Diagnosis of a Level of Simple Mental Computational Skills
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
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