Abstract:

Metaphorical transfer helps to establish a connection between the more developed knowledge field, from which terms are borrowed, and the semantically poor field of knowledge. Various metaphor-models allow to model the learning process and to understand its essence better. From positions of the information-cybernetic approach the following metaphors are of great interest: 1) "the teacher and the student are an information system of the type: the source => the communication channel => the receiver"; 2) "the brain is the decoder of messages" or "the brain is the communication channel between the sense organs and the pupil's memory". The creation and improvement of new metaphors, their use for building qualitative and mathematical models are an actual problem of the education theory.

The purpose of this research is as follows: 1) to analyze the features of the mathematical modelling of didactic system (DS); 2) to develop and deepen the metaphors "the brain is the message decoder” or “the brain is the communication channel”; 3) to define the concept “the complexity profile of the message (text)”, 4) to create the mathematical model of the student’s understanding of the teacher's message.

The methodological basis of the research is the works on theoretical pedagogy and didactics (E. G. Gel’fman, M. A. Kholodnaya, B. M. Velichkovsky, V. I. Zagvyazinsky, T. P. Zinchenko), mathematical theory of learning (R. Atkinson, G. Bauer, R. Bush, E. Crothers, O. G. Gokhman, L. P. Leontiev, V. V. Mayer, F. Mosteller, F. S. Roberts), simulation modelling (R. Shannon), processing of semantic information (I.P. Kuznetsov), cognitive models of the brain information processing (D. Broadbent, A. Deutsch, D. Deutsch, D. Norman, E. Traisman), speech communication (O.Ya. Gokhman, T. M. Nadeina). We use the “black box” method, when the DS is divided into separate blocks (internal structure and mechanism of functioning of this blocks are not discussed) and their reactions to external influences are analyzed. This allows to build qualitative and mathematical models of the DS, based on the facts that: 1) the teacher and student form an informational semantic system; 2) learning сan be considered as perceiving (listening or reading) a sequence of educational texts of increasing complexity; 3) as the student learns more complex LMEs, the “brain decoder” throughput capacity increases due to the “zone of proximal development”. For study of the mathematical model of DS the spreadsheet MS Excel is used.

The article defines the concepts of "brain decoder transfer coefficient", "volume and information comprehension coefficients", "dependence of the transfer coefficient on the complexity of elementary statements". It is shown that the message transmitted from the teacher (textbook) to the student we can decompose into elementary phrases and evaluate their complexity. This allows to create a complexity text profile, i.e. the dependence graph of the number of elementary phrases on their complexity. The student's "brain decoder" is considered as a communication channel with limited bandwidth; its transfer coefficient depends on the complexity of incoming phrases and the degree of the student’s training. The article contains five figures that help to understand the dependence of the knowledge acquired by the student on the bandwidth of his/her "brain decoder" and the complexity profile of the text, as well as to explain the phenomenon of partial understanding of the educational text.

Keywords:

decoding, informativeness, metaphor, modeling, training, memory, complexity, educational text.