ti-nspire as a technological support in learning conics...

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.

A. HomeroFloresSamaniegoahfs@unam.mx

AdrianaGómezReyesorodelsilencio@yahoo.com.mx

G.Xochitl ChávezPérezmatematica60_xch@hotmail.com

That’sallfolks