In his book, Issues in Teaching Numeracy in Primary School, Ian Thompson states some basic reasons why mental calculations are necessary:
Mental arithmetic develops and promotes a better understanding of numbers. Mental calculations encourage children to develop short cuts to solve number problems, and in doing so, they gain a greater insight into the workings of numbers.
Mental work develops problem solving skills. Regular sessions of mental computation may improve problem solving performance. Mental calculations encourage the need to select an appropriate strategy and method for the numbers in the problem and the following of a sequence of steps to execute the calculation. These skills are also crucial for problem solving.
The use of mental arithmetic also helps children later on with other aspects of written work. Mental work helps children to become clear, logical and quick thinkers.
Mental arithmetic helps with memory recall as it requires knowing number facts, along with understanding the properties of the number system in order to work out, for example, the sum of a two digit pair of numbers.