УПРОВАДЖЕННЯ ПРИНЦИПУ ГЕНЕРАЛІЗАЦІЇ ЗНАНЬ У ПОВТОРЮВАЛЬНИЙ КУРС ЕЛЕМЕНТАРНОЇ МАТЕМАТИКИ В ТЕХНІЧНИХ ЗАКЛАДАХ ВИЩОЇ ОСВІТИ

Abstract

The fundamentalization of mathematical preparation of future specialists at higher educational establishments (HEE), as the basis of their professional technical preparation, is a process of generalization of mathematical knowledge. This process should ensure the emphasis of the core of classical and applied mathematical disciplines, which guarantees further high-quality innovative professional preparation. A prerequisite for introduction of fundamentalization of mathematical preparation into the educational process of technical HEE is the presence of strong initial knowledge and creative abilities in elementary mathematics of future specialists. The article draws attention to the decrease in the level of mastering the school course of mathematics by modern entrants HEE for objective circumstances. The most characteristic shortcomings of modern school mathematical preparation are allocated. A number of necessary key abilities in elementary mathematics of technical HEE students are presented at the same time. The contradiction between the frequent lack of indicated key abilities of the first – year undergraduate students and requirements for having these abilities for successful mathematical preparation at the HEE under the conditions of fundamentalization is identifed. As a consequence, the introduction of a repetitive course of elementary mathematics at technical HEE is proposed. References of scientists to similar experience of higher schools of Europe and the USA are provided. The necessity of introduction of the principle of generalization of knowledge to the indicated repetitive course is proved. The authors present their own examples of generalized, creaive statement of certain aspects of the repetitive course of elementary mathematics as a result of the introduction of the principle of generalization of knowledge. In particular, the use of three schemes of solving of equations is proposed in the generalized presentation of the topic "Irrational equations” and recommendations for the use of these schemes are provided. Classification and summary of the main ideas on the solution of exponential equations are demonstrated. The urgency of the continuation of the research in terms of the development of the didactic basis of the generalized statement of the repetitive course of elementary mathematics and the creation of appropriate methodological support is noted. Key words: fundamentalization of mathematical preperation, generalization of knowledge, repetitive course of elementary mathematics, generalized statement.