Abstract:

The didactic process can be presented as the pupil’s solution of the sequence of the learning tasks (LT). The condition for successful learning is the correct sequence of the LTs presentation to the learner, in which an important didactic principle “from simple to complex” is realized. Therefore, the development of methods for assessing the complexity of explaining the task is an actual problem of didactics. Its solution will allow to determine the didactic complexity of the LT for the tests, exams and correctly assess the students’ knowledge. LT should be understood as any educational task that requires intellectual action (tasks in mathematics, physics, chemistry, a specific formula derivation, proof of the theorem, etc.). As components of LT complexity various scientists in didactics call the number and complexity of elements, relations, closed circuits or loops, logical operations, formulas; the abstraction degree of the concepts and models; the presence of implicit factors that influence the study process; the redundancy of the LT conditions; the LT belonging to several types of tasks or to various subjects; the need for complex or cumbersome mathematical transformations, etc. At present, there is no effective method of “measuring” the complexity of the LT solution.

The purpose of the study is to develop an effective method for determining the didactic complexity of the LT solving, based on an analysis of its explanation and taking into account the used terms complexity. It is assumed that the didactic complexity of LT is proportional to the amount of semantic information in explaining its solution. To determine it, we propose calculating the total complexity of all terms. The methodological basis of this study is the works by E.G. Gelfman, M.A. Kholodnaya (the textbook theory), Zerkal O.V., N.M. Solomatin (the semantic information), B. Davis, D. Sumara (the didactic objects complexity), A.I. Uemov, S.I. Shapiro (the knowledge folding), A.M. Sokhor (the educational texts informational capacity), V.I. Shalak (the content analysis), A.V. Gidlevsky, A.N. Kolmogorov, I.L. Lerner (the learning tasks complexity), N.K. Krioni, A.D. Nikin (the automated assessment of the text complexity).

The novelty of the work lies in the fact that the method for assessing the complexity of LT solving has been developed. It consists in the following:
1) to code the task condition and its solution (formulas and explanations) in the text file F1;
2) to create text file F2, containing the list of terms used in the task solving;
3) to assess the terms complexity by calculating the number of words in the definitions;
4) with help of special program to analyze file F1 containing the task solving and determine the total complexity of the text, its volume and the average information folding coefficient.

The complexity of 10 physical tasks from different sections of the physics course is estimated, the general informativeness of explanations and the average folding coefficient of information are determined. It has been established that the overall information content of the standard task explanation varies quite significantly (from 70 to 760 conventional units of information), and the average coefficient of folding is in the range of 1.5 – 7.7. The method of automated counting of terms will allow to evaluate the didactic complexity of any information block containing an explanation of the LT solution, the formula derivation, the theorem proof, etc.

Keywords:

Informativeness, information folding, semantic information, complexity, thesaurus, educational task.