Excerpts from
World Cultures in the Mathematics Class
HIMED Conference, Leicester, UK
April 7-9, 1990
By Claudia Zaslavsky

The mathematics eduction community in the United States is embarking upon a program to reach all students. As stated in the Curriculum and Evaluation Standards for School Mathematics (NCTM): "It is crucial that conscious efforts be made to encourage all students, especially young women and minorities, to pursue mathematics." (p.68) Recognition is given to the varied backgrounds and interests of the students: "Students should have numerous and varied experiences related to the cultural, historical and scientific evolution of mathematics. (p. 5) Students' cultural backgrounds should be integrated into the learning experiences. (p.68)
"The ethnic groups that have lived longest in the Americas -- and who have been most oppressed -- are the Native peoples and the Africans who were brought to the New World in chains, to serve as slaves to European plantation owners. Now their descendants are determined to reassert their cultural heritage."
It is not only children of "minority" groups who benefit from the inclusion of topics relating to their heritage. Students in our "global village" must learn to respect and appreciate the contributions of peoples in all parts of the world. Educators are beginning to recognize the value of infusing mathematics with the achievements of world cultures, to "multiculturalize the curriculum." (Bishop, D'Ambrosio, Gerdes)
In this presentation I shall describe some of the mathematical practices of African peoples and of the indigenous peoples of the Americas, suitable for incorporation in the curriculum at the primary and middle grade level.
All peoples have developed numeration systems to the extent of their needs. The English language system of numeration and most European systems are based on grouping by tens and powers of ten. Why is ten commonly used as a base? Is it because we have ten fingers (digits)? The peoples of West Africa and Middle America, as well as the Inuit of the far northern group by twenties. In some languages, such as Mende of Sierra leeone, the word for twenty means "a whole person" -- all the fingers and toes.
Children can learn about numeration systems by examining the construction of larger numbers. In the Yoruba (Nigeria) language, for example, the name for 65 means "take five and ten from four twenties," using the operations of multiplication and subtraction, rather than multiplication and addition, as in most European languages. These are different solutions to the same problem, one just as good as the other. (Zaslavsky. Africa Counts, 207)
Finger gestures to express numbers are commonly used by people who do not speak each other's languages. These gestures may be related to the number words, or, again, they may be quite different. When the indigenous peoples of North America were pushed westward by European settlers, tribes speaking different languages were thrown together. Of necessity, they developed systems of finger signs, including signs for numbers. (Zaslavsky, "It's OK")
The peoples of Middle America developed their own systems of written numerals, dating back at least two thousand years in the case of the Maya. The systems were based on twenty and powers of twenty, and included the use of zero,positional notation, addition, and the repetition
of symbols.
Another aspect of number is the ability to do mental arithmetic. The year 1990 marks the 200th anniversary of the death of the slave Thomas Fuller, known as the African Calculator. Shipped to North America in 1724 at the age of fourteen, he developed remarkable powers of calculation, although he was forbidden access to any kind of schooling, as were all slaves, and he could neither read nor write. Late in his life he was used by anti-slavery advocates to demonstrate the mental capacity of Black people. (Fauvel & Gerdes)
Conclusion: The introduction of multicultural, interdisciplinary perspectives into the mathematics curriculum has many points in its favor:
(1) Students become aware of the role of mathematics in all societies. They realize that mathematical practices arose out of a people's real needs and interests.
(2) Students learn to appreciate the contributions of cultures different from their own, and to take pride in their own heritage.
(3) By linking the study of mathematics with history, language arts, fine arts and other subjects, all the disciplines take on more meaning.
(4) The infusion into the curriculum of the cultural heritage of people of color builds their self-esteem and encourages them to become more interested in mathematics. As one eleven-year-old boy wrote in his evaluation of a classroom activity based on African culture, "As you probably don't know I feel very strongly and am in deep thurst (sic) with my black people, and the math has made me feel better." There is little to be added to this heart-felt comment!
Bishop. A.J. Mathematical Enculturation (Dordrecht Kluwer, 1988).
D'Ambrosio, Ubiratan, "A research program and a course in the history of mathematics: Ethnomathematics," Historia Mathernatica 16 (1989), 285-6.
Fauvel, John & Gerdes, Paulus, "African slave and calculating prodigy: Bicentenary of the death of Thomas Fuller," Historia Mathematica 17 (1990) (to appear)
Gerdes, Paulus, "On culture, geometrical thinking and mathematics education," Educational Studies in Mathematics 19(1988), 137-162.
National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, 1989)
Zaslavsky, Claudia, Africa Counts: Number and Pattern in African Culture (Brooklyn: Lawrence Hill Books, 1979).
Zaslavsky, Claudia, "It's OK to count on your fingers," Teacher 96 (1979) 54-56.