Cognitive Aspects of Mental Calculation

Mental math to better understand working memory and image schemata

29 May 2020  (Wall Street International)*  — This article describes five world records of mental calculation and memorization to better understand working memory and image schemata from a cognitive perspective set by Paolo Fabiani. The purpose of the records is to demonstrate that the potential and limits of working memory are closely connected with the image schemes¹.

On January 19, 2019, at a conference open to everyone, Paolo Fabiani gave a lecture on mental calculation and memorization. The conference took place in the public library of Rufina in the metropolitan city of Florence, Italy.

Inside the conference, in front of an independent jury composed by public officials and experts, Paolo Fabiani performed successfully these five different mental calculation exercises: set time to mentally sum ten random binary numbers of seven digits each and give the result in a decimal number (18.45 seconds); set time to mentally sum seven random square numbers (10.93 seconds); set time to mentally calculate the average of five random square numbers (10.17 seconds); set time to mentally sum two random numbers of 30 digits each (calculus: 1.59 minute) doing calculations aloud, column by column and writing the result without looking at the addends; set time to mentally sum five random dice seen for only 0.1 (a tenth of a) second (3.06 seconds).

The tests were designed to highlight some specific features of image schemata. Some of these aspects are:

1) use specific mental images to facilitate the calculation of large numbers;
2) the conversion from binary numbers to decimals; count from bottom to top;
3) make arithmetic sums proceeding from left to right;
4) convert images into numbers and then “add” the images thinking about numbers.

We can considerably improve the performance in mental calculations by using the knowledge of the operating mechanisms of the schemes. Furthermore, we can note that these records consist in mentally performed arithmetic operations without any kind of material support or other form of help. They are made with numbers consisting of many random digits (up to thirty).

It is not a matter of simple “mechanical” (rote) mental calculations, nor of pure memorization of numbers, but rather they are the integration of the calculation with the memorization of the partial results that are obtained column by column up to the solution of very complex arithmetic operations, much more complex than what has been done until now.