Towards a Philosophy of Critical Mathematics Education

253 Pages·1994·5.047 MB·English

by  Ole Skovsmose (auth.)

TOWARDS A PHll..OSOPHY OF CRITICAL MATHEMATICS EDUCATION
Mathematics Education Library
VOLUME 15
Managing Editor
A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board
H. Bauersfeld, Bielefeld, Germany
J. Kilpatrick, Athens, US.A.
C. Laborde, Grenoble, France
G. Leder, Melbourne, Australia
S. Turnau, Krakow, Poland
TOWARDS A PHILOSOPHY
OF CRITICAL
MATHEMATICS EDUCATION
by
OLE SKOVSMOSE
Aalborg University, Denmark
SPRINGER-SCTENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-4425-9 ISBN 978-94-017-3556-8 (eBook)
DOI 10.1007/978-94-017-3556-8
Printed on acid-free paper
All Rights Reserved
© 1994 Springer Science+ Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1994
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
CONTENTS
Acknowledgements ix
Introduction 1
Chapter 1: Critique and Education 11
1. Crisis 12
2. Critique 14
3. Emancipation? 19
4. Critical Education 21
5. Literacy and Mathemacy 24
Chapter 2: Democracy and Education 28
1. Links between 'Democracy' and 'Education' 28
2. Basic Democratic Ideas 31
3. Democratic Competence 34
4. A Problem of Democracy in a Highly Technological
Society 38
5. Education for Miindigkeit 40
Chapter 3: Mathematics-A Formatting Power? 42
1. Technology and the Vico Paradox 43
2. Mathematics and Technology 48
3. Abstractions 50
4. Formalisations 53
5. Mathematics as Critical 56
Chapter 4: A Thematic Approach in Mathematics Education 59
1. Some Sources of Inspiration 60
2. Planning a Thematic Approach 62
3. Comments on the Project 68
4. The Diary and the 'Results' 70
5. Exemplarity 73
v
vi CONTENTS
Chapter 5: "Golfparken" and "Constructions" 79
1. Opinions about Mathematics 80
2. "Golfparken" 82
3. "Construction" 86
4. Comments on the Projects 90
Chapter 6: Reflective Knowing 97
1. Reflective Knowing: A First Delineation 98
2. Reflections and Modelling 102
3. Reflective Knowing in Educational Practice 114
4. Six Entry Points to Reflective Knowing 118
5. A Note about 'Knowing' 122
Chapter 7: "Family Support in a Micro-Society" 125
1. The Structure of the Project 125
2. Comments on the Project 129
3. Reflective Knowing in the Project 133
4. Understanding 'Formatting' 136
5. A Note about Challenging Questions 138
Chapter 8: "Our Community" 141
1. The Structure of the Project 142
2. Comments on the Project 148
3. Reflective Knowing-An Open Concept 152
Chapter 9: "Energy" 155
1. The Structure of the Project 155
2. Comments on the Project 163
3. Formal Language versus Natural Language 166
4. Comments on Mathemacy 170
Chapter 10: Intentionality 175
1. Dispositions, Intentions and Actions 176
2. Learning as Action 181
3. Different Forms of Epistemic Development 184
4. Personal Fatalism, Servility and Achievement 189
5. Some Comments on the Projects 192
CONTENTS vii
Chapter 11: Knowing, An Epilogue 196
1. Knowledge-A Controlled Concept 196
2. Knowing -An Open Concept 199
3. Mono-Logical Epistemic Theories 201
4. Dia-Logical Epistemic Theories 205
5. Knowing-An Explosive Concept 206
Notes 210
Bibliography 227
Name Index 237
Subject Index 241
ACKNOWLEDGEMENTS
In 1988 the Danish Research Council for the Humanities decided to set
up the research initiative 'Mathematics Education and Democracy in
Highly Technological Societies'. The overall intention of this project
was to discuss mathematics education as part of democratic endeavour
in a highly technological society. The initiative ran for a period of
five years. The members of the group directing the initiative were
Gunhild Nissen (chairperson), University of Roskilde; Jens Bj~meboe
(secretary); Morten Blomh~j (secretary), University of Roskilde; Peter
Bollerslev, Ministry of Education; Vagn Lundsgaard Hansen, Technical
University of Copenhagen; Mogens Niss, University of Roskilde; and
Ebbe Thue Poulsen, University of Aarhus. My work forms a part of
this overall initiative. It has been supported financially by the Danish
Research Council and the University of Aalborg; additional support has
been received from Den Obelske Familiefond.
My attempt to develop a philosophy of a critical mathematics edu
cation has had much help and inspiration from experimental work car
ried out in relation to the overall initiative. The teachers and schools
who have contributed the most to my work include Henning B~tkjer,
Klarup skole; Jens J~rgen Andersen, Ole Dyhr and Thue 0rberg, Aal
borg Friskole; Ib Trankjrer, Nyvangskolen in Randers; and J~rgen Boll
and J~rgen Vognsen, R~nbrekskolen in Hinnerup. In addition Andreas
Reinbolt from Aalborg Teacher Training College has co-ordinated much
of the experimental work. Several researchers have been involved in
'Mathematics Education and Democracy in Highly Technological So
cieties'. In particular, I have had inspiration and support from Morten
Blomh~j and Lena Lindenskov, University of Roskilde; Dan Eriksen,
Royal Danish School of Educational Studies; Kirsten Gr~nbrek Hansen,
University of Copenhagen; and Helle Air~ and Then Maj Christiansen,
University of Aalborg. Karin Beyer, University of Roskilde, has given
me useful suggestions for improving parts of the manuscript. In addition
I have received most valuable criticism, of the whole manuscript, from
Marcelo Borba, State University of Sao Paulo at RioC laro.
I want to thank the directors of the initiative as well as the teachers and
the researchers involved for their support as well as for their comments
on both my work and my manuscript.
ix
X ACKNOWLEDGEMENTS
During the year 1990-1991, I visited the Department of Education,
University of Cambridge where I gained much advice from Alan Bishop,
not only about how to begin my investigation and how to finish the
book, but also about what comes in between. Alan Bishop has made
it possible for me to publish my work in the Mathematics Education
Library. Marilyn Nickson, University of Cambridge, has carefully gone
through the whole manuscript and made the final linguistic corrections.
I want to express my gratitude to both Alan Bishop and Marilyn Nickson
for their encouragement and efforts.
Aalborg, November 1993
Ole Skovsmose
INTRODUCTION
In Nineteen Eighty-Four George Orwell gives a description of different
forms of suppression. We learn about the telescreens placed everywhere,
through which it is possible for Big-Brother to watch the inhabitants of
Oceania. However, it is not only important to control the activities of
the inhabitants, it is important as well to control their thoughts, and the
Thought Police are on guard. This is a very direct form of monitoring
and control, but Orwell also outlines a more imperceptible and calculated
line of thought control.
In the Appendix to Nineteen Eighty-Four Orwell explains some struc
tures of 'Newspeak', which is going to become the official language of
Oceania. Newspeak is being developed by the Ministry of Truth, and
this language has to substitute 'Oldspeak' (similar to standard English).
Newspeak should fit with the official politics of Oceania ruled by the
Ingsoc party: "The purpose of Newspeak was not only to provide a
medium of expression for the world-view and mental habits proper to
the devotees of Ingsoc, but to make all other modes of thought impos
sible. It was intended that when Newspeak had been adopted once and
for all and Oldspeak forgotten, a heretical thought - that is, a thought
diverging from the principles of Ingsoc - should be literally unthink
able, at least as far as thought is dependent on words. Its vocabulary
was so constructed as to give exact and often very subtle expression
to every meaning that a Party member could properly wish to express,
while excluding all other meanings and also the possibility of arriving at
them by indirect methods. This was done partly by the invention of new
words, but chiefly by eliminating undesirable words and by stripping
such words as remained of unorthodox meanings, and as far as possible
of all secondary meanings whatever. To give a single example. The
word free still existed in Newspeak, but it could only be used in such
statements as 'This dog is free from lice' or 'This field is free from
weeds'. It could not be used in its old sense of 'politically free' or
'intellectually free', since political and intellectual freedom no longer
existed even as concepts, and were therefore of necessity nameless." 1
I am not going to consider life in Orwell's Oceania, nor the activity of
the Thought Police or the role of Big-Brother; but I want to take a closer
look at the presumption that a language could prestructure a world-view
1