Elementary Mental Computational Skills And Success In School
Math
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The article "Elementary Mental Computational Skills and Success in School
Math" is about reference and education, it was written by Victor Guskov.
To teachers and parents: if your kids have problems in
mathematics, reed that article, please. Maybe the cause of the
difficulties is very simple.
For success in school mathematics it is necessary to master
elementary metnal computational skills at first. This statement
is obvious not only for teachers. Everybody konws 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 otfen is insufficient for secondary school. During last
twenty years I invetsigated why some pupils can not study
mathematics successfully. Now I am sure - the first of the
causes is poor metnal arithmetic. 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? The answer seems very
simple. Mental computations must be siwft 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 cuased not only by lack of
skills. There are many other outside causes - a bad condition of
a pupil, a brief distraction of attention and so on. Therefore a
probability of occurrence of an error, which must be
sufficiently low but not equal to zero, must be taken as the
second criterion.
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 matheamtics without big
problems. They cuold not work at lessons of full value and do
homework themselves. Their knowledge and skills were very bad.
In contrary, in those cases when it was possible to improve
their elementary mental computational skills, they began to make
progress.
If you want to know more about the implemented study, you can go
to
http://www.Simplar.Boom.Ru
You can find there a description of the study with some figures
and diagrams, a test for diagnosis of elementary mental
computational skills and a description of two effective ways for
improvement of the skills: 1) The testing tbales which are an
effective means for training work. Their using lets to brnig up
quickly the elementary mental computational skills to the level
exceeding the calculated permissible limits of the considered
parameters. 2) The teaching computer program for improvemnet of
elementary mental computational skills. It makes a diagnosis of
a level of the skills; carries out the work on improvement of
the skills; carries out control by a psycho-physical state of a
pupil and by a level of permissible working load; allows
controlling the results of working.
For confirming the influence of quality of elementary mental
computational skills over success in school mathematics bad
achieving pupils (from one to three years after the
multiplication table was completely studied) were chosen.
The
work upon dveelopment of the skills, which level had been very
bad, was carried out with each of them individually. In 85% of
cases the level was brought to stable corrsepondence to the
calculated values of parameters.
The results exceed the limit
values of the parametres significantly. After that a work upon
main basic topcis of school math (common fractions, algebraic
equations and so on) was carried out with the pupils.
The work
was successful, and all of them had not enormous problems in their
subsequent math's learnnig. It must be noted that the level of
elementary mental computational skills of actively working
pupils only do not decreases in due course.
If a pupil works
passively at lesosns and does not carry out home works
himself/herself, the level decreases gradually. In some time it
leads to difficulties in math's learning.
Thus a level of elementary mental computational skills is a good
means of determination of pupil's preparendess for successful
studies. The limit values of the considered parameters define
the first threshold of school math's learning ability. The
pupils who have not crsosed that threshold are doomed to poor
progress. It means that results of testing of the skills may be
used for prediction of failure in school mathematics.
MAIN INFERENCES 1) Unsatisfactory development of the elementary
mental computational skills adverse affects progress in school
mathematics. The skills must be driven to autoamtism. That is
the obliagtory 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 claculated (http://www.Simplar.Boom.Ru)
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Elementary Mental Computational Skills and Success in School
Math
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