Search

The machinery of power series for representing functions and solving various problems of mathematics and mechanics was used systematically by Newton starting in the l660’s. However it was left to the eighteenth century to perfect the technique of operating with power series, the series used by Newton being supplemented by the series of Taylor and Lagrange. In the eighteenth century, mostly at the initiative of Euler. infinite products, partial fraction expansions, integral representations (gamma function, elliptic integrals), and continued fractions were applied along with power series.

The problem of improving education under the present conditions of the scientific-technological revolution is now being confronted by many countries of the world. It would be fundamentally wrong, however, to assume that these problems can be resolved in the same way for both the socialist and the capitalist countries, as well as for the developing countries, regardless of the differences in social systems.

The basic problem to which all remaining problems are subordinate is the problem of the content of the instruction: what mathematics should be taught at the present time in a general education school? This problem can be solved with relative ease for schools that have a clear mathematics orientation and that prepare their graduates for further deep studies in mathematics. In the final analysis in such cases, the question is how the schoolteacher and the university professor will reach an agreement on how to divide between them the time and work in solving a common problem: preparation of a professional mathematician. The requirements of the profession are the decisive factor in the selection of material for study in such a school, in its arrangements into a given system, and in the methods of presenting it to the students.

We are at the decisive phase in the reform of the content of school education. The changeover to the new content of education was stipulated by a decree of the Central Committee of the CPSU and the USSR Council of Ministers on the school in 1966, based on recommendations on curricula and syllabuses by the Commission of the Academy of Sciences and the Academy of Pedagogical Sciences. This decree formulated the following principles that determine the nature of the new content of education: the relevance of education to the development of science, technology, and culture; continuity in the study of the principles of science from the 1st to the last grade; a more rational distribution of subject matter throughout the years of schooling; the commencement of systematic instruction in the principles of science beginning with the fourth year of instruction; the elimination of superfluous detail and second-rate [vtorostepennogo] material from curricula and textbooks to avoid overburdening pupils.

The contemporary state of mathematical science is characterized by a vast extension of its field of application. Mathematics as a science that has important uses has enjoyed high esteem and respect throughout the ages; but till several decades ago these uses were limited mainly to mechanics, physics, astronomy and geodesy.

The tremendous scope of pedagogical research in our country and the remarkable prospects for the further growth and development of these investigations make the problem of coordination in the pedagogical sciences ever more urgent.

(1967). An Interview: Stages of School Education. Childhood Education: Vol. 44, No. 3, pp. 183-184.

A European Conference on Secondary Curricula took place in Paris from April 8th to 18th. Delegations from 25 European countries, including the USSR, Poland, Czechoslovakia, Bulgaria, Rumania, Hungary, and Yugoslavia, participated in the Conference. In addition to the delegates, observers of a number of non-European countries attended the Conference (Brazil, Canada, India, etc.).