Abstract:

The development of the simulation method has created the preconditions for application of the information-cybernetic approach for the didactic systems analysis. The present paper is devoted to the creation of the computer model of the cybernetic system “teacher – pupil” which takes into account its structure, the major information flows and the control circuits. It is possible to assume, that the similar model of the didactic system will more precisely study the basic features of the training process and will promote development of the mathematical training theory.

The methodological basis of the research are the works by S.I. Arhangel'skij, Ju.K. Babanskij, J.L. Bermudez, V.P. Bespal'ko, R.R. Bush and F.A. Mosteller, M.V. Jadrovskaja, V.M. Krol', A.V. Solovov, V. I. Zagvjazinskij, T.P. Zinchenko, I.A. Zimnjaja, D. Gibson and P. Jakl, R.B. Johnson and L. Christensen, B. Joyce and M. Weil, L.P. Leont'ev and O.G. Gohman, J. Murray, A. Pritchard, V.V. Majer, A.P. Sviridov, B.M. Velichkovskij, J. Wellington. Also we used the system approach, basics of the control theory, pedagogical cybernetic, soft systems methodology, theory of complexity, cognitive psychology, methods of computer simulation.

In the paper the cognitive scheme of didactic process, which is taking into account the major factors and links, influencing on training, is constructed. The mathematical model of system “teacher – pupil”, considering psychological regularities, basic information flows and control circuits, is offered.

Thus it is supposed:
1) while training the quantity of the pupil’s “weak” knowledge increases, and a part of “weak” knowledge transforms into “strong” knowledge;
2) the “weak” knowledge is forgotten faster then ”strong” knowledge.

On the basis of the mathematical model the computer program which simulates behavior of the didactic system at various control modes has been created. It contains the cycle on time, which the teacher’s requirements level and the quantity of knowledge, skills and abilities of the learner on the following time step are calculated. The proposed computer model allows to analyze behavior of the system “teacher – pupil”, changing its parameters and the regulation law.

The model takes into account that:
1) at increase of the pupil's lagging behind the teacher’s requirements the pupil’s efforts first increase, reaches a maximum, and then decrease;
2) at increase of the material complexity or the information speed, at first the transfer coefficient of the communication channel is constant and equal to 1, and then decreases down to 0;
3) the information of the pupil’s condition comes through the reverse communication channel to the teacher with some delay;
4) the teachers can control the training process, changing new information transfer speed or organizing the revision of the studied material.

The article analyses six situations, in which the teacher manages the educational process, adapting to the pupil in this or that way. The graphs of dependences of the teacher's requirements and pupil's knowledge on time are submitted. It is shown, that the results of functioning of the cybernetic system “teacher – learner” are high, when the teacher adapts to the pupil’s possibilities so that learner should apply maximum efforts. There is a maximal speed at which the learner can assimilate the new information; it depends on the pupil’s parameters.

Keywords:

Assimilation, computer modeling, didactics, forgetting, learning material, pupil, teacher, training.