To teachers and parents: if your children have problems in mathematics, reed this article, please. For success in school mathematics it is necessary to master elementary mental computational skills at first. Everybody knows that addition and subtraction within the limits of 20, multiplication and division within the limits of 100 are the foundation of all next arithmetical and algebraic topics. But my practice shows that a level of the skills, which maybe is suitable for primary school, very often is insufficient for secondary school.

During last twenty years I investigated why some pupils can not study mathematics successfully. If elementary mental computational skills are not enough good, a pupil has no chances to understand and master more complicated topics.
How can we diagnose a lack of the skills? Mental computations must be swift and errorless. We may say that the skills must be driven to automatism (the top quality of skills) which means quick and errorless mental implementation of the simple arithmetical operations.
Thus the computational speed is the first criterion of the automatism. Meanwhile an error may be caused not only by lack of skills. The results of my study allow determining permissible limits of the average time of implementation of one operation and relative frequency of occurrence of errors while a pupil implements a sequence of simple uniform operations. All pupils who had not reached the limits could not learn mathematics without big problems. In contrary, in those cases when it was possible to improve their elementary mental computational skills, they began to make progress.