What Counts in Teaching Mathematics: Adding Value to Self and Content

208 Pages·2011·2.21 MB·English

by  Sandy Schuck

WHATCOUNTSINTEACHINGMATHEMATICS
Self-StudyofTeachingandTeacherEducationPractices
Volume11
SeriesEditor
JohnLoughran,MonashUniversity,Clayton,Australia
AdvisoryBoard
MaryLynnHamilton,UniversityofKansas,USA
RuthKane,MasseyUniversity,NewZealand
GeertKelchtermans,UniversityofLeuven,Belgium
FredKorthagen,IVLOSInstituteofEducation,TheNetherlands
TomRussell,Queen’sUniversity,Canada
Forfurthervolumes:
http://www.springer.com/series/7072
WHAT COUNTS IN TEACHING
MATHEMATICS
Adding Value to Self and Content
Editedby
Sandy Schuck
UniversityofTechnologySydney,Sydney,Australia
Peter Pereira
DePaulUniversity,Chicago,USA
123
Editors
SandySchuck PeterPereira
UniversityofTechnologySydney DePaulUniversity
POBox222 2320Kenmore
Lindfiel ChicagoIL60614
NSW2070 USA
Australia [email protected]
[email protected]
ISSN1875-3620
ISBN978-94-007-0460-2 e-ISBN978-94-007-0461-9
DOI10.1007/978-94-007-0461-9
SpringerDordrechtHeidelbergLondonNewYork
©SpringerScience+BusinessMediaB.V.2011
Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby
anymeans,electronic,mechanical,photocopying,microfilming recordingorotherwise,withoutwritten
permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificall forthepurpose
ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Series Editor’s Foreword
WhentheInternationalHandbookofSelf-StudyofTeachingandTeacherEducation
Practices (Loughran, Hamilton, LaBoskey, & Russell, 2004) was launched at the
American Educational Research Association Annual conference in 2004, the dis-
cussant,DenisPhillipsofStanfordUniversityposedaninterestingquestionforthe
S-STEPcommunity.Denisaskedhowthefiel mightfurtherdevelopandprogress
in the wake of the achievement of publishing a Handbook that so thoroughly cap-
turedtheresearchliteratureandideasaroundself-study.Hewasoftheviewthatin
publishingtheHandbooktheS-STEPcommunitymightfeelasthoughthe‘jobhad
beendone’andthatfurtheringthecoreintentofself-studymightbeovertakenbyan
approachtogate-keepingthatcouldlimittheinfluenc ofself-studyontheveryfiel
itwasdesignedtofoster–teachingandteachereducation.ThisbookbySchuckand
Pereira,likethatofCrowe’s(2010)inSocialStudies,offersanotherclearandstrong
responsetoPhillips’insightfulchallengetotheS-STEPcommunity.
SchuckandPereirahaveassembledanimpressivegroupofmathematicseduca-
tors, each of whom offers new ways of thinking about the teaching and learning
of mathematics as a consequence of their involvement in self-study. The catalyst
for their writing was a concern to “help our students develop mathematical peda-
...
gogicalcontentknowledgeaswellassubjectcontentknowledge [becauseour]
soon to be teachers of maths in primary and secondary schools need to recognise,
andknowhowtoreduce,theconceptualdifficultie thatoftenariseforschoolstu-
dents”.Theseauthors’effortsinsodoingarecapturedinthechaptersofthisbook
in ways that demonstrate an abiding commitment to teaching and learning about
mathematicsteachingthatisthecorebusinessofmathematicsteachereducation.
Theoutcomeofaseriousconsiderationofaself-studymethodologyinresearch-
ing the teaching and learning of mathematics is clearly evident in each of the
chapters. Each of the authors demonstrates how they had to challenge their own
conceptions of mathematics teaching and learning in order to develop deeper
understandings of their own practice because, ultimately, they were concerned to
genuinely challenge their own students’ approach to, and understanding of, math-
ematics. It is this focus on their students’ learning that has been so important in
shapingtheirownlearningaboutpracticeandisclearlyanoutcomederivedfroma
thoughtfulapproachtoresearchingpracticethroughself-study.
v
vi SeriesEditor’sForeword
Becauseself-studyhasbeenaguidingmethodologytotheresearchinthisbook,
itisnotsurprisingthatotherkeyaspectsofteachingandlearningalsoemerge.For
example,thebookis“looselydividedintotwoparts”.Thefrstpartoffersinsights
gained as a consequence of learning though mentoring and collaboration – a key
aspectofself-study.Thesecondpartdelvesintothetensionsandconflict inherent
in challenging students’ attitudes and beliefs about mathematics and mathematics
teaching. Through these two separate but closely related organizing principles, a
coherent, thoughtful and honest account of salient issues in researching the teach-
ing and learning of mathematics is portrayed for the reader in a most accessible
andmeaningfulway.SchuckandPereirahavecertainlyassembledacoregroupof
mathematics educators whose work demonstrates quality and scholarship in ways
thatoffermanyinvitationsandopportunitiesforotherstobuildupon.
This book brings to the surface the value of learning with, and from, others
through collaboration, mentoring and challenging the status-quo. Key concepts of
reflectio (Dewey, 1933) and framing and reframing (Schön, 1983) continually
emerge in the chapters as the authors draw attention to the need to recognize and
reconsidertaken-for-grantedaspectsofpracticethataresofrequentlyoverlookedor
ignoredinpractice.Insodoing,theabilitytolookagainintotheheartofteaching
andlearninginordertopurposefullydeveloplong-lastingpedagogicalrelationships
in teacher education emerges as a theme that binds these chapters together into a
coherentwhole.
The editors describe self-study as “challenging, unsettling and uncomfortable”.
However, as they make clear, and as each of the chapters in this book more than
illustrates,inacceptingthechallengetolookintopracticeinnewways,thesenseof
being unsettled and uncomfortable clearly leads tonew learning that enhances the
pedagogicalexperienceforallofthoseinvolved.Acrucialoutcomeofself-studyis
to build on and expand our knowledge of teaching and learning about teaching in
waysthatmatterfortheprofession.Inthisbook,SchuckandPereirahavedonejust
thatbydrawingontheexperiencesofarangeofauthorswho,throughtheircommon
focusonmathematics,helptoofferbreakthroughsinafiel inwaysthatgenuinely
modelinnovativeapproachestostudyingmathematicsteachingandlearning.
Thisbookisafin additiontothegrowingbodyofliteratureofsubject-specifi
self-study. It illustrates how understanding and responding to the self is impor-
tant, but of itself, not sufficien for developing a pedagogy of teacher education
(Korthagen,etal.,2001;Loughran,2006;Ritter,2007).Despitethesuperficia inter-
pretations of those not involved in self-study but who often have opinions about
the work as being too concerned with the self, this book makes clear that looking
beyond the self is central to knowledge growth and development in ways that do
makeadifferenceforteachingandlearningaboutmathematicsteaching.
Inapreviousself-studySchuck(2009)highlightedthevalueoflisteningto,and
learning from, her students of teaching. Likewise, Pereira (2005) has illustrated
how to learn from the tensions and dilemmas associated with learning about how
tobecomeateacherofmathematics.Togethertheyhavecreatedaformidableedito-
rialteamandhavedevelopedaqualityproductthatinyearstocomewillbeseenasa
seminalworkinthefiel ofself-studyofteachereducationpracticesinmathematics.
SeriesEditor’sForeword vii
References
Crowe,A.(Ed.)(2010).Advancingsocialstudieseducationthroughself-studymethodology:The
power,promise,anduseofself-studyinsocialstudieseducation.Dordrecht,TheNetherlands:
Springer.
Dewey,J.(1933).Howwethink.Lexington,MA:D.C.HeathandCompany.
Korthagen,F.A.J.,Kessels,J.,Koster,B.,Langerwarf,B.,&Wubbels,T.(2001).Linkingtheory
andpractice:Thepedagogyofrealisticteachereducation.Mahwah,NJ:LawrenceErlbaum
AssociatesPublishers.
Loughran,J.J.(2006).Developingapedagogyofteachereducation:Understandingteachingand
learningaboutteaching.London:Routledge.
Loughran,J.J.,Hamilton,M.L.,LaBoskey,V.K.,&Russell,T.(Eds.)(2004).Internationalhand-
bookofself-studyofteachingandteachereducationpractices.Dordrecht,TheNetherlands:
KluwerAcademicPublishers.
Pereira,P.(2005).Becomingateacherofmathematics.StudyingTeacherEducation,1(1),69–83.
Ritter, J. K. (2007). Forging a pedagogy of teacher education: The challenges of moving from
classroomteachertoteachereducator.StudyingTeacherEducation:Ajournalofself-studyof
teachereducationpractices,3(1),5–22.
Schön,D.A.(1983).Thereflectiv practitioner:Howprofessionalsthinkinaction.NewYork:
BasicBooks.
Schuck, S. (2009). How did we do? Beginning teachers teaching mathematics in elementary
schools.StudyingTeacherEducation,5(2),113–123.
J.JohnLoughran

Contents
1 WhatCountsinMathematicsEducation? . . . . . . . . . . . . . . 1
SandySchuckandPeterPereira
PartI CollaborationsandCriticalFriends
2 TensionsofMentoringMathematicsTeachers:Translating
TheoryintoPractice . . . . . . . . . . . . . . . . . . . . . . . . . . 13
PaulBetts
3 Team-TeachingAboutMathematicsforAllCollaborative
Self-Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
ð
HafdísGu jónsdóttirandJónínaValaKristinsdóttir
4 Growing Possibilities: Designing Mathematical
andPedagogicalProblemsUsingVariation. . . . . . . . . . . . . . 45
CynthiaNicol
5 Resisting Complacency: My Teaching Through
anOutsider’sEyes . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
SandySchuck
PartII ExaminingOurPractice:Conflicts DilemmasandIncongruities
6 How Students Teach You to Learn: Using Roundtable
Reflectve Inquiry to Enhance a Mathematics Teacher
Educator’sTeachingandLearning . . . . . . . . . . . . . . . . . . 77
RobynBrandenburg
7 MakingSenseofStudents’FractionalRepresentations
UsingCriticalIncidents . . . . . . . . . . . . . . . . . . . . . . . . 93
NellB.Cobb
8 ReformingMathematicsTeacherEducationThroughSelf-Study . 111
JoanneE.Goodell
ix