Mathematics Curriculum in School Education PDF
Preview Mathematics Curriculum in School Education
Advances in Mathematics Education SeriesEditors: GabrieleKaiser,UniversityofHamburg,Hamburg,Germany BharathSriraman,TheUniversityofMontana,Missoula,MT,USA InternationalEditorialBoard: UbiratanD’Ambrosio(SãoPaulo,Brazil) JinfaCai(Newark,NJ,USA) HelenForgasz(Melbourne,Victoria,Australia) JeremyKilpatrick(Athens,GA,USA) ChristineKnipping(Bremen,Germany) OhNamKwon(Seoul,Korea) Forfurthervolumes: www.springer.com/series/8392 Yeping Li (cid:2) Glenda Lappan Editors Mathematics Curriculum in School Education Editors YepingLi GlendaLappan Dept.Teaching,Learning&Culture MichiganStateUniversity TexasA&MUniversity EastLansing,MI,USA CollegeStation,TX,USA ISSN1869-4918 ISSN1869-4926(electronic) AdvancesinMathematicsEducation ISBN978-94-007-7559-6 ISBN978-94-007-7560-2(eBook) DOI10.1007/978-94-007-7560-2 SpringerDordrechtHeidelbergNewYorkLondon LibraryofCongressControlNumber:2013954441 ©SpringerScience+BusinessMediaDordrecht2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Series Preface The eighth volume of the series Advances in Mathematics Education on “Mathe- matics Curriculum in School Education” edited by Yeping Li and Glenda Lappan commencesfromoneofthemostimportantperspectivesonmathematicseducation inschool,namelyquestionsonthecurriculum.Curricularstructuresaredecisivefor theorganizationandstructureofmathematicseducation,astheydirectlyinfluence teachingandlearningprocesses.However,despitethisstronginfluenceofthecur- riculumoneducationingeneralandlearning-and-teachingprocesses,extensiveem- piricalresearchhasnotbeencarriedoutsofar.Theinternationalcomparativestudies onmathematicsandscienceeducationimplementedbytheIEAalreadyintroduced the differentiation of the intended, the implemented and the achieved curriculum intheSecondInternationalStudyonMathematicsandScienceEducation(SIMS). However,thesedistinctionshavenotledtoextensivestudiescomparingthesediffer- ent kinds of curricula. Studies accompanying the Third International Mathematics and Science Study (TIMSS) brought forward the cultural dependency of the cur- riculum and pointed out the difficulty in finding a common curricular core for the schoolsubjectofmathematicsallovertheworld. Thisisoneofthefoundationpointsofthepresentbook,inwhichcontributions fromEasternandWesternmathematicseducatorsarecollected.Inthisrespect,the book represents an extension of an issue of ZDM—The International Journal on Mathematics Education on ‘Curriculum Research to Improve Mathematics Teach- ingandLearning:PracticesandApproachesinChinaandtheUnitedStates’edited byYepingLiandGeraldKulmin2009,whichwasrestrictedtoChinaandtheUSA. Thepresentbookcontainsacollectionofstudiesonmathematicscurriculumfrom morethanteneducationsystemsacrosstheworldwithadditionalreflectivechapters acrossvariouscountries. Withthisimpressiveoverviewoncurricularpracticesallovertheworldthisbook willprovideaninsightfuloverviewontheroleandtheinfluenceofthemathematics curriculuminternationally,whichthereaderwillhopefullyfindinteresting. Hamburg,Germany GabrieleKaiser Missoula,USA BharathSriraman v Acknowledgements We want to take this opportunity to thank and acknowledge all of those who have been involved in the process of preparing this book. This has been a wonderful experience.Theworkonthisbookhasnotonlybroughttogetherlongtimefriends andcolleagues,butalsocreatednewprofessionalconnectionsandfriends.Wewant tothankallthosewhoweresoreadyandwillingtocontributetothetopicthathas now been proven to be indispensable to the international mathematics education community. Indeed, this book wouldn’t be possible without the dedicated group of 54 con- tributors from 14 education systems across the world (Australia, Brazil, Canada, China,HongKong,Israel,Japan,Singapore,SouthKorea,Taiwan,theNetherlands, Turkey,U.K.,andtheU.S.)andwethankthemfortheircontributions.Thisgroupof contributorsalsoworkedtogetherasateamtohelpblindreviewthechapters.Their collectiveeffortshelpensurethisbook’squality. Thanksalsogotoagroupofexternalreviewerswhotookthetimetohelpreview many chapters of the book. They are Richard A. Askey, Ana Canavarro, Janice Grow-Maienza, Minsung Kwon, Arne Mogensen, and Ji-Won Son. Their reviews andcommentshelpedimprovethequalityofmanychapters.Wealsowanttothank NikkiButchersforherassistanceinproofreadingmanychaptersofthebook. Last but not least, we want to thank our families for their love and continuous supportalongtheway.Thebookwouldn’thavebeencompletedwithouttheirsup- portandunderstanding.Wewanttoletthemknowagainthatwearesogratefulfor theirpatienceandsupportthatmakeourworkpossible. vii Contents PartI IntroductionandPerspectives MathematicsCurriculuminSchoolEducation:AdvancingResearch andPracticefromanInternationalPerspective . . . . . . . . . . . 3 YepingLiandGlendaLappan CurriculumDesignandSystemicChange . . . . . . . . . . . . . . . . . 13 HughBurkhardt Mathematics Curriculum Policies and Practices in the U.S.: The CommonCoreStateStandardsInitiative. . . . . . . . . . . . . . . 35 BarbaraJ.Reys ReflectionsonCurricularChange . . . . . . . . . . . . . . . . . . . . . 49 AlanH.Schoenfeld PartII CurriculumandPolicy MathematicsCurriculumPolicies:AFrameworkwithCaseStudies fromJapan,Korea,andSingapore . . . . . . . . . . . . . . . . . . 79 KhoonYoongWong,MasatakaKoyama,andKyeong-HwaLee DecisionMakingintheMathematicsCurriculaamongtheChinese Mainland,HongKong,andTaiwan . . . . . . . . . . . . . . . . . . 93 HakPingTam,Ngai-YingWong,Chi-ChungLam,YunpengMa,Lije Lu,andYu-JenLu Potential Impact of the Common Core Mathematics Standards ontheAmericanCurriculum . . . . . . . . . . . . . . . . . . . . . 119 Hung-HsiWu BriefConsiderationsonEducationalDirectivesandPublicPolicies inBrazilRegardingMathematicsEducation . . . . . . . . . . . . . 143 AntonioVicenteMarafiotiGarnica ix x Contents TheAustralianCurriculum:Mathematics—HowDiditComeAbout? WhatChallengesDoesitPresentforTeachersandfortheTeaching ofMathematics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 MaxStephens PartIII CurriculumDevelopmentandAnalysis ThreePillarsofFirstGradeMathematics,andBeyond . . . . . . . . . 183 RogerHowe Forging New Opportunities for Problem Solving in Australian MathematicsClassroomsthroughtheFirstNationalMathematics Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 JudyAnderson Freedom of Design: The Multiple Faces of Subtraction in Dutch PrimarySchoolTextbooks . . . . . . . . . . . . . . . . . . . . . . . 231 MarcvanZantenandMarjavandenHeuvel-Panhuizen Changes to the Korean Mathematics Curriculum: Expectations andChallenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 JeongSukPang The Singapore Mathematics Curriculum Development—A Mixed ModelApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 NganHoeLee School Mathematics Textbook Design and Development Practices inChina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 YepingLi,JianyueZhang,andTingtingMa PartIV Curriculum,Teacher,andTeaching TeachersasParticipantsinTextbookDevelopment:TheIntegrated MathematicsWiki-bookProject . . . . . . . . . . . . . . . . . . . . 333 RuhamaEvenandShaiOlsher MathematicsTeacherDevelopmentintheContextofDistrictManaged Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 MaryKayStein,JuliaKaufman,andMirayTekkumruKisa Curriculum,TeachersandTeaching:ExperiencesfromSystemicand LocalCurriculumChangeinEngland . . . . . . . . . . . . . . . . 377 MargaretBrownandJeremyHodgen Teaching Mathematics Using Standards-Based and Traditional Curricula:ACaseofVariableIdeas . . . . . . . . . . . . . . . . . 391 JinfaCai,BikaiNie,JohnC.Moyer,andNingWang Contents xi Supporting the Effective Implementation of a New Mathematics Curriculum: A Case Study of School-Based Lesson Study ataJapanesePublicElementarySchool . . . . . . . . . . . . . . . 417 AkihikoTakahashi Does Classroom Instruction Stick to Textbooks? A Case Study ofFractionDivision. . . . . . . . . . . . . . . . . . . . . . . . . . . 443 RongjinHuang,Z.EbrarYetkinerOzel,YepingLi,andRebeccaV. Osborne PartV CurriculumandStudentLearning CurriculumIntent,TeacherProfessionalDevelopmentandStudent LearninginNumeracy . . . . . . . . . . . . . . . . . . . . . . . . . 473 VinceGeiger,MerrilynGoos,andShelleyDole The Impact of a Standards-Based Mathematics Curriculum on Classroom Instruction and Student Performance: TheCaseofMathematicsinContext . . . . . . . . . . . . . . . . . . 493 MaryC.Shafer CurriculumandAchievementinAlgebra2:InfluencesofTextbooks andTeachersonStudents’LearningaboutFunctions . . . . . . . . 515 SharonL.Senk,DenisseR.Thompson,andJamieL.W.Wernet Learning Paths and Learning Supports for Conceptual Addition and Subtraction in the US Common Core State Standards andintheChineseStandards . . . . . . . . . . . . . . . . . . . . . 541 KarenC.FusonandYepingLi TheVirtualCurriculum:NewOntologiesforaMobileMathematics . . 559 NathalieSinclairandElizabethdeFreitas PartVI Cross-nationalComparisonandCommentary Forty-Eight Years of International Comparisons in Mathematics Education from a United States Perspective: What Have We Learned? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 ZalmanUsiskin (Mathematics)Curriculum,TeachingandLearning . . . . . . . . . . . 607 Ngai-YingWong,QiaopingZhang,andXiaoqingLi ImprovingtheAlignmentBetweenValues,PrinciplesandClassroom Realities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 MalcolmSwan Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637 AuthorIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 AuthorBiographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649 Part I Introduction and Perspectives
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