ti-nspire as a technological support in learning conics...
TRANSCRIPT
TI-Nspire as a technological support in learning conics: the
case of ellipse
CCHSur,UNAMCienciaForense,UNAMCECyT 13,IPN
Á. HomeroFloresS.AdrianaGómezR.
G.XochitlChávezP.
Introduction
WewilltalkabouthowstudentsreactwhentheyinvolveinMathematicalModelling(MM)tasks,andabouttheirperformancewiththeaidofCAScalculators.
ThiswillbeillustratedwithoneexamplefromanAnalyticalGeometrystudent-basedcourseattheSouthCampusoftheColegio deCiencias yHumanidades (CCH)-UNAM.
WefocusonaMMactivityconcerningtheconceptofellipseasalocus.
StudentCenteredApproach
LearningMathematics,DoingMathematicsteachingmodelservedastheoreticalbackgroundaswellasamethodologicalsupport.
ItisbasedonthetheoreticalassumptionsofVigotsky,DeweyandBrousseau(amongothers).
StudentCenteredApproach
Students’learningisachievedthroughexploring,andproblemsolvingactivities.
Learningactivitiesaredevelopedinateaching-learningenvironmentimmersedinaformativeassessmentcontext.
Theseactivitiesaretakenasteachingexperimentsandformativeassessmenttoolsareusedasresearchtools.
ModellinginaStudentCenteredMathCourse
IntermediateModel
Mathematization
ModelVerification
Translationintophenomenon
terms
Problematization
PhenomenonIdentificaction
MathematicalModel
ModellinginaStudentCenteredMathCourse
Modellingmathactivitiescouldbeaddressedfromtwostandpoints:thinkandactperspective,andfittingcurveperspective
ContextandDevelopment
WedidthestudywiththreethirdsemesterclassesatCCH(agesbetween16-17).
OneoftheclassesdidnotuseCAScalculators.
Studentssolvedtheproblemsworkingin2-3membersteams;theinformationofthesolvingprocesswasgatheredonworksheets.
ContextandDevelopment
Assessment,andthusresearch,informationwastakenfromthreeMathematicalModellingproblems:TheTable:wherestudentsshoulduseellipse’sdefinitioninordertosolvetheproblem.TheBridge:inwhichthereistheneedtofindanellipseequationanddosomecalculations.Whispers:wherestudentsexploresomecharacteristicsofellipsesconcerningthetwofociandsoundwaves.
ThetableI
Ifyouwanttomakeanellipsoidaltableandyouwantedtocutitfromarectangularwoodensheet,1.5mx3m,astohavethemaximumareapossibleonthetable.Howcanwedrawtheellipseonthewoodensheetusingastring?Whereshouldwelocatethefociandwhatlengthshouldourstringhave?Explainyouranswers.Giveanequationforsuchanellipse.
ThetableII
Ifyouwanttocutanellipsoidaltableoutofarectangularwoodensheet(1.5mx3m)insuchawaythatyouhavethemaximumtablearea,howcanyoudrawtheellipseonthesheetusingastring?What’sthelengthofthestring?What’stheequationofyourellipse?Explainyouranswers.
Development1
Development2
Development3
Development4
Results
Concerningtheperformanceofourstudentswecanhighlightthreeaspects:a) Theconceptionsthatteachershaveontheirabilityto
understandandsolvethiskindofproblems;thisleadustodelivertwoversionsofthesameproblem.
b) TheperformancewasbetterwhenusingaCAScalculator.Wethinkthatthisissobecausecalculatorsallowafasterandmoreaccurateverificationofproblemresults.
c) Studentshavetodomorealgebraandpracticetheiralgebraskills.
Results
ConcerningthereactionsontheuseofCAScalculatorsourstudentsweremoremotivatedthanwhentheyuseonlypaper,pencilandascientificcalculator(notCAS).
Somestudentsmanifestedtheirenthusiasmbycallingthem“thelittlemagicalmachines”.
Studentsfeltmotivateddevelopingmathmodelling activities.
Someconclusions
TheuseofCAStechnologyisabetterwaytoexploremathematicalmodellingproblems,becauseitfostersamoreelaboratedmanipulationofalgebraicexpressions.
CAStechnologyallowsstudentstoquicklyverifythecorrectnessoftheirsolutionsandabetterunderstandingoftheproblemathand.
CAStechnologyinmathematicalmodelingactivitiesmotivatesstudentsonthelearningofmathematics.
