English language proficiency and spatial visualization in middle school students' construction of the concepts of reflection and rotation using The Geometer's Sketchpad

192 Pages·1995·3.4 MB·English

by  Dixon, Juli Kim

ENGLISHLANGUAGEPROFICIENCYANDSPATIALVISUALIZATIONIN
MIDDLESCHOOLSTUDENTS'CONSTRUCTIONOFTHECONCEPTSOF
REFLECTIONANDROTATIONUSINGTHEGEOMETERSSKETCHPAD
JULIKIMDIXON
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
1995
Copyright1995
by
JuliKimDixon
Thisdissertationisdedicatedtothreegenerationsoflifeandlove.
Inlovingmemoryofmygrandfather,
AlbertP.Harap,
whosebeliefinmewasinvaluable,
tomyparents,
HarveyandJoyInventasch,
whoinstilledinmearespectforeducation,
andtomyhusband,
MarcToddDixon,
whorespectedmydreamandmadeithisown.
ACKNOWLEDGEMENTS
Mygratitudeisextendedtothemanypeoplewhohaveprovided
academicandemotionalsupportthroughoutthedissertationprocess.
ToProfessorMaryGraceKantowski,mychairandmentor,who
providededucationalchallengesandsupport, Iowemyfuture
contributionsasamathematicseducator. Iamthankfultomy
committeemembers,eachofwhomprovidedguidancethroughoutthe
dissertation process. Professor David Millershared hisstatistical
expertise. ProfessorClemensHallmanledmetoadeeper
understandingoftheneedsofstudentswith limited English
proficiencyand providedfinancial supportthrough the Bilingual
EducationandMinorityLanguagesAffairsFellowship. Professor
DonaldBernardcontributedtomygrowththroughhisexperiencesas
aneducator. ProfessorCharlesNelsonenhancedmyunderstandingof
mathematicsfromtheviewpointofa mathematics educator.
IamgratefultoSusanLeeandthemathematicsfacultyand
studentsofthecentral Floridamiddleschoolformakingthe
research for mydissertation possible.
IamespeciallyindebtedtoNickJackiwofKeyCurriculum
Pressforprovidingmewiththeexperimentalversionof The
Geometer's Sketchpadusedinthestudyandprovidingparticipating
teacherswith The Sketchpadforthecontinuedusewiththeir
students. Nickalsoprovidedongoingandgreatlyappreciated
technical support.
IV
IamgratefulforthefinancialassistanceprovidedbyDr.
CharlieT.CouncilandtheFloridaEducationalResearchCouncilin
supportofthisstudy.
Iamforevergratefultomyfamily,especiallytomyparents,
HarveyandJoyInventasch,myhusband,MarcToddDixon,andmy
friend,ThomaseniaLottAdamswhomIconsiderfamily. Thesevery
specialpeoplehaveprovidedmewiththeloveandsupportthatonly
familycanprovide. Iwouldneverhavebecomethepersonand
mathematicseducatorIamtodaywithouteachandeveryoneof
them.
TABLEOFCONTENTS
page
ACKNOWLEDGEMENTS iv
ABSTRACT viii
CHAPTERS
I DESCRIPTIONOFTHESTUDY
Introduction 1
Statementofthe Problem 5
SignificanceoftheStudy 8
OrganizationoftheStudy 9
II LITERATUREREVIEW
Overview 11
Theorietical Background 11
Studies on Transformations 17
Visualization 33
Limited English Proficient Students 46
Summary 49
III METHODOLOGY
Research Objective 52
Measures 53
Pilot Study 56
Sampling Procedures 61
ExperimentalTreatmentand Procedures 62
ResearchDesign 67
VI
V
I RESULTS
Descriptive Statistics 70
Limitations ofthe Study 78
V QUALITATIVERESULTS
Methodology 81
Computer Projects 83
Observations 90
Data from Reflection/Rotation Instruments 105
Icon Questionnaire 108
VI CONCLUSION
Summary 110
Discussion 116
Implications 123
Recommendations 124
SuggestionsforFutureResearch 127
APPENDICES
AB PPAAPPEERRAANNDDPPEENNCCIILLRREEFFLLEECCTTIIOONN//RROOTTAATTIIOONNIINNSSTTRRUUMMEENNTT....129
OVERLAYS 140
C TRAININGLESSONS 147
D ANGLEANDDISTANCEMEASUREACTIVITIES 150
E EXPERIMENTALTREATMENTLESSONS 158
F REFLECTIONANDROTATIONKEYS 165
G REFLECTIONGAMESCREEN 170
REFERENCES 171
BIOGRAPHICALSKETCH 180
vii
AbstractofDissertationPresentedtotheGraduateSchoolofthe
UniversityofFloridainPartialFulfillmentoftheRequirementsfor
theDegreeofDoctorofPhilosophy
ENGLISHLANGUAGEPROFICIENCYANDSPATIALVISUALIZATIONIN
MIDDLESCHOOLSTUDENTS'CONSTRUCTIONOFTHECONCEPTSOF
REFLECTIONANDROTATIONUSINGTHEGEOMETER'SSKETCHPAD
By
JULIKIMDIXON
May1995
Chairman: EleanoreL.Kantowski
MajorDepartment: Instructionand Curriculum
Thisstudywasdesignedtoinvestigatetheeffectsofadynamic
instructional environment, English proficiency, and visualization
level, independentlyand interactively, on middleschool students'
constructionoftheconceptsofreflectionand rotation. Also
examinedweretheeffectsofadynamicinstructionalenvironment
onstudents'two-andthree-dimensionalvisualization.
Thedynamicinstructional environmentinvolved exclusive use
ofThe Geometer'sSketchpadwithlessonscreatedforthepurpose
ofallowing forstudentdiscoveryofproperties ofreflection and
rotation. Studentswerealsoprovidedextensiveopportunitiesto
perform the transformations.
After controlling for initial differences, it was concluded that
students experiencing the dynamic instructional environment
VIII
significantly outperformed students experiencing a traditional
instructionalenvironmentoncontentmeasuresoftheconceptsof
reflection and rotation aswellason measuresoftwo-dimensional
visualization. Thestudents' instructional environmentdid not
significantly affect their three-dimensional visualization. There
was nostatisticallysignificantdifferenceson anyofthedependent
variables betweenthe performances of limited English proficient
studentsandthoseoftheirEnglishproficientpeerswhenthesame
instructional environmentwas experienced.
Observationsprovidedexamplesofhowstudentscommunicate
aboutmathematics,visualizemovement,andconstructconceptsof
reflection and rotation while experiencing a dynamic instructional
environment. Concreteinformationwasgainedregardingthedepth
ofstudents'knowledgeaboutconceptsinvolvedwith reflectingand
rotating. Insightwasobtainedintotheclassattitudesaboutand
understanding of transformations.
ix
DESCRIPTCIHOANPOTFERTHIESTUDY
Introduction
TheCurriculumandEvaluationStandardsforSchool
Mathematics(NationalCouncilofTeachersofMathematics(NCTM),
1989) includethefollowing objectives in the standardformiddle
levelgeometry:"Ingrades5-8,themathematicscurriculumshould
includethestudyofthegeometryofone,two,andthreedimensions
inavarietyofsituationssothatstudentscanvisualizeand
representgeometricfigureswith special attention to developing
spatial sense; [and] exploretransformations ofgeometricfigures"
(p.112). Thisstandardisnotbeingimplementedinmanymiddle
schoolsintheUnitedStates.The SecondInternationalMathematics
Study: ReportfortheUnitedStates(SIMS) (Crosswhite, 1985)
identifiedtopicstaughtin othercountrieswhichwere notcovered
bythemajorityofeighth-gradeclassesintheUnitedStates. "For
example,topicsintransformational geometry, taughtin some
countries,werereportedtaughtbyonly12%ofUnitedStateseighth
gradeteachers"(p.20). Furthermore,theresultsofthestudy
indicated thatteachers primarilytaughtaccording totheirtextbook
withvery little useofmanipulativesorother materials not included
1