Table Of ContentAdvances in Mathematics Education
Scott A. Chamberlin
Bharath Sriraman E ditors
Aff ect in
Mathematical
Modeling
Advances in Mathematics Education
Series Editors
Gabriele Kaiser, University of Hamburg, Hamburg, Germany
Bharath Sriraman, University of Montana, Missoula, MT, USA
Editorial Board Members
Ubiratan d’Ambrosio (Sa˜o Paulo, Brazil)
Jinfa Cai (Newark, NJ, USA)
Helen Forgasz (Melbourne, VIC, Australia)
Jeremy Kilpatrick (Athens, GA, USA)
Christine Knipping (Bremen, Germany)
Oh Nam Kwon (Seoul, Korea)
Moreinformationaboutthisseriesathttp://www.springer.com/series/8392
(cid:129)
Scott A. Chamberlin Bharath Sriraman
Editors
Affect in Mathematical
Modeling
Editors
ScottA.Chamberlin BharathSriraman
SchoolofTeacherEducation DepartmentofMathematicalSciences
UniversityofWyoming UniversityofMontana
Laramie,WY,USA Missoula,MT,USA
ISSN1869-4918 ISSN1869-4926 (electronic)
AdvancesinMathematicsEducation
ISBN978-3-030-04431-2 ISBN978-3-030-04432-9 (eBook)
https://doi.org/10.1007/978-3-030-04432-9
LibraryofCongressControlNumber:2019936163
©SpringerNatureSwitzerlandAG2019
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Contents
PartI
CommentaryonAffect,CognitionandMetacognition
inMathematicalModelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
JoneiCerqueiraBarbosa
Chapter1:TheConstructofAffectinMathematicalModeling. . . . . . . 15
ScottA.Chamberlin
Chapter2:MetacognitioninMathematical
Modeling–AnOverview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
KatrinVorhölter,AlexandraKrüger,andLisaWendt
Chapter3:PrinciplesforDesigningResearchSettings
toStudySpontaneousMetacognitiveActivity. . . . . . . . . . . . . . . . . . . . . 53
MartaT.MagieraandJudithS.Zawojewski
Chapter4:EngagementStructuresandtheDevelopment
ofMathematicalIdeas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
LisaB.WarnerandRobertaY.Schorr
PartII
TheWhatandtheWhyofModeling. . . . . . . . . . . . . . . . . . . . . . . . . . . 89
AlanH.Schoenfeld
EngagingStudentsinMathematicalModeling:
ThemesandIssues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
PeterKloosterman
Chapter5:ExploringaConativePerspective
onMathematicalEngagement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
GeraldA.Goldin
v
vi Contents
Chapter6:ExploringTeacher’sEpistemicBeliefs
andEmotionsinInquiry-BasedTeachingofMathematics. . . . . . . . . . . 131
InésM.Gómez-ChacónandConstantinoDelaFuente
Chapter7:MathematicsLearningExperiences:
ThePracticeofHappinessandtheHappinessofPractice. . . . . . . . . . . . 159
AdiWiezel,JamesA.Middleton,andAmandaJansen
Chapter8:DevelopmentofModellingRoutines
andItsRelationtoIdentityConstruction. . . . . . . . . . . . . . . . . . . . . . . . 177
JuhainaAwawdehShahbari,MichalTabach,andEinatHeyd-Metzuyanim
PartIII
CommentaryonPartIII:ConnectionstoTheory
andPractice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
MortenBlomhøj
Commentary:FlowandMathematicalModelling:
IssuesofBalance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
LynD.English
Chapter9:TheComplexRelationshipBetweenMathematical
ModelingandAttitudeTowardsMathematics. . . . . . . . . . . . . . . . . . . . 219
PietroDiMartino
Chapter10:TeachingModellingProblemsandItsEffects
onStudents’EngagementandAttitudeTowardMathematics. . . . . . . . 235
ZakiehParhizgarandPeterLiljedahl
Chapter11:AffectandMathematicalModelingAssessment:
ACaseStudyonEngineeringStudents’ExperienceofChallenge
andFlowDuringaCompulsoryMathematicalModelingTask. . . . . . . . 257
ThomasGjestelandandPaulineVos
Chapter12:FlowandModelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
MinnieLiuandPeterLiljedahl
Chapter13:ACodaonAffect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
BharathSriraman
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Part I
Commentary on Affect, Cognition
and Metacognition in Mathematical
Modelling
JoneiCerqueiraBarbosa
Abstract Inthischapter,IreacttothetextsbyChamberlin(2019);Vorhölteretal.
(2019); Magiera and Zawojewski (2019); and Warner and Schorr (2019), which
provide powerful insights to analyze mathematical modelling in terms of affect,
cognition, and metacognition. Particularly, I use the sociocultural and sociocritical
lenstodiscusstheideaspresentedbytheauthorsandtoproposeotherquestions.
Keywords Affect·Cognition·Metacognition·Socioculturalperspective·
Sociocriticalperspective
Introduction
The past decades have witnessed important theoretical insights on the practice of
mathematical modelling in educational settings (Schukajlow et al. 2018). The
community of researchers has given more attention to the analysis and theorising
of what happens when mathematical modelling has been developed in educational
environments.Oneofthefocusesreferstostudents’psychologicalprocesses,which
I understand initially as dispositions for action, ways of thinking, and ways of
communicating.
InthecaseofthesectiononeofthisbookAffectinMathematicalModelling,the
chapters by Chamberlin (2019); Vorhölter et al. (2019); Magiera and Zawojewski
(2019);andWarnerandSchorr(2019)addresstheconceptsofaffect,cognition,and
metacognition. They present powerful ideas that provoke us into thinking about
students’ doings in mathematical modelling activities. These concepts were origi-
nallyformulatedinthefieldofpsychology,buttheyhavebeenborrowedbythosein
thefieldofmathematicseducation.AsLerman(2010)underlines,ourareahasweak
grammar,whichmeansthatitdoesnotproduceunambiguousempiricaldescriptions.
Many conceptualizations compete in the fields, giving rise to what the sociologist
J.C.Barbosa(*)
FederalUniversityofBahia,Salvador,Brazil
e-mail:[email protected]
©SpringerNatureSwitzerlandAG2019 3
S.A.Chamberlin,B.Sriraman(eds.),AffectinMathematicalModeling,Advancesin
MathematicsEducation,https://doi.org/10.1007/978-3-030-04432-9_1
4 J.C.Barbosa
B. Bernstein called horizontal structures of knowledge. As a result, I acknowledge
thatthosedescriptionspresentedbytheauthorsofthebooksectionhavetheoretical
affiliationsthatcompeteinthefieldofmathematicseducationaswellasothersareas
suchaspsychologyandphilosophy.
Thefollowingcommentaryismoreofadiscussionbasedonmyreflectionofthe
textsthanasummary.Icannotseparatemyselffromthetheoreticalperspectivesused
in my research, which are based on the sociocultural theory (Barbosa 2010), the
theoryofcodesbyBasilBernstein(OliveiraandBarbosa2013),andWittgenstein’s
latephilosophy(SouzaandBarbosa2014).
Thus,whatfollowsisaconstructivedialoguewiththeauthorsontheconceptsof
affect, cognition, and metacognition and how they are used to analyse students’
doings in mathematical modelling practice. To help the discussion, I am going to
present an illustrative episode of a classroom, which will be used as part of my
arguments. I will clarify my perspective on mathematical modelling so that the
reader might understand how it unfolds in the following discussion. Lastly, I will
examinethenotionsofaffect,cognition,andmetacognitionpresentedbythesection
authors.
A Classroom Episode
The following episode was extracted from one of Teacher Marcelo’s first mathe-
matical modelling-based lessons. It took place in a public school located in the
BraziliancityofSalvador.Usually,mathematicslessonsattheschoolfollowedthis
Fig. 1 Bay of All Saints, where Salvador City and the island of Itaparica are located. (Source:
https://www.google.com/maps)
