Mental calculation

Mental calculation: Mental calculation consists of performing mathematical calculations using only the brain , without the help of other instruments such as calculators or even pencil and paper or fingers to easily count. The use of the brain and body can also be considered mental calculation.


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  • 1 Fundamental part of mathematics
  • 2 Purpose of mental math
  • 3 The practice of mental math
  • 4 Exact calculation and rough calculation
  • 5 Sources

Fundamental part of mathematics

Mental math is a fundamental part of mathematics. Thanks to it, people find tools to respond flexibly and appropriately to different situations in everyday life, such as the ability to quickly decide whether to buy a product under a certain discount, or the approximate amounts of food needed to make a recipe.

Traditionally, the teaching of mental arithmetic has emphasized the repeated practice of operations in order to solve them as quickly as possible “in the head”, without the need to use a pencil and paper. However, this view is not entirely complete, as being good at mental arithmetic means more than just accumulating a series of isolated numerical facts in memory. On the contrary, to be agile in the calculation you have to be able to interconnect, understand and master a large number of ideas and concepts. In other words, good computational power does not depend so much on a large storehouse of isolated facts, operations, or results, as on good number sense.

Children who are proficient in number and arithmetic relationships have been shown to be better at calculating (Baroody, 2006 ). Understanding that a number can be composed and broken down into different parts, and that this can be done in many different ways, helps children develop different mental calculation strategies. An especially useful one is to transform certain combinations into other simpler expressions, as in the following example, where the expression 8 + 9 can be modified to facilitate the calculation: Sum of doubles plus one: 8 + (8 + 1) = 16 +1 = 17, or Sums of 10: (7 + 1) +9 = 7 + 10 = 17.

Thus, it would be more correct to conceive mental calculation as the invention and application of strategies based on the characteristics of the number system and arithmetic operations. According to this perspective, mental arithmetic is described as “think with your head”, rather than “operate in your head”, and advocates favoring number sense

Mental math good number sense

Purpose of mental calculation

Mental arithmetic is a mathematical tool that helps us “keep our minds in shape.”

A multitude of daily acts require starting the mind to perform quick mathematical calculations. However, deducting the return of a purchase, a discount in a store and other operations, often simple but that many would find more comfortable if they were carried out with a pencil on paper, are easier to solve if they learn and apply different mental calculation strategies and techniques. Encouraging this exercise among students helps them explore different ways to calculate and operate with numbers and promotes the acquisition of concentration and attention skills.

As established in the official curricula, developing and applying personal mental calculation strategies is one of the basic competences that primary and secondary school students must acquire. The essential thing is that students understand that there are different ways of working with numbers and that they just have to choose the most appropriate for each calculation.

The practice of mental math

Exercising this practice contributes to acquiring the understanding and sense of number, provides versatility and independence of procedures and helps in reflection to decide and choose. This method “awakens interest and the ability to concentrate.” On the Internet, you can access a good number of applications and teaching resources aimed at exercising the mental calculation skills of children. The vast majority are designed in the form of interactive games to be more entertaining and attractive for students.

Exact calculation and rough calculation

We can distinguish the exact calculation and the approximate or rounded calculation.

The exact calculation: It is the search for the result of an operative exercise using mathematically valid procedures; It can be done in writing, orally, or supported by a calculator.

The approximate calculation: It consists of looking for an interval in which the result of the exercise that is presented or a single approximate value is found. With great frequency in daily life approximate mental calculation is used, when it is not necessary to make use of written calculation, when we are not in a position to do it to control calculations made by written procedures or with a calculator. The purpose of learning calculation is to ensure that students have different ways of making reliable and fast calculations, have a repertoire of calculation procedures and use those that are appropriate to the numbers with which they have to operate, to the relationship between them and to the precision of the result demanded by the situation in which the need for this calculation arose.


by Abdullah Sam
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