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History and Epistemology in Mathematics Education

Le Rôle de L' Association Des Professeurs de Mathématiques de L' Enseignement in elementary arithmetic — in everyday language and waiting by now another ...



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HistoryandEpistemology

inMathema ticsEducation

Proceedingsofthe

5 th

EuropeanSummerUniver sity

Prague

July19-24,2007

Publisher:Vydavatelsk!servis,Plze"

Editors:EvelyneBarbi n,Na

aSt ehlíková,ConstantinosTzanakis,2008

ISBN978-8 0-86843-19-3

3

Contents

Preface13

1.History andEpistemologyasto olsforanin terd isciplinarya pproachin

theteac hingandlearningofMathemati csandtheSci ences15

PlenaryLecture

1.1LeoCO RRY

AxiomaticsBetweenHilbertandthe NewMath:DivergingViewson MathematicalResearchandt heirConsequencesonEducation....................17 Workshopsbasedonhi storicaland epistemological material

1.2Didi erBESSOT

CalculusbyAugustin Fres nel(1788-1827)toImprovetheE ciencyofParabolic

1.3Franti ˇsekKU

RINA,Chr istianSIEBENEICHER

AlgebraandGeometry inElement aryandSecondarySchool.....................29

1.4Fr´ ed´ericMETIN

AdamFrita ch'sNewFortification...............................................39

1.5Yanni sTHOMAIDIS,Const antinosTZANAKIS

OriginalTextsintheCl assroom.................................................49 Workshopsbasedonpe dagogicalanddi dacticalmateria l

1.6Mic helROELENS

TheVolu meofaPyramidThr oughtheA ges: Tosliceornottoslice,that's the

Oralpresentations

1.7Chri stianGERINI

LesAnna lesdeMath´ematiquesdeGergonne:Un journaldu 19 `eme si`ecle

num´eris´eetm´ediatis´eaub´en´eficed'unei nterdisciplinarit´eentremath´ematiques,

histoire,didactiqueetphilosophie ...............................................71

1.8RogerGOD ARD

LinearProgrammi ngandItsMathematicalRoots................................83

1.9Ladis lavKVASZ

HistoricalandEpistemological Aspects ofTeachingAlgebra......................91

1.10Konst antinosNIKOLANTONAKIS

Didweha ve"Rev olutions"inMa thematics?ExamplesfromtheHistoryo f MathematicsinthelightofT. S.Kuhn 'shisto ri calphilosophyofsc ience.........97 4

1.11Syl viePROVOST

Pourquoi"fairehistoire» dansl 'industrie,larecher cheetl'enseignement ,selon C.Combes (1867),W.H.B ragg(1912),P .L angevin(1926)?....................107

1.12Man-K eungSIU

HarmoniesinNature:ADialo guebet weenMathematicsand Phy sics.............115

1.13Atha nassiosSTRANTZALOS

GeometricTransformationsas aMeansfortheIntroductionofInterdisciplinarit y andofEdu cationalElemen tsinHighSchool.....................................125

Shortor alpresentations

1.14Ji

´ıCIHL

A

R,Pe trEISENMANN,Magda lenaKR

ATK

A,Pe trVOP

ENKA

1.15Mirand aISAIAS

LinearMovementofO bjects:D i

erencesbetweenAr istotle'sand highsc hoolstudents 'analysis(abstract).........................................143

1.16Anna MariaMERCURIO,N iclaPALL ADINO

Onth eResoluti onofAlgebraicEquations(abstract).............................145

1.17Ra

aelePISANO EvaristeGalois'GroupThe ory:Epis temologicalnotesonitslogical structure

1.18Sevim SEVG

I Harmonographapplicationintoourle ssons(abstract)...........................149

1.19Domi niqueTOURN

ES

GeometricalApproachtoDi

erentialEquations:From historytomathematics

2.Intro ducingahistoricaldimensioni nthe teachingandlearningof

Mathematics153

PlenaryLecture

2.1Luis PUIG

ResearchingtheHistoryofAlgebra icIdeasfr omanEducationalPoint ofView

Paneldiscussion

2.2Evely neBARBIN,FritzSCHWEI GER,LuisRADFORD,FrankSW ETZ

MathematicsofYesterdayan dTeaching ofToday................................157 5 Workshopsbasedonh istoricala ndepistemologi calmaterial

2.3Rit aBASTOS,Eduardo VELOSO

Episodesofthe History ofGeom etry:TheirInterpretationThrough Models inDy namicGeometry..........................................................171

2.4RobertB URN

TowardsaDefinitionof Lim it...................................................181

2.5Renau dCHORLAY,Philipp eBRIN

UsingHistor icalTextsintheClassroom:Exa mplesinStatisti csandPr obability

2.6CarlosC ORREIADESÁ

ConqCoutbes AvecLeurH istoire:laQuadrat rice,laSpirale,laConc ho¨ıde,la Cisso¨ıdeet laCyclo¨ıde..........................................................195

2.7Ale jandroS.GONZ

ALEZ-MART

IN,C arlosCORREIADES

A NewTea chingPractices.........................................................211

2.8Odil eKOUTEYNIKOFF

AboutFibonac ci'sBookofSquares:Howelementaryt oolscansolve quite elaborateproblems ..............................................................225 Workshopsbasedonpe dagogicalanddi dacticalmateria l

2.9Mic helBALLIEU,Marie-France GUISSARD

PourUneCu ltureMath ´ematiqueAccessible`aTous..............................237

2.10Adri anoDEMATT

E HistoricalDocumentsinEverydayC lassroomWork.............................251

2.11Isabel CristinaDIAS

Fromtheori ginaltext sofPedroNunestothemathe maticsclassroo mactiv ities

2.12Vict orKATZ

HistoricalModulesfortheTeac hingandLearningofMathema tics...............261

2.13Mich aelKOURKOULOS,Constan tinosTZANAKIS

EnhancingStudents 'UnderstandingontheMethodofLeastSqu ares:an InterpretativeModelInspiredByHistorical andEpistemologi calConsiderations..271

2.14Mich elaMASCHIETTO,FrancescaMARTIGNONE

ActivitieswithMathematicalM achines:Pant ographsandCurveDrawers........285

2.15Theo dorusPASCHOS,VassilikiF ARMAKI

TheIn tegrationofGeneticMomentsintheHi stor yofMathematicsandPhysics inth eDesigningofD idacticActivitiesAimingtoInt roduce First-Year 6

2.16Chri sWEEKS

UsingHistor icalMaterialintheMathematic sClassroom:Condorcet'sPa radox..311

2.17Robin WILSON

SolvingDottyProble ms(abstract)...............................................319

2.18Greis yWINICKI-LANDMA N

PlayingwithF ractionsaLaL eibniz.............................................321

Oralpresentations

2.19EvaC AIANIEL LO

LePr oblemeD'Oiseaux:Procede sdeResolutionDansL'Histoirede s

2.20Kathleen CLARK

ReflectionandRevision:Firs tExperien ceswithaUsingHistoryCou rse.........343

2.21JohanH DEKLERK

HistoryandEpistemolo gyAsToo lsinTeachingMathematics....................353

2.22EleniD IMITRIADOU

DidacticalandEpistemological Issues RelatedtotheConceptofProof:Some mathematicsteachers'ideasabo uttheroleofproofinGreeksec ondarycurriculu m363

2.23Mich aelR.GLAUBITZ

TheU seofOriginalSo urces intheClassroom:The oreticalPerspectivesand EmpiricalEviden ce.............................................................373

2.24HansN ielsJAHNK E

StudentsWorkingonThe irOwnIdeas:Bernoulli 'sLec turesontheDi erential

2.25Po-Hu ngLIU

InvestigationofStudents'Perceptionsofth eInfinite:A HistoricalDime nsion....385

2.26Andr easPOULOS

2.27Mariad oC´euSILV A

BentoFernan des'TratadodaArtedeArismetica(P orto,1555)(abstract).......405

2.28Frank J.SWETZ

HistoricalProblems:AValuable ResourceforMathematicsClas sro omInstruction

Shortor alpresentations

2.29OscarJo˜aoAB DOUNUR

AnEx hibitionAsaTooltoApproachDida ctical and HistoricalA spects ofthe RelationshipBetweenMathematicsand Music(abstract).........................409 7

2.30Fun daGONULATES

MathematicsTheather:Mathematician sonStage(abstract).....................411

2.31Gavi nHITCHCOCK

ApproachingMathematicalAnalys iswiththeHelpofItsHistory(abstract).......413 2.32U eTh omasJANKVIST

2.33JimJ .TATTE RSALL

BringingRamanujanInto theClassroom(abstract)..............................417

2.34PaolaG ALLOPIN,LucianaZ UCCHERI

MathematicalMethodsinApproachingthe ConceptsofA rea andVolume

3.Histor yandEpistemologyin Mathematicstea cherseducation 421

PlenaryLectur e

3.1Frit zSCHWEIGER

TheGr ammarofMathematicalSymb olis m......................................423 Workshopsbasedonhi storicaland epistemological material

3.2Giorgio T.BAGNI,Cateri naVICEN TINI

HistoryandEpistemol ogyofC alculusandAlgebra,CelebratingLeonhardE uler's

Tercentenary:CooperativeLearningand E

ectivenessofPerspectiveTeacher

3.3Jind ˇrichBE

CV A

R,Vlas timilDLAB,DagHRUB

Y,Fr antiˇsekKU

RINA EducationofMathematicsT eachers(InAlgebra andGeometry,inParticular)...441

3.4AnneBOY

E WhenHighSc hoolStudents AreTaughtChasles':" G´eom´etrieSup´ erieure" Lorsquel'onenseigna itla"g´eom´etriesup´ erieure"deChasles`alafinducursus

3.5Mich aelN.FRIED,AlainBERNAR D

ReadingandDoingMat hematicsi ntheHumanistTr adition:AncientandModern

3.6Jean- PaulGUICHARD

Vi`eteandt heAdventofLit eralCalculus........................................475

3.7Martin eB

UHLER,AnneMICHEL-P AJUS

AboutDi

erentKindofPro ofsEncounter edSpe cificallyinArithmeti c(Fermat's LittleTheorem):Fe rmat'sLittleTheorem.......................................489 8

3.8Ste liosNEGREPONTIS,DionysiosLAM PRINIDIS

ThePlat onicAnthyphaireticInterpret ationofPappus'AccountofAnalysisand

3.9Irene POLO-BLANCO

RegularandSemi-Regu larPolyto pes:AdidacticapproachusingBoole Stott's

3.10LuisR ADFORD

GeneralityandMathematicalIndetermin acy:Variables,U nknownsand Parameters,andtheirSymbolizatio ninHisto ryandintheClass room(abstract).521 Workshopsbasedonpe dagogicalanddi dacticalmateria l

3.11Mil anHEJN

Y,Na aSTEH LÍKOVÁ DidacticSimulationofHist oricalDiscoveriesinMathemat ics....................523

3.12Nits aMOVSHOVITZ-HAD AR

Today'sMathematical NewsAreTomorrow'sHistory:Interweavi ngMathNews SnapshotsintheTeachingo fHighSch oolMath..................................535

3.13LeoROGER S

EarlyMethodsforSolvin gRealProblems(abstract).............................547

3.14BjørnSM ESTAD

VariousMaterialsfor PrimarySchoolTeacherTraini ng: Or:Cany oudosomet hingevenif youca n'tdomuch?...........................549

Oralpresentations

3.15Marti naBE

VÁ

OVÁ

HistoryofMathematic sasaPa rtofMathematicalEducation....................561

3.16Alain BERNARD

HistoryofScienceandTec hnology intheFrenchSyste mforTe acherTraining: AboutaRecent Ini tiative........................................................569

3.17Anton ´ınJAN &A'

IK TheIn fluenceofITontheDevelopmentofMathemati csandont heEducation ofFu tureTeachers..............................................................577

3.18James F.KIERNAN

HowMuch HistoryofMath ematicsShouldanEle mentary MathematicsTeacher

3.19Bernadete MOREY

NavigationInstrumentsandTeacher Training...................................587

3.20Sifis PETRAKIS

TheRole oftheFifth Postulate intheEu clideanCons tructionofParallels.......595 9

3.21Klaus VOLKERT

ThePr oblemoftheDimensi onso fSpaceintheHi storyofGeometry.............605

Shorto ralpresentations

3.22Kamila

MEJRKOV

A SolvingLogicalPr oblemsandCommunicativeSk illsBytheGroupsofPupils

3.23E.Meh met OZKAN,HasanUNAL

InfluenceofMathematiciansinH istory onPre-ServiceMathematicsTea chers' BeliefsA bouttheNatur eofMathemati cs(abstract)..............................613

3.24David STEIN

SomeQuestio nsRegardingtheHistorica lRoleofConstructivisminMa thematic s

3.25Lucian aZUCCHERI,Veren aZUDINI

TheQu estionofChangingMathematicsSecon darySchoolCu rriculainVen ezia GiuliaAfter theFirstWorldWar(1918-1923)(abstract).......................617

4.Cu lturesandMathematics619

PlenaryLecture

4.1Ulric hREBSTOCK

MathematicsintheService oftheIs lamicComm unity...........................621 Workshopsbasedonhi storicaland epistemological material

4.2Chris tinePROUST

4.3Marie-N o¨elleRACINE

FemmesMathemati ciennesDansL'Histoire.....................................641 Workshopsbasedonp edagogicalandd idacticalmateri al

4.4GailE .FITZSIMON S

MathematicsandthePersonalCul tures ofStuden ts..............................651

Oralpresentations

4.5Adri anaCESARDEMATTOS

TheP rocessofRecognitionint hehis toryofMathematics.......................659

4.6Harald GROPP

TheR elationsBetweenMathema ticsandMusicinDi

erentRegionsandPeriods ofWor ldHistory(abstract).....................................................667quotesdbs_dbs23.pdfusesText_29
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