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.

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).

Abstract: The object of this research is an important and relevant question of modern education – the realization of educational activity with application of the information and communication technologies. The subject is the assessment of the quality of math classes with application of the information and communication technologies. Special attention is given to the development of mechanism for creating the system of models considered as exemplary for the math class (content area, presentation style, etc.). The article describes (from various perspectives) the criteria for the system of exemplary models that allow assessing the quality of the content of math class. Methodology of the research is based on the modelling theory. The following conclusions were made: 1) the content of math class, developed with implementation of the formalized system of exemplary model, produces the more extensive pedagogical effect that the content selected by certain private methods; 2) the described system of exemplary models can be used not only as an apparatus for assessing the quality of the existing mathematical content, but also as instrument of projecting the new math disciplines; 3) the suggested approach can be applied to the assessment of quality not only of the mathematical educational content, but also other areas of education. Unlike the existing studies on the questions of application of the information and communication technologies in math education, the accent is made not on the quality of content solution, but rather the quality of the content of math classes. The proposed approach allows harmoniously combine the unification and diversification of presentation of the educational discipline, as well as ensure to the student a possibility of structuring of an individual educational trajectory.

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.