C&B Notes

Shells, Beans, & Bars

Luis Fernando Magana, a physicist originally from Mexico’s Yucatan, reintroduced a form of math practiced by the ancient Mayans on the peninsula.  Present-day schools are now using the concepts to try to improve Mexico’s poor competency in math.  Despite being Latin America’s second-biggest economy, Mexico ranks 58th out of the 72 OECD countries measured.

In a classroom in south-east Mexico, eight-year-old Verónica Yuritzi Martín Puc’s hand shoots up with the answer.  On her desk is a sheet of paper with a simple grid drawn on it.  She has put two dried black beans in one of the squares on her grid and a shell of dried pasta in another.  More beans, pasta and some thin wooden blocks lie unused in piles on the desk.  Yuri, as she is known, is learning maths — but not the way most children do. Instead, she is following a method invented thousands of years ago by her Maya ancestors.

In a bid to fix an education system that struggles to teach children the most basic numeracy and literacy skills, Yuri’s teachers have gone old school — literally.  They are breathing new life into the ancient counting system that helped the Maya become some of the world’s most sophisticated early mathematicians and astronomers.  Celtún, the tiny village of thatched huts where Yuri lives, is in the state of Yucatán, less than an hour’s drive from Chichén Itzá, one of the most stunning ruined cities of the Maya civilization, which flourished across southern Mexico and Central America.  Scholars believe it originated around 2000BC, peaking in its classical era from AD200 to AD900.

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The potential benefits of Maya maths for early learning are huge.  Proponents of the method say simple sums can be mastered even by preschool children, as soon as they are able to count. More complicated maths, including multiplication, division and square roots, can also be worked out using the Maya tablero, or grid…

The laws of Maya maths are simple: a bean is worth one unit, five beans make a bar, zero is a pasta shell.  Maya numbers are set out vertically, read from top to bottom.  The bottom row of the grid records the units from zero to nine, the next one up tens, the one above that hundreds, and so on.  When a bean is in the bottom row of the grid, it represents a single unit.  Move it up a level and it becomes 10, up again and it is worth 100.  In the same way, a bar in the bottom row is worth five, move it up and it becomes 50, up again and it is 500.

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The Ignacio Ramírez Calzada primary school, where Yuri studies, began teaching the Maya system last September.  New headmaster, José Manuel Cen Kauil, who teaches the school’s only other class (of nine- to 11-year-olds), wanted to improve basic maths skills.  Aside from an initial investment in teacher training, the method has been almost laughably low-cost.  His class uses grids drawn on cardboard, dried corn kernels for units and slim strips of cardboard for bars.

“It’s empowering,” says Manuel Gil Antón, a sociologist at the Colegio de México in Mexico City and an education specialist.  “Maths itself is not the objective,” he says.  “These teachers in the Yucatán are not aiming to teach maths per se. It’s a tool… it’s about consolidating elementary structures of logic, which fundamentally benefits abstract thought.  Maths is at the service of logical structure.”

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Prof Magaña happened to open the book at Chapter 24, a description of the Maya counting system. He was hooked.  “I abandoned my thesis for a month and went to the library,” he chuckles, sitting in his present-day office at the National Autonomous University of Mexico (UNAM) in Mexico City.  He began to read anything he could lay his hands on about the extraordinarily sophisticated arithmetical system the Maya had developed using a vigesimal, or base 20, method of counting — inspired, scholars believe, by our number of fingers and toes.

“The Maya were the first to discover zero, 600 years before cultures in India,” Prof Magaña says.  Some mathematicians dispute which civilization came first, but agree the Maya arrived at the concept of zero earlier than most — scholars point to around the fourth century AD, although some place it earlier.  The Maya also apparently discovered zero independently.  “When the Europeans learnt about zero, the Maya had had it for 1,500 years,” Prof Magaña says.

The Maya also developed one of the earliest writing systems in Mesoamerica (the area of pre-Spanish native cultures in Central America), considered the most sophisticated and featuring 800 glyphs.  “In writing, they were way ahead of the game,” says Elizabeth Graham, an archaeologist specializing in Mesoamerica at University College London.  “They certainly developed astronomy to the highest degree,” she adds.  Observing the stars using only the naked eye and sticks to guide them, they were able to calculate the length of a year with astonishing precision — to 365.242 days.


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