ZDM 98/5 mathematical knowledge Section III: Considering interactions between culture and mathematical knowledge Section IV: Reconsidering what counts as mathematical knowledge Section V: Ethnomathematical praxis in the curriculum Section VI: Ethnomathematical research Rather than reflecting the different traditional disciplines, the editors have skilfully structured the book in terms of the goals and foci of the writings, thus representing as well some of the motives and aspirations of the different authors. This is important because as the editors say in their acknowledgments: "What is particularly significant about the academic discipline of ethnomathematics is that it emerged from intellectual influences of emancipatory struggles worldwide and that interest and work in the discipline has not been limited to the academy" (p. xi). There is thus no doubt that this book is a socio-political documentation of some of the challenges to orthodoxy and entrenched traditions in academic mathematics and its related fields. 3. The chapters Section I This section is basically an introductory section to the book and it sets the scene with two of the fundamental papers in the field. The first, by d'Ambrosio, "Ethnomathematics and its place in the history and pedagogy of mathematics" grew out of his plenary address at the InterNational Congress of Mathematics Education in Adelaide, Australia, in 1984. The title reveals that in those early days the field which helped to legitimise the new area of study was history. In contrast, and indicating some of the challenge which this new field represented, the second chapter, by the Aschers, "Ethnomathematics" was, as they say, written in the early 1980s but did not find journal acceptance for several years. This paper was firmly in the field of anthropology, a field which traditionally had not been a great contributor to disciplinary thinking about mathematics and mathematics education. Section II In this section are three of the key papers which directly challenge the orthodox views of the history of mathematical ideas, and which, the editors claim, get to the heart of Eurocentrism. As if to illustrate this point, the first chapter by Joseph is entitled "Foundations of Eurocentrism in mathematics". In this he documents the historical "gaps" concerning the roles of the Arabs, and the Africans, which are fundamental to understanding the history of mathematical development. The next chapter, by Bernal, "Animadversions on the origins of Western science", develops this theme further by describing the contribution of the Egyptians to science, and shows how the traditional history of Western science fails to recognise that contribution in giving much greater credit to the work of the Greeks. The third chapter in this section is by Lumpkin, "Africa in the mainstream of mathematics history", who argues that although for thousands of years Africa was in that mainstream, that fact is rarely acknowledged by orthodox

ZDM 98/5 historians of mathematics. Section III This section, which could in this reviewer's view have been much longer, tackles the issue of the relationship between culture and mathematics. In some sense this is the focus which is at the disciplinary heart of the ethnomathematics movement. For this section the editors have selected only 3 papers of the many which could have been chosen. The first by Ginsberg, "The myth of the deprived child: new thoughts on poor children" exposes the dominant cultural underpinnings of many societal assumptions about academic failure by so-called "poor" children. The next chapter by Martin, "Mathematics and social interests" is perhaps less well known to mathematics educators but is a powerful demonstration of the way that mathematical ideas, which have usually been portrayed as culture-free and value-free, have been crucially influenced by societal interests and pressures. His chapter finishes with this remark with indicates perhaps better than any other the driving force behind the whole book, "Exposing the links between mathematics and social interests should not be seen as a threat to "mathematics" but rather as a threat to the groups that reap without scrutiny the greatest material and ideological benefits from an allegedly value-free mathematics" (p. 169). Another unfamiliar paper by Struik is the third chapter in this section. It is called "Marx and mathematics" and shows how a particular perspective affects one's views of mathematical constructs, in this case how "dialectical materialism" influenced Marx's theoretical ideas on the calculus. Section IV This section focuses our attention on what counts as mathematical knowledge and on who considers it thus. The first chapter by Walkerdine, "Difference, cognition, and mathematics education" discusses some of the issues related to class and gender resulting from her research on the learning of mathematics by young children. The second chapter by Harris, "An example of traditional women's work as a mathematical resource" continues the theme of gender stereotyping in the definition of mathematical knowledge. The third by Gerdes, "On culture, geometrical thinking and mathematics education" focuses on the issues from the perspective of a developing country, Mozambique. All three chapters in this section force us to confront the power of the dominant groups in determining the nature of orthodox mathematical knowledge, an orthodoxy which of course has many educational implications. Section V This section, with 4 chapters, represents one of the predominant foci of contest in mathematics education, namely the mathematics curriculum. Developments in ethnomathematics have added a different dimension to this contestation, with particular implications in educational situations of difference. Borba's chapter "Ethnomathematics and education" sets the scene well by discussing the relative "efficiency" and "efficacy" of ethnomathematics and orthodox mathematics in the classroom, in terms of the methods to be used in a particular context, and the avail-

Book Reviews ability of ideas for aiding learning. Fasheh, in his chapter "Mathematics, culture, and authority", critiques standard mathematics teaching in the context of a non-Western culture and a Third World society, and discusses the authority issues associated with trying to change the curriculum in that kind of situation. Anderson, in "Worldmath curriculum: fighting Eurocentrism in mathematics" shows how including historical information about the mathematical knowledge of African, Asian and Latin American peoples can help students from marginalised cultures in USA classrooms. Zaslavsky in "world cultures in the mathematics class" continues this theme by arguing that exposure to such multi-cultural ideas can, and should, benefit all students, not just those from minority cultures. Section VI This section is concerned with some of the developments taking place in ethnomathematical research and demonstrates that not only is the research continuing but the contests are still continuing. Gerdes' "Survey of current work in ethnomathematics" presents a huge coverage of the main developments, with references from p. 357371. Pinxten, an anthropologist, uses his specific knowledge to discuss some "Applications in the teaching of mathematics and the sciences" with a traditional Native American group in mind. Knijnik contributes the final chapter of the section "An ethnomathematical approach in mathematics education: a matter of political power" from the perspective of the landless peasants in Brazil. 4. Conclusion As was stated in the introduction, this book is an important "reader" for those who are new to the field, but it is also important to recognise that this is not a mere random collection of papers and articles in the field. There are many other papers and writings which could have been chosen to constitute a reader in ethnomathematics. This collection has been skilfully and deliberately constructed to represent a particular perspective on ethnomathematics and its development, one which catches the aims, arguments and contexts of those who see it as the main hope for the necessary challenge to Eurocentrism. This is not a neutral anodyne account of the development of a field. It is a lively, partial, and political expose of both the contest and the contestants over the definition and ultimately the control of mathematical knowledge. One could argue with many aspects of course, such as whether Eurocentrism is the appropriate target, or whether Westernism might be more appropriate nowadays, given the major roles that the USA has played in this century concerning the proselytising of Western, contrasted with European, values. One could certainly also argue with some of the choices of papers; for example there is little which represents the struggle for appropriate articulations of mathematical knowledge in workplace education and training, and there are no chapters discussing Chinese mathematical knowledge and culture, so important in East Asia nowadays. The fact remains that ethnomathematics presents a viable and crucial challenge to Eurocentric thinking in mathematics and mathematics education, and this book with its 147

Book Reviews reworked papers mainly from 1982-94, documents much of the dynamic of its genesis during that period. The world of mathematics and mathematics education will certainly never be the same again, and the editors are to be complimented on their contribution to our knowledge. 5. References Powell, A. B.; Frankenstein, M. (1994): Towards liberatory math- ematics: Paulo Freire's epistemology and ethnomathematics. In: P. L. McLaren; C. Lankshear (Eds.), Politics of liberation: Paths from Freire. London: Routledge Author Bishop, Alan J., Prof., Monash University, Faculty of Educa- tion, Clayton, VIC 3168, Australia. E-mail: [email protected]

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ZDM 98/5

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New books on mathematics/Computer Science education as well as books of general interest are reviewed in detail in the review section of ZDM. Readers are encouraged to participate in ZDM by offering book reviews and / or proposing books for a review to the editorial office of ZDM.

148

AB Powell, M Frankenstein

Deutschunterricht mit Migrantenkindern: bilinguale, kommunikative, interkulturelle und ganzheitliche Ansätze, 167 pages, 1.04 Mb

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