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Scientific research on mental arithmetic


Mental arithmetic is a system that allows to make quick and accurate arithmetic calculations using imagined Abacus (old computational tool) in the mind. Wide expansion of this technique worldwide prompted scientists to know whether mental arithmetic helps develop intellectual abilities in children or not?

And this question has forced scientists – Michael Frank from Stanford University and David Barner from University of California to go to India, and to shed light on the way in which mental abilities are developed through training in mental arithmetic.

According to previous studies, it has been suggested that the process of submission of abacus in mind is due to short-term visual memory (i.e., a person’s ability to perceive and retain in memory of visual images, play them in your mind for a certain period of time), but this hypothesis has not given explanation on how children could hold all abacus bones in mind, as the conventional Abacus has 15 spokes, with 5 bones on each. It is well known that many people find it very difficult and sometimes impossible to imagine images of various objects in the mind at the same time.

In one experiment, M.Frank and D.Barner studied children who have learned to count on the physical abacus for one year and only recently started training to perform arithmetic calculations on a mental level. The researchers asked the children to make complex arithmetic calculations involving addition. Many of them were difficult to perform calculations with a three-digit, four-digit numbers. Based on this, Frank suggested that the children imagine only three or four spokes of abacus in a certain time interval.

In the second experiment, the researchers conducted a study involving 15 children who have perfectly mastered the technique of mental accounts: these children were asked to make complex arithmetic calculations listening to the tale of Ali Baba and the Forty Thieves, and at the same time they had to repeat every word of the tale, while listening to it (that is, the task on the hearing), or tapping their fingers on the table (task on motility).

Representation of image in the mind

Tasks on the hearing and motor skills a bit hampered the process of calculating in mind, however, it was easier to do the task on hearing rather than on motor activity. In contrast, for students of the University of California, who have never trained on mental arithmetic, task to perform complex arithmetic operations while listening to a fairy tale was almost impossible.

M.Frank consolidates that all this suggests that mental calculations is not much related to the language system. Many of us need words to imagine such numbers as 134,789, i.e. we express these numbers with the words «one hundred thirty four thousand seven hundred eighty-nine» while for those who have mastered this technique mental calculations on the abacus is an assignment for visual perception.

«Our results confirm and at the same time provides a more comprehensive explanation of the fact that mental calculations do not operate the system of language, but in fact are based on the visual image», – said M. Frank.

Abacus design makes it not only a powerful computing tool, but it also facilitates the process of visualization (representation of the image in the mind). Grouping bones in sets of numbers eases the retention of these numbers in the visual memory as well as we group telephone numbers in the three-digit or four-digit number to remember. «Since the physical abacus bones are grouped in several rows, it is easier to keep a mental image in your head», – adds M. Frank.

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