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European Education
ISSN: 1056-4934 (Print) 1944-7086 (Online) Journal homepage: http://www.tandfonline.com/loi/meue20
The Politics of Anti-Racist Mathematics
George Gheverghese Joseph
To cite this article: George Gheverghese Joseph (1994) The Politics of Anti-Racist Mathematics,
European Education, 26:1, 67-74, DOI: 10.2753/EUE1056-4934260167
To link to this article: http://dx.doi.org/10.2753/EUE1056-4934260167
Published online: 08 Dec 2014.
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The Politics of Anti-Racist
Mathematics
Anti-Racist/Multicultural Mathematics: Common Perceptions
At the Annual Conservative Party Conference in 1987, Prime
Minister Margaret Thatcher declared:
Children who need to count and multiply are being taught antiracist mathematics, whatever that may be.
Mrs. Thatcher's puzzlement is shared by many, including a
number of teachers. Multicultural/anti-racist mathematics is perceived as a strange and incongruous subject introduced into an
already overladen mathematics syllabus rather than as an approach which permeates all topics within the syllabus.
This view is best captured by the section on ethnic and cultural diversity (paragraphs 10.18-10.23) of the preliminary National Curriculum Report (DES, 1988) entitled Mathematics for
Ages 5 to 16.
It is sometimes suggested that the multicultural complexion of
society demands a "multicultural" approach to mathematics, with
children being introduced to different numeral systems, foreign
currencies, and non-European measuring and counting devices.
This is a revised version of a paper presented to the First lntemational Conference on
Political Dimensions of Mathematics Education held at the Institute of Education,
University of London, on 1 4 April 1990.
Dr. George Gheverghese Joseph is a Senior Lecturer in the Department of Econometrics and Social Statistics at the University of Manchester, U.K. His books, The Crest of
the Peacock: Non-European Roots of Mathematics (1992) and Multicultural Mathematics (1993), develop the historical and pedagogical issues discussed in this article.
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68 POLITICS OF ANTI-RACIST MATHEMATICS
We are concerned that undue emphasis on multicultural mathematics, in these terms, could confuse young children. While it is
right to make clear to children that mathematics is the product of
a diversity of cultures, priority must be given to ensuring that
they have the knowledge, understanding, and skills which they
will need for adult life and employment in Britain in the twentyfirst century. We believe that most ethnic parents will share this
view. . . . (Paragraph 10.22)
These quotations summarize well the widespread reservations
that exist about multicultural mathematics. It is seen as something irrelevant or peripheral, a sop for or a way of patronizing
ethnic minority children, not particularly useful in providing
training for adult life and employment, educationally unsound
because it may confuse children, involving adding extra bits to
the existing curriculum which would further burden teachers and
children.
Anti-Racist/Multicultural Mathematics
Anti-racist education in Britain, as readers of this journal are
aware, is not a matter of bits, but a holistic approach to education. It involves organization, ethos, teaching styles, and every
area of the curriculum-including
mathematics. The Swann
Report (1985) and more recent reports have highlighted the
existence of racism in British society and British schools. The
mathematics teacher, like teachers in other subjects, needs to
be aware of the ways in which racism enters the classroom and
how it can be countered. An ILEA publication, Everyone
Counts (1985), contains the following checkpoints of how bias
or insensitivity to racial minorities may creep into a mathematics lesson:
a. Lifestyles Implied in Classroom Examples Unduly Restrictive
Illustration: Using the common "statistics" example of ownership of pets in a class with a large number of children of
Asian or African origin among whom keeping pets may be
uncommon.
GEORGE GHEVERGHESE JOSEPH
69
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b. Ignoring or Devaluing Certain Ethnic Groups
Illustration 1 : Accepting the stereotype of a child of Afro-Caribbean origin being "no good7' at mathematics compared to an
Asian child.
Illustration 2: Before the coming of the European, the African
had a primitive counting system. That was all that was needed in
a simple society.
c. Being Insensitive to the Position of Minority Groups in Society
Illustration: Refusing to recognize that issues of racial discrimination and power relations within the wider society are proper
subjects of study in a mathematics classroom.
The use of mathematics to affect social attitudes in colonial
and postindependent Mozambique is brought out well by Gerdes
(1985). During Portuguese rule, questions beginning, "In a factory, the men earned 45$, women 30$ and apprentices 15$ . . . ,"
"In Loren20 Marques, Mr. Abilo has a house rented to four
tenants who pay . . . " legitimized gender inequality and landlordltenant relations respectively as much as questions beginning, "23 peasants are working in a field. At midday 6 Frelimo
guerrilla fighters arrive to help them. . . . " "Yesterday there
were 22 women in a literacy class. Today 5 more women joined
the class . . . " emphasized the social role of the Frelimo fighters
and the importance of literacy for women respectively.
The very fact that many teachers would be prepared to accept
the first two questions from the colonial period, while having
reservations about the nature of the example that refers to guerrilla fighters indicates how meaningless is the concept of a "politics-free" mathematics for the classroom.
At a conference convened to respond to the sections on ethnic
and cultural diversity contained in the National Curriculum documents on mathematics and science documents, we recommended
that paragraph 10.20, quoted earlier, should be replaced by:
The mathematics curriculum must provide opportunities for all
pupils to recognize that all cultures engage in mathematical activity and no single culture has a monopoly on mathematical
70 POLITICS OF ANTI-RACIST MA THEMATICS
Figure 1. An Alternative Trajectory
\
WESTERN
/
El
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SICILY
achievement. All pupils must be given the opportunity to enrich
their mathematical experience by selection of appropriate materials to stimulate and develop the knowledge, understanding, and
skills they will need for adult life and employment in Britain in
the twenty-first century. Mathematical experience may be enriched by examples from a variety of cultures--e.g., Vedic arithmetic enhances understanding of number, Islamic art patterns are
based on complex geometric construction, and the Chinese had a
rod numeral method of solving simultaneous equations that leads
naturally to methods used in higher mathematics.
I quote this passage not because of any subsequent reaction
from the politicians or bureaucrats. Indeed the deafening silence
that greeted the criticisms of the "ethnic and cultural diversity"
section of the National Curriculum document was followed by
the jettisoning of this section from later reports. However, our
suggested replacement paragraph highlights two aspects which
tend to be swept under the carpet in most discussions of the need
for antiracist/multicultural inputs into the National Curriculum.
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GEORGE GHEVERGHESE JOSEPH
71
First, it emphasizes the need for exemplars from cultures and
traditions that have been ignored or devalued for far too long.
Second, it also conveys by implication what is sometimes identified as the "hidden" objective of promoting the permeation of
multiculturalism into the mathematics curriculum. A multicultural approach to mathematics is seen as part of a general strategy
of making mathematics more accessible and less anxiety-arousing among a wider public. It is part of a challenge of the overall
content and pedagogy of the standard curriculum in its signal
failure to make mathematics more accessible to working-class,
female, and black students. It counters the view of mathematics
as a sequence of unconnected skills, taught in isolation from the
real world of applications and preparing those who have the
ability and commitment to join a tiny, inward-looking group,
speaking their language and sharing their enthusiasm for the
subject. The vast majority, however, after their experience at
school, are relieved to be rid of it once they leave.
History and Anti-Racist/MulticulturalMathematics
The neglect or devaluation of non-European cultures is best seen
in the manner in which the historical development of the subject
is perceived. The "classical" Eurocentric trajectory views mathematical development as taking place in two areas separated by a
period of stagnation lasting for a thousand years-Greece (from
about 600 BC to AD 300) and post-Renaissance Europe from the
15th century to the present day. The intervening period of inactivity is labeled as the "Dark Ages9'-a convenient label which
was both an expression of post-Renaissance prejudices about its
immediate past and of the intellectual self-confidence of those
who saw themselves as the true inheritors of the "Greek miracle"
that occurred on Ionian soil two thousand years earlier. This
view of history served as a useful rationale for a colonial ideology of dominance in the past. Traces of it remain today, despite
evidence of significant mathematical developments in Mesopotamia, Egypt, China, pre-Columbian America, India, and the Arab
world, to mention a few places, and despite growing evidence
that Greek mathematics owed a significant debt to the mathematics of some of those cultures.
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72 POLITICS OF ANTI-RACIST U4THEMATICS
A somewhat grudging acceptance of the debt owed by Greek
mathematics to earlier civilizations and of the seminal contributions of the Arabs led some historians of mathematics in recent
years to accept the "modified" Eurocentric trajectory. Even in
this scenario, the role of other cultures is ignored or marginalized. For example, in those texts where India and China make an
appearance, the discussion is often confined to a single chapter
which may go under the misleading title of "Oriental" mathematics. There is little indication of how these cultures contributed to the mainstream development of mathematics and no attempt to take account of recent research into the mathematics of
these and other areas. They are included in histories of mathematics as a "residual dump" to be ignored without affecting the
main story. The figure on page 70 provides an "alternative"
trajectory of such transmissions between the eighth and fifteenth
centuries, the period described as the "Dark Ages." The exchange and transmission between different cultural areas and the
critical role of the Arabs in taking mathematics westward are
brought out by the figure. They will not be discussed here but
the interested reader may wish to consult Joseph (1987, 1992).
There are certain lessons to be learned for the classroom from
a less Eurocentric perspective to mathematical development. We
will consider just two.
i. It is important to recognize the misleading aspects of naming
mathematical constructs only after Greeks and Europeans. For
example, the earliest known demonstrations of the Theorem of
Pythagoras are found in an ancient Chinese text, Chou Pei Suan
Ching, conservatively dated around the latter half of the first millennium BC and in the Sulbasutras (ca. 800-600 BC) from India.
Earlier antecedents of the Pascal triangle or the Gregory series or
the Homer's method are all to be found outside Europe.
ii. If we accept the principle that teaching should be tailored to
students' experience of the social and physical environment in
which they live, mathematics should draw on these experiences,
including the mathematical heritage of different ethnic minority
groups in Britain. The rangoli patterns that decorate the homes
of Hindu and Sikh families, the geometric art that forms the
basis of the Islamic designs in mosques and wall coverings, the
calendars that determine the Jewish and Chinese new year, are
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GEORGE GHEVERGHESE JOSEPH
73
all part of the rich heritage that can be brought to life in a
mathematics lesson. Drawing on the traditions of these groups,
indicating that their cultures are recognized and valued, would
also help to counter the entrenched historical devaluation of
them. Again, by promoting such an approach, mathematics is
brought into contact with a wide range of disciplines, including
art and design, history, and social studies, which it conventionally ignores. Such a holistic approach would serve to augment
rather than fragment a child's understanding and imagination.
Conclusion
In the final analysis, the principal purpose of antiracist mathematics is to combat racism through mathematics. The mathematics teacher, like teachers in other subjects, needs to be aware of
the ways in which racism enters the classroom and how it can be
countered. Both history and the social context of mathematics
provide useful exemplars for teachers who wish to do so. A
growing number of such exemplars are now available, references
to which are found in the Bibliography.
Bibliography
Gerdes, P. "Conditions and Strategies for Emancipatory Mathematics Education in
Underdeveloped Countries." For the Learning of Mathematics, 5 (1985), 15-20.
Gerdes, P. "On Possible Uses of Traditional Angolan Sand Drawings in the Mathematics Classroom." Educational Studies in Mathematics, 19 (1988), 3-22.
Hemmings, R. "Mathematics" in Curriculum Opportunities in a Multicultural Society,
ed. A. Craft and G. Bardell. London: Harper and Row, 1984.
Hudson, B. Global Statistics. York: University of York, 1987.
. "Global Perspectives in the Mathematics Classroom," Educational Studies in
Mathematics, 21 (1990), 129-36.
Inner London Education Authority. Everyone Counts. London, 1985.
Joseph, G. G. "The Multicultural Dimension." Times Educational Supplement, Mathematics Extra, 5 October 1984.
. "An Historical Perspective" TimesEducational Supplement, 11October 1985.
. "A Non-Eurocentric Approach to School Mathematics," Times Educational
Supplement, 4 (2), 1986.
. "Foundations of Eurocentrism in Mathematics" Race and Class, 28 (1987),
13-28.
. "Turning the Tables," Times Educational Supplement, Mathematics Extra, 5
May 1989.
. The Crest of the Peacock: Non-European Roots of Mathematics. London:
Penguin, 1992.
74 POLITICS OF ANTI-RACIST MA THEMATICS
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Joseph, G.G., Nelson, R. D., and Williams, J. Multiculhual Mathematics. Oxford:
Oxford University Press, 1993.
The Mathematical Association. Mathematics in a Multicultural Society. Leicester,
1989.
Schools Councils Project. Statistics in Your World. Foulsham Slough, 1980.
Swetz, F . J., and Kae, T.I. Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China. Pennsylvania State University Press, 1977.
Zaslavsly, C. Africa Counts. New York: Lawrence Hill, 1979.
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