Оценка сложности формул и методов, применяемых при решении школьных задач по механике

Abstract

The problem of estimating the complexity of formulas and methods used in solving school tasks in mechanics is considered. A content analysis of standard school textbooks and tasks books was car-ried out, all formulas on mechanics were written out and 9 topics were identified, each of which corresponds to its own method of solving tasks. To assess the semantic complexity, the formulas were encoded with a verbal code and presented in a text file Formuli.txt . The complexity of the concepts denoting physical quantities is evaluated separately; their list is placed in a file Slovar.txt. With the help of a special computer program, the semantic complexities of formulas (or their corresponding theoretical propositions) are determined, and the coefficient of information folding is calculated for each ones. At that the difference between formulas-definitions and formulas expressing functional dependencies was taken into account. The distributions of formulas and methods in the space of their characteristic features are analyzed. This made it possible to identify the most com-plex formulas and methods for solving tasks in mechanics. The number of formulas in each method is also taken into account, the choice uncertainty of formulas and the corresponding complexity of the choice in the independent solution of a single-formula task are estimated. It is shown how the choice uncertainty of formulas can be taken into account when solving two- and three-formula tasks.