Compendium for Early Career Researchers in Mathematics Education PDF
Preview Compendium for Early Career Researchers in Mathematics Education
ICME-13 Monographs Gabriele Kaiser Norma Presmeg Editors Compendium for Early Career Researchers in Mathematics Education ICME-13 Monographs Series Editor Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität Hamburg, Hamburg, Germany Each volume in the series presents state-of-the art research on a particular topic in mathematics education and reflects the international debate as broadly as possible, while also incorporating insights into lesser-known areas of the discussion. Each volumeisbasedonthediscussionsandpresentationsduringtheICME-13congress and includes the best papers from one of the ICME-13 Topical Study Groups, DiscussionGroupsorpresentationsfromthethematicafternoon. More information about this series at http://www.springer.com/series/15585 Gabriele Kaiser Norma Presmeg (cid:129) Editors Compendium for Early Career Researchers in Mathematics Education Editors Gabriele Kaiser Norma Presmeg Faculty of Education Mathematics Department UniversitätHamburg Illinois State University Hamburg,Germany Normal, IL, USA ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN978-3-030-15635-0 ISBN978-3-030-15636-7 (eBook) https://doi.org/10.1007/978-3-030-15636-7 LibraryofCongressControlNumber:2019934361 ©TheEditor(s)(ifapplicable)andTheAuthor(s)2019.Thisbookisanopenaccesspublication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adap- tation,distributionandreproductioninanymediumorformat,aslongasyougiveappropriatecreditto the originalauthor(s)and the source, providealink tothe CreativeCommonslicense andindicate if changesweremade. The images or other third party material in this book are included in the book’s Creative Commons license,unlessindicatedotherwiseinacreditlinetothematerial.Ifmaterialisnotincludedinthebook’s CreativeCommonslicenseandyourintendeduseisnotpermittedbystatutoryregulationorexceedsthe permitteduse,youwillneedtoobtainpermissiondirectlyfromthecopyrightholder. Theuse ofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc. inthis publi- cationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromthe relevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Early career researchers represent the future of the field, insofar as they will shape thefurtherdevelopment ofresearchwithinthe field. Hence theimportance,for the futureofhigh-qualityresearchinthefieldofmathematicseducation,ofsupporting and encouraging new scholars as they enter this community of researchers. It has nowbecomecommonforlargeinternationalandnationalconferences,andnotonly those in mathematics education, to offer specific activities for early career researchersinordertointroducethemtotheimportantresearchmethodswithinthe field, toprovide them withsurveys and overviews on topics significant tothe field andtointroducethem toacademicwriting andpublishing. Overall, these activities aimtoinductearlycareerresearchersintothecommunity,helpthembecomeaufait with its research standards and provide insight on the state-of-the-art results achieved so far by those who have already worked in this community for a long time and who are identified as experts in the field. At the 13th International Congress on Mathematical Education (ICME-13), which took place from 24 to 31 July 2016, an Early Career Researcher Day was therefore organized to take place directly before the congress on 24 July 2016, which attracted 450 participants. This Compendium and its chapters are based on workshops that were presented as part of this activity, with a few additional chapters on important themes in mathematics education. Although the Early Career Researcher Day, and ICME-13 itself, followed the structure of summer schools in general and special workshops from various net- works (e.g. the European Researchers on Mathematics Education, or activities of the German community), the question arises whether early career researchers needspecificofferingsor,ingeneral,whytheprogrammewasstructuredinsucha way, and why we structured the Compendium as it is. We have seen in the last two decades a strong development towards higher quality standards of research in mathematics education. Rigorous standards of qualityneedtobemetincarryingoutresearchinfulfilmentoftherequirementsfora Ph.D.,oratpost-doclevel.Oneoftheserequirementsistohaveaclearconceptual frameworkincludingreferencetowell-knowntheoriesfrommathematicseducation, either as home-grown theories, or invoking those borrowed from other disciplines. v vi Preface Thestandardsconcerningmethodologieshavealsobeenraisedasthefieldmatures. One aspect of this concern with standards of methodology is the increasing importance of large-scale studies in mathematics education. The high standards of psychometric research have long been unquestioned, but what are the implications when themethods of social and naturalistic research are also recognized as having significance is answering current questions of research in the field? This develop- ment leads to the question of what constitutes quality, both in qualitatively and in quantitatively oriented research. It is recognized that qualitative and quantitative methods have different goals, differ in their applicability, and above all, answer different questions in mathematics education research. While qualitative research often enables depth of perception of why a certain phenomenon is happening, quantitativeresearchaddressesthequestionofhowwidespreadsuchaphenomenon is. Both kinds ofresearch havetheirplace, and they may complementeachother. Thequalitystandardsofobjectivity,reliabilityandvaliditycommoninstatistical research are not questioned, but what does that mean for qualitatively oriented research focusing quite often on a single case, with no chance of repetition or controlgroups?Variousmixedmethodsapproachesmayofferonekindofsolution; however, these questions are essential for the future development of research in mathematics education. With the proliferation of journals and conference proceedings, dissemination of research results through publication has assumed increasing importance in recent years,withgrowingpublicationpossibilities.Publishingastudynowadaysneedsto fulfilmanyrequirementsconcerningtheclarityofthetheoreticalframeworkandthe methodologyused.Whatistheroleofhome-grownstandardsinpublishing?Dowe wishtofulfilthestandardsimplementedbypsychometricresearch?Dowewishto orient towards educational research standards, which are often more qualitatively oriented? It is not by accident that we use the standards of the American Psychological Association (APA) for referencing in many journals of mathematics education. The Early Career Researcher Day at ICME-13 and its outcome, the Compendium for Early Career Researchers in Mathematics Education, are char- acterized by a combination of presentations on methodological approaches and theoretical perspectives shaping the field in mathematics education research. Overall, the book provides a state-of-the-art overview of important theories from mathematics education and the broad variety of empirical approaches currently widely used in mathematics education research. This Compendium supports early career researchers in selecting adequate theoretical approaches and adopting the mostappropriatemethodologicalapproachesfortheirownresearch.Furthermore,it helps early career researchers in mathematics education to avoid common pitfalls andproblemswhilewritinguptheirresearchanditprovidesthemwithanoverview ofthemostimportantjournalsforresearchinmathematicseducation,helpingthem to select the right venue for publishing and disseminating their work. The strong emphasis on academic writing and publishing, supported by descriptions of the major journals in mathematics education by their (former or associate) editors, offers strong insight into the theoretical and empirical bases of research in Preface vii mathematicseducationfor earlycareerresearchers inthisfield.Suchknowledgeis necessaryfornewandseasonedresearchersalike,fortheproductionofhigh-quality research papers in mathematics education. We would like to thank Armin Jentsch and Thorsten Scheiner, who were strongly involved in organising the Early Career Researcher Day at ICME-13 and shaped it with their ideas. Furthermore, we thank Ferdinando Arzarello, who welcomed the participants in his role as ICMI-president. We hope that this Compendium for Early Career Researchers in Mathematics Education will foster further similar activities and support the development of an international network for Early Career Researchers in Mathematics Education. Hamburg, Germany Gabriele Kaiser Normal, USA Norma Presmeg Contents Part I Empirical Methods 1 Argumentation Analysis for Early Career Researchers. . . . . . . . . . 3 Christine Knipping and David A. Reid 2 Topic-Specific Design Research: An Introduction . . . . . . . . . . . . . . 33 Koeno Gravemeijer and Susanne Prediger 3 ANaturalisticParadigm:AnIntroductiontoUsingEthnographic Methods for Research in Mathematics Education. . . . . . . . . . . . . . 59 Judit N. Moschkovich 4 An Introduction to Grounded Theory with a Special Focus on Axial Coding and the Coding Paradigm . . . . . . . . . . . . . . . . . . 81 Maike Vollstedt and Sebastian Rezat 5 Interactional Analysis: A Method for Analysing Mathematical Learning Processes in Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 101 Marcus Schütte, Rachel-Ann Friesen and Judith Jung 6 Planning and Conducting Mixed Methods Studies in Mathematics Educational Research . . . . . . . . . . . . . . . . . . . . . . 131 Nils Buchholtz 7 The Research Pentagon: A Diagram with Which to Think About Research. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Angelika Bikner-Ahsbahs 8 Qualitative Text Analysis: A Systematic Approach. . . . . . . . . . . . . 181 Udo Kuckartz 9 Problematising Video as Data in Three Video-based Research Projects in Mathematics Education. . . . . . . . . . . . . . . . . . . . . . . . . 199 Man Ching Esther Chan, Carmel Mesiti and David Clarke ix x Contents Part II Important Mathematics Educational Themes 10 Approaching Proof in the Classroom Through the Logic of Inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Ferdinando Arzarello and Carlotta Soldano 11 A Friendly Introduction to “Knowledge in Pieces”: Modeling Types of Knowledge and Their Roles in Learning . . . . . . . . . . . . . 245 Andrea A. diSessa 12 Task Design Frameworks in Mathematics Education Research: An Example of a Domain-Specific Frame for Algebra Learning with Technological Tools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Carolyn Kieran 13 Gender and Mathematics Education: An Overview . . . . . . . . . . . . 289 Gilah C. Leder 14 Theoretical Aspects of Doing Research in Mathematics Education: An Argument for Coherence. . . . . . . . . . . . . . . . . . . . . 309 Stephen Lerman 15 The Professional Development of Mathematics Teachers . . . . . . . . 325 Björn Schwarz and Gabriele Kaiser Part III Academic Writing and Academic Publishing: Academic Writing 16 Pleasures, Power, and Pitfalls of Writing up Mathematics Education Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 Norma Presmeg and Jeremy Kilpatrick 17 Scholarly Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 Helen J. Forgasz Part IV Academic Writing and Academic Publishing: Description of Major Journals in Mathematics Education 18 Educational Studies in Mathematics: Shaping the Field. . . . . . . . . . 377 Merrilyn Goos 19 For the Learning of Mathematics: An Introduction to the Journal and the Writing Within It . . . . . . . . . . . . . . . . . . . . 393 Richard Barwell and David A. Reid 20 The International JournalofScience andMathematicsEducation: A Beginner’s Guide to Writing for Publication. . . . . . . . . . . . . . . . 407 Peter Liljedahl
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