New opportunities of computer assessment of knowledge based on fractal modeling

Abstract

In this article the urgent problem of control systems modeling of professional competences and mathematical knowledge assessment of students is discussed. Pedagogical expediency in management of students` cognitive activity by using of new informational technologies instruments in monitoring and assessment of knowledge is proved. The possibility of fractal methods application in perfecting of the system of computer monitoring of mathematical knowledge of students as a part of the adaptive training systems is considered and realized. The design of the technology of computer monitoring of students` knowledge on the basis of fractal methods includes the following stages: development of cross-disciplinary fractal and organized base of key mathematical concepts; the creation of the expansible bank of educational and cognitive and research tasks, which is coordinated with fractal structure of the conceptual framework; the development of the program module, which is  focused on individual estimation of quality of students` educational cognitive activity in two characteristics — depth of knowledge based on the Hurst exponent and the size of synergetic effect of educational cognitive activity. The software realization of technology of the computerized control of training in mathematical disciplines quality as a part of the adaptive training system is enabled in the programming language C#. The experience of implementation and operation of the controlling systems realized in the adaptive training systems based on the fractal model operation showed reliability of their work and allowed to increase the quality of educational process management and its effectiveness in general. Using of fractal techniques in computer assessment of mathematical knowledge of students makes it possible to increase the accuracy and speed of evaluation of the students` knowledge.