DOI: 10.25136/2409-8736.2019.4.31402

Abstract: The object of this research is the process of teaching mathematics. The subject of this research is the strategy of teaching. The author suggest and examines the internal algebraic perception of teaching strategy viewed as the mechanism for creating the teaching plan. Earlier on, Y. B. Meknikov has proposed the interpretation of algebraic approach towards modelling as the system consisting of three components: 1) system of basic models; 2) system of typical transformations and standard combinations of models; 3) approximation mechanism intended for a similar understanding of the model in form of a result of typical transformations and standard combinations of basic models. The internal algebraic understanding of the strategy is distinguished by the fact that basic elements represent the components of the strategy, rather than the external perception, where the basic elements are a part of other strategies. The research carries a theoretical character, though some of its results have already been implemented into educational practice in the Ural State University of Economics. The theoretical framework relies on the modelling theory of Y. B. Melnikov, which is based on the formal-constructive interpretation of the model. The scientific novelty primarily consists in structuring of model of the strategy as a mechanism for creating plan of action, as well as distinction of the postulates of strategy that help to define the typical transformations and standard combinations of the plans of action. The author proposes an internal algebraic approach towards the concept of strategy, where the algebraic concept means a system consisting of three components: a) system of basic elements; b) system pf typical transformations and standard combinations of the elements; c) approximation mechanism intended for understanding of strategy in form of a result of application of typical transformations and standard combinations of the basic elements.

DOI: 10.25136/2409-8736.2018.4.27930

Abstract: The object of this research is the process of teaching mathematics to the economists and engineers. The subject of this research is the formation of skills for comprehensive and multilateral assessment of adequacy of the phenomena under consideration in the process of teaching mathematics to the economists and engineers. The goal of this work lies in structuring the model of multilateral assessment of mathematical activity (its objectives, methods, and results) and the application of mathematics as the component of economic and engineering education. The authors suggest the multi-criteria approach towards assessing the indicated phenomena on the basis of the original theory of modelling and theory of adequacy. The estimation of quality of the model in the theory of adequacy is defined via comparing the assessable model with the stated reference model. Research methodology includes the theoretical analysis of the modern mathematical education, theory of modelling, competence and activity approaches. In Y. B. Melnikov’s theory of modelling, the estimation of adequacy of the model is viewed as a result of comparison of the assessable and reference models. Evaluation of adequacy is viewed as a function, which arguments are the assessable and reference models. This allowed acquiring new scientific results: formalization of a specific attribute of adequacy can begin either with the structuring of reference model (with further concretization of the corresponding functions), or with the formation of the comparison method (with further determination of referenced model and formalization of the corresponding function).

DOI: 10.25136/2409-8647.2018.4.28207

Abstract: The subject of this research is the process of creating a work plan using the methods of bottom-up and top-down analysis. The authors based upon the hypothesis that every point of planning by the executive and planner is perceived either as a reference to a known algorithm of actions, or as a goal setting for work without concretization of means of achieving it. The goal is being viewed as a system of example models of results meant for planning and assessment of adequacy of results, both planned and achieved. The research carries a theoretical character and employs results of research in the area of management, modeling theory of Y. B. Melnikov, which is based on formal-constructive interpretation of the model and analysis of management decisionmaking process. Authors examine the process of transformation of the original plan, consisting of a single point (formulation of goal), towards a plan of which all main points are perceived by the executive as references to known to him algorithms of actions. The authors’ original interpretation of the methods of bottom-up and top-down analysis is schematically illustrated by the examples from the taxation practice.

DOI: 10.7256/2409-8736.2017.1.22616

Abstract: The subject of the study is a very important and urgent issue of modern education - the training of competent professionals who are able to make weighted management decisions in various fields of activity.The subject of the study is the role and significance of mathematical culture in enhancing the professional competence of students in economic and related areas of training.Particular attention is paid to the study of the connection between mathematical culture and professional competence. The modern state of mathematical education is described, the relation of mathematics and computer science is analyzed, the use of information and computer technologies in mathematical education is analyzed.The methodology of the study is based on the theory of modeling, based on the formal-constructive interpretation of the model. Methods of research: analysis of own pedagogical practice of mathematical education, analysis and synthesis of advanced Russian and foreign research, modeling.The main findings of the study are:1. The mathematical culture of the graduate and specialist remains one of the key components of the culture of modern society.2. The professional competence of the graduate and specialist includes a cultural component, of which the mathematical culture is an integral part.3. A specially organized mathematical education at the economic university allows successfully to solve the problem of increasing the professional competence of the graduate.The novelty of the research is that at the basis of this special organization is the model of mathematical culture as an infrastructure for the perception and processing of information and the exchange of information consisting of a system of phenomena, a system of relations, a system of interfaces and a management system.