Mathematics in Central Africa
Mathematics in Central Africa encompasses a rich tapestry of indigenous practices and concepts across countries including Angola, the Central African Republic, Chad, and others. A prominent aspect of this mathematical landscape is the counting game Mancala, which exists in numerous variations, particularly in the Congo and Cameroon. These versions, often with complex rules and structures, require significant logical thinking and arithmetic skills. Additionally, Central African art is deeply intertwined with mathematics, showcasing intricate geometric patterns that can be found in pottery, cloth, and tattoos. Notably, the Kuba and Chokwe peoples are renowned for their sophisticated designs, which reflect cultural stories and mathematical ideas, including concepts like Eulerian graphs and fractals.
Despite the cultural richness of mathematics in the region, educational challenges persist, such as low school attendance, high student-to-teacher ratios, and limited access to resources. Some educators advocate for integrating these traditional mathematical concepts into school curriculums to promote a holistic educational approach. Cameroon stands out with a more developed education system and a significant number of mathematics Ph.D.s, potentially positioning it as a future leader in the region's mathematics education.
Mathematics in Central Africa
Summary: Central African contributions include counting games and decorative geometric patterns.
Central Africa comprises Angola, the Central African Republic, Chad, Congo, the Democratic Republic of the Congo, Equatorial Guinea, Gabon, and Sao Tome and Principe. Mathematical concepts developed in central Africa include variations of the counting game Mancala and the sophisticated geometric patterns used in traditional art. These patterns, in sand art and pottery, woven into mats and baskets, and displayed in tattoos, include complex symmetries and fractals. Some educators have advocated incorporating these indigenous African manifestations of mathematics into school curriculums.
Mancala
As with much of Africa, variations of the mathematical counting game Mancala were played throughout the region. The mathematics of Mancala games are discussed in more detail in the entry “Africa, East,” but some description here is warranted. The Complete Mancala Games Book gives rules for 28 different versions of this game played in central Africa. These variations arise throughout much of central Africa but especially in Cameroon and the Congo. While the version of Mancala best known in the United States is a two-row version (also called Wari or Oware), many of the variations played in the Congo have four rows, which adds substantially to the complexity of the game, as well as the complexity of the arithmetic calculations and logical thinking required to play them well. Even with the two-row version, the Congolese variation Mbele uses a complicated game board (a two-row version with many holes in each row, with the rows pinched together near the ends). Again, this adds mathematical complexity to the game.
Geometric Patterns
Many of the most interesting mathematics developed by the peoples of central Africa have been geometric in nature. A significant part of African art traditions include quite complex—and mathematically sophisticated—geometric patterns. These patterns include symmetries in various combinations, between different elements, and between various colors. Claudia Zaslavsky writes: “If one wanted to survey the whole field of geometric design in Africa, one would have to catalogue almost every aspect of life.” In central Africa, such geometric patterns are found on pottery, cloths, mats, carvings, baskets, bowls, tattoos, and other objects of daily use.
The Kuba people of the Congo are particularly famous for such art, especially their raffia embroidered cloth. Both Africa Counts and Geometry From Africa show many examples of Kuba artwork, along with artwork of other African peoples. The woven mats of the Yombe women of the Congo are another example of complex geometric design. Paulus Gerdes has studied these mat designs as an interplay between cultural values and mathematics.
The art of the Chokwe people of the Congo and Angola includes a mathematically challenging art form called “sona,” usually drawn in the sand. These drawings are made with a single line continuously weaving through an arrangement of dots, such as the “Lion With Cubs” drawing of the accompanying figure. The heads and tails of the animals are added after the principal line is drawn. These drawings represent stories, morals, or values of the Chokwe, or just an animal or object from their environment. The techniques for determining which dot arrangements will generate such one-line drawings are fundamentally mathematical in nature. Drawings that can be done in a single line, without retracing, are a mathematics topic known as Eulerian Graphs. This artwork of the Chokwe is strongly connected to this mathematical idea, and was being investigated by the Chokwe artists about the same time that the idea was first studied by European mathematicians in the mid-eighteenth century.
The geometric patterns of central Africa extend to include fractal designs. Fractals are a mathematical structure that can be viewed as a repetition of the same shapes at many different sizes or scales. For example, trees have branches, each with smaller branches, and then even smaller branches. Western architecture often has rectangular blocks with rectangular houses, but rarely are such shapes repeated at more than two scales, and rarely is this a conscious shape imitation. African fractals often use circular, oval, or diamond shapes at several scales, with smaller shapes inside or around the larger shapes. There is substantial evidence that at least some of these fractal designs are a conscious choice of the artists and builders, and not accidental. African Fractals shows several Cameroonian examples of fractal designs in cities and villages, and even in hair braiding. This book also shows a similar style of pattern, using increasingly smaller but otherwise identical shapes in the art of the Mangbetu people of the Congo.
Education
Several African educators have suggested incorporating these traditional mathematical elements into their schools. The Cameroonian educator A. N. Boma writes: “In African traditional education, the curriculum was organized holistically rather than in discipline areas such as mathematics, history.…Education for all cannot afford the luxury of isolating education in terms of disciplines, rather it should take the holistic approach in developing a total person.…” The ideas described here integrate mathematics with cultural, artistic, and other elements to achieve this holistic approach. Unfortunately, the schools in Central Africa cannot easily incorporate such ideas. The 2009 Mathematics in Africa report describes low percentages of the population attending schools, high student-to-teacher ratios, heavy use of recycled European mathematics textbooks, and few prepared teachers in most of central Africa outside of Cameroon. All of these facts make it difficult to customize mathematics education for African students. Cameroon has a more developed education system, but at the college level it is struggling with filling the mathematics faculty positions that have been approved, and most mathematics teaching there is done in large classes by low-level staff. Nevertheless, with more than half of the central African Ph.D.s in mathematics, Cameroon may become a leader in mathematics education for the region.
Bibliography
Boma, A. N. “Some Lessons From Traditional Practices for Present-Day Education in Africa.” In African Thoughts on the Prospects of Education for All. Dakar, Senegal: United Nations Educational, Scientific and Cultural Organization (UNESCO)-United Nations Children’s Fund (UNICEF), 1990.
Eglash, Ron. African Fractals: Modern Computing and Indigenous Design. Piscataway, NJ: Rutgers University Press, 1999.
Gerdes, Paulus. African Doctorates in Mathematics: A Catalogue. Maputo, Mozambique: Research Centre for Mathematics, Culture and Education, 2007.
———. Geometry From Africa. Washington, DC: Mathematical Association of America, 1999.
Gerdes, Paulus, and Ahmed Djebbar. Mathematics in African History and Cultures: An Annotated Bibliography. Cape Town, South Africa: African Mathematical Union, 2004.
International Mathematical Union. “Mathematics in Africa: Challenges and Opportunities.” 2009. http://www.mathunion.org/publications/reports-recommendations.
Russ, Laurence. The Complete Mancala Games Book. New York: Marlowe Co., 1999.
Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Cultures. 3rd ed. Chicago: Chicago Review Press, 1999.