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### Correct reasoning in solving logical problems

Yaremko N.N., Tikhonova N.B.

Penza state University, Faculty of physical, mathematical and natural Sciences Russia, 440026, Penza, Krasnaya str., 40, Tel.: (8412) 56-35-11, E-mail: yaremki@yandex.ru Penza state University, Faculty of pedagogy, psychology and social Sciences Russia, 440026, Penza, Krasnaya str., 40, Tel.: (8412) 54-88-15, E-mail: tixru@mail.ru

The development of students ' ability to build correct reasoning is one of the most important goals of studying the school mathematics course. Such skills are especially important when solving logical problems. Analysis of Russian and International Olympiad logic problems in mathematics showed that the ability to build correct reasoning and the ability to draw conclusions is the key to solving most of these problems. In mathematical logic, " a rule of inference is said to be correct if, for every example of that rule whose premises are identically true, its conclusion is also identically true." Evidence-based reasoning based on the correct rules of inference will be correct: conclusion, negation, counterposition, syllogism.

How to teach students to build correct reasoning and draw conclusions? Our experience has shown that to achieve this goal effective the following methods: addition of text reasoning in accordance with the conditions of the problem; selecting the right arguments proposed; comparison of different methods of reasoning; a comparison of the results obtained with the text of the problem; hypotheses, testing, drawing inferences, etc. [1]. Examples of the use of these techniques in the process of teaching younger students to solve logical problems can be found in the manuals [2]. When using these methods, logical problems become an effective means of teaching younger students to build correct reasoning.

Literature

1. Istomina N. B., Tikhonova N. B. Formation of the ability to reason in the process of solving logical problems / / journal Elementary school. 2014. No. 7.

2. Istomina N. B., Tikhonova N. B. Learning to solve logical problems. Mathematics and computer science. Notebooks for 1-2, 3 and 4 classes of General education organizations-Smolensk: Association XXI century, 2019. - 64 p.

3. Selyutin V. D., Yaremko N. N. teaching bachelors mathematics on the basis of the concept of "correctness": monograph-eagle: OSU. I. S. Turgenev, 2019. – 184 p.

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