# Mental Calculations and Thinking

### June 20, 2016

**Reading Time: 2 minutes**

Many of us tend to think that being great at math is all about being able to calculate fast. This perception is reinforced through popular media and entertainment channels where individuals who can mentally calculate fast are labeled geniuses.

Math is much more than calculations. Being able to calculate fast is only a subset of math ability in general. Some of the world’s best mathematicians are only average when it comes to mental calculations. Also, the ability to calculate fast is almost never tested on competitive academic or professional exams. For example, in one of the most competitive exams of the world – the IIT JEE (joint entrance exam) – what is tested is not the ability to calculate fast but the ability to think from first principles.

Given this,** the ability to calculate fast is a good-to-have skill, but not a must-have-skill. **Children need to be taught something far more fundamental. Let us illustrate this with an example.

Ritesh* was a Grade-6 child who could calculate exceptionally fast, because he was part of one of these calculation programs where they teach children how to use a mechanical counting device to calculate fast. He could multiply two-digit numbers in his head effortlessly. During our interaction with him, we posed this question to him: If the price of a book is Rs. 18,** what will be the price of twelve such books? In response to this question, he asked us: Should I add these numbers, or should I multiply them?**

This is an unfortunate example of what happens when you teach children to calculate mechanically, but not teach them to think or apply. Ritesh could calculate much faster than an average adult, but he could not tackle even basic applications of those calculation skills. In such a scenario, one is forced to ask this question. What is the use of teaching the child to calculate using a mechanical device, when there is no thinking involved in that process? How is it any better than using a digital calculator?

Here’s another example of the consequence of children being trained to calculate mechanically. In a Cuemath survey, a group of Grade-6 and Grade-7 children were asked the following question: If all the numbers from 21 to 31 are multiplied, what will be the units digit of the product? All these children had been attending various calculation programs for the past many months. The response of most children to this question was to explicitly carry out the multiplication: 21 x 22 = 462, 462 x 23 = 10626, and so on. However, no student realised that the answer is directly evident: there’s a 30 in the product, so the units digit of the product will be 0.

Attending these programs makes the children so accustomed to the process of calculation itself that they lose the ability to consider a problem from any other perspective.

Cuemath, of course, has a very different objective. Through a strong emphasis on fundamentals and by exposing children to the logical interconnections between various mathematical ideas, Cuemath strives to make children fall in love with math, and hence to make them great at math.** Cuemath focuses on creating thinkers, not calculators.**