Abstract:

The cybernetic model of the didactic process based on the metaphor “the student's brain is a decoder with limited throughput capacity” is proposed. The didactic system includes:
1) the person managing learning (PML), who formulates the goals and objectives of learning, chooses teaching methodology and means of training, time and place;
2) the sources of educational information (teacher, textbooks, the Internet, etc.);
3) the student, who can be considered as a system consisting of sensory organs, a “brain decoder”, long-term memory and manipulators, that is, hands, with which the student writes in a notebook, leafs through textbooks, controls electronic devices, etc.;
4) notebooks for writing-down-and-reading important thoughts and examples of completing educational tasks;
5) control and test materials for PML to determine the student’s knowledge level, implementing feedback.

The student perceives the flow of verbal information, which can be presented in the form of a text and decomposed into separate learning material elements (LME, i.e. words, elementary phrases). Using the method of counting words in definitions, as well as the paired comparisons method, it is possible to assess the complexity of individual terms or elementary statements. This allows to analyze the distribution of LME by complexity, building a complexity profile of the message (text), i.e. the dependence graph of the LME number in the teacher's message by their complexity.

The student’s “brain decoder” is considered as a communication channel with noise, the throughput capacity of which depends on the complexity of words (ideas) and the student’s training degree. This takes into account: 1) the distribution of the studied LME by complexity; 2) mathematical regularities of assimilation and forgetting; 3) the student's ability to understand more than he/she knows, and to assimilate issues from the “nearest development zone”; 4) the limited throughput capacity of the "brain decoder".

A computer program in the Pascal has been created, with the help of which it was possible to simulate: 1) slow knowledge increase without training, but only due to the presence of the student in the information environment created by other people, the Internet, television, etc.; 2) training without any control of the knowledge level (open didactic system): when the teacher “breaks away” from the student, the knowledge growth stops, it can start being forgotten; 3) training with control of the knowledge level (closed didactic system), in which the student's knowledge is periodically monitored; 4) interrupted learning, when the complexity of the studied issues is sharply reduced, which leads to a decline in total knowledge and a decrease in the understanding threshold.

Training results are characterized by differential and integral learning coefficients. On the computer screen, for various points in time, the complexity profiles of the studied and assimilated educational information are built, as well as the dependency graphs of the comprehension coefficient on complexity, the total knowledge level and understanding threshold on time. The paper contains 8 figures that depict a cybernetic learning system and more than 50 different graphs. The considered model contributes to the development of the information-cybernetic approach to the didactic system analysis and the mathematical learning theory.

Keywords:

Didactics, cybernetic approach, computer modeling, learning, complexity, control theory, feedback.