Logical problems solving as a basis for the development of logical thinking and ability to solve problems

Abstract

The purpose of the article is to focus teachers’ attention on the fact that the solution of logical problems is both interesting and available to most students; it
allows to teach students to deal with common-type problems and use general methods of their solving. Solution of mathematical problems develops logical thinking. Since most students will not be mathematicians, neither mathematical objects nor mathematical problems posing is close to them. Meanwhile, logical problems are interesting for the majority of students from the 5th form up to the 5th year at the university and older. They are simply and clearly formulated through familiar objects in everyday life. Hence, students are enthusiastically taking to solving. Even if a student does not succeed in solving the problem, there is motivation to learn about possible ways of its solution. For getting the maximum benefit from problem solving or familiarization with the process, the teacher –after the problem having been solved - should emphasize the following: 1) the process of obtaining the solution is based on the sequence of methods and their results; 2) each particular problem statement made it possible to solve it in the proposed sequence of actions; 
3) it is necessary to identify the common type of the problems, give examples of other ones of the similar type and consider methods of their solution.
It is also important to bind specific techniques with the forms of logical thinking: deduction, induction, generalization, analogy, analysis, synthesis, synthesis through analysis. For most logical problems, several methods that allow even a small number of problems to demonstrate a large number of techniques are
consistently applied.In the article there were analyzed solutions of logical problems which solving demanded the use of such methods as deduction, reformulation of problem requirements, creation of an adequate mathematical model, constriction of solution search area, questions and answers framing, comparison, formation of a virtual situation and its comparison with the real one, search and use of the invariant of transformation and the method of inverse transformation. For some problems, a generalized type of the problem was formulated.