Visualization in Mathematics, Reading and Science Education

111 Pages·2010·1.438 MB·English

by  Linda M. Phillips, Stephen P. Norris, John S. Macnab (auth.)

VISUALIZATIONINMATHEMATICS,READING
ANDSCIENCEEDUCATION
Models and Modeling in Science Education
Volume 5
SeriesEditor
ProfessorEmeritusJ.K.Gilbert
InstituteofEducation,TheUniversityofReading,UK
EditorialBoard
ProfessorD.F.Treagust
ScienceandMathematicsEducationCentre,CurtinUniversityofTechnology,
Australia
ProfessorJ.H.vanDriel
ICLON,UniversityofLeiden,TheNetherlands
Dr.RosáriaJusti
DepartmentofChemistry,UniversityofMinasGerais,Brazil
Dr.JaniceGobert
WorchesterPolytechnicInstitute
Forfurthervolumes:
http://www.springer.com/series/6931
Visualization in
Mathematics, Reading
and Science Education
Linda M. Phillips
UniversityofAlberta,Edmonton,Canada
Stephen P. Norris
UniversityofAlberta,Edmonton,Canada
John S. Macnab
EdmontonPublicSchools,Edmonton,Canada
123
Prof.LindaM.Phillips Prof.StephenP.Norris
UniversityofAlberta UniversityofAlberta
CanadianCentreforResearchonLiteracy CentreforResearchinYouth,
653EducationSouth ScienceTeachingandLearning
Edmonton,Alberta 7-104EducationNorth
T6G2G5 Edmonton,Alberta
Canada T6G2G5
[email protected] Canada
[email protected]
JohnS.Macnab
AspenDriveEast4208
EdmontonAlberta
T6J2A9
Canada
ISBN978-90-481-8815-4 e-ISBN978-90-481-8816-1
DOI10.1007/978-90-481-8816-1
SpringerDordrechtHeidelbergLondonNewYork
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Preface
Science education at school level worldwide faces three perennial problems that
have become more pressing of late. These are to a considerable extent interwoven
withconcernsabouttheentireschoolcurriculumanditsreceptionbystudents.
Thefirstproblemistheincreasingintellectualisolationofsciencefromtheother
subjectsintheschoolcurriculum.Scienceistoooftenstilltaughtdidacticallyasa
collectionofpre-determinedtruthsaboutwhichtherecanbenodispute.Asaconse-
quence,manystudentsdonotfeelany“ownership”oftheseideas.Mostotherschool
subjectsdosomewhatbetterintheseregards.Forexample,inlanguageclasses,stu-
dentssuggestdifferentinterpretationsofatextandthendebatetherelativemeritsof
thecasesbeingputforward.Moreover,ideasthatareofuseinsciencearepresented
tostudents elsewhere andthenre-taught,oftenusingdifferentterminology, insci-
ence.Forexample,algebraistaughtintermsof“x,y,z”inmathematicsclasses,but
studentsarelaterunabletoseetherelevanceofthattothemeaningoftheuniversal
gas laws in physics, where “p, v, t” are used. The result is that students are con-
fusedandtoooftenalienated,leadingtotheirfailuretoachievethat“extractionof
aneducationfromaschemeofinstruction”whichJeromeBrunerthoughtsohighly
desirable.
The second of these is how to accommodate a “science education for citizen-
ship”, one that is relevant to the needs of all students, in a curriculum which has
traditionallybeenfocusedonthepurpose(albeitusuallydistorted)of“scienceedu-
cation as a preparation to be a scientist/engineer”. While there are commonalities
betweenthetwo,therewillbedifferencesbetweenwhatistaught,howitistaught,
and why it is taught. Teachers need a justifiable basis on which to distinguish
betweenthetwotreatmentsofscience.
Thethirdoftheseisaconsequenceoftheexponentiallyincreasinggapbetween
thephenomenainwhichscienceiscurrentlyinterestedandwhatscienceeducation
seemsabletoaddress.Theinabilityofplannerstoagreetoarollingevolutionofthe
contenttaughthasledtoacurriculumwhichis,toasubstantialdegree,permanently
overloadedandoutofdate.Whilesciencefacesthemodernworld,scienceeducation
seemstooconcernedwiththechallengesofyesteryear.
If science education is to seem important and relevant to young people, then it
must be based, to a far greater degree than at present, on concepts that transcend
setsofalliedphenomenaandtoalesserdegreeonconceptsthataretiedtospecific
v
vi Preface
facts. The current emphasis on “nature of science” is an honest attempt to do so.
Onemajorproblemwiththisapproachisthelackofaconcisedefinitionof“nature
of science”—there is no such thing as “the nature of science”—which arises from
thefactthatscienceisacollectionoftoolsthatareapplicabletoahugediversityof
phenomena,fromthestudyofvirusestothestudyofgalaxies.Asecondmajorprob-
lem isthat the resources available to, as well as the social conditions of, scientific
enquiryareverydifferentfromthoseofschoolscienceeducation.Asattemptscon-
tinuetobemadetoevolveauthenticapproachestotheconductofscientificenquiry
inschools,aworthwhilestepforwardistofocusontheintellectualskillsthatwould
beanintegralpartofallsuchapproaches.Ofthese,learninghowtoproduceanduse
models,thethemeofthisbookseries,hasaverystrongclaimforattentioninthatit
includesskillsthatarevitalnotonlyinsciencebutalsoinothercoresubjects,such
asreading/languageandmathematics.
Modellingisthementalproductionandsubsequentdisplaytoothersofasimpli-
fiedrepresentationofanobject,idea,system,event,process,initiallyproducedfor
aparticularpurpose.Thatpurposeistoprovideanexplanation,whetherofphysical
constitution,behaviour,orcausality,orbetterstillallthree,ofaphenomenon.While
models,theoutcomesofmodelling,ultimatelyresideinthemind,theycanbeshared
with other people in some or all of gestural, material/concrete, visual, verbal, and
mathematical forms. The key element in modelling is visualization which is often
taken to mean either the formation of a mental image or the presentation of that
imageintheworld-as-experienced;however,manyotherassociatedinterpretations
aretobefoundintheliterature.
In “Visualization in Mathematics, Reading and Science Education”, Linda
M.Phillips,StephenP.Norris,andJohnS.Macnabhavebroughttogetherandcrit-
icallyreviewedtheresearchliteratureonthepsychologyofvisualizationaswellas
its relevance to and manifestation in the teaching and learning of the three school
subject areas. It is perhaps a consequence of the range of definitions for “visual-
ization” in use that firm conclusions are difficult to arrive at. The situation might
be summarized as follows: the science education community is convinced on the
valueofvisualizationsinteachingandlearning,thelanguageeducationcommunity
believing it to be useful for particular purposes, while the mathematics educa-
tion community is not at all sure about its place and value. However, the current
stronginterestinresearchaboutvisualizationcould,itistobehoped,leadtofirmer
conclusions.
Such a resolution could provide the basis of an address to the three challenges
faced by science education and outlined above. In respect to intellectual isolation,
mathematical modelling techniques (usually in the form of equations and graphs)
are an invaluable approach to scientific modelling. If such techniques, with their
inbuilt use of visualization, were systematically taught in mathematics education,
then their transfer into and use by science education should be eased. As regards
didactic teaching, the widespread use of visualization in the teaching of the inter-
pretationofwrittentextscouldbetranslatedintoscienceeducation,withbeneficial
outcomes.“Scienceeducationforcitizenship”shouldincludeanintroductiontothe
useandinterpretationofthatsetofvisualizations—heremeaningdiagramsandthe
like—in common cultural use yet which have their origins in science. That set of
Preface vii
representationswillformamajorpartinthepublicpresentationsoftopicalscientific
ideas,theformerthusenablingeasieraccesstothelatter.
Switchingthefocusonvisualizationfromscienceeducationintheforegroundto
the background, considerable benefits can be seen for both reading education and
mathematicseducation.Theseformoneclearargument:scienceprovidesabodyof
phenomena,facts,andideasthatcanbevisualizedthroughbothreadingandmathe-
maticalrepresentations.Thebringingtogetherofthesethreeeducationalareasunder
theumbrellaofvisualizationshouldenablestudentstobecomebettereducatedand
not merely instructed in separate subjects. Phillips, Norris, and Macnab are thus
veryappropriatelyplacedwithinthe“ModelsandModellinginScienceEducation”
series.
London,UK JohnK.Gilbert
Contents
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
PartI AnIntroductionToVisualization
1 ACommonsenseViewandItsProblems . . . . . . . . . . . . . . . . 3
Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
WhyVisualizationMightBeUseful . . . . . . . . . . . . . . . . . . . 6
2 AHistoryofVisualizationinPsychologyandScience. . . . . . . . . 9
EarlyPsychologicalResearch . . . . . . . . . . . . . . . . . . . . . . . 9
RecentTheoriesofVisualizationinCognitivePsychology. . . . . . . . 10
TheDevelopmentofVisualizationinScience . . . . . . . . . . . . . . 13
TheIntroductionofComputerstoScientificVisualization . . . . . . . . 16
ConcludingComments . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 TheConceptofVisualization . . . . . . . . . . . . . . . . . . . . . . 19
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
TheDefinitionsofVisualization . . . . . . . . . . . . . . . . . . . . . 22
WhatConstitutesaGoodVisualization? . . . . . . . . . . . . . . . . . 27
Colour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Realism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Relevance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Interactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Animation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
ConcludingComments . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 CognitiveTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
CognitiveCodingofVisualImages . . . . . . . . . . . . . . . . . . . . 35
UsingCognitiveTheoriestoDesignEffectiveVisualizationObjects . . 37
ConcludingComments . . . . . . . . . . . . . . . . . . . . . . . . . . 41
ix
x Contents
PartII CurrentEducationalResearch
5 VisualizationsandMathematics . . . . . . . . . . . . . . . . . . . . 45
Visual–SpatialImages. . . . . . . . . . . . . . . . . . . . . . . . . . . 46
ComputerVisualizationsandVisualRepresentations . . . . . . . . . . 48
ConcludingComments . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6 VisualizationsandReading . . . . . . . . . . . . . . . . . . . . . . . 51
VisualizationObjectsasMotivators. . . . . . . . . . . . . . . . . . . . 51
Comprehension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
RelevantPropertiesofVisualizationObjects . . . . . . . . . . . . . . . 57
Multimedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
ConcludingComments . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7 VisualizationsandScience. . . . . . . . . . . . . . . . . . . . . . . . 63
VisualRepresentations,Diagrams,andAnimation . . . . . . . . . . . . 63
DynamicMediaandLearningPerformance . . . . . . . . . . . . . . . 66
Animations,Visualizations,andConceptualChange . . . . . . . . . . . 67
ConcludingComments . . . . . . . . . . . . . . . . . . . . . . . . . . 74
PartIII CautionsandRecommendations
8 ResearchandGuidelinesonComputer-GeneratedVisualizations . . 77
9 ConcludingComments,Recommendations,andFurther
Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
VisualizationObjects . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
AnimationsandComputer-BasedVisualization . . . . . . . . . . . . . 86
RecommendationsforTeachers . . . . . . . . . . . . . . . . . . . . . . 87
AreasforFutureResearch . . . . . . . . . . . . . . . . . . . . . . . . 88
FinalWord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
AuthorIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
SubjectIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Overview
Thistimeisbothexcitingandcontroversialforresearchonvisualization.Itisexcit-
ing because computers have made it possible for graphics, images, illustrations,
animations, and virtual reality to reach new heights in colour, realism, interactiv-
ity,appeal,andcomplexity.Manyproducersofvisualizationmediasimplyassume
thatvisualizationmakeslearningeasier.Infact,someadvocatesimplythatvisual-
izationsarethebestwaytolearn.Itisacontroversialtimebecausetheevidenceis
sometimesequivocalandfrequentlyunclearonwhetherthesenewheightsachieved
throughpowerfulcomputersactuallyenhancelearning.Nonetheless,theincreased
use of technology and the visualizations it can make available for teaching and
learningcannotbeignored.
This book is about the history of visualizations dating back to the 1880s, the
evolution of the concept since the first studies were conducted in the early 1960s,
and a comprehensive analysis and synthesis of empirical studies across the disci-
plines of mathematics, reading, and science education. The questions of whether
there is a defensible model of visualization and whether the use of visualizations
haspedagogicalmeritareraisedanddiscussed.Comments,recommendations,and
suggestionsforfutureresearchareproposed.
There is a dearth of research and scholarship on visualizations. The total num-
berofempiricalresearcharticlesweidentifiedinmathematics,reading,andscience
education on the topic of visualization for the last 50 years is approximately 250,
whichisremarkablylowwhenplacedinthecontextofallthejournalarticlespub-
lishedacrossthesethreesubjectareasduringthesameperiodoftime,whichnumber
in the thousands. One important conclusion of this book is that there are a num-
ber of important open questions with regard to the development and utilization of
visualizationobjectsandactivitiesineducationthatwarrantfurtherempiricalstudy.
A recent GoogleTM search on “visualization and education” yielded about
800,000results.Giventhecomparativelysmallnumberofempiricalarticlesinthe
area, this is a remarkable number. Whatever visualization in education is believed
to be and whatever the evidence is for its efficacy, a lot of people are taking note
of it. A number of distinct ideas seem to be rolled into the current discourse on
visualization.Onecommonusageinvolvestheideathatvisualizationissomething
thatpeopledo—theyvisualize.Thisprocessistypicallyseenasamentalprocessin
whichcertainthoughtshavecontentthatisrelatedto—perhapsisidenticalto—the
xi