Table Of ContentEFFECTIVENESSOFCONCRETEANDCOMPUTERSIMULATED
MANIPULATIVESONELEMENTARYSTUDENTS'LEARNINGSKILLSAND
CONCEPTSINEXPERIMENTALPROBABILITY
By
FELICIAM.TAYLOR
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHE
UNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHE
REQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
2001
Thisdissertationisdedicatedtomymother,
LauraAnnRoberts,
whoseloveandbeliefIwasneverwithout
and
tomyhusband,
ReginaldEugeneTaylor,
mymateandfriend.
ACKNOWLEDGMENTS
Mygratitudeisextendedtothemanypeoplewhoprovidedagreatdealofsupport
formebeforeandduringthedissertationprocess.
ToDr.ThomaseniaLottAdams,mychairandmentorwhoprovidedsupportand
educationalchallenges, Iowemyfuturecontributionsasamathematicseducator. Iam
thankfultomycommitteemembers,eachofwhomprovidedguidancethroughoutthe
dissertationprocess. ToDr.Miller,Iowegreatthanksforhisstatisticalandprofessional
advice. ToDr.SebastianFoti,andDr.Li-ChienShen,Iowethanksfortheiracademic
guidance.
IamespeciallyindebtedtoDr.IsraelTribbleoftheFloridaEndowmentFundfor
HigherEducationforsupportingmeasaMcKnightDoctoralFellowfinanciallyand
emotionally.
Iamforevergratefultomyfamily,especiallymyhusbandReginaldEugene
Taylor,whowasallIneededhimtobe;mymother,LauraRoberts;mysiblings,Carolyn,
Prudence,Eric,andChantell;andmyfather-in-law,EddieLeeTaylor,whomI
consideredmyfather. Theseveryspecialpeoplehaveprovidedmewiththeloveand
supportthatonlyfamilycanprovide. Ioweacontinuousefforttoimproveselfand
empowerothersthrougheducation.
iii
TABLEOFCONTENTS
Page
ACKNOWLEDGMENTS
iii
ABSTRACT vi
CHAPTERS
1 DESCRIPTIONOFTHESTUDY 1
Introduction 1
PurposeandObjectivesoftheStudy 12
RationalefortheStudy 13
SignificanceoftheStudy 14
OrganizationoftheStudy 16
2 LITERATUREREVIEW 17
Overview 17
TheoreticalFramework 17
Constructivism-GroundedResearch 22
ConcreteManipulativesforTeachingMathematics 44
TechnologyandSimulatedManipulativesintheClassroom 56
Probability 62
Summary 68
3 METHODOLOGY 71
OverviewoftheStudy 71
ResearchObjective 71
DescriptionoftheResearchInstruments 72
PilotStudy 74
ResearchPopulationandSample 78
Procedures 79
DataAnalysis 82
IV
4 RESULTS 84
OtherFindings 89
LimitationsoftheStudy 91
5 CONCLUSION 93
Summary 93
Discussion 94
Implications 96
Recommendations 97
APPENDICES
A EXPERIMENTALPROBABILITYINSTRUMENT 100
B EXPERIMENTALFRACTIONINSTRUMENT 108
C TREATMENTLESSONS '. 112
D TEACHERCONSENTFORM 140
E PARENTALCONSENTFORM 142
F STUDENTCONSENTSCRIPT 145
REFERENCES 146
BIOGRAPHICALSKETCH 161
AbstractofDissertationPresentedtotheGraduateSchoolofthe
UniversityofFloridainPartialFulfillmentoftheRequirementsfor
theDegreeofDoctorofPhilosophy
EFFECTIVENESSOFCONCRETEANDCOMPUTERSIMULATED
MANIPULATIVESONELEMENTARYSTUDENTS'
LEARNINGSKILLSANDCONCEPTSIN
EXPERIMENTALPROBABILITY
By
FeliciaM.Taylor
August2001
Chairperson: ThomaseniaLottAdams
MajorDepartment: SchoolofTeachingandLearning
Thisstudywasdesignedtoinvestigatetheimpactofusingconcrete
manipulativesandcomputer-simulatedmanipulativesonelementarystudents'learning
skillsandconceptsinexperimentalprobability.Ofprimaryinteresttotheresearcherwas
students'abilitytopredictoutcomesofsimpleexperiments.Asecondaryinterestwasthe
incidentalfractionlearningthatmightoccurasstudentsengageintheexperimental
probabilityexperiences.
Theresearchsampleconsistedof83fifth-gradestudents. Therewerefour
treatmentgroups. TreatmentGroupIstudentsreceivedcomputerinstruction. Treatment
GroupIIstudentsreceivedmanipulativeguidedinstruction. TreatmentGroupIII
studentsreceivedbothcomputerinstructionandmanipulativeguidedinstruction.
TreatmentGroupIVservedasacontrolgroupandreceivedtraditionalinstruction. The
researcherusedananalysisofcovariance(ANCOVA). Aftercontrollingforinitial
VI
differences,theresearcherconcludedthatstudentsexperiencingthecomputerinstruction
onlysignificantlyoutperformedstudentsexperiencingatraditionalinstructional
environmentregardingexperimentalprobabilitylearningskillsandconcepts.
Vll
CHAPTER
1
DESCRIPTIONOFTHESTUDY
Introduction
WhilethecurriculumintheUnitedStatescontinuestofocusonbasicskillswell
pastthefourthgrade,classroomsinJapanandGermanyemphasizemoreadvanced
concepts—includingalgebra,geometry,andprobability(Riley,1998). Theaimofthe
UnitedStatesistobefirstinscienceandmathematics,teachersmayneedtointroduce
childrentomoreadvancedtopicsatearliergradelevels. PrinciplesandStandardsfor
SchoolMathematics,publishedbytheNationalCouncilofTeachersofMathematics
(NCTM,2000),recognizesprobabilityasanadvancedtopicthatshouldbelearnedby
studentsintheK-12curriculum.InthePrinciplesandStandards,emphasisisplacedon
introducingthesametopicsandconceptsthroughoutthePreK-12curriculum. Young
childrenneedtoexploretheprocessofprobability.Thestudyofprobabilityintheearly
gradesprovidesastrongerfoundationforhighschoolstudents(NCTM,2000). Bruner
(1960)statedinhisdiscussionofthespiralcurriculum,
Iftheunderstandingofnumber,measure,andprobabilityis
judgedcrucialinthepursuitofscience,theninstructioninthese
subjectsshouldbeginasintellectuallyhonestlyandasearlyas
possibleinamannerconsistentwiththechild'sformsofthought.
Letthetopicsbedevelopedandredevelopedinlatergrades,
(pp.53-54)
Healsobelieved,
Ifonerespectsthewaysofthoughtofthegrowingchild,ifoneis
courteousenoughtotranslatematerialintohislogicalformsand
challengingenoughtotempthimtoadvance,thenitispossibleto
introducehimatanearlyagetotheideasandstylesthatinlaterlife
makeaneducatedman. (p.52)
Theforegoingreasonsseemtopointtotheteachingofexperimentalprobabilityconcepts
beginningintheelementarygrades.
Probability
"Aswithotherbeautifulandusefulareasofmathematics,probabilityhasin
practiceonlyalimitedplaceinevensecondaryschoolinstruction"(Moore,1990,p.119).
Thedevelopmentofstudents'mathematicalreasoningthroughthestudyofprobabilityis
essentialindailylife. Probabilityrepresentsreal-lifemathematics. Probabilityalso
connectsmanyareasofmathematics,particularlynumbersandgeometry(NCTM,1989).
"Researchinmedicineandthesocialsciencescanoftenbeunderstoodonlythrough
statisticalmethodsthathavegrownoutofprobabilitytheory"(Huff,1959,p.11).Moore
(1990)stated,
Probabilityisthebranchofmathematicsthatdescribesrandomness.
Theconflictbetweenprobabilitytheoryandstudents'viewofthe
worldisdueatleastinparttostudents'limitedcontactwith
randomness. Wemustthereforepreparethewayforthestudyof
chancebyprovidingexperiencewithrandombehaviorearlyinthe
mathematicscurriculum,(p.98)
Anunderstandingofprobabilitytheoryisessentialtounderstandsuchthingsaspolitics,
weatherreports,genetics,statelotteries,sports,andinsurancepolicies.AsshownTable
1,thelistofquestionspresentedinthedifferentareasshowstheneedforexperimental
probability. Thesequestionsrequireconsiderationsofprobabilitiesandwhattheymean
(Huff,1959).
Table1
RealLifeMathematicsUsingExperimentalProbability
Example Description
Politics Arandomsurveyofvotersshowthat381outof952areplanning
tovoteforCandidateMcCainintheprimaryelection. Whatis
theprobabilitythatarandomlyselectedvoterwillvotefor
CandidateMcCain?
WeatherReports Theprobabilityofraintodayis70%. Whataretheoddsinfavor
ofrain? Whataretheoddsagainstrain?
Genetics Ingenetics,wecanuseprobabilitytoestimatethelikelihoodfor
brown-eyedparentstoproduceablue-eyedchild.Thegenefor
browneyesinhumansisdominantoverthegeneforblueeyes.If
eachparenthasadominantbrownandarecessivebluegene,
whatisthechancethattheirchildwillhaveblueeyes?
StateLotteries Alotteryconsistsofchoosing6numbers,thefirst5numbers
beingoneofthedigits0-9andthesixthnumberbeingfrom0-
39. Howmanypossiblesetsoflotterynumbersareavailablefor
selection?Ifthewinningnumbersarerandomlyselected,what
istheprobabilityofwinningwithasingleticket?
Sports Softballstatistics(NCTM,1989,p.111)
Home runs 9
Triples 2
SDionugblleess 2146
WOaultkss 3181
Total 1OO
Aboveistherecordofaplayer'slast100timesatbatduringthe
softballseason. Whatistheprobabilitytheplayerwillgeta
homerun? Whatistheprobabilitythattheplayerwillgetahit?
InsurancePolicies Insurancecompaniesusetheprincipleofprobabilityto
determineriskgroups. Onewayoffiguringoutwhatinsurance
youneedisbylookingattheprobabilityoftheeventandthe
financiallossitwouldcause.Whatistheprobabilityofmen
between18-25yearsofagebeinginvolvedinacaraccident?
Determineifthecostofeachoccurrenceishighorlow.
