Mancala games motivate young mathematicians
Looking for activities to motivate your school-aged kids to count and think strategically?
Try out mancala.
known as "count and capture" games, mancala games encourage kids to
conduct thought experiments, counting tokens and comparing tactics in
their heads before they move a game piece. Such qualities have
inspired educators in Africa, Europe, and the United States to bring
mancala into the classroom.
Does playing mancala actually sharpen math and thinking skills? To date, nobody has performed the relevant experiments to find out. However, competent performance requires counting and the mental movement of game tokens across a game board. And research suggests that good players use abstract or hypothetico-deductive reasoning (Retschitzki et al 1986).
Here I provide an overview of the games, and I describe two popular variants of mancala: Kalah and Oware. If you want to play the games with your kids, you can buy a game board. But one of the great things about mancala is that the game equipment is easily made from everyday materials at home. You can make your own macala set using an egg cartoon, two bowls, and some dried seeds, beans, or pebbles.
Mancala games are played throughout the world, but especially in Africa, the Caribbean, South Asia and Southeast Asia. The earliest evidence of mancala may come from Eritrea, where archaeologists have found game boards dating from the 6th or 7th centuries AD.
Though there are many variants of mancala, most versions share these elements:
• A set of counters (e.g., seeds)
• A series of small pits arranged in 2 or 4 rows
• Two large storage pits (where players keep the seeds they “capture”)
• General rules of play that include
(1) beginning the game by placing a specified number of counters in each small pit,
(2) having players take turns “sowing” and “capturing” seeds.
A player “sows” seeds by choosing a pit, scooping up all the seeds in that pit, and--moving in a specified direction--dropping one seed in each of the pits immediately adjacent to the starting pit.
Depending on which variant of mancala is played, there are different rules for capture. In most versions, the object is to capture the most seeds.
Let’s review two mancala games. The first, Kalah, is usually considered a children’s game. The second, Oware, can be enjoyed by older children. However, it is considered a more complex, grown-up game.
Kalah is one of the most popular mancala games for kids. Inspired by traditional mancala games, the rules for Kalah were invented an American, William Julius Champion.
Kalah is sometimes called “Mancala” in the United States.
In Kalah, the game board consists of two rows of 6 small pits (or “houses”), with a large storage pit at each end. Picture an egg carton with a bowl at each end.
At the beginning of the game, you and your opponent sit on opposite sides of the game board.
The row in front of you is your row.
The storage pit to your right is your storage pit.
Four seeds are placed in each of the 12 houses.
And then play begins:
The game continues, often with these additional mancala rules:
To make the game more challenging, begin with more seeds--5 or 6--in each small house.
Want to play online? Check out Mancala snails, an electronic version of Champion’s Mancala.
Oware, a West African variant of mancala, is a more sophisticated game. It’s recommended for adults and older kids (11 and up).
In Oware (also called Wari and Awale), the game board resembles that used for Kalah, consisting of
The “sowing” is also similar to that practice in Kalah. When it’s your turn:
But here’s where the rules diverge from those of Kalah.
First, you don’t drop seeds into the storage pits as you sow—-sow seeds only in the small pits or “houses.”
Second, the rules for capture are different. If you’ve ended your move in one of your opponent’s houses (as opposed to one of your own houses), then you count the seeds in that house. Are there 2 or 3 seeds in it (no more and no less)?
If the answer is no, your turn is over and your opponent gets to sow seeds.
But if the answer is yes, you get to collect the seeds and keep them in your storage pit. Then you examine the next-to-last house. If that house belongs to your opponent, and it contains 2 or 3 seeds, then you get to collect those seeds as well. Continue working backwards until you get to a house that doesn’t contain the correct number of seeds.
Mancala as a group activity
Games like Kalah and Oware are often played one-on-one. But they can also be played as team games. In Africa, people sometimes play with very large boards in a party-like atmosphere. Multiple players might work together on a team, or—if there are just two opponents in the game—the players get lots of free advice from very enthusiastic, vocal, and involved onlookers (Townsend 1979).
Included are the instructions for four different mancala games, and other board games, puzzles, crafts, and games of chance. Zavlasky offers historical and cultural explanations of each activity, as well as clear, well-illustrated instructions and questions designed to get kids analyzing underlying mathematical and strategic concepts.
Retschitzki J, N’Guessan A, and Loesch-Berger MC. 1986. Etude
cognitive et genetique des styles de jeu et des strategies de jouers
d’awele. Archives de Psychologie 54: 307-340.
Townsend P. 1979. African Mankala in anthropological perspective. Current Anthropology 20: 794-796.
de Voogt A. 2001. Mancala: Games that count. Expedition 43(1): 39-46.
Image of Cape Verde Uril / mancala game players by DuncanCV / wikimedia commons