Discrete Analogues of the Continuous Mathematics Concepts in the Comprehensive Teaching of Mathematics in a Specialized School
https://doi.org/10.31161/1995-0659-2022-16-1-2-115-120
Abstract
The aim is on the basis of the methodological principles of integrated teaching in mathematics, develop an effective methodological toolkit for identifying categorical features in the interactions of methodological objects of continuous and discrete mathematics in order to create and implement appropriate technologies for teaching mathematics at various levels of education.
Methods. Analysis of the interaction of methodological objects of continuous and discrete mathematics, the analogy of the manifestation of their categorical features and the synthesis of various approaches in the context of interdisciplinary integration in the field of education.
Results. The ontological unity of the concepts of the derivative of a continuous function and the finite difference of a discrete function has been methodically substantiated. The discovered analogies of the properties of the operations of differentiation of a continuous function and the finite difference of a discrete function made it possible to generalize the Newton Leibniz formula for a certain class of functions and apply it to study recurrent formulas and calculate the sums of terms of some rational sequences of a given degree.
Conclusions. The combination of ideas and methods of continuous and discrete mathematics contributes to the holistic perception of methodological objects, forming the corresponding competencies in students, and the generalization of basic mathematical concepts at different levels of education, thereby ensuring the continuity and continuity of mathematical education as a whole.
About the Authors
G. A. Yarakhmedov
Dagestan State Pedagogical University
Russian Federation
Russian Federation
Gadzhiakhmed A. Yarakhmedov, Ph. D. (Physics and Mathematics), Assistant Professor, the chair of Higher Mathematics
Makhachkala
T. S. Hajiyev
Dagestan State University
Russian Federation
Russian Federation
Tazhudin S. Hajiyev, Ph. D. (Physics and Mathematics), Assistant Professor, the chair of Information Technologies and Computer Systems Security
Makhachkala
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Review
For citations:
Yarakhmedov G.A., Hajiyev T.S. Discrete Analogues of the Continuous Mathematics Concepts in the Comprehensive Teaching of Mathematics in a Specialized School. Dagestan State Pedagogical University. Journal. Psychological and Pedagogical Sciences. 2022;16(1-2):115-120. (In Russ.) https://doi.org/10.31161/1995-0659-2022-16-1-2-115-120
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