Mancala
Count, Capture, Play and Think: Mancala and Math
We have all had the experience of playing board games. They are the staple of family game nights and inside recesses. Board games have been around in various forms throughout history and one of the oldest is the family of count and capture games known under the umbrella term of Mancala, which is an Arabic word meaning "to move". This game can, of course be played for fun, but it can also be used in its different forms to teach simple math and strategy (University of Waterloo 2010). Mancala can be traced back to ancient Egypt in the 15th or 11th century BC. The game has been played throughout Asia, Africa and the Middle East. Through the slave trade Mancala made its way to the Caribbean. It …show more content…
has, until recently not been known in non-Islamic Europe and the American continents (University of Waterloo 2010).
For the most part the game is played simply for the pleasure of it.
Some cultures have limitations on who plays it and who they play it with once a person reaches adulthood. In the Sudan for example, it is said that playing mancala takes commitment and woman often don't have time to play it. According to an essay written in 1952 the author observes that in the "Old World" mancala is played after the day's work is finished or when rain makes outdoor work impractical. In most places in Africa the game doesn't have a religious or superstitious nature, but in Suriname in South America it is associated with death. Mancala is played to entertain the spirit of the recently deceased while the body awaits burial (Murray, 1952); (BBC News, …show more content…
2010). As Mancala is a family of games it is known by many names depending on what culture is playing it there are also many variations The mancala board is made up of rows of shallow indentations (which I will call “houses” which is the term used in the University of Waterloo article) and in many version two more indentations on either end of the board (which I will call “banks”. Term also from the Waterloo article). The number of rows and whether or not there are banks, depends on what culture is playing the game. For example in the Philippines the Chuncajon board has twelve houses and two banks, while the Ugandan Omweso board has thirty-two houses split into four rows and no banks. For the purposes of this paper I will be looking at three variations played on a board with two rows of six houses and two banks and I will refer to the games played as: “Basic", "Kalah", and "Oware". The “Basic” version is called such because it is a very simple version used by a teacher for her Kindergarten students to easily understand and play. (Teaching Ace, 2013); (Dewar, 2009). Played on the twelve-house-two-bank board (which is rectangular in shape) Mancala is simple in concept; each of the houses are filled with four tokens (three can also be used).
Two players sit at the long sides of the rectangle, the row in front of them is their row and the store to their right is their store. The board and tokens can be as simple as holes dug in the ground in the configuration of the board using pebbles or seeds; or as ornate as elaborately carved board and marbles. Each of the variations I will discuss have different levels of difficulty that can be used to teach the mathematics needed to win (BBC News, 2013) (University of Waterloo,
2010).
The most basic variation is played thusly: The players decide who goes first then Player One choses a house from their row, picks up all of the tokens and, moving counter-clockwise drops tokens into the houses, their own and Player Two's. Tokens can be dropped in to the player's own bank, but not their opponents. If the last token dropped lands in Player One's bank then Player One has another turn. If the last token doesn't land in the store then their turn ends and Player Two's turn begins. Play continues this way until the houses on one side are cleared into that player's store. Tokens are then counted and whoever has the most tokens wins. The remaining tokens on the other players side goes into their bank. (Teaching Ace, 2013).
This variation has a few learning opportunities, a few are obvious - young kids will learn turn taking and sportsmanship, as they would with any board game. The game also teaches counting and simple adding and subtracting skills. Mancala can also teach strategy. Unlike games with dice that decides how many places to move, mancala doesn’t involve chance. More like checkers or chess, strategies can be developed to think a head to how one might win the game. Mancala's math based game play requires the players to count, not only their tokens and how many houses they can cover with the tokens in any turn, but also to think abstractly about how many tokens they might have in the turns ahead. Other than trying to drop the last token into your bank, giving yourself extra turns and therefore more opportunities to put tokens into your bank, the basic version doesn’t really have any occupying strategies. The other variations do have ways to plan ahead.
A mancala game known as Kalah adds another element into how a kid might strategize. Kalah is played exactly as the basic form but with another opportunity to "capture" your opponent’s tokens. If the last token a player drops into one of their own empty houses then they can take the tokens out of their opponent’s house directly across from it and put them in their own bank. This added capturing opportunity also brings another counting strategy into play. Now, the only goal is not to move the tokens into the bank, drop the last token into your bank for an extra turn, but also to plan out a way to take your opponents tokens. This requires forethought and the ability to keep more than one strategy in play (Dewar, 2009).
There are a couple of strategies to win at Kalah. It is usually best to go first because the first player can choose the fifth house from the bank and drop the last token into the bank there by earning another turn. With the added element of capturing this extra turn can be used to get an early lead. Using the free turn Player One can then choose the second to last house in their row to distribute the tokens so that the last one lands in their empty house allowing them to capture all of the tokens from their opponent’s house directly across from it (eHow Hobbies, Games & Toys Editor, 2008).
Hoarding is another strategy, and one that can be employed by both players. To hoard, treat a one of your houses as a small bank. This accomplishes a couple of things: It keeps more tokens on your side of the board, and if your opponent clears their side first then it gives your bank a boost because you then put all of those tokens into your bank. Hoarding also gives your opponent fewer tokens to work with. There is a risk with this strategy however, it leaves a prime house for your opponent to capture. So it is best to keep an eye on the other side of the board and try to also distribute tokens on to that side and not allow the house across from your hoard to stand empty (eHow Hobbies, Games & Toys Editor, 2008).
There is also a way to hoard for part of the game and then use that hoard to capture your opponent’s tokens. By planning a head and using a full house to loop the board you can hopefully land your last token in one of your empty houses and then take the tokens directly across from this house. This requires you to keep track of how many tokens are in the house you wish to use because one too many or one too few and you’re not able to capture anything and you have given your opponent more tokens.
Once a lead is established, defensive play is a good technique. The idea behind this is to keep as many of your tokens on your side of the board as possible, so while your opponent tries to catch up they run the risk of running out of tokens leaving you to bank what is left on your side and giving your bank another boost in addition to the lead you already had (eHow Hobbies, Games & Toys Editor).
Mancala games are played by all ages, but with adjustments to make the game more challenging for older kids and adults. Oware still has the core of the basic and Kalah, but requires even more advanced mathematical thinking. Oware is played on the same board and is started with four tokens in each house, play still moves in a counter clockwise direction. However the banks are not used. Tokens are only dropped into house and capturing is more complicated. If your last token is dropped into your opponent’s house then you count the number of tokens in that house. If there are less than two or more than three tokens in the house your turn ends and the other player's turn begins (Dewar, 2009).
If there are two or three tokens in the house then you can take those tokens and then the banks are used for captured tokens. Then you look to the next-to-last house. If that house is your opponent’s, and it contains two or three tokens, then you get to capture those tokens as well. Continue working backwards until you get to a house that doesn’t have two or three tokens (Dewar, 2009). A variation of the hording trick can be used to further your advantage and limit your opponent’s. By collecting twelve or more tokens in one house can ensure that you can do a complete lap of the board, because of the more complex capturing rule, this strategy could allow you to collect a large amount of tokens (Soler, 2014).
With the Oware variation, if the players keep their strategy and try to discern their opponent’s strategy then it is possible to clear the board in very few turns. This not only requires mathematical thinking but complex forethought and the ability to multitask by focusing on both sides of the board. Logical thinking is also required (Dewar, 2009).
By using a game to build these skills it links them to a feeling of fun rather than a feeling of frustration. Hopefully this link to a pleasurable activity will reduce the feeling of math anxiety in kids that find math difficult and translate to working with math outside of the game.
Mancala can also be played in groups. Boards can be very large and each side can be worked by teams. The game can also be played one on one but with a large group choosing sides and enthusiastically offering encouragement and advice to their chosen player (Murry, 1952).
The Mancala game is a predecessor to another math based family of games that requires even more advanced thought: Nim. Nim games require a lot of strategic thinking and goes beyond the scope of this paper. This game can be expressed in binary code, even though it is an ancient game that's origins are hard to pin down (University of Cambridge, 2015); (Encyclopædia Britannica, 2015).
The Mancala family of count and capture games bring math, strategic thinking to playtime and can, when applied in the context of teaching, hopefully associate math with fun and also instill confidence in the players’ and enhance their relationship with numbers.
We have all had the experience of playing board games. They are the staple of family game nights and inside recesses. Board games have been around in various forms throughout history and one of the oldest is the family of count and capture games known under the umbrella term of Mancala, which is an Arabic word meaning "to move". This game can, of course be played for fun, but it can also be used in its different forms to teach simple math and strategy (University of Waterloo 2010). Mancala can be traced back to ancient Egypt in the 15th or 11th century BC. The game has been played throughout Asia, Africa and the Middle East. Through the slave trade Mancala made its way to the Caribbean. It …show more content…
has, until recently not been known in non-Islamic Europe and the American continents (University of Waterloo 2010).
For the most part the game is played simply for the pleasure of it.
Some cultures have limitations on who plays it and who they play it with once a person reaches adulthood. In the Sudan for example, it is said that playing mancala takes commitment and woman often don't have time to play it. According to an essay written in 1952 the author observes that in the "Old World" mancala is played after the day's work is finished or when rain makes outdoor work impractical. In most places in Africa the game doesn't have a religious or superstitious nature, but in Suriname in South America it is associated with death. Mancala is played to entertain the spirit of the recently deceased while the body awaits burial (Murray, 1952); (BBC News, …show more content…
2010). As Mancala is a family of games it is known by many names depending on what culture is playing it there are also many variations The mancala board is made up of rows of shallow indentations (which I will call “houses” which is the term used in the University of Waterloo article) and in many version two more indentations on either end of the board (which I will call “banks”. Term also from the Waterloo article). The number of rows and whether or not there are banks, depends on what culture is playing the game. For example in the Philippines the Chuncajon board has twelve houses and two banks, while the Ugandan Omweso board has thirty-two houses split into four rows and no banks. For the purposes of this paper I will be looking at three variations played on a board with two rows of six houses and two banks and I will refer to the games played as: “Basic", "Kalah", and "Oware". The “Basic” version is called such because it is a very simple version used by a teacher for her Kindergarten students to easily understand and play. (Teaching Ace, 2013); (Dewar, 2009). Played on the twelve-house-two-bank board (which is rectangular in shape) Mancala is simple in concept; each of the houses are filled with four tokens (three can also be used).
Two players sit at the long sides of the rectangle, the row in front of them is their row and the store to their right is their store. The board and tokens can be as simple as holes dug in the ground in the configuration of the board using pebbles or seeds; or as ornate as elaborately carved board and marbles. Each of the variations I will discuss have different levels of difficulty that can be used to teach the mathematics needed to win (BBC News, 2013) (University of Waterloo,
2010).
The most basic variation is played thusly: The players decide who goes first then Player One choses a house from their row, picks up all of the tokens and, moving counter-clockwise drops tokens into the houses, their own and Player Two's. Tokens can be dropped in to the player's own bank, but not their opponents. If the last token dropped lands in Player One's bank then Player One has another turn. If the last token doesn't land in the store then their turn ends and Player Two's turn begins. Play continues this way until the houses on one side are cleared into that player's store. Tokens are then counted and whoever has the most tokens wins. The remaining tokens on the other players side goes into their bank. (Teaching Ace, 2013).
This variation has a few learning opportunities, a few are obvious - young kids will learn turn taking and sportsmanship, as they would with any board game. The game also teaches counting and simple adding and subtracting skills. Mancala can also teach strategy. Unlike games with dice that decides how many places to move, mancala doesn’t involve chance. More like checkers or chess, strategies can be developed to think a head to how one might win the game. Mancala's math based game play requires the players to count, not only their tokens and how many houses they can cover with the tokens in any turn, but also to think abstractly about how many tokens they might have in the turns ahead. Other than trying to drop the last token into your bank, giving yourself extra turns and therefore more opportunities to put tokens into your bank, the basic version doesn’t really have any occupying strategies. The other variations do have ways to plan ahead.
A mancala game known as Kalah adds another element into how a kid might strategize. Kalah is played exactly as the basic form but with another opportunity to "capture" your opponent’s tokens. If the last token a player drops into one of their own empty houses then they can take the tokens out of their opponent’s house directly across from it and put them in their own bank. This added capturing opportunity also brings another counting strategy into play. Now, the only goal is not to move the tokens into the bank, drop the last token into your bank for an extra turn, but also to plan out a way to take your opponents tokens. This requires forethought and the ability to keep more than one strategy in play (Dewar, 2009).
There are a couple of strategies to win at Kalah. It is usually best to go first because the first player can choose the fifth house from the bank and drop the last token into the bank there by earning another turn. With the added element of capturing this extra turn can be used to get an early lead. Using the free turn Player One can then choose the second to last house in their row to distribute the tokens so that the last one lands in their empty house allowing them to capture all of the tokens from their opponent’s house directly across from it (eHow Hobbies, Games & Toys Editor, 2008).
Hoarding is another strategy, and one that can be employed by both players. To hoard, treat a one of your houses as a small bank. This accomplishes a couple of things: It keeps more tokens on your side of the board, and if your opponent clears their side first then it gives your bank a boost because you then put all of those tokens into your bank. Hoarding also gives your opponent fewer tokens to work with. There is a risk with this strategy however, it leaves a prime house for your opponent to capture. So it is best to keep an eye on the other side of the board and try to also distribute tokens on to that side and not allow the house across from your hoard to stand empty (eHow Hobbies, Games & Toys Editor, 2008).
There is also a way to hoard for part of the game and then use that hoard to capture your opponent’s tokens. By planning a head and using a full house to loop the board you can hopefully land your last token in one of your empty houses and then take the tokens directly across from this house. This requires you to keep track of how many tokens are in the house you wish to use because one too many or one too few and you’re not able to capture anything and you have given your opponent more tokens.
Once a lead is established, defensive play is a good technique. The idea behind this is to keep as many of your tokens on your side of the board as possible, so while your opponent tries to catch up they run the risk of running out of tokens leaving you to bank what is left on your side and giving your bank another boost in addition to the lead you already had (eHow Hobbies, Games & Toys Editor).
Mancala games are played by all ages, but with adjustments to make the game more challenging for older kids and adults. Oware still has the core of the basic and Kalah, but requires even more advanced mathematical thinking. Oware is played on the same board and is started with four tokens in each house, play still moves in a counter clockwise direction. However the banks are not used. Tokens are only dropped into house and capturing is more complicated. If your last token is dropped into your opponent’s house then you count the number of tokens in that house. If there are less than two or more than three tokens in the house your turn ends and the other player's turn begins (Dewar, 2009).
If there are two or three tokens in the house then you can take those tokens and then the banks are used for captured tokens. Then you look to the next-to-last house. If that house is your opponent’s, and it contains two or three tokens, then you get to capture those tokens as well. Continue working backwards until you get to a house that doesn’t have two or three tokens (Dewar, 2009). A variation of the hording trick can be used to further your advantage and limit your opponent’s. By collecting twelve or more tokens in one house can ensure that you can do a complete lap of the board, because of the more complex capturing rule, this strategy could allow you to collect a large amount of tokens (Soler, 2014).
With the Oware variation, if the players keep their strategy and try to discern their opponent’s strategy then it is possible to clear the board in very few turns. This not only requires mathematical thinking but complex forethought and the ability to multitask by focusing on both sides of the board. Logical thinking is also required (Dewar, 2009).
By using a game to build these skills it links them to a feeling of fun rather than a feeling of frustration. Hopefully this link to a pleasurable activity will reduce the feeling of math anxiety in kids that find math difficult and translate to working with math outside of the game.
Mancala can also be played in groups. Boards can be very large and each side can be worked by teams. The game can also be played one on one but with a large group choosing sides and enthusiastically offering encouragement and advice to their chosen player (Murry, 1952).
The Mancala game is a predecessor to another math based family of games that requires even more advanced thought: Nim. Nim games require a lot of strategic thinking and goes beyond the scope of this paper. This game can be expressed in binary code, even though it is an ancient game that's origins are hard to pin down (University of Cambridge, 2015); (Encyclopædia Britannica, 2015).
The Mancala family of count and capture games bring math, strategic thinking to playtime and can, when applied in the context of teaching, hopefully associate math with fun and also instill confidence in the players’ and enhance their relationship with numbers.