Table Of ContentAdvances in STEM Education
Series Editor: Yeping Li
Yeping Li
W. James Lewis
James J. Madden Editors
Mathematics
Matters in
Education
Essays in Honor of Roger E. Howe
Advances in STEM Education
Serieseditor
YepingLi,TexasA&MUniversity,CollegeStation,Texas,USA
InternationalAdvisoryBoard
SpencerA.Benson,UniversityofMacau,Macau,China
RichardA.Duschl,PennsylvaniaStateUniversity,USA
DirkIfenthaler,UniversityofMannheim,Germany
KennethRuthven,UniversityofCambridge,UK
KaranL.Watson,TexasA&MUniversity,USA
Advances in STEM Education is a new book series with a focus on cutting-edge
research and knowledge development in science, technology, engineering and
mathematics (STEM) education from pre-college through continuing education
aroundthe world. It is open to all topics in STEM education,both in and outside
ofclassrooms,includinginnovativeapproachesandperspectivesinpromotingand
improving STEM education, and the processes of STEM instruction and teacher
education. This series values original contributions that view STEM education
eitherintermsoftraditionallydefinedsubject-basededucationorasaneducational
undertakinginvolvinginter-connectedSTEMfields.Theseriesisopentonewtopics
identified and proposed by researchers internationally, and also features volumes
frominvitedcontributorsandeditors.ItworkscloselywiththeInternationalJournal
ofSTEMEducationandJournalforSTEMEducationResearchtopublishvolumes
ontopicsof interestidentifiedfromthe journalpublicationsthatcallforextensive
andin-depthscholarlypursuit.
Researchers interested in submitting a book proposalshould contact the Series
Editor: Yeping Li ([email protected]) or the Publishing Editor: Melissa James
([email protected])forfurtherinformation.
Moreinformationaboutthisseriesathttp://www.springer.com/series/13546
Yeping Li • W. James Lewis • James J. Madden
Editors
Mathematics Matters
in Education
Essays in Honor of Roger E. Howe
123
Editors
YepingLi W.JamesLewis
DepartmentofTeaching,Learning DepartmentofMathematics
andCulture UniversityofNebraska–Lincoln
TexasA&MUniversity Lincoln,NE,USA
CollegeStation,TX,USA
ShanghaiNormalUniversity
Shanghai,China
JamesJ.Madden
DepartmentofMathematics
LouisianaStateUniversity
BatonRouge,LA,USA
ISSN2520-8616 ISSN2520-8624 (electronic)
AdvancesinSTEMEducation
ISBN978-3-319-61433-5 ISBN978-3-319-61434-2 (eBook)
DOI10.1007/978-3-319-61434-2
LibraryofCongressControlNumber:2017949175
©SpringerInternationalPublishingAG2018
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Acknowledgments
ThisbookisascholarlyproductthatisderivedfromtheworkshopinhonorofRoger
Howe,heldontheoccasionofhis70thbirthdayin2015atTexasA&MUniversity.
Firstandforemost,wewouldliketotakethisopportunitytothankRogerHowefor
hisinspirationandcontributionstomathematicseducationandalsoforcontributing
hischaptertothisbook.
The gathering of many mathematicians, mathematics educators, and other
scholars made the workshop both memorable and productive. With a follow-up
conferencethatalreadytookplace,andmoreplannedforthefuture,theworkshop
was a catalyst for furtheringconnectionsand communicationsamong mathemati-
cians, mathematicseducators,and practitionersof mathematics. We would like to
acknowledgeandthankallworkshopparticipantsfortheirparticipationandsupport.
Wealsotakethisopportunitytoacknowledgeandthankallthosewhohavebeen
involved in preparing and contributing to this volume. This book would not have
been possible without the dedicated group of 20 contributors from more than 15
universitiesorinstitutesacrosstheUnitedStates, manyof whomalso volunteered
theirtimetoreviewchapters.Theircollectiveeffortshelpensurethisbook’squality.
The resulting book is a wonderful Festschrift in honor of Roger Howe for his
contributionstomathematicseducationasaninterdisciplinaryfield.
Thanks also go to a dedicated group of external reviewers, including James
Epperson,AlexanderForan,RobertGustafson,andDickStanley,fortakingthetime
tohelpreviewchaptersofthisbook.Theirreviewsandcommentshelpedimprove
the quality of many chapters, and on behalfof all the contributors,we extend our
appreciationtothem.
WewanttothankKeWangforhisassistanceindrawingfiguresforthisbook,and
Melissa James (a senior editorat Springer)forher patience andsupport.Working
withMelissahasbeenaproductiveandpleasantexperience,withthisbook’stimely
publicationasthefirstvolumeofthenewbookseries.
Finally, we want to express our deep appreciation to the workshop’s host
institution, the College of Education and Human Development at Texas A&M
University and especially the Department of Teaching, Learning and Culture, for
v
vi Acknowledgments
theirgreatsupportthatmadetheworkshoppossible.Theselflesssupportfrommany
dedicatedstaffandgraduatestudentswasbeyondthecallofduty.
Note:TheeditorsacknowledgethatLewis’workasaconferenceorganizerand
co-editor of this book was supported by the National Science Foundation. Any
opinion, findings, and conclusionsor recommendationsexpressed in this material
are those of the author(s) and do not necessarily reflect the views of the National
ScienceFoundation.
Contents
PartI Introduction
1 “MathematicsMattersin Education” to Roger E. Howe
andtoAll:AnIntroduction ............................................... 3
YepingLi,W.JamesLewis,andJamesJ.Madden
2 AboutRogerE.HoweandHisContributionstoMathematics
Education.................................................................... 9
YepingLiandW.JamesLewis
3 CulturalKnowledgeforTeachingMathematics ........................ 19
RogerE.Howe
PartII Knowing and Connecting Mathematics in Teaching
andTeacherEducation
4 TheContentKnowledgeMathematicsTeachersNeed ................. 43
Hung-HsiWu
5 KnowingRatioandProportionforTeaching............................ 93
JamesJ.Madden
6 HowFutureTeachersReasonedwithVariablePartsandStrip
DiagramstoDevelopEquationsforProportionalRelationships
andLines .................................................................... 117
SybillaBeckmannandTorreyK.Kulow
7 GivingReasonandGivingPurpose ...................................... 149
YvonneLai,MaryAliceCarlson,andRuthM.Heaton
8 WhoAretheExperts? ..................................................... 173
JohnEwing
vii
viii Contents
PartIII IdentifyingandStructuringCoreIdeasandPractices
inK-12MathematicsCurriculum
9 BuildingonHowe’sThreePillarsinKindergartentoGrade6
Classrooms .................................................................. 185
KarenC.Fuson
10 IstheRealNumberLineSomethingtoBeBuiltorOccupied? ....... 209
HymanBass
11 WhatContentKnowledgeShouldWeExpectinMathematics
Education? .................................................................. 219
RichardAskey
12 ApproachingEuclideanGeometryThroughTransformations........ 233
ZalmanUsiskin
13 CurricularCoherenceinMathematics................................... 245
AlCuocoandWilliamMcCallum
PartIV Supporting and Engaging Mathematicians in K-12
Education
14 Attracting and Supporting Mathematicians for the
MathematicalEducationofTeachers .................................... 259
AmyCohen
15 TheContributionsofMathematicsFacultytoK-12Education:
ADepartmentChair’sPerspective ....................................... 277
SolomonFriedberg
16 Supporting Education and Outreach in a Research
MathematicsDepartment.................................................. 287
JerryDwyerandLawrenceSchovanec
Index............................................................................... 301
Part I
Introduction
