ANOMALIES IN THE IMPLEMENTATION OF METHODS OF TEACHING MATHEMATICS AND THEIR CONSEQUENCES

Abstract

The article deals with the negative trends in the development of school mathematics education in the context of the relationship of inductive and deductive methods of teaching educational material. It is stated that the dominance of deduction in teaching of mathematics in high school and its separation from inductive explanations to students of mathematical concepts, definitions, rules, formulas indicates a complete disregard for pedagogical experience and K.F. Lebedyntsev and D. Polya’s methodical research. The historical causes of excessive application of the deductive method of teaching mathematics are revealed: the centuriesold practice of imitating the method of “Beginnings” by Euclid; historically short (about four centuries) period of induction method formation in scientific research; even shorter period of pedagogical induction applications practice. In order to more fully revealing the pedagogical significance of inductive methods of teaching mathematics, a brief analysis of the methodical features of lectures course on algebra, developed and delivered by I. Newton to the students of Cambridge University, was carried out.It is found out that this course has a strong inductive orientation and revealed this genius English scientist’s conviction that teaching mathematics is an art in which solving examples and problems is more important and useful than rules. It is emphasized that this I. Newton’s conviction was significantly ahead of other Western European mathematicians. The purposefulness and persistence of national mathematicians-teachers M.G. Kurganov, F.I. Busse, P.S. Guriev, O.M. Strannolyubsky, S.I. Shohor-Trotsky, K.F. Lebedyntsev in substantiating the pedagogical significance of the inductive method of teaching mathematics and its practical implementation were noted. The important general didactic significance of F.I. Busse’s views on the implementation of learning consciousness principle has been revealed. Examples of M.M. Luzin’s high school education and modern practice of training mathematics teachers are given. They show that the lack of inductive explanations of the main thing in the content of the lesson turns deductive learning into formal-deductive, accompanied by the substitution of understanding by thoughtless mechanical memorization of educational material. The exceptional relevance of the practical implementation of the methodical heritage of K.F. Lebedyntsev and D. Polya’s in the context of solving the problem of improving the quality of school mathematical education is substantiated. The most important task of of the considered problem – determinating the practical ways of its decision – is formulated.