Table Of ContentAdvances 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
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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
