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Explorations in Ethnomathematics and Ethnoscience in Mozambique

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Explorations in Ethnomathematics and Ethnoscience in Mozambique Copyright © 2014 by Paulus Gerdes www.lulu.com http://www.lulu.com/spotlight/pgerdes 2 Paulus Gerdes (Editor) EXPLORATIONS IN ETHNOMATHEMATICS AND ETHNOSCIENCE IN MOZAMBIQUE 2014 3 Title: Explorations in Ethnomathematics and Ethnoscience in Mozambique Editor: Paulus Gerdes C. P. 915, Maputo, Mozambique [email protected] First edition (1994): Ethnomathematics Research Project Instituto Superior Pedagógico (since 1995: Universidade Pedagógica) Maputo, Mozambique Authors: 1 Mário Baloi: M.Ed. (Physics, Gustrow, Germany), Department of Physics. ISP, P. O. Box 3276, Maputo José Barros: M.Ed. (Chemistry, Gustrow, Germany), Department of Chemistry, ISP, P. O. Box 3276, Maputo Marcos Cherinda: M.Ed. (Mathematics, Gustrow, Germany), Department of Mathematics, ISP, P. O. Box 2923, Maputo Jan Draisma: M.Sc. (Mathematics, Amsterdam, Netherlands), Department of Mathematics, ISP, P. O. Box 2025, Beira Abdulcarimo Ismael: M.Ed. (Mathematics, Dresden, Germany), Department of Mathematics, ISP, P. O. Box 2923, Maputo Felisberto Lobo: M.Ed. (Biology, Gustrow, Germany), Department of Biology, lSP, P. O. Box 3276, Maputo Abílio Mapapá: M.Ed. (Mathematics & Physics, Maputo), Department of Mathematics, lSP, P. O. Box 2923, Maputo Adão Matonse: M,Ed. (Physics, Dresden, Germany), Department of Physics, ISP, P. O. Box 3276, Maputo 1 See “Where are the authors in 2014” on pages 93-96. 4 Cristiano Pires: M.Ed. (Biology, Gustrow, Germany), Department of Biology, ISP, P. O. Box 3276, Maputo Luís Ramos: M.Ed. (Chemistry, Gustrow, Germany), Department of Chemistry, ISP, P. O. Box 3276, Maputo Horácio Simão: M.Ed. (Mathematics & Physics, Maputo), Department of Physics, ISP, P. O. Box 2923, Maputo Daniel Soares: M.Ed. (Mathematics, Gustrow, Germany), Department of Mathematics, ISP, P. O. Box 2025, Beira Linguistic revision: Jill Gerrish & Joanna Smith: Department of English, ISP, Maputo Second edition (2014): Faculty of Natural Sciences and Mathematics, Pedagogical University, Maputo, Mozambique International distribution (Printed version and eBook): www.lulu.com/spotlight/pgerdes Copyright © 2014 Paulus Gerdes 5 Map of Mozambique 6 Contents page Map of Mozambique 6 0 Preface (Paulus Gerdes) 9 1 On the Origin of the Concepts of “Even” and 13 “Odd” in Makhuwa Culture (Abdulcarimo Ismael) 2 Mathematical-educational exploration of 21 traditional basket weaving techniques in a children’s “Circle of Interest” (Marcos Cherinda) 3 Popular counting methods in Mozambique 31 (Daniel Soares & Abdulcarimo Ismael) 4 How to handle the theorem 8+5=13 in (teacher) 39 education? (Jan Draisma) 5 Symmetries and metal grates in Maputo – 63 Didactic experimentation (Abílio Mapapá) 6 Symmetric ornamentation on wooden spoons 71 from Sofala Province – a study in progress (Daniel Soares) 7 Strip patterns on wooden spoons from 75 Inhambane Province – a study in progress (Marcos Cherinda) 8 Ideas about Nature: Traditional Interpretations 79 of Thunder and Lightning in Catembe and Physics Teaching (Mário Baloi) 9 Perspectives in Ethnophysics (Mário Baloi, 87 Adão Matonse & Horácio Simão) 10 Perspectives in Ethnobiology (Cristiano Pires 91 & Felisberto Lobo) 11 Perspectives in Ethnochemistry (José A. Barros 95 & Luís Ramos) Where are the authors in 2014? 99 7 Cover of the 1994 edition 8 and Ethnoscience in Mozambique Paulus Gerdes Prefácio Three important publications on the challenges to the South in general and to education in Africa in particular, appeared in 1990: * “The challenge to the South”, The Report of the South Commission, led by the former President of Tanzania, Julius Nyerere (Nyerere, 1990); * “African Thoughts on the Prospects of Education for All”, selection from papers commissioned for the Regional Consultation on Education for All, Dakar, 27-30 November 1989 (UNESCO, 1990); * “Educate or Perish: Africa’s Impasse and Prospects”, study directed by Joseph Ki-Zerbo. These studies delineate the societal and educational background that must be taken into account in any reflection on Mathematics and Science Education in Africa for the 21st Century. “The challenge to the South” criticizes development strategies that minimize cultural factors. Such strategies only provoke indifference, alienation and social discord. The development strategies followed until now “have often failed to utilize the enormous reserves of traditional wisdom and of creativity and enterprise in the countries of the Third World”. Instead, the cultural wellsprings of the South should feed the process of development (Nyerere, p. 46). An important feature of “African thoughts” is the fact that two themes keep recurring in all contributions: the focus on the crisis in African contemporary culture and the theme of African languages (as vehicles of culture and media of education). The crux of the crisis of African cultures is the issue of African cultural identity (UNESCO, p. 9). A people’s cultural identity (including their awareness of such an identity) is seen as the springboard of their development effort (UNESCO, p. 10). 9 Explorations in Ethnomathematics Africa needs culture–oriented education that would ensure the survival of African cultures, if it emphasized originality of thought and encouraged the virtue of creativity (UNESCO, p. 15). Scientific appreciation of African cultural elements and experience is considered to be “one sure way of getting Africans to see science as a means of understanding their cultures and as a tool to serve and advance their cultures” (UNESCO, p. 23). “Educate or Perish...” shows that today’s African educational systems favour foreign consumption without generating a culture that is both compatible with the original civilization and truly promising. Unadapted and elitist, the existing educational systems feed the crisis by producing economically and socially unadapted people, and by being heedless of entire sections of the active population. Education for all, as discussed by Ki-Zerbo, should be an attempt to encourage the development of initiative, curiosity, critical awareness, individual responsibility, respect for collective rules, and a taste for manual work. Africa needs a “new educational system, properly rooted in both society and environment, and therefore apt to generate the self- confidence from which imagination springs “ (Ki-Zerbo, p. 104). Reminding us of the apt African proverb “When lost, it’s better to return to a familiar point before rushing on”, Ki-Zerbo stresses “Africa is in serious trouble, not because its people have no foundations to stand on, but because ever since the colonial period, they have had their foundations removed from under them” (Ki-Zerbo, p. 82). This is probably particularly true in the case of mathematics and science. Here lies one of the principal challenges to African mathematics and science educators. Many African children (and teachers too!) experience mathematics and natural science as rather strange subjects, imported from outside Africa. In order to overcome this psychological and cultural blockage to the learning and development of mathematics and science; the African scientific heritage, traditions and practices have to be embedded’ or ‘incorporated’ into the curriculum. How should we respond to this challenge? Ki-Zerbo (1990, p. 87) stresses that all educational renovation in Africa has to be based on research. This appeal is indeed necessary, as, according to Hagan in “African thoughts”, “In Africa, there is 10 and Ethnoscience in Mozambique generally a surprising lack of research to back up proposals for educational reforms” (p. 24). It is in the context of trying to contribute to a response to the aforementioned challenge, that research begun in ethnomathematics and ethnoscience in Mozambique. 1 Ethnomathematical and ethnoscientific studies analyse * scientific traditions that have survived colonization, and activities in peoples daily life with scientific components, and look for ways to incorporate them into the curriculum; * cultural elements that may serve as a starting point for doing and elaborating mathematics and science, both in and outside school. A type of mathematics and science education is intended that succeeds in valuing the scientific knowledge inherent in the culture by using this knowledge to lay the foundations of providing quicker and better access to the scientific heritage of the whole of humanity. At Mozambique’s Institute Superior Pedagógico, ethnomathematical research started at the end of the 1980, continuing earlier research done at the Eduardo Mondlane University from the end of the seventies. 2 Ethnoscientific research began more recently. “Explorations in Ethnomathematics and Ethnoscience” presents a collection of papers written by various lecturers at the Instituto Superior Pedagógico, based both in Maputo, situated in the South of Mozambique, and in Beira, in the central Sofala Province. The ethnomathematical papers reflect on some mathematical ideas involved in basket and mat making in the North of the country; on languages and mental arithmetic, on popular counting practices all over Mozambique; on symmetries and metal grates; and on the decoration of spoons in Sofala and the South-eastern lnhambane Province. A paper on the traditional interpretation of lightning and thunder in the southern Catembe region and physics teaching is a first 1 Cf. e.g. the book by the U. D’Ambrosio, “father” of ethnomathematics and ethnoscience in the context of education (D’Ambrosio, 1990). 2 Cf. the list of books published by the “Ethnomathematics Research Project” on the last page of this
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