Table Of ContentICME-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
