If you are worried about the future of the school mathematical education or about concrete pupil?s lack of success in math, then do not hasten to think that the problem of elementary mental computational skills is insignificant or trivial. The level of progress in simple mental computations defines the first threshold of school math?s learning ability. To put it mildly, it is a little bit higher than the level of standard requirements. The pupils who have not crossed this threshold are doomed to poor progress.
Many children in secondary school have bad results in mathematics. My experience show that problems start in primary school ? the root is in bad practical skills in count and simple mental computations. All kids who have problems with addition and subtraction within the limits of 20, multiplication and division within the limits of 100 can not master many basic topics of school math successfully. They have difficulties with common fractions, simple algebraic transformations, simple equations and so on.
When make a diagnosis of quality of the simple mental computational skills we must pay attention not only to correctness but to swiftness of computations too. It is a very important criterion, but we often underrate its significance. Slow mental computations are one of possible causes of failure in understanding more complicated operations: reducing to a common denominator, operations with brackets and similar terms, solving simple equations.
The results of my investigations have allowed figuring criteria of permissible level of the simple mental computational skills for different ages. All pupils who have not reached this level could not learn mathematics without big problems. In contrary, in those cases when it is possible to improve the skills, they begin to make progress.
I offer you a simple computer test for diagnosis of a level of simple mental computational skills. You can download it free at my site
You can find there also a short description of the implemented study with some figures and diagrams and a description of two effective ways for improvement of the skills.
Undoubtedly you have one or several familiar persons more or less successfully (maybe more or less unsuccessfully) gnawing a granite of sciences in a primary or secondary school. If they have learnt the multiplication table already, offer them this simple test and you will see that many of them will not pass it. A pupil must implement a sequence of 64 simple operations not only nearly errorless but quickly also. The speed of mental computation is one of the two criteria of automatism ? the top quality of skills. Whereas a minimal number of errors is permissible (an error will be caused not only by lack of knowledge), a testing will end in failure because of slowness even if there will be no mistakes. The values of parameters using in the test were figured experimentally in correspondence with time passed after the multiplication table was completely studied.