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.
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Author
RICHARD E. MAYER,Professorand Chairof Psychology,Universityof California,Santa
Barbara,CA 93106.Specializations.humanlearningandproblemsolving,proseprocessing.
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