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. Submit your article to this journal Article views: 2 View related articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=meue20 Download by: [Florida Atlantic University] Date: 25 October 2017, At: 02:54 Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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. 67 Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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 Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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 Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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. Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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. Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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 Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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 Downloaded by [Florida Atlantic University] at 02:54 25 October 2017 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.