Целесообразно ли изучение уравнений детьми 7–8 летнего возраста?
Is it Worth to Teach Equations 7–8 Year Old Children?

Summary/Abstract: Experts in the field of mathematical education know well facts of meaningless learning of mathematical concepts by school children. Some of them are: the so-called problem “How old is the captain?”, “transportation problem”. The first fact was found out by staff of the Scientific Research Institute of Mathematical Education in France (IREM) in 1979. The research group from the Institute studied the quality of mathematics achievement of elementary school pupils. Among tasks in the test there was a problem: “There are 26 sheep and 10 goats on a ship. How old is the captain?” 76 out of 97 seven year old children (78%) “solved” the problem providing a numerical answer by adding 26 and 10. A similar fact was revealed in 1983 by the National Assessment of Educational Progress (NAEP) in USA. 79% of pupils proposed an absurd solution of the problem. The difference in the volumes of the samples in France (97 pupils) and in USA (about 150 000 pupils) is significant but in percentage the results are approximately identical - 78% and 79%. Facts received from different countries reveal much (see, for example, 6, 16). Most of experts consider that these facts testify a lack of training pupils in mathematics. In our opinion such explanation is not exhaustive. Sept sent twenty two 7–8 year old children from Belarus and Lithuania participated in the research. The object of the research was the quality of understanding of equation solution methods by children: x + a = b, a + x = b, x – a = b, и a – x = b. The method of research was that the test included 10 equations. 7 of them were standard (for example, х + 4 = 7, 8 – х = 2). Other equations (х + 7 = 4, 6 + х = 3, 2 – х = 8) were incorrect: they had no natural roots and, consequently, no sense for children. It was supposed that test results will allow to evaluate how pupils understand the sense of equations solution. If a pupil solves a standard equation and refuses to solve a senseless equation he has understanding of the concept of equation.Equations and verbal problems essentially differ mathematically by and methodologically. Results solving wrongly made up equations are very close to data by IREM and NEAP: percentages of mistakes are 82%, 78% and 79% accordingly. Explanations by children in our experiment and in the experiment by IREM are also very similar. In our opinion, similar results of Belarusian, Lithuanian, French and American researches cannot be explained only by insufficient teaching. The content of elementary mathematical education, methods of teaching, social and cultural conditions in Belarus, Lithuania, France and USA are essentially different. It is necessary to assume that the source of the phenomena is a common feature of the development of mentality of 7–9 year old children.

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