Whiz Kids Use Imaginary Abacus to Solve Complex Math Calculations

In a highly impressive display of mental prowess, young South Asian children are able to solve complex math calculations within seconds simply by flicking their fingers through thin air. Their secret tool –  an imaginary abacus.

News reports on the Mind Mathlon 2014 program held at the Robotics Lab of the Karachi Institute of Technology and Entrepreneurship in March described young children raising and flicking their fingers to keep track of long series of numbers and solve calculations with mind-blowing accuracy.  They were apparently taught to use their hands as the beads of an abacus – an ancient calculating tool – to add and subtract at the speed of a calculator.


Photo: The Express Tribune

The technique is actually quite simple, but requires years of practice to master. The fingers on the right hand represent unit digits, while an open right thumb is interpreted as the number five. Each finger on the left hand is used to tally tens, and the left thumb corresponds to the number 50. So two thumbs up to a student of mental math would indicate the number 55.

What’s more amazing by this effective technique is that it can be used by anyone; a visually impaired child who participated in the Mind Mathlon program was able to calculate just as well as any other student. An 11-year-old could multiply strings of 10-digit numbers and even find the square root of a six-digit number, without the use of a calculator, pencil or paper.


Yasin Altaf, founder and CEO of Robotics labs, revealed that mental math could also be used to compute a longer range of numbers and is also useful for multiplication, division and more complex mathematical operations. He explained that the students were taught to move beads on an abacus in their imagination, so they don’t really need to carry one around.

Mental math techniques are popular among school children in several Asian countries such as India, China, and Japan. Intrigued by the results, Michael Frank of Stanford University and David Barner of the University of California, traveled to a school in Gujarat, India, to observe the mental abacus program and conduct experiments and understand how it works.


 Photo: The Hindu

Frank and Barner wanted to understand in particular, how children were able to keep track of all 15 columns of an abacus, when most people have trouble simultaneously visualizing three or four. So they studied children who had spent a year learning the technique – these children were unable to perform calculations with numbers that had more than three or four digits, which means they were only able to imagine three or four columns of the abacus in their minds.

Expert mental abacus students, on the other hand, were able to perform more complex calculations. So Frank and Barner increased the complexity by setting them a language task (listening to and repeating a story) and a motor task (drumming their fingers on the table) while performing the calculations. In both cases, the tasks somewhat hindered the childrens’ mental calculations, with the language task posing less of a distraction.


This indicated that the mental abacus does not depend on language systems. While most others need to represent numbers with verbal names, mental abacus appears to be entirely a visual task. “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,” said Frank. “Because the physical abacus groups beads into columns, it’s easier to hold a mental image of the abacus in your head.”

According to Altaf, mental math is for everyone – anyone can use it to sharpen their minds and improve listening skills. You would have to pay attention though and work hard, so if you’re one to daydream in class, the technique might not be for you.

Sources: NewScientist, The Express Tribune

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