Can We Improve Simple Mental Computational Skills?

Three years ago I tried to pay attention to importance of simple mental calculations for success in school math. Now it must be not only attempt, it must be an appeal to all who worried about the future of mathematical education.

My last studies show that the skills of pupils are getting worse and worse. Last year I have tested 106 final-year pupils of primary school in mental addition and subtraction (within the limits of 20), multiplication and division (within the limits of 100). Standard tables including 64 elementary operations on addition, subtraction, multiplication and division were used for determination of the level of the skills. You can see specimens of the tables at my site Prevention of Failure in School Mathematics (Improvement of Elementary Computational Skills, Tables).

The results turned out worrying: 52% of the sample has failed in addition and subtraction; 75% of the sample has failed in multiplication and division. In comparison with the data which had been obtained five years ago there is considerable deterioration (25 – 30 %). My earlier investigations show that all of these pupils have no chances to understand and master more complicated topics. If the trend will not change, very soon school math will turn into “knowledge for minions of fortune” and will become a sort of magic for other pupils.

Can we improve the situation? My answer is yes. I have chosen one class (20 pupils) with next results:

on addition: good – 2, uncertainly – 8, bad – 10;
on subtraction: good – 2, uncertainly – 7, bad – 11;
on multiplication: good – 5, uncertainly – 1, bad – 14;
on division: good – 4, uncertainly – 1, bad – 15.

During half a year we worked with standard tables. In total the pupils have completed eight tables on each arithmetical operation. Besides that the tables were constantly used as homework. In February the class has implemented a control test. Here are the results:

on addition: good – 16, uncertainly – 2, bad – 2;
on subtraction: good – 14, uncertainly – 5, bad – 1;
on multiplication: good – 10, uncertainly – 5, bad – 5;
on division: good – 9, uncertainly – 5, bad – 6.

Success on addition and subtraction is evident. You may say that on multiplication and division the results are not so good. But we must take into consideration that such a work must be implemented much earlier – at the second and third grades. Teachers of secondary school have not enough time to improve simple mental computational skills. It is a job of primary school.

If we want the greater part of our pupils will understand math in future, we must teach them some simple things in present. The first of these things are simple mental computations.