Proficiency and Beliefs in Learning and Teaching Mathematics: Learning from Alan Schoenfeld and Günter Törner

310 Pages·2013·2.33 MB·English

by  Yeping Li

PROFICIENCYANDBELIEFSINLEARNINGANDTEACHINGMATHEMATICS
MATHEMATICS TEACHING AND LEARNING
Volume 1

Series Editor:
Yeping Li, Texas A&M University, College Station, USA

International Advisory Board:
Marja Van den Heuvel-Panhuizen, Utrecht University, The Netherlands
Eric J. Knuth, University of Wisconsin-Madison, USA
Suat Khoh Lim-Teo, National Institute of Education, Singapore
Carolyn A. Maher, Rutgers – The State University of New Jersey, USA
JeongSuk Pang, Korea National University of Education, South Korea
Nathalie Sinclair, Simon Fraser University, Canada
Kaye Stacey, University of Melbourne, Australia
Günter Törner, Universität Duisburg-Essen, Germany
Catherine P. Vistro-Yu, Ateneo de Manila University, The Philippines
Anne Watson, University of Oxford, UK

Mathematics Teaching and Learning is an international book series that aims to
provide an important outlet for sharing the research, policy, and practice of
mathematics education to promote the teaching and learning of mathematics at all
school levels as well as teacher education around the world. The book series strives
to address different aspects, forms, and stages in mathematics teaching and
learning both in and out of classrooms, their interactions throughout the process of
mathematics instruction and teacher education from various theoretical, historical,
policy, psychological, socio-cultural, or cross-cultural perspectives. The series
features books that are contributed by researchers, curriculum developers, teacher
educators, and practitioners from different education systems.

For further information:
https://www.sensepublishers.com/catalogs/bookseries/mathematics-teaching-and-
learning/
Proficiency and Beliefs in Learning
and Teaching Mathematics
Learning from Alan Schoenfeld and Günter Törner
Editedby
YepingLi
TexasA&MUniversity,USA
and
JuditN.Moschkovich
UniversityofCalifornia,SantaCruz,USA
SENSEPUBLISHERS
ROTTERDAM/BOSTON/TAIPEI
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ISBN978-94-6209-297-6(paperback)
ISBN978-94-6209-298-3(hardback)
ISBN978-94-6209-299-0(e-book)
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ThephotoonthefrontcovershowsGünterTörnerandAlanSchoenfeld atMarksburgCastleinthe
RhineValley,Germany,inMarch2013
Photocredit:JaneSchoenfeld,2013
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TABLE OF CONTENTS
Acknowledgements vii
PartI:Introduction
1.ProficiencyandBeliefsinLearningandTeachingMathematics–
AnIntroduction 3
YepingLiandJuditN.Moschkovich
2.AboutAlanH.SchoenfeldandHisWork 9
HughBurkhardtandYepingLi
3.AboutGünterTörnerandHisWork 19
HansHeinrichBrungsandYepingLi
PartII:ProficientPerformance,Beliefs,andMetacognitionin
MathematicalThinking,ProblemSolving,andLearning
4.DevelopingProblemSolvingSkillsinElementarySchool–
TheCaseofDataAnalysis,Statistics,andProbability 33
KristinaReiss,AnkeM.Lindmeier,PetraBarchfeldandBeateSodian
5.TransmissiveandConstructivistBeliefsofIn-ServiceMathematics
TeachersandofBeginningUniversityStudents 51
ChristineSchmeisser,StefanKrauss,GeorgBruckmaier,StefanUfer
andWernerBlum
6.BuildingonSchoenfeld’sStudiesofMetacognitiveControltowards
SocialMetacognitiveControl 69
MingMingChiu,KarrieA.JonesandJenniferL.Jones
PartIII:ProficientPerformance,Beliefs,andPracticesinMathematics
Teaching,andWaystoFacilitateThem
7.TheCAMTEFramework–AToolforDevelopingProficientMathematics
TeachinginPreschool 89
PessiaTsamir,DinaTirosh,EstherLevenson,RuthiBarkaiand
MichalTabach
v
TABLEOFCONTENTS
8.IntegratingNoticingintotheModelingEquation 111
MiriamGamoranSherin,RosemaryS.RussandBruceL.Sherin
9.TeachingasProblemSolving–CollaborativeConversationsasFound
Talk-AloudProtocols 125
IlanaSeidelHorn
10.ResearchingtheSustainableImpactofProfessionalDevelopment
ProgrammesonParticipatingTeachers’Beliefs 139
StefanZehetmeierandKonradKrainer
11.CapturingMathematicsTeachers’ProfessionalDevelopmentinTerms
ofBeliefs 157
BettinaRoesken-Winter
12.MathematiciansandElementarySchoolMathematicsTeachers–
MeetingsandBridges 179
JasonCooperandAbrahamArcavi
PartIV:IssuesandPerspectivesonResearchandPractice
13.MethodologicalIssuesinResearchandDevelopment 203
HughBurkhardt
14.AMathematicalPerspectiveonEducationalResearch 237
CathyKessel
15.IssuesRegardingtheConceptofMathematicalPractices 259
JuditN.Moschkovich
PartV:ReflectionsandFutureResearchDevelopment
16.LookingBackandAhead–SomeVerySubjectiveRemarkson
ResearchinMathematicsEducation 279
GünterTörner
17.Encore 287
AlanH.Schoenfeld
AuthorBiographies 303
Index 313
vi
ACKNOWLEDGEMENTS
The book was principally conceived to celebrate the work of two outstanding
scholars: Alan Schoenfeld and Günter Törner. First and foremost, we would like
toacknowledgeandthankthemforsupportingtheideaofpublishingsuchabook
andcontributingtheirrespectivechapters.
Wealsowanttotakethisopportunitytothankandacknowledgeallotherswho
havebeeninvolvedintheprocessofpreparingthisbook.Thishasbeenawonderful
experience.Hereareafewhighlightsoftheprocess:
1. Thisbookresultedfromthetypicalprocessofrequesting,contributingandedit-
ingchapters.However,thecurrentvolumeisnottypicalinitscontentbecause
all the chapters refer to and build upon these two scholars’ work. Although
mathematicseducationasafielddoesnothavealonghistory,therehavebeen
manybookspublishedonmathematicseducationresearchandpractice.How-
ever, there are few books that focus on what we can learn from and how we
can build on others’ work as this volume does. We would especially like to
acknowledgethe scholarswho contributedchaptersto this volume. This vol-
ume wouldnot have been possible withouttheir contributionsdetailingways
tobuilduponandexpandtheworkofothers.
2. Although it may seem that the contributors were all close friends, this book
has actually brought together people who had never collaborated before and
has provided the opportunity to develop new professional relationships. For
example,althoughJuditisaformerstudentofAlan’s,shehadnotmetGünter.
YepingfirstformallymetGünterinAugust2011inCollegeStation,Texasand
startedtheconversationaboutthepossibilityandvalueofeditingandpublish-
ingsuchabook.Thus,theworkonthisbookhasnotonlybroughttogetherlong
timefriendsandcolleagues,butalsocreatednewprofessionalconnectionsand
resulted in new friends. We want to thank all those who were so ready and
willingtoworkwithnewcolleaguesandcreatenewconnections.
It is easy to see that the volume is the product of an international collaboration
of scholars from different countries and disciplines. This book would not have
been possible without the dedicated group of 31 contributors from six countries
(Austria, Canada, Germany,Israel, UK,and the US) and we thankthem for their
contributions.Thisgroupofcontributorsalsoworkedtogetherasateamtoreview
the chaptersof this publication.Their collective effortshelpedensure this book’s
quality.
vii
ACKNOWLEDGEMENTS
Thanks also go to a group of external reviewers who took the time to help
review many chapters of the book. They are Ann Ryu Edwards, Rongjin Huang,
JenniferLewis,KatieLewis,HéliaOliveira,andConstantaOlteanu.Theirreviews
andcommentshelpedimprovethequalityofmanychapters.
Finally, we want to thank Nikki Butchers for her assistance in proofreading
manychaptersofthisbookandMichelLokhorst(publisheratSensePublishers)for
hispatienceandsupport.Michel’sprofessionalassistancehasmadethepublication
a smooth and pleasantexperience,with this book’stimely publicationas the first
volumeofthenewbookseriesonMathematicsTeachingandLearning.
viii
PART I
INTRODUCTION
YEPINGLIANDJUDITN.MOSCHKOVICH
1. PROFICIENCYANDBELIEFS IN LEARNING AND
TEACHINGMATHEMATICS
AnIntroduction
INTRODUCTION
ThisvolumewassparkedbythefactthatAlanSchoenfeldandGünterTörnerwere
bothcelebratingtheir65thbirthdaysinJuly2012.Thebookstartedoutaspartof
a Festschrift to celebrate that event. Although the volume was not ready in time
for their birthdays, the result is a belated celebration in print to recognize their
contributionsto the field of mathematicseducation.Alan and Günter share much
more than simply their birth month and year. In addition to being colleagues in
mathematicseducation,AlanandGünterarelongtimefriendsandmathematicians
bytraining.Theirbackgroundinmathematicsledthemtopaycloseattentiontothe
details of mathematical work. Although Alan and Günter followed differentpro-
fessionaltrajectoriesinthefieldofmathematicseducation,theirworkexemplifies
how mathematicians can make importantcontributionsto mathematicseducation
research.AlanandGünterarewellrespectedintheinternationalmathematicsed-
ucationcommunityfortheirwork,andthisvolumeismeanttobeatributetotheir
scholarlyachievement.
Thisvolume,however,isnotacollectionofpaperswrittenbyAlanandGünter.
Instead, this is a collection of papers that show how other researchers have con-
nected to, learned from, and built upon Alan and Günter’s work. In Alan’s own
words this volume is, “... a chance for some goodscholars to advance the field,
withtheirownworkasoutgrowthsofthingstheymayhavedonewithGünterand
me.Andcontributingtothefieldiswhatbooksshouldbefor!”(personalcommu-
nication).Itisinthisspiritofmovingthefieldofmathematicseducationforward
thatweofferthisvolumetoshowourdeepappreciationoftheworkdonebyAlan
andGünter.
Identifying a theme for the volume was at once easy and challenging. On
one hand, it was not difficult to find a theme because Alan and Günter’s
works have covered such a broad scope of topics. However, attempts to cover
these varied topic areas would not have generated a coherent volume. On the
other hand, because Alan and Günter have devoted their efforts to studying
key questions in learning and teaching mathematics, we found that the themes
of understanding and improving mathematics teaching and learning should be
at the core of such a volume. This has been a central theme in mathemat-
ics education, as researchers aim to not only understand the nature of profi-
ciency, beliefs, and practices in mathematics learning and teaching, but also
identify and assess possible influences on students’ and teachers’ proficiency,
Y.LiandJ.N.Moschkovich(eds.),ProficiencyandBeliefsinLearningandTeaching
Mathematics,3–7.
©2013.SensePublishers.Allrightsreserved.