Prognosis of Failure in School Math

It is obvious that for success in school mathematicsfrom the first group had no problems, 87% of the
it is necessary to master elementary mentalpupils from the second and third groups had big
computational skills at first - addition and subtractionproblems, and the other pupils' results were, to put it
within the limits of 20, multiplication and division withinmildly, very poor. Therefore it was confirmed that
the limits of 100. In spite of this there are kids inunsatisfactory development of the elementary
third, fourth, and fifth grade who cannot - without amental computational skills in primary school was the
calculator - add 8 to 5, subtract 7 from 12, multiply 7first cause of difficulties in math's learning. It means
by 8, divide 54 by 9 and so on. Just those very pupilsthat results of testing of the skills may be used for
have considerable difficulties while learning the otherprognosis of failure in school mathematics.
basic topics of arithmetic and algebra. They cannotIt is evident that the population of pupils with
master well operations with two and three digitsatisfactory skills may be represented only by the
numbers, common fractions, negative numbers, likepupils from the first group. That's why the
terms, brackets, simple equations etc. Evenparameters of the first group were used as the basis
calculators cannot help them.for computing limits of values of the considered
For confirming the influence of quality of elementaryparameters. In view of the fact that sample statistics
mental computational skills over success in schoolonly approximately estimate parameters of
mathematics I had decided to investigate a level ofpopulation, the top border under which 90% of
the skills of pupils in graduation-classes of primarysamples means lie was considered as the
school (the multiplication table had been completelystarting-point (the sample mean of satisfactory
learnt a year and a half ago) and their achievementsachieving pupils), and only the 99th percentile of thus
in algebra three years later. The study was carriedachieved normal distribution was taken as the limit for
out in period from 1994 to 2004 years. The sampletime and the last value of thus achieved Poisson's
includes 403 pupils. Standard tables including 64distribution which probability is not less than 0.01 was
elementary operations in addition, subtraction,taken as the limit for number of errors. This method
multiplication and division were used for determinationof determination of limit values gives approximation
of the level of the skills. You can see specimens ofwith surplus only. Therefore the permissible limits of
the tables at my site Prevention of Failure in Schooltime and errors may be considered as sufficiently mild
Mathematics (Improvement of Elementarydemands.
Computational Skills, Tables).The limit values were calculated for the standard
The pupils completed the tables in written form. Thetables including 64 similar elementary operations. For
time from the starting point to the finishing point wasfinal-year pupils of primary school (the multiplication
measured. For estimation of the level two criteriatable had been completely learnt a year and a half
were used - a total time of completion of a table andago) the next limit values had been obtained:
a number of occurred errors. Statistical analysis ofAddition - 11 minutes 02 seconds and not more than
the results had shown that there is possible to single4 errors.
out four uniform groups in the sample:Subtraction - 11 minutes 35 seconds and not more
1) Pupils completed the tables quickly and made notthan 4 errors.
more than 3 mistakes.Multiplication - 9 minutes 46 seconds and not more
2) Pupils completed the tables significantly slowerthan 3 errors.
than the pupils from the first group but made notDivision - 9 minutes 06 seconds and not more than 3
more than 1 mistake.errors.
3) Pupils completed the tables at middle pace andThis level of elementary mental computational skills is
made 3-6 mistakes.a good means for determination of pupil's
4) Either a time or a number of errors, or bothpreparedness for successful studies. The limit values
together were evidently "good-for-nothing".of the considered parameters define the first
Statistical analysis of the parameters of the firstthreshold of school math's learning ability. The pupils
groups (separately for addition, subtraction,who have not crossed this threshold are doomed to
multiplication and division) confirmed (significance atpoor progress. The prediction of their failure in math
5% level) their internal uniformity: distribution in time iswill be right in about 95 cases of 100.
normal, and distribution in errors submits to Poisson'sIt must be noted in conclusion that the level of
law. In different cases these groups included fromelementary mental computational skills of actively
50% to 70% of corresponding samples. According toworking pupils only do not decreases in due course. If
the criteria of rejecting extreme values they werea pupil uses a calculator instead of mental
sufficiently good isolated (significance at 5% level)computations, works passively at lessons and does
from the other parts of the samples.not carry out home works himself/herself, then the
In three years after the testing the current results inlevel decreases gradually. In certain cases it leads to
algebra (of the pupils which had been tested) duringdifficulties in math's learning.
five months was studied. It turned out that all pupils