Transitions Between Contexts of Mathematical Practices

252 Pages·2002·2.513 MB·English

by  Guida de Abreu, Norma C. Presmeg (eds.)

Transitions Between Contexts of Mathematical Practices
Mathematics Education Library
VOLUME 27
Managing Editor
A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board
H. Bauersfeld, Bielefeld, Germany
J.P. Becker, Illinois, U.S.A.
G. Leder, Melbourne, Australia
A. Sfard, Haifa, Israel
O. Skovsmose, Aalborg, Denmark
S. Turnau, Krakow, Poland
The titles published in this series are listed at the end of this volume.
Transitions Between Contexts
of Mathematical Practices
Edited by
Guida de Abreu
Department of Psychology, University of Luton, U.K.
Alan J. Bishop
Faculty of Education, Monash University, Melbourne, Australia
and
Norma C. Presmeg
Department of Mathematics, Illinois State University,
Normal, Illinois, U.S.A.
KLUWER ACADEMIC PUBLISHERS
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eBookISBN: 0-306-47674-6
Print ISBN: 0-7923-7185-2
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CONTENTS
Acknowledgements vii
List of Contributors ix
Editors’ Prelude: Researching mathematics learning: the need for
a new approach 1
Chapter 1: Mathematics learners in transition 7
Guida de Abreu, Alan Bishop and Norma Presmeg
Chapter 2: Immigrant children learning mathematics
in mainstream schools 23
Núria Gorgorió, Núria Planas and Xavier Vilella
Chapter 3: The transition experience of immigrant secondary
school students: dilemmas and decisions 53
Alan Bishop
Chapter4: Thinking about mathematical learning with
Cabo Verde Ardinas 81
Madalena Santos and João Filipe Matos
Chapter 5: Exploring ways parents participate in their children’s
school mathematical learning: cases studies in
multiethnic primary schools 123
Guida de Abreu, Tony Cline and Tatheer Shamsi
Chapter 6: Transitions between home and school mathematics:
rays of hope amidst the passing clouds 149
Marta Civil and Rosi Andrade
Editors’ Interlude: Theoretical orientations to transitions 171
Chapter 7: Towards a cultural psychology perspective on
transitions between contexts of mathematical
practices 173
Guida de Abreu
Chapter 8: Mathematical acculturation, cultural conflicts, and 193
transition
Alan Bishop
Chapter 9: Shifts in meaning during transitions 213
Norma Presmeg
vi CONTENTS
Editors’ Postlude: The sociocultural mediation of transition 229
Author Index 239
Subject Index 241
ACKNOWLEDGEMENTS
This bookrepresents asharedjourney undertaken by researchers workingindiffer-
ent contexts and different situations but sharing similar educational concerns and
research aspirations. The course of thejourney involved the collaboration of many
people andinstitutions towhomwewouldliketoexpress our gratitude.
Wewishtothankfirstofall thepeoplewhohave participatedinour researchpro-
jects, without their contribution this volume would not be possible. Teachers and
schoolmanagers have allowedusintotheirclassrooms. Parentshaveallowed usinto
theirhomes. Childrenhavebeenpatientin answering ourquestions andintolerating
our observations. Workers have allowed our presence, even intrusion, into their
everydaypractices andhavegivenus insightsonwhattheydoandwhy.Wearevery
grateful toallofthemforopeningtheir doorsandallowingusin.
Alltheempiricalworkreportedinthebook wasfunded byNationalAgencies and
wealsowish to expressourthanks tothese organisations.Namely:
Catalan Ministry of Education, Fundació Propedagògic, Catalonia – Spain, funded
the research presented by Núria Gorgorió, Núria Planas and Xavier Vilella in
chapter 2;
Australian Research Council – funded the research reported by Alan Bishop in
chapter 3, in a collaborative project undertaken with Gilah Leder, Chris Brew and
Cath Pearn;
Fundação Ciência e Tecnologia, Portugal (Grant PRAXIS-PCSH-C-CED-146-96),
funded the research reported by Madalena Santos and João Filipe Matos in chapter
4;
ESRC – Economic and Social Research Council in the UK (Grant R000222381),
funded the research reported in chapter 5 by Guida de Abreu, Tony Cline and
Tatheer Shamsi;
Educational Research and Development Centers Program (PR/ Award Number
R306A60001), OERI – U.S. Department of Education, funded the research reported
by Marta Civil and Rosi Andrade in chapter 6.
Of course many other institutions, including our own Universities or Schools,
have supported the authors’ development of the ideas presented in the book by
giving us time, space and the resources to undertake the research and to participate
in local and international research meetings. We are very grateful for this support
and wish to take the opportunity to thank all the colleagues who shared and ques-
tioned our ideas.
We also wish to thank those that helped us to transform what we learned in our
journeys into a book. Here we wouldespecially like to acknowledge NúriaGorgorió
and her colleagues at the Faculty of Education, University Autonoma of Barcelona,
for the organisation of the first TIEM 98 (Trimestre Intensiu en Educació
Matemàtica) in Barcelona. It provided a rare opportunity for the editors to meet. It
was during TIEM, in our offices at the CRM (Centre de Recerca Matemàtica), that
viii ACKNOWLEDGEMENTS
the first outline of the book structure and the planning of the first group meeting,
which tookplace during PMEin SouthAfricain 1998, weredrafted. We arealso in
debt to the reviewers ofthe first outline we submitted to Kluwer. Their comments
were certainly provocative, and have helped us to produce the book in the current
shape. Thanks to themthe group had amostenjoyable meeting pre-CIEAEM 51, in
the University College ofChichester in 1999. And, here we cannot omit our grati-
tudetoAfzalAhmed, theChairofCIEAEM 51, whoprovidedtheinfrastructure for
our group meeting.
Many other names of colleagues who have supported, guided and challenged us
come to our minds. It would make a long list to single each one out. The same will
be true about the support each of us has received from our families. To all of them
we conclude with a message of deep gratitude and appreciation.
LIST OFCONTRIBUTORS
Guida de Abreu Núria Planas
Department of Psychology Facultat Ciències de l’Educació
University of Luton Universitat Autònoma de Barcelona
Park Square, Luton, Beds Edifici G G-5 140
LU1 3JU Bellaterra
UK 08193 Barcelona
Spain
Rosi Andrade
Department of Mathematics Norma Presmeg
University of Arizona Mathematics Department
617 N. Santa Rita 313 Stevenson Hall
Tucson AZ 85721 Illinois State University
USA Normal, IL 61790-4520
USA
Alan Bishop
Faculty of Education Madalena Santos
P.O Box 6, Monash University, School: Escola Básica 2-3 de Paço
Victoria 3800 d’Arcos
Australia Research Centre: Centro de
Investigação em Educação
Tony Cline
Faculdade de Ciências
Department of Psychology
Universidade de Lisboa
University of Luton
Campo Grande, C1
Park Square, Luton, Beds
1700 Lisboa
LU1 3JU
Portugal
UK
Tatheer Shamsi
Marta Civil
Department of Psychology
Department of Mathematics
University of Luton
University of Arizona
Park Square, Luton, Beds
617 N. Santa Rita
LU1 3JU
Tucson AZ 85721
UK
USA
Xavier Vilella
Núria Gorgorió
Facultat Ciències de l’Educació
Facultat Ciènciòs de 1’Educació
UniversitatAutonoma de Barcelona
Universitat Autònoma de Barcelona
Edifici G G5-142
Edifici G G5-142
Bella Terra
Bellaterra
08193 Barcelona
08193 Barcelona
Spain
Spain
João Filipe Matos
Departamento de Educação
Faculdade de Ciências
Universidade de Lisboa
Campo Grande, C1
1700 Lisboa, Portugal
EDITORS’ PRELUDE
RESEARCHING MATHEMATICS LEARNING:
THE NEEDFORA NEWAPPROACH
We begin this book by sharing with the reader three vignettes which provide a snap-
shot of the experiences of learners who have to cope with differences between math-
ematical practices in their school and out-of-school contexts.
VIGNETTE1(BRAZIL, YEAR 5 – PRIMARY SCHOOL)
‘I’m the worst, because as I said there’s no way I can get it into my head, even though I pay
attention’ (Abreu, 1993, p. 124).
This was how Severina, daughter of an unschooled sugar-cane farm worker,judged
her performance in school mathematics. She entered school at the age of 6. At 14 she
was still in year 5. She repeated year 4 three times. After school she worked on the
production of manioc flour, and also helped her father in sugar-cane farming during
the harvest. She acknowledged that people in sugar-cane farming could do sums:
‘Yes, they do, but I think they do sums in their heads like my father. But writing they
do not do’. Doing sums orally using out-of-school methods, however, did not have
the same importance as using school-written methods, since for Severina, these
defined for her the places people can access. Referring to the sugar-cane workers she
remarked: ‘If they had studied they would not be working in that place. This is an
example of those who have never been to school, like my father’. Ironically it is
Severina’s unschooledfather who still helps her with her homework: ‘I ask him how
much is 3 times 7 or 8 and he answers. How much is 3 plus 12? He answers every-
thing.’ The various conflicts – cognitive, affective, valorative – which emerged from
the differences seem to remain with Severina.
VIGNETTE 2 (CATALONIA, SPAIN, YEAR 3 – SECONDARY SCHOOL)
‘I am wrong in your class. ... I do the same mathematics as boys, but I will not do the same
work ... I do not want to be a mechanic. Please can I do mathematics for girls?’ (Gorgorió,
Planas & Vilella, chapter 2).
Saima, a 16 year-old Indian girl, arrived in Barcelona 9 months before she made the
above comment to her classroom teacher. She learned the language quite quickly
G. de Abreu, A.J. Bishop, and N.C. Presmeg (eds.), Transitions Between Contexts of Mathematical
Practices, 1–5.
© 2002 Kluwer Academic Publishers. Printed in Great Britain.
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