe lesson +73 (Mayer,Dyck, & Cook, 1984,Exp. 2) (Bromage& Mayer, 1981, Exp. 2) +46 (Mayer,in press,Exp. 1) +23 (Mayer,in press,Exp. 2) (Mayer, 1975, Exp. la)
(Mayer,1975, Exp. lb) (Mayer,1985, Exp. 2) (Mayer,1976,Exp. lb) (Bayman& Mayer, 1988, Exp. 1)
Creative problem solving
-14
+83
-26
+45 +92
+129
-
-
-14
+245 +100 +132 +42 +29
-5
-8
+61 +65 +64 +460 +52
+33 +21
Note. Scoresindicatepercentagedifferencesbetweencontroland experimentalgroupsbased on the formula(experimental- control)/control.Dashes(-) indicatethatno measurewas taken. Density. Mayer, Dyck, and Cook (1984, Experiment 1) asked students to read a 450-word passage on density that was representative of high school physics textbooks. Prior to reading the passage, some students were given a model sheet, as summarized in Figure 6, whereas other students were not. The model showed a diagram of a cube of city air along with a verbal definition of volume and a diagram showing particles in a cube of city air along with a definition of mass. Thus, the model helped concretize the concept of volume as a three-dimensional container and mass as the amount of material in the container. As predicted, the model students recalled 144% more of the conceptual information, scored 26% lower on 50
4
CIRCUIT: A CIRCUIT CONSISTS OF A BATTERY, A WIRE, AND A BULB. POSITIVE TERMINAL
?
?
??? -?
NEGATIVE TERMINAL
ELECTRONS
o?0O? tO 0@
(?? ) W
C?~G-
BATTERY (POTENTIAL DIFFERENCE): A BATTERY SEPARATES NEGATIVES (ELECTRONS) FROM POSITIVES. FIGURE 5. Modelfor understandingOhm'slaw
Volume tells us how much space an object takes up. Finding the volume of an object is like finding how many individual cubes there are in a specific object. In the case below, volume is 3 x 4 x 2 = 24 cubes.
3 inches
4 inches 2 inches We could theoretically
even take one cube out.
^1i inch
1 inch 1 inch
Mass is the number of particles within an object. Obviously, some substances may have more particles in them than others. For example:
BOX A Mass = 3 particles
BOX B Mass = 6 particles
BOX B has two times as many particles and thus twice the gravitational pull.
FIGURE 6. Modelfor understanding density 52
Modelsfor Understanding verbatimretention,and solved45%more of the transferproblemsthan the control students. Data base systemprogramming.In a seriesof three studies,studentsreada 10pagemanualfor usinga database managementsystem(Mayer,1980, Experiments 1, 4, & 5). Some studentswere introducedto a concrete model of the computer system prior to readingthe manual (model group),whereasother studentswere not (controlgroup).As shown in Figure7, the model of the computerincludeda file cabinetto representlong-termstorageof records;an in basket,a save basket, and a discardbasketto representthe sortingfunction of the system;an erasable scoreboardwith labeled spaces to representdata tabulation;and a note pad to representthe outputfunction.Studentsgiven the model produced92%and 129% more correct answers to tests of problem-solvingtransfer in a series of two experiments(Experiments1 & 4, respectively);finally,model studentsrecalled26% more of the conceptualinformationthan controlstudents(Experiment5). BASIC computerprogramming.In a series of studies, studentsread a 10-page manualdescribinga simplifiedBASICprogramminglanguage(Mayer,1976;Mayer & Bromage, 1980). Some students were introducedto a concrete model of the computersystempriorto readingthe manual(model group)whereasotherswere not (control group).Figure 8 shows a typical version of the model used in these studies;the model includes a memory scoreboardto help representthe memory functionof the computer,an input windowwith in and out boxes to representthe data entry function, a programlist with pointer arrow to representthe control FILE CABINET
SORTING BASKETS RECORD
FILEX 0 FILEQD FILEP POINTER
IN
FILEZ
ARROW
v
SAVE
X
DISCAR
FILER
FILEX
MEMORYSCOREBOARD COUNT
33 COUNT1
7 COUNT2
TOTAL
212 TOTAL1
3 AVERAGE1
0
0
TOTAL2
AVERAGE2
55
714
102
COUNT3
TOTAL3
AVERAGE3
12
33
1
COUNT4
TOTAL4
AVERAGE4
150
50
3
OUTPUT PAD
AVERAGE
2
data baseprogramming FIGURE 7. Modelfor understanding
53
Richard E. Mayer
MEMORY SCOREBOARD A
B
C
D
E
F
G
H
INPUT POINTER PROGRAM OUTPUT PAD WINDOW ARROW LIST IN
1 2
OUT
3 4
elementaryBASICprogramming FIGURE 8. Modelfor understanding
function,and an outputpad to representthe output function.The model students recalled43%,44%,and 30%moreconceptualinformationthanthe controlstudents acrossthreestudiesthat evaluatedrecall(Mayer& Bromage,1980, Experiment1, Experiment2-Immediate Test, and Experiment2-Delayed Test), and correctly solved 245%, 100%,and 132%more transferproblemsthan the control students acrossthree studiesthat evaluatedproblemsolving (Mayer, 1976, Experiment1, Experiment2-Experimenter Control,and Experiment2-Subject Control). Model Withinthe Lesson This section reviewsstudiesin which a conceptualmodel was embeddedwithin a lesson, includingthe reorganizationof the lesson to fit within the context of the model. Nitrogencycle.Mayer,Dyck, and Cook (1984, Experiment2) askedstudentsto reada 670-wordpassageon the nitrogencycle adaptedfrom a high school biology book (Slesnick,Balzer,McCormack,Newton & Rasmussen,1980) or a conceptual model versionthat emphasizedthe majorsteps in the nitrogencycle. The model versioncontainedthe model shown in Figure9 and was organizedaroundthe five steps:fixation,in whichbacteriacatch and convertatmosphericnitrogen(N2)into ammonia(NH3);nitrification,in whichbacteriain the soil convertammonia(NH3) into nitrate(NO3);assimilation,in which cells in plantstake in nitrates(NO3)and convert them into protein (NH2);ammonification,in which bacteriain the soil convertprotein(NH3)from decayingplantsand wastesinto ammonia (NH3);and denitrification,in which bacteriain the soil convertnitrates(NO3) in the soil back into atmosphericnitrogen(N2).The model studentsremembered73%more of the conceptualinformationcommon to both passages,scored 14%less on verbatim retention, and correctly solved 42% more transferproblems than the control students. Camera.Bromage& Mayer(1981, Experiment2) askedstudentsto readan 800word passageabout how to use a 35mm camera (control group) or an enlarged 54
Modelsfor Understanding
denitrification
FIGURE 9. Modelfor understanding the nitrogencycle
versionof the passagethat includedmodels of the internalworkingsof the camera (model group). As summarizedin Figure 10, the models describedhow fuzzy picturesubjectsand backgroundsare relatedto raysof lightin the cameraand how overexposedor underexposedor blurredpicturesare relatedto the amount and timing of light enteringthe cameraand the particledensityof the film. The results indicatedthat the model studentsexhibitedsystematicthinkingby producing29% more creativeproblem-solvinganswersthan the controlstudents. Brakes.In a recentset of studiescarriedout in our laboratory(Mayer,in press, Experiment1 & Experiment2), studentsreada 1200-wordpassageon how brakes work, adapted from the WorldBook Encyclopedia(1986). Some students read passagesthat includedfourlabeleddiagrams,as summarizedin Figure11, whereas others read passageswithout diagrams.The diagramsshowed the major parts of the brakes-such as cylinders, pistons, tubes, drums, and shoes for hydraulic brakes-and showedthe majorchain of eventswhen the brakepedalis activatedsuch as the piston moving forwardin the master cylinder,brake fluid moving throughthe tube to the wheel cylinder,the wheel moving forward,the brakeshoe pressinginto the brakedrum,and the wheel slowingdown. The wordsused in the diagramswere identicalto those used in the text. In the two studies,respectively, the model studentsrecalled46% and 23% more of the conceptualinformation, scored5%and 8%loweron verbatimretention,and produced61%and 65%more creativesolutionsto transferproblemsas comparedto the controlstudents. BASICcomputerprogramming.Complementingthe foregoingstudieson computer programming,anotherserieswas conductedin which studentsread BASIC programmingmanuals that either contained and referredto a concrete model (model group)or did not (controlgroup).Figure 12 summarizesthe model used 55
AIR
GLASS
Light waves passing into glass along normal.
Light waves passing into glass at angle.
FIGURE 10. Modelfor understandinghow cameraswork
Modelsfor Understanding
HYDRAULIC DRUMBRAKES Tube =-
Wheel Cylinder Smaller Pistons
O|C
1 |-Brake
Drum
Brake Shoe
When the driver steps on the car's brake pedal... A piston moves forward inside the master cylinder (not shown). The piston forces brake fluid out of the master cylinder and through the tubes to the wheel cylinders. In the wheel cylinders, the increase in fluid pressure makes a set of smaller pistons move. When the brake shoes press against the drum both the drum and the wheel stop or slow down. FIGURE 11. Modelfor understanding how brakeswork
by Bayman& Mayer(1988), which containeda memoryscoreboard,input queue with pointer,outputscreen,programlist with pointer,scratchpad workspace,and run-waitlight.Acrossfive separatestudiesthat evaluatedproblem-solvingtransfer performance(Mayer 1975, Experiment1-No Flow Chart,Experiment1-Flow Chart, and Experiment2; Mayer, 1976, Experiment 1; and Bayman & Mayer, 1988, Experiment1), the model group outperformedthe control group by 64%, 460%, 52%, 33%, and 21%.
Conclusion Can ConceptualModelsImproveStudents'SystematicThinking? We beganwith the hypothesisthatprovidingconcretemodelswouldhelp novices learnto thinksystematicallyaboutto-be-learnedscientificinformation.If providing conceptualmodels helps to fostersystematicthinking,we can predicta patternin 57
RichardE. Mayer CONTROL LIGHT MEMORYSCOREBOARD J J JJ WAIT
OUTPUT SCREEN
r
] RUN I
LOVE PROGRAMMING
GO
]
0 J
PROGRAMLIST
DATALIST .-
55 12 3
SCRATCHPAD
*
10PRINT "I" 20 PRINT"LOVE"
790 88
30 PRINT "PROGRAMMING"
2
40 END
FIGURE 12. Modelfor understanding BASICprogramming which students who learn with concrete models recall more conceptual information, perform more poorly on verbatim retention of information, and most important, generate more creative solutions on transfer problems, as compared to students who learn without models. Table 3 summarizes how well these three predictions were supported by the research results. Prediction 1. Models will improve conceptual retention. The first prediction is that conceptual recall will be higher for the model group than the control group. The rationale for this prediction is that the model helps students direct their attention toward the conceptual objects, locations, and actions described in the lesson. As summarized in Table 3, there were 10 separate tests in which the conceptual recall of a model group was compared to the conceptual recall of a control group. In all 10 tests, the model group outperformed the control group with a median improvement of 57%. TABLE 3 Evaluationof threepredictions
Type of test Conceptualrecall Verbatimretention Problemsolvingtransfer
58
Number of tests
Percentage consistent with predictions
Median percentage increaseor decrease
10 5 16
100% 100% 100%
+57% -14% +64%
Modelsfor Understanding Prediction2: Models will reduce verbatimretention.The second predictionis that verbatimretentionwill be lower for the model groupthan the controlgroup. The rationalefor this predictionis that the model helps studentsreorganizethe materialto fit in with theirconceptualmodel and when studentsactivelyreorganize the materialthey tend to lose the originalpresentationformat. In five separate comparisonsof the verbatimretentionby model and controlstudents,the control studentsoutperformedthe model studentsin all five tests. The median reduction in performancefor the model studentswas 14%,as summarizedin Table 3. Prediction3. Models will improveproblem-solvingtransfer.The most crucial predictionis that models will improvethe abilityof studentsto transferwhat they have learned to creativelysolving new problems. The ability to generatenovel solutionsto new problemsis the hallmarkof systematicthinking;if studentshave built models that they can mentallymanipulate,they will be better able to solve transferproblems. As summarizedin Table 3, this review yielded 16 separate comparisonsbetweenmodel and control studentson problem-solvingtransfer;in each of these comparisons,the model groupoutperformedthe controlgroup,with a medianimprovementof 64%. These resultsprovideconsistentsupportfor the idea that conceptualmodels for scientifictext can lead to changesin the way that studentsthink aboutthe material. It shouldbe notedthatthis reviewhas focusedon dependentmeasures-conceptual recall, verbatim retention, and problem-solvingtransfer-that are intended to evaluatedifferencesin systematicthinking.Hadwe focusedon traditionalmeasures such as overallamount recallor overallamount correcton a comprehensiontest, we would not have found strongdifferencesbetween model and control groups. Whatis wrongwith overallrecallor comprehensionperformance?These measures are not useful for the present review because they do not provide information concerninghow models help studentsto select, organize,and use scientificinformation. In contrast,to examine students'uriderstandingrequiresa focus on the threedependentmeasuresused in this study as well as more fine grainedanalyses that shouldbe a partof futureresearch. How Should ConceptualModelsBe Used in Instruction? this reviewprovidesa consistentlyaffirmativeanswerto the question Although of whethermodelscan fosterstudentunderstanding,it also raisesseveraladditional questionsconcerningthe what, when, where, who, and why of using conceptual models in instruction. Question1. Whatis a good model?The firstquestionconcernsthe characteristics of good models. Of course,this question must be revisedin orderto describethe purposeof the model; in light of this reviewwe can ask: "Whatis a good model for improvingnovices'transferperformance?"The foregoingreviewsuggests,but does not adequatelytest, severalcharacteristicsof good models for transferthat warrantfutureresearchstudy: Complete.Good modelscontainall of the essentialparts,states,or actionsof the systemas well as the essentialrelationsamongthem, so that the learnercan be able to see how the systemworks. Concise.Good models are presentedat a level of detail that is appropriatefor the learner.Ratherthan provideso much detail that the studentis overwhelmed, good models summarizeand epitomize the system they seek to explain. Rather 59
RichardE. Mayer than providea "bloodand guts"descriptionof each part,good modelsdescribethe generalfunctionsof each part.Eachof the modelsdescribedin this reviewinvolved a small numberof steps or states-generally about five-and only a few partsgenerallyless than a dozen. Coherent.Good modelsmake intuitivesenseto the learnerso that the operation is transparent;the model or analogy used is a logical system that contains parts and rulesfor how the partsinteract. Concrete.Good models are presentedat a level of familiaritythat is appropriate for the learner,includingphysicalmodels or visual models. Conceptual.Good models are based on materialthat is potentiallymeaningful, that is, on materialthat explainshow some systemoperates. Correct.Good models correspondat some level to the actual events or objects they represent.The majorpartsand relationshipsin the model correspondto the majorpartsand relationshipsin the actualobjector event. Considerate.Good models are presentedin a mannerthat is appropriateto the learner,usinglearnerappropriatevocabularyand organization. In short,models are "good"with respectto certainlearnersand certaininstructional goals. The currentreview,althoughconsistentwith the seven characteristics listed above, does not confirmthem. Systematicresearchis neededto identifythe relative contributionsof each characteristicand to establish better operational definitionsof each. Question2: Whereshould models be used?The second question concernsthe conditionsunder which models should be used. In the foregoingreview, models were effectivefor explanativematerial,that is, materialthat explainedhow some system worked.Correspondingly,visual mnemonic techniqueshave been shown to be highly effective for helping students to remember rote lists and paired associates(Levin, 1981). Question 3: When should models be used? The third question concerns the placementof modelswithin a lesson. Severalof the studiesin the foregoingreview providedevidencethat modelsareeffectivewhen placedeitherbeforeor integrated within a lesson but not when placedafter a lesson (Mayer, 1976, 1980; Mayer& Bromage,1980). Question4: Whois a modelgoodfor?The fourthquestionasksaboutindividual differencesin the effectivenessof models. The resultssummarizedin Table 3 are basedon studentswho had low priorknowledgeand low aptitudefor the material in the lesson. In studies that also included high-aptitudestudents, the positive effectsof modelson systematicthinkingwereeliminated;forexample,high-aptitude model students did not perform better than high-aptitudecontrol students on problemsolving(Bayman& Mayer,1988;Mayer,1980,Experiment4) or on recall of conceptualinformation(Mayer& Bromage,Experiment1). The high-aptitude studentsare more likely to come to the lessonwith alreadyexistingmodels (or the ability to rapidly construct them); for these students, the simplified, teachergeneratedmodels in the model groupsmay conflict with their more sophisticated models. Question5. Why use models?The final question concerns instructionalgoals. The models describedin the foregoingreview were intended to foster student understanding,as manifestedin creative problem-solvingtransferperformance. When the goal of instructionis student understandingof potentiallymeaningful 60
Modelsfor Understanding explanations, conceptual models can be effective tools. Apparently, conceptual models can provide an assimilative context for students to build useful mental models. In summary, the results of this review encourage continued development of theory and practice for using models to promote understanding. One particularly exciting avenue concerns the role of interactive computer graphic simulations as a vehicle for expanding the power of conceptual models (White, 1984). APPENDIX A Threetypesof cognitiveprocessing Definition: Example:
Guide attention Readertransferscertainidea units fromthe passageto short-termmemory. Readerattendsto 20 of the 78 idea units in the radarpassage.
Definition: Example:
Buildinternalconnections Readerorganizesidea units in short-termmemoryinto coherentstructure. Readeruses 'process'structure,so that idea units are arrangedinto five steps (see AppendixB).
Definition: Example:
Buildexternalconnections Readerintegratesnewstructurewithexistingknowledgein long-termmemory. Readerrelatesradarto bouncingball (see AppendixB).
APPENDIX B Some internaland externalconnectionsfor the radarpassage Internalconnections Transmission:First,a radiopulse is sent out from an antenna. Reflection:Second,the pulse strikesa remoteobject. Reception:Third,the reflectedpulse returnsto the antenna. Measurement:Fourth,the tripout and backtakesa certainamountof time. Conversion:Fifth,this time correspondsto the distanceof the remoteobject. Externalconnections Transmissionis like throwinga ball. Reflectionis like the ball hittinga wall. Receptionis like catchingthe ball afterit bouncesoff the wall. Measurementis like determininghow long it took for the ball to come back. Conversionis like noticingthat the furtherawayyou are from the wall the longerit takes for the ball to come back. Note A conceptualmodelcan be thoughtof as a specialkindof comparativeadvanceorganizer (Ausubel,1968)or a specialkindof text illustration(Lumsdaine,1963),thatis, as an organizer or illustrationthat showshow the partsand operationsof a systemfit together. References Alesandrini,R. L. (1984). Picturesand adultlearning.InstructionalScience,13, 63-77. Anglin, G. J., & Stevens,J. T. (1986). Prose-relevantpicturesand recallfrom science text. Perceptualand MotorSkills, 63, 1143-1148.
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RichardE. Mayer Ausubel,D. P. (1968). Educationalpsychology.A cognitiveview. New York:Holt, Rinehart and Winston. Bayman, P., & Mayer, R. E. (1988). Using conceptualmodels to teach BASIC computer programming.Journalof EducationalPsychology,80, 291-298. Bromage,B. K., & Mayer, R. E. (1981). Relationshipbetween what is rememberedand creativeproblem-solvingperformancein sciencelearning.Journalof EducationalPsychology, 73, 451-461. Clarke,D. (1977). The encyclopediaof how it works.New York:A & W Publishers. research Cormier,S. M., & Hagman,J. D. (Eds.).(1987). Transferof learning:Contemporary and applications.San Diego:AcademicPress. Curtis,R. V. (1988). When is a science analogylike a social studiesanalogy?A comparison of text analogiesacrosstwo disciplines.InstructionalScience,13, 169-177. Curtis,R. V., & Reigeluth,C. M. (1984). The use of analogiesin writtentext. Instructional Science,13, 99-117. Dean, R. S., & Enomoth,P. A. (1983). Pictorialorganizationin proselearning.Contemporary EducationalPsychology,8, 20-27. deKleer,J., & Brown,J. S. (1981). Mentalmodels of physicalmechanismsand theiracquisition. In J. R. Anderson(Ed.),Cognitiveskillsand theiracquisition(pp. 258-310). Hillsdale, NJ: Erlbaum. deKleer, J., & Brown, J. S. (1983). Assumptionsand ambiguitiesin mechanisticmental models.In D. Gentner& A. L. Stevens(Eds.),Mentalmodels(pp. 155-190). Hillsdale,NJ: Erlbaum. Gentner, D. (1983). Structuremapping:A theoreticalframeworkfor analogy. Cognitive Science, 7, 155-170. Gentner,D., & Gentner,D. R. (1983). Flowingwatersor teemingcrowds:Mentalmodelsof electricity.In D. Gentner& A. L. Stevens(Eds.),Mental models (pp. 99-129). Hillsdale, NJ: Eribaum. Gentner,D., & Stevens,A. L. (Eds.).(1983). Mentalmodels.Hillsdale,NJ: Erlbaum. Hayes, D.A., & Henk, W.A. (1986). Understandingand rememberingcomplex prose augmentedby analogicand pictorialillustration.Journalof ReadingBehavior,18, 63-78. Herron,W. B., Palmer,N. P., & Joslin,P. H. (1972). Matter,life, and energy.Chicago:Rand McNally. Holmes, B. C. (1987). Children'sinferenceswith print and pictures.Journalof Educational Psychology,79, 14-18. Levie,W. H., & Lentz,R. (1982).Effectsof text illustrations:A reviewof research.Educational Communicationand Technology,30, 195-232. Levin,J. R. (1981). The mnemonic '80s:Keywordsin the classroom.EducationalPsychologist, 16, 65-82. Levin, J. R., & Berry,J. K. (1980). Children'slearningof all the news that's fit to picture. EducationalCommunicationand Technology,28, 177-185. Levin,J. R., & Lesgold,A. M. (1978). On picturesin prose.EducationalCommunicationand Technology,26, 233-243. Luchins,A. S., & Luchins,E. H. (1970). Wertheimer'sseminarsrevisited.Problemsolving and thinking(Vol. 1). Albany,NY: SUNY Press. Lumsdaine,A. (1963). Instrumentsand mediaof instruction.In N. L. Gage(Ed.),Handbook of researchon teaching.Chicago:Rand McNally. Mayer,R. E. (1975).Differentproblem-solvingcompetenciesestablishedin learningcomputer programmingwith and without meaningfulmodels. Journalof EducationalPsychology, 67, 725-734. Mayer,R. E. (1976). Some conditions of meaningfullearningfor computerprogramming: Advanceorganizersand subjectcontrolof frameorder.Journalof EducationalPsychology, 68, 143-150.
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Richard E. Mayer White,R. T., & Mayer,R. E. (1980). Understandingintellectualskills.InstructionalScience, 9, 101-127. WorldBookEncyclopedia.(1986). Chicago:WorldBook Encyclopedia. Author RICHARD E. MAYER,Professorand Chairof Psychology,Universityof California,Santa Barbara,CA 93106.Specializations.humanlearningandproblemsolving,proseprocessing.
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