Do you know an answer to a following question. In my previous article Can We Improve Simple Mental Computational Skills? At the grades after the fourth there is no need in supplementary exercises. Uniform big amount operations brings about transformation of quantity into quality finally. At this time I’ll try to detail my methods.
After the publication I began to get letters with one question -how can we do such a work? Both for determination of a level of simple mental computational skills and for improving them I use tables including 64 uniform elementary operations. Required accidental selection numbers simulates spontaneous appearance of corresponding operations in ordinary computations. Gradually, one after another, they will begin to calculate correctly and quickly. Each table contains operations on the arithmetical rules -addition, subtraction, multiplication or division. Earlier necessity may appear to teach some pupils to add or subtract in some cases. That’s right! Offer pupils to fill in the tables at class and indoors.
Pupils fill in the tables in written form.
When we make a diagnostics of simple quality mental computational skills, we must pay attention not only to correctness but to swiftness of computations too. You see, we often underrate its significance, it is a very important criterion. You need a more or less good timer. Actually, the time from the start point to the finish point must be measured. Slow mental computations are one of possible causes of failure in understanding more complicated operations.
It is not difficult to measure time, if you work with one pupil. Do not hurry pupils while working -rush can increase number of errors. You must fix the time and write down it, when a pupil gives back a table. This is the case. All pupils must understand how to fill in the tables and get accustomed to implementation of big series of elementary operations. The work has to be started simultaneously for all pupils, if you work with a class. It is necessary to note that you must carry out training for the first test. An optimum time will be reached by even rate of work. Each pupil will choose the suitable for him/her speed of working after a preliminary training. Needless to say, it is handy when several pupils bring their tables at the same time. On p of that, as a rule I approximate results to five seconds.
Two criteria are used for estimation of a level of simple mental computations -total running time and number of occurred errors.
The following maximum values were obtained for the pupils finished primary school recently. Multiplication -7 minutes 10 seconds and not more than 3 errors. Division -6 minutes 30 seconds and not more than 3 errors. Usually, addition -8 minutes 40 seconds and not more than 3 errors. Just think for a moment. You can find the description at my site, if you want to know how I did it. Subtraction -8 minutes 55 seconds and not more than 4 errors.
My method of determination of maximum values gives approximation with surplus only.
I can describe the most difficult case from my practice occurred last year. The first test showed that her elementary mental computational skills were very bad. It happens within the limits from three to eight cycles. Sometimes it will require much more efforts to this effect. My practice shows that these parameters limits should be overcome significantly. In September my friends asked me to help Irena, a fifth pupil grade. With that said, the permissible limits of time and errors might be considered as sufficiently mild demands.
Addition -9 minutes 50 seconds, 3 errors. Subtraction -11 minutes 5 seconds, 1 error. Multiplication -18 minutes 50 seconds, 17 errors. Of course, almost any time she filled in the tables on four arithmetic operations. At that time I did not even think about division because of awful multiplication skills. Consequently, I gave her the tables as homework. Irena twice during weekends. So, for short I’ll list only the results on multiplication to show progress. Also, in tal Irena filled more than 35 tables on addition, 45 tables on subtraction, 70 tables on multiplication and 60 tables on division.
Oct.
Now you can see the results obtained in March and compare them with the first results test. Although.
Addition -2 minutes 15 seconds, 0 errors. Division -2 minutes, 0 errors. Subtraction -2 minutes 35 seconds, 0 errors. Multiplication -2 minutes 15 seconds, 0 errors. It does not guarantee automatic removal of these problems, its implementing creates a base for solving other problems. Actually, it is necessary to notice that good and even excellent elementary computational skills are only the first required condition for good progress in school math.