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 AC.I.P.recordforthisbookisavailablefromtheLibraryofCongress. ISBN978-94-6209-297-6(paperback) ISBN978-94-6209-298-3(hardback) ISBN978-94-6209-299-0(e-book) Publishedby:SensePublishers, P.O.Box21858,3001AWRotterdam,TheNetherlands https://www.sensepublishers.com/ ThephotoonthefrontcovershowsGünterTörnerandAlanSchoenfeld atMarksburgCastleinthe RhineValley,Germany,inMarch2013 Photocredit:JaneSchoenfeld,2013 Printedonacid-freepaper Allrightsreserved©2013SensePublishers Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby anymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwritten permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework. 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.