Lawrence Shirley

Ethnomathematics as a Fundamental of Instructional Methodology

Over the past two or three decades, various political, cultural, and educational forces have brought ethnomathematics and multiculturalism in general into widespread use. Thus, it is important to include ethnomathematical studies in teaching methodology and especially teacher education programs.

The role of ethnomathematics in mathematics education

Kay Owens (Charles Stuart University, Dubbo, NSW, Australia) presented a paper illustrating how schools can change when funds are available to assist schools and communities to implement appropriate and effective professional development, to establish partnerships between school and community, to revise teaching approaches and curriculum, to overcome disadvantage, and to value family and Aboriginal cultural heritage.

Some Conclusions About Ethnomathematics: Looking Ahead

This final chapter reviews the 13 contributions in the volume, organizing them using the four categories of mathematics of cultural groups, classroom applications, cross-cultural situations, and theoretical basis of ethnoamthematics. Taken together, the featured works provide examples of new trajectories for research, and they offer a glimpse of future directions in the field of ethnomathematics, especially its role in advancing inclusive and culturally relevant mathematics education.

In Guise of Conclusion

With the growth of ethnic and linguistically diverse student populations in schools, curricula should reflect the intrinsic, social, and cultural learning of students and teachers should be supported in their preparation to address such differences. Ethnomathematics draws from the sociocultural experiences and practices of learners, their communities, and society at large, using them not only as vehicles to make mathematics learning more meaningful and useful, but, more importantly, to provide students with insights of mathematical knowledge as embedded in diverse environments.

Otthava: making baskets and doing geometry in the Makhuwa culture in the Northeast of Mozambique, by Paulus Gerdes

For more than 20 years, Paulus Gerdes of the Centre for Mozambican Studies and Ethnoscience at the Universidade Pedagógica in Maputo, Mozambique, has been investigating activities of everyday life in nonWestern cultures, especially in Mozambique and other areas of southern Africa, looking for mathematical thought and seeking ways that traditional work can demonstrate or lead to mathematical concepts. He has published his work in scattered publications in several languages in Europe, America and Africa. This book represents a consolidation of several past works with new material, published in a more accessible Englishlanguage format. The central argument of much of his writing is that geometrical and other mathematical ideas are neither discovered as mathematics in the Platonic sense, nor are they the product of passive observation of the geometric shapes in nature. Rather, they come from active design and the making of tools and other everyday products. Often the material structures used in these activities and the necessity for maximum strength or volume or other engineering properties dictate the shapes and geometrical relationships that emerge. From these physical requirements, he suggests early people came to recognize not only circles and straight lines, but also such specialized shapes as hexagons and pentagons and properties such as the Pythagorean relationship. Ethnomathematics reports are sometimes criticized for being just that – reports. An outsider (usually) visits a non-Western culture (usually) and learns about their interesting system of counting words or their interesting patterns of design and then writes up a description. This is useful in adding to the knowledge bank of ethnomathematical examples, especially for researchers seeking a wider range of samples or teachers looking for new classroom examples. However, unless the report’s author can offer some cultural context or some reasoning about how the observed system may have developed within the culture or what meaning may be inferred, the report’s value is limited. Some have even complained that this type of report may show disrespect or a colonialist attitude, simply grabbing some information and exploiting it without really understanding it. Happily enough, this is not the way of Gerdes’ ethnomathematical research. Although he is Dutchborn, he came to Mozambique as a young lecturer in 1975 and stayed, becoming a Mozambican citizen three decades ago, and marrying into a family of several Mozambican cultures, including the Makhuwa, whose weaving technique he writes about in this book. He has not only observed and reported, but has learned the techniques and the structural engineering of the weaving, and has recognized cultural influences and interactions. He incorporates his findings for local and international use in research and pedagogy, even to the establishment of the Center for Mozambican Studies and Ethnoscience. The biggest part of this book demonstrates the technical details of how certain geometrical notions emerge from the activities. In the process, Gerdes teaches the reader specifics about basket-weaving, pottery-making and other traditional activities. Several chapters take up specific objects, mostly woven objects, for discussion – a funnel, a hat, a fish trap and both flat and solid weaving designs. In these chapters, the object and its cultural and practical purposes are discussed and the often-complicated weavings are explained in detail. Certain shape features of the object – cones, special curvatures, corners; and extra features like rims, handles and holes – require special techniques, all of which mean special approaches to the weaving – and usually, resulting mathematical thinking. All of these are discussed in detail – enough that with careful reading and experimental practice with actual materials, the reader could probably become at least an apprentice weaver of these objects. In fact, weaving constructions are often suggested as exercises for the reader to gain tactile experience with the techniques and the resulting patterns and mathematical structures. However, this book is not intended as an instructional manual of Mozambican weaving practice. Gerdes is not an engineering anthropologist, but an ethnomathematician. Hence, for every object and every weaving detail, he makes note of the mathematics that is involved and the mathematics that emerges from the work. He has argued elsewhere that mathematics is ‘frozen’ in the design of materials. The people who developed the design, without formal mathematics