Robert Maier

Education and development of schoolchildren is closely connected with reading, so improving the text reading efficiency is one of the problems intensively studied by various scientists in the field of didactics, psychology and linguistics. Reading involves extracting information from the text, which requires decoding phonetic relationships between letters and sounds, as well as understanding the meaning. The result of reading depends on the parameters of the reader and the text he/she reads. The aim of the work: 1) using the information-cybernetic approach, to create a simulation model of the reader’s (pupil’s) activity, taking into account the psychological patterns of perception, remembering and forgetting information, that would allow us to investigate the main regularities of reading texts; 2) to study the behavior of this model under different characteristics of the reader and the text; to explain the results obtained. The system-cybernetic approach is applied, as well as methods of qualitative, mathematical and computer modeling. In the proposed simulation model, human memory is modeled by three matrixes in which syllables, words and sentences are «remembered». Numbers from the intervals [0; 1] are matrix elements, which are equal to the probabilities of correct reproduction of these components of the text. Syllable recognition is modeled as a random process with a probability 0.05 – 1. When the pupil has read all the syllables correctly, he understands the word being read, and the corresponding element of the matrix is assigned 1. After reading the sentence, the pupil tries to understand its meaning; the result depends on the degree of understanding and memorization of the words that make up this sentence. The model takes into account: 1) the multilevel structure of the reader's memory; 2) the probabilistic nature of reading syllables, understanding words and sentences; 3) the exponential law of forgetting uncomprehended information (syllables); 4) the logistic law of forgetting comprehended information (words, sentences); 5) the effect of feedback on the repeated reading of words and sentences in case of their incomprehension; 6) reducing the speed of forgetting information during re-reading. As a result of the pupil’s reading simulation, we obtain the graphs of the level of the entire text and separate sentences comprehension dependence on time; it is shown that the time of reading the text depends seriously on the «reader’s» characteristics and the text parameters. The situations when the reader (pupil) poorly reads syllables, slowly understands and quickly forgets the read text are also considered here. The computer program used is written in the Free Pascal environment and consists of nested loops that correspond to the reading of syllables, words and sentences. The novelty lies in the fact that an imitational model of the reader was created, with the help of which the dependence of the student’s knowledge on time, the student’s working time with text on reading speed, the degree of understanding of various sentences on their ordinal number with different text parameters was studied.

One of the didactics development directions is associated with the improvement of the mathematical theory of training (MTT), which makes it possible to explain the basic regularities of didactic systems functioning using the analysis of their mathematical models. An actual problem of MTT is the mathematical solution of the optimization task of training, which consists in determining the conditions of the educational process organization, when its effectiveness is the highest. The result of optimization depends on the learner's assimilation coefficient, classes duration, distribution of learning material elements (LME) according to their complexity and importance. The aim of the work is to build the computer model of the didactic system and to find optimal study duration of LMEs which have various complexity and importance in conditions of the fixed classes duration. The methods of mathematical and computer modeling of the learning process are used, as well as the method of stochastic optimization with a return. It presumes creation of the computer program which makes a step in random direction in the multidimensional environment of optimized values and simulates the study of the given set of issues (LMEs) for new study durations. If the test results at the end of training are not better than at the previous step, then the computer returns to the previous state and repeats everything again. If the test results are higher, then the changes of the optimized values are accepted, and the next step is made from the new state. Gradually, the program approaches the optimal values of the study durations for LMEs. The main results of the work include: 1) the computer program which makes it possible to calculate the optimum values of study durations at different distributions of LMEs on the complexity categories; 2) the graphs of the optimal durations for studying LMEs, the student’s knowledge levels of specific LMEs and the total knowledge levels of different importance LMEs depending on their complexity. The theoretical significance of the article is due to the fact that it sets and solves the problem of optimizing the study durations of specific issues (LMEs) that are different in complexity and importance; this problem is a particular optimization task of the mathematical theory of training.

The improvement of the computer modeling teaching technique assumes the development of physical sys-tems simple computer models. In this article the author suggests the Visual Basic Application macroses which allow to study by method of computer modeling: 1) forced swings of a spring pendulum; 2) chaotic swings of Duffing’s pendulum; 3) Van-der-Pole’s auto oscillations; 4) Lorenz’s attractor; 5) electrical oscilla-tions in oscillatory circuit. The developed programs provide series of the computational experiments realiza-tion with various researched system parameters, initial conditions and external influences.

In the paper the method of imitating modeling of studying by the student of some hypothetical discipline which is calculating on 15 weeks and coming to an end with examination is considered. On the basis of fundamental psychology and pedagogical regularities of learning the mathematical multicomponent model of training is constructed. It is taking into account: 1) the division of the student's knowledge in dependence of the memory strength into three categories; 2) the duration of lessons and intervals between them; 3) the distribution of educational information on themes and on time; 4) complexity of the training material; 5) repeated studying of some themes during preparation for the test or examination; 6) the degree of the using of educational material of the previous themes when studying the current theme. The result of modelling are represented.

The author suggests the technique of the content analysis of various topics of school course of the physics. It is based on definition of the following indicators: 1) complexity of the physical objects, represented on drawings; 2) complexity of used physical models. The corresponding scales are developed, the assessment of physical complexity of 27 subjects is made, and topics with high and low level of complexity are revealed.