Diagnostics

 Simple Test (free renovated version)

If you worry about the future of the school mathematical education or about concrete pupil's lack of success in math, 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 pupils' ability to master school math. To put it mildly, this level is a little bit higher than the level of standard requirements. The pupils who have not crossed this threshold are doomed to poor progress. They cannot master many basic topics of school math (common fractions, algebraic equations and so on).

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 error-free but quickly also. The speed of mental computations is one of the two criteria of automatism - the top quality of skills. While minimal number of errors is permissible (an error may be caused not only by lack of knowledge), a testing will end in failure because of slowness even if there are not be mistakes. The values of parameters used in the test were figured out experimentally in accordance with pupils' age (during five years after the multiplication table had been completely studied).

 Influence of a Level of Elementary Mental Computation Skills upon Success in School Mathematics (article)

MAIN INFERENCES
1) Unsatisfactory development of the elementary mental computational skills adversely affects progress in school mathematics. The skills must be driven to automatism. That is the obligatory condition for success in school mathematics.
2) A level of the skills may be determined by two parameters: average time of implementation of one operation and relative frequency of occurrence of errors.
3) For testing it is handy to use the standard tables, for which the permissible limits of time and errors were calculated.
4) The testing tables are an effective means for training work. Their using lets to bring up quickly the elementary mental computational skills to the level exceeding the calculated permissible limits of the considered parameters.