Mathematics in Eastern Africa

Summary: East African contributions include Mancala, logic games, and games similar to Tic-Tac-Toe.

Eastern Africa is the birthplace of the human species, and includes Burundi, Comoros, Djibouti, Eritrea, Ethiopia, Kenya, Madagascar, Malawi, Mauritius, Mayotte, Mozambique, Reunion, Rwanda, Seychelles, Somalia, Tanzania, Uganda, Zambia, and Zimbabwe. Mancala, an ancient counting game with many variations throughout the continent, originates in East Africa, which is also home to complicated geometric patterns in woven art and a number of logic puzzles and other mathematical games. The quality of mathematics education continues to be a serious concern.

Mancala

Eastern Africa is home to an impressive variety of mathematically based games. The most well known are the many variations of Mancala, often called the “African national game.” Although there are hundreds of variations, the general idea is: (1) stones or seeds are placed in pits laid out with two to four rows and several pits per row; (2) players collect the seeds from one pit and “sow” them one at a time into other pits around the board; (3) under some circumstances, the player picks up the seeds from the final pit and continues sowing those seeds; (4) when the move ends, the player will, in some cases, capture seeds from his or her opponent. These games generally involve a substantial amount of counting, adding, and subtracting (for example, to determine where the final seed will land), as well as consideration of multiple possibilities, analysis to calculate where an opponent can move afterward, strategy, and logic. It is no wonder that some leaders (including Tanzanian president Julius Nyerere) were first noticed as good Mancala players. It is uncertain where the game originated, but the oldest dated game boards come from Ethiopia and Eritrea about 1300 years ago. The game is surely older than that, possibly as much as 3300 years old. The Complete Mancala Games Book includes 61 different variations of this game played in eastern Africa, including variations specific to every country except Burundi.

Other Puzzles and Games

Logic puzzles come in many forms. One puzzle type common to eastern Africa is the river-crossing puzzle. For example, a man with a wolf, a goat, and a cabbage must use a boat to cross a river except that (1) he can take only one item across at a time; and (2) the goat cannot be left alone with the wolf (who would eat it) or the cabbage (which it would eat). These kinds of puzzles are mathematical because, as Marcia Ascher writes, “A stated goal must be achieved under a given set of logical constraints.” Variations of this puzzle, with different logical constraints, appear in Ethiopia, Zambia, and Mozambique.

Several “three-in-a-row” games, related to Tic-Tac-Toe, are played in eastern Africa. In Shisima, from Kenya, players start with an octagonal board, the eight corners, a center point, and lines connecting opposite corners through that center. Players start with three stones each, on the corners closest to them. During a turn, players move one of the stones to one of the nine points (eight corners and the center) connected to it, if it is empty. The goal is to get three stones in a row (a straight line), which must include the center and two corners opposite each other. Africa Counts describes two other three-in-a-row games from Zimbabwe, each of which begins like Tic-Tac-Toe where players place stones on points on the board, then continues like Shisima with players moving their stones to get a triple. In Tsoro Yematatu, the board has seven spots, each player has three stones, and one spot is always empty. In African Morris, there are 24 spots, and each player has 12 stones. Here, it could happen that the board becomes filled, but if there is a three-in-a-row during that stage, the player does not win; instead, the player captures an opponent’s stone. Hence, the game usually continues into the second phase. These three-in-a-row games are logic puzzles and are examples of games of position, which have been widely studied in mathematics.

Geometric Patterns

The geometric patterns of art from eastern Africa contain a great deal of mathematical and geometric structure and symmetry. Some of the most well known of such crafts are the woven sipatsi baskets of Mozambique, and other types of woven baskets and mats from Mozambique, Kenya, Tanzania, Uganda, and Madagascar. This artwork contains varied types of symmetries and dramatic patterns. Paulus Gerdes writes that this art “reveals the force of the imagination and the artistic and geometric creativity of the women and men who weave [these baskets].” Examples exist in the Ba-ila settlement in Zambia and in Ethiopian processional crosses.

Mathematical Education

Mathematical education in eastern Africa shares many of the challenges that exist throughout the continent, especially the lack of prepared teachers at the secondary level. As the South African mathematics educator Jan Persons writes, “At the departure of the Portuguese from Mozambique in the early 1970s, there were only a handful of qualified secondary mathematics teachers. In general, starving the local population of decent and effective education was used as a weapon to halt or, at least, retard development.”

This issue has been a major problem in eastern and central Africa, which combined have 48% of Africa’s population but have produced less than 8% of Africa’s mathematics Ph.D.s. Kenya has a strong college-level mathematics program, having produced nearly half of all Ph.D.s in eastern Africa. Unfortunately, as also happens in central Africa, most of the mathematics students are attracted into professions other than teaching because of the low salaries for teachers. There are several efforts in place to improve mathematics education in these countries, but much work on the educational structures remains to be done throughout this region.

Bibliography

Ascher, Marcia. “A River-Crossing Problem in Cross-Cultural Perspective,” Mathematics Magazine 63, no. 1 (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.