OK, now transfer it to your mind (Image: F1 Online/Rex Features)

When 11-year-old Priyanshi Somani multiplies strings of 10-digit numbers or finds the square root of a six-digit number, she doesn’t use a calculator or even pencil and paper. Instead, like other specially trained youngsters, the young Mental Calculation World Cup champion manipulates an imaginary abacus.

Now studies on a group of children trained to use a “mental abacus” suggest the technique frees mathematics from its usual dependence on language.

In some parts of the world, particularly India, China and Japan, schoolchildren sign up for intense training programmes that teach them how to perform complex calculations in their heads using a mental abacus.


Intrigued, Michael Frank of Stanford University in California and David Barner at the University of California, San Diego, travelled to a school in Vadadora in Gujarat, India, where children learn mental abacus in a 3-year-long after-school programme.

Ali Baba

Previous research has suggested that mental abacus relies on visual working memory, but it wasn’t clear how children kept track of all the columns: a typical abacus might have more than 15 columns, yet most people have trouble simultaneously visualising more than three or four distinct items in their minds.

In one experiment, Frank and Barner studied children who had spent a year learning to work a physical abacus and had recently begun practicing mental abacus. The pair asked the students to perform challenging additions. Most of them had difficulty performing calculations with numbers that had more than three or four digits. Frank suggests that the children only represent three or four columns of an abacus in their minds at any given time.

In a second experiment, the pair asked 15 expert mental abacus students to do complex calculations while listening to the story Ali Baba and the Forty Thieves. At the same time, these children had to repeat each word of the tale as they heard it – a language task – or drum their fingers on the table – a motor task – or do both.

Visual representation

The language and motor tasks somewhat hindered the expert children’s mental calculations, with the language task interfering slightly less than the motor task. In contrast, a group of undergraduates from the University of California with no experience in mental abacus found it almost impossible to perform complex calculations while listening to the story.

All of this suggests that for practiced experts, mental abacus does not depend strongly on language systems, says Frank. Most of us need words to represent a number like 134,789 – we rely on concepts represented by verbal numbers like “seven-hundred and eighty-nine” – but mental abacus may be largely a visual task for those who master it.

“What we found confirms and extends previous work suggesting that mental abacus is not based on language, but is really a mental image of some sort, a visual representation,” Frank adds.

The design of the abacus not only makes it a powerful physical tool, it also facilitates mental visualisation. Grouping beads into a few sets makes them easier to hold in visual memory – just as dividing long telephone numbers into three or four-digit chunks helps us remember them. “Because the physical abacus groups beads into columns, it’s easier to hold a mental image of the abacus in your head,” says Frank.

Journal reference: Journal of Experimental Psychology, DOI: 10.1037/a0024427