Collaborating to Meet Language Challenges in Indigenous Mathematics Classrooms

310 Pages·2012·5.472 MB·

by  Tamsin Meaney, Tony Trinick, Uenuku Fairhall (auth.)

Collaborating to Meet
Language Challenges
in Indigenous Mathematics
Classrooms
Mathematics Education Library
VOLUME 52
ManagingEditor
A.J.Bishop,MonashUniversity,Melbourne,Australia
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· ·
Tamsin Meaney Tony Trinick
Uenuku Fairhall
Collaborating to Meet
Language Challenges
in Indigenous Mathematics
Classrooms
123
Dr.TamsinMeaney TonyTrinick
CharlesSturtUniversity UniversityofAuckland
SchoolofEducation FacultyofEducation
WaggaWaggaNewSouthWales POBox92109
Australia 1020Auckland
[email protected] FisherBldg.
NewZealand
[email protected]
UenukuFairhall
TeKuraKaupapaMa¯oriOTe
Koutu
POBox379
Rotorua
NewZealand
[email protected]
ISBN978-94-007-1993-4 e-ISBN978-94-007-1994-1
DOI10.1007/978-94-007-1994-1
SpringerDordrechtHeidelbergLondonNewYork
LibraryofCongressControlNumber:2011935852
©SpringerScience+BusinessMediaB.V.2012
Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby
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He mihi aroha
Hewhakahokingamihitepukapukaneikinga¯ ta¯ngatakatoaiputaatuai.Hemihi
ki a koutou me to¯ koutou kaha i ora Ma¯ori mai ai nga¯ mahi tätaitai. Hei aha? Hei
wh¯ıtikimo¯ a¯ tätoutamariki,mo¯ äta¯toumokopuna.
No¯ reira, te¯na¯ ra koutou o Te Koutu! Kaiako mai, mätua mai, tamariki mai, hoa
mai–tena¯ koutoukatoa!
Hemihihokikiakoe,ePiri,ipiritahiaimatoutokotoru.
Keiwarewarehokio¯ ma¯touhoarangatira.Te¯na¯ koutouimanawanuimaina¯!
Tena¯ hokikoe,eTeReo!Tetaongaemanahauaitengäkau.Aue¯,taukurie¯!
v
Acknowledgements
Thisbookisdedicatedtotheteachers,students,andwidercommunityofTeKura
Kaupapa Ma¯ori o te Koutu, both past and present. Without their enthusiasm and
commitment,therewouldhavebeennoschool,noMa¯ori-mediummathematicsreg-
isterresearch,andnoprojectstoreportuponinthisbook.Wetakeinspirationfrom
themandcelebratetheirachievements.
Forus,astheauthors,ourconnectionwithTeKoutuhasbeenvaluablenotjust
work-wise but also for the friendships that we have forged over the years. It has
involvedusinmuchdiscussion(heatedattimes),muchlaughter,hugeamountsof
food,andafewbottlesofredwine.Whenwebeganworkingtogether,wedidnot
realisethatadecadelaterwewouldstillbetalkingandworkingwiththeteachersat
TeKoutu.Thelongevityoftheworkbeingdoneinthisschoolmakesitaremarkable
projecttowriteaboutbutevenmorefascinatingtobepartof.
Overtheyears,ourunderstandingofwhatwasoccurringatTeKoutuhasbecome
moreinsightfulfromthemanyconversationsthatwehavehadwithcolleaguesand
students both at Te Koutu and in the teacher education programmes that we have
taught.Thankyouforyourinsights.
We also acknowledge the role that Bill Barton, presently professor at the
University of Auckland, has played in introducing us to each other in 1997 and
the initial academic influence he had on our research, which is reported in this
book.
Anothersubstantialinfluenceonourresearchhasbeenthefundingwereceived
from the Ministry of Education’s Teaching and Learning Research Initiative
for the work that we carried out between 2005 and 2007. This funding was
provided specifically for research projects based around issues highlighted by
teachers and schools and which could be done in collaboration with university
researchers.
Therehavebeenmany,manypeoplewhohavecontributedtothecollection,tran-
scription, and translation of the data. Without you the book would have been the
poorer. We know that many of you have also been inspired by the school, and we
hopethatseeingthedatapresentedinabookmakesthoseroutinetasksworthwhile.
Finallytoourfamilies,bothimmediateandextended,wewouldliketoexpress
our thanks. They have put up with our colonisation of each other’s free time, and
vii
viii Acknowledgements
sometimestheyhavehadtoendureconversationsofwhichtheymayhavebeenable
to make no sense. We do not expect you to read this book but thank you for your
patience whilst it has been created. Without your support, it would not have been
started,letalonecompleted.
“Na¯uano¯ au!”
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
WeroandtheStoryofMa¯ui . . . . . . . . . . . . . . . . . . . . . . . 2
TheSchoolandtheData . . . . . . . . . . . . . . . . . . . . . . . . . 3
UsingCaseStudies . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
TheComplexityofLearningMathematicsinanIndigenousLanguage. 6
MeetingandOvercomingChallenges . . . . . . . . . . . . . . . . . . 10
OverviewoftheChapters . . . . . . . . . . . . . . . . . . . . . . . . 11
PartI MeetingPoliticalChallenges
2 The Development of a Mathematics Register
inanIndigenousLanguage . . . . . . . . . . . . . . . . . . . . . . 19
TeWeroNo¯ Waho–TheExternalChallenge . . . . . . . . . . . . . . 21
TeWeroNo¯ Roto–TheInternalChallenge . . . . . . . . . . . . . . . 23
The Process of Expanding the Mathematics Register
inTeReoMa¯ori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
TheStandardisingProcess . . . . . . . . . . . . . . . . . . . . . . . . 31
Challenges to Te Reo Ma¯ori from Developing
theMathematicsRegister . . . . . . . . . . . . . . . . . . . . . . . . 32
MeetingChallenges . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 TheHistoryofTeKuraKaupapaMa¯orioTeKoutu–The
PoliticisationofaLocalCommunity . . . . . . . . . . . . . . . . . 37
TheHistoryofTeKoutu . . . . . . . . . . . . . . . . . . . . . . . . . 40
GovernanceandWha¯nauInvolvementintheSchool . . . . . . . . . . 47
MeetingChallengesinEstablishingandOperatingTeKoutu . . . . . . 51
4 It Is Kind of Hard to Develop Ideas When You Can’t
UnderstandtheQuestion:DoingExamsBilingually . . . . . . . . . 53
NationalCertificateofEducationalAchievement . . . . . . . . . . . . 54
MakingtheExamsBilingual . . . . . . . . . . . . . . . . . . . . . . 54
ResultsfromBilingualNCEAExaminations . . . . . . . . . . . . . . 57
EquivalenceinBilingualEducation . . . . . . . . . . . . . . . . . . . 62
ImprovingtheQualityoftheTeReoMa¯oriExaminations . . . . . . . 66
ix
x Contents
Students’ResponsestoDoingExamsBilingually . . . . . . . . . . . 68
MeetingtheChallengeofDoingExamsBilingually . . . . . . . . . . 73
PartII MeetingMathematicalChallenges
5 The Resources in Te Reo Ma¯ori for Students
toThinkMathematically . . . . . . . . . . . . . . . . . . . . . . . . 81
ResourcesinTeReoMa¯ori . . . . . . . . . . . . . . . . . . . . . . . 82
LinguisticMarkers . . . . . . . . . . . . . . . . . . . . . . . . . . 84
TransparencyWithinTerms . . . . . . . . . . . . . . . . . . . . . . 85
LogicalConnectives. . . . . . . . . . . . . . . . . . . . . . . . . . 87
LinguisticComplexity . . . . . . . . . . . . . . . . . . . . . . . . . . 89
LearningHowtoGiveSpokenExplanations . . . . . . . . . . . . . . 92
KanikaniPa¯ngarau–DancingMathematics . . . . . . . . . . . . . . . 95
MeetingChallengesAroundThinkingMathematically . . . . . . . . . 97
6 WritingtoHelpStudentsThinkMathematically . . . . . . . . . . 99
TheRoleofLiteracyWithinaTraditionallyOralCulture. . . . . . . . 99
WritingtoSupportReflection . . . . . . . . . . . . . . . . . . . . . . 100
TypesofWritinginMathematics . . . . . . . . . . . . . . . . . . . . 104
WritinginMathematicsatTeKoutu. . . . . . . . . . . . . . . . . . . 105
Whakaahua. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Whakama¯rama . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Parahau. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
JudgingtheQualityofMathematicalWriting . . . . . . . . . . . . . . 111
Students’ViewsAboutWritinginMathematics . . . . . . . . . . . . 115
ChallengesinWritingtoSupportMathematicalThinking . . . . . . . 119
7 TheCaseofProbability . . . . . . . . . . . . . . . . . . . . . . . . 121
StudentsLearningAboutProbability . . . . . . . . . . . . . . . . . . 123
LearningtoThinkAboutProbability . . . . . . . . . . . . . . . . . . 129
DevelopingtheIdeaofLikelihoodintheBeginningSchoolYears . . 129
DevelopingIdeasAbouttheProbabilityofEventsattheEnd
ofPrimarySchool . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Developing Ideas About the Probability of Events in
IntermediateandHighSchool . . . . . . . . . . . . . . . . . . . . 142
MeetingtheChallengeofUsingLanguageforThinking
Probabilistically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
PartIII MeetingCommunityChallenges
8 UsingtheMathematicsRegisterOutsidetheClassroom . . . . . . 153
TeReoMa¯oriandBroadcasting . . . . . . . . . . . . . . . . . . . . . 156
TheUseoftheMathematicRegisteronMa¯oriTelevision . . . . . . . 159
The Use of Te Reo Ma¯ori by Students Once They Finish
TheirMa¯ori-MediumSchooling . . . . . . . . . . . . . . . . . . . . . 165
Contents xi
UsingTeReoMa¯oriforFurtherStudy . . . . . . . . . . . . . . . . 165
UsingTeReoMa¯oriatWork . . . . . . . . . . . . . . . . . . . . . 167
UsingTeReoMa¯oriforSocialising. . . . . . . . . . . . . . . . . . 168
Meeting the Challenge of Having Te Reo Ma¯ori Spoken
intheCommunity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
9 TeachersasLearnersoftheMathematicsRegister . . . . . . . . . 171
LanguageKnowledgeasPartofPedagogicalContentKnowledge . . . 173
InitialTeacherEducationforMa¯ori-MediumTeachers . . . . . . . . . 179
LearningontheJob:TheSituationatTeKoutu . . . . . . . . . . . . . 182
StrategiesforLearningtheMathematicsRegisterWhilstatWork . . . 185
Professional Development for Teachers of Mathematics
inTeReoMa¯ori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Meeting the Challenges of Teachers Learning
theMathematicsRegister . . . . . . . . . . . . . . . . . . . . . . . . 191
PartIV MeetingPedagogicalChallenges
10 “They Don’t Use the Words Unless You Really Teach
Them”:MathematicalRegisterAcquisitionModel . . . . . . . . . 199
MathematicsRegisterAcquisitionModel(MRA). . . . . . . . . . . . 201
Kitenga/Noticing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Akoranga/Intake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Taunga/Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Putanga/Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
CombiningStrategiesforEffectiveness . . . . . . . . . . . . . . . . . 215
LanguageAcquisitionStrategiesandYearLevel . . . . . . . . . . . . 216
TheEffectoftheNewnessoftheTopiconStrategyUse . . . . . . . . 219
Meeting the Challenge of Documenting How Teachers
SupportedStudentstoAcquiretheMathematicsRegister . . . . . . . 220
Appendix:Year6Teacher’sScaffoldingStrategies . . . . . . . . . . . 221
11 “Ma¯oriwereTraditionalExplorers”:Ma¯oriPedagogical
Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
WhatarePedagogicalPractices? . . . . . . . . . . . . . . . . . . . . 227
WhatareMa¯oriPedagogicalPractices? . . . . . . . . . . . . . . . . . 228
TeAhoMatua . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
PedagogicalPracticesatTeKoutu . . . . . . . . . . . . . . . . . . . . 232
TeIraTangata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
TeReo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Nga¯ Iwi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
TeAo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
A¯huatangaAko . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
TeTinoUaratanga . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
MeetingtheChallengeofWorkingWithinMa¯oriPedagogy . . . . . . 247