1.Introduction.

According to the provisions of the Federal State Educational Standard, cognitive meta-subject learning outcomes are associated, in particular, with mastering the ability to build logical reasoning.

In assessing the ability to build logical reasoning, we relied on the concept of two types of cognitive activity, developed in dialectical logic [3] and implemented in psychological research (see, for example, [1], [4]).

According to these ideas, a person’s knowledge of the surrounding world can be aimed at reflecting the internal connections of objects and phenomena (theoretical, meaningful, reasonable knowledge) and at reflecting their external connections (empirical, formal, rational knowledge).

In the first case, human cognitive activity is quite effective, since its result is an understanding of the causes of changes in objects of knowledge. In the second case, cognitive activity is not effective enough, since its result is only a description and ordering of the observed features of the change in cognizable objects.

When assessing the formation of the ability to build logical reasoning, it was assumed that in one case the inference can be based on the true relations of the proposed judgments, in the other case, on their false relations. When relying on true relationships, the action of constructing reasoning will be meaningful, when relying on false relationships, it will be formal.

The purpose of our work was to develop and test a task for diagnosing the characteristics of the formation of logical actions associated with the ability to build reasoning and make inferences in secondary school students, in particular, sixth graders.

At the same time, we proceeded from the fact that such a task should include verbal-logical tasks containing judgments of various types.

2.Materials and methods.

Thus, in logical science (see, for example, [2]), simple judgments are divided into attributive (ie, property judgments) and relational (ie, relational judgments).

Qualitatively, attributive judgments are characterized, firstly, as affirmative (if some property is attributed to the subject of the statement), for example: «… the square is red …». Secondly, attributive judgments are characterized as negative (if the subject of the utterance lacks some property), for example: «… the square is not red …».

Among the relational ones, there are judgments that reflect symmetrical and asymmetric relations. In the first case, when the members of the relation are rearranged, its character does not change (if A is equal to B, then B is equal to A), for example: “… if Dima was the same age as Kolya, then Kolya was the same age, how many Dima … «.

In the second case, when the previous and subsequent members of the relation are interchanged, it changes to the opposite (if A is greater than B, therefore, B is less than A), for example: «… if Dima is older than Kolya, then Kolya is younger than Dima …».

Thus, when characterizing logical actions, one should use tasks composed of relational judgments of both types.

2.1. Characterization of problems with relational judgments

When including problems with relational judgments in a diagnostic technique, a number of the following provisions should be taken into account.

First, there should be several tasks of each type — with symmetrical and asymmetric judgments.

Secondly, tasks of each type — with symmetrical and asymmetric judgments — should be of three degrees of complexity: simple (two judgments), less simple (three judgments) and complex (four judgments).

Thirdly, in each pair of problems with relational symmetric judgments of the same degree of complexity (first, second, and third), the combination of judgments must be different. In particular, the following two variants of combinations are possible.

For tasks of the first degree of complexity (with two judgments in the conditions), the following two options for combining judgments in the conditions of the tasks are implemented: task 1 “Misha is as strong as Gena. Gena is as strong as Dima. Which of the schoolchildren is stronger, Misha or Dima?” task 2 “Misha is as strong as Gena. Misha is as strong as Dima. Which of the schoolchildren is stronger, Misha or Dima?”

For problems of the second degree of complexity (with three judgments in the conditions), the following two combinations of judgments are implemented in the conditions of the problems: task 3 “Vova is as cheerful as Borya. Borya is as cheerful as Alik. Alik is as cheerful as Ivan. Which of the boys is more fun, Vova or Ivan?”; task 4. “Vova is as cheerful as Borya. Vova is as cheerful as Alik. Alik is as cheerful as Ivan. Which of the boys is more fun, Borya or Ivan?”

For problems of the third degree of complexity (with four judgments in the conditions), the following two combinations of judgments are implemented in the conditions of the problems: problem 5 “Vova is as cheerful as Borya. Borya is as cheerful as Alik. Alik is as cheerful as Ivan. Ivan is as cheerful as Oleg. Which of the boys is more fun, Vova or Oleg?”; task 6. “Vova is as cheerful as Borya. Vova is as cheerful as Alik. Alik is as cheerful as Ivan. Alik is as cheerful as Oleg. Which of the boys is more fun, Borya or Ivan?”

Fourth, in each pair of problems with relational asymmetric judgments of the same degree of complexity, the combination of judgments must be different. For example, the following two combinations are possible.

For tasks of the first degree of complexity (with two judgments in the conditions), the following two options for combining judgments in the conditions of the tasks are implemented: task 1 “Misha is weaker than Gena. Gena is weaker than Dima. Which of the schoolchildren is weaker, Misha or Dima?”;task 2 “Misha is stronger than Gena. Misha is weaker than Dima. Which of the schoolchildren is stronger, Misha or Dima?”

For problems of the second degree of complexity (with three judgments in the conditions), the following two combinations of judgments are implemented in the conditions of the problems: problem 3 “Vova is lower than Borya. Vova is lower than Alik. Alik is shorter than Ivan. Which of the boys is lower, Vova or Ivan?”; task 4. “Vova is taller than Borya. Vova is lower than Alik. Alik is shorter than Ivan. Which of the boys is taller, Vova or Ivan?”

For problems of the third degree of complexity (with four judgments in the conditions), the following two combinations of judgments are implemented in the conditions of the problems: problem 5 “Vova is lower than Borya. Vova is lower than Alik. Alik is shorter than Ivan. Ivan is shorter than Oleg. Which of the boys is lower, Vova or Oleg?”;task 6. “Vova is taller than Borya. Vova is lower than Alik. Alik is shorter than Ivan. Oleg is taller than Ivan. Which of the boys is taller, Borya or Oleg?”

2.2. A series of problems with relational judgments

Considering the features of constructing a series of problems with relational symmetric and asymmetric judgments, it should be noted that in the first two problems (problems 1 and 2, with two judgments in the conditions), – in particular, in problem 1 with symmetric judgments (“Misha is just as strong , like Gena. Gena is as strong as Dima. Which of the schoolchildren is stronger, Misha or Gena?”) and in task 2 with asymmetric judgments (“Misha is weaker than Gena. Gena is weaker than Dima. Which of the schoolchildren is weaker than — Misha or Gena?») conclusion about, respectively, «Which of the schoolchildren is stronger?» or “Which of the students is weaker?” carried out directly, i.e. by one comparison of two judgments directly presented in the conditions of the tasks.

In the second pair of problems of the discussed methods (i.e., in problems 3 and 4, with three judgments in the conditions), a comparison of directly presented judgments cannot answer the questions in these problems, – in particular, the question of problem 3 with symmetrical judgments ( Misha is as strong as Gena Gena is as strong as Dima Dima is as strong as Yegor Which of the schoolchildren is stronger, Misha or Yegor?) and tasks 4 with asymmetric judgments (Misha is weaker than Gena. than Dima. Dima is weaker than Yegor. Which of the schoolchildren is weaker, Misha or Yegor?).

In order to answer the questions of problems constructed in this way, it is necessary to make not one, but two comparisons of judgments. In this case, the first comparison should be made with two (out of three) directly presented judgments, for example: “Misha is as strong as Gena. Gena is as strong as Dima» or «Misha is weaker than Gena. Gena is weaker than Dima.» As a result, an intermediate conclusion was obtained that, respectively: «Misha is as strong as Dima» and «Misha is weaker than Dima.»

The second comparison is also made with two judgments, but at the same time one of them is not directly presented in the condition of the problem — this is an intermediate conclusion obtained as a result of the first comparison and held in the internal plan. For a problem with symmetrical judgments, this will be the judgment «Misha is as strong as Dima», for a problem with asymmetric judgments — «Misha is weaker than Dima».

Another judgment with which the intermediate conclusion is compared is the judgment directly presented in the conditions of the problem, i.e. the remaining third judgment, respectively: «Dima is as strong as Yegor» and «Dima is weaker than Yegor.»

Thus, the answers to the questions, respectively: “Which of the schoolchildren is stronger, Misha or Yegor?” and “Which of the schoolchildren is weaker, Misha or Egor?” are displayed only as a result of the second comparison.

In the third pair of problems (i.e., in problems 5 and 6, with four judgments in conditions): in problem 5 with symmetrical judgments (“Misha is as strong as Gena. Gena is as strong as Dima. Dima is the same strong as Egor. Egor is as strong as Kolya. Which of the schoolchildren is stronger, Misha or Kolya?») and in problem 6 with asymmetric judgments («Misha is weaker than Gena. Gena is weaker than Dima. Dima is weaker than Yegor Yegor is weaker than Kolya, which of the schoolchildren is weaker, Misha or Kolya?»), the answer is obtained only as a result of three comparisons.

The first comparison is made on the material of directly presented judgments (“Misha is as strong as Gena. Gena is as strong as Dima”) and (“Misha is weaker than Gena. Gena is weaker than Dima”), the first intermediate conclusion is made, respectively, («Misha is as strong as Dima») and («Misha is weaker than Dima»).

The second is drawn on the material of the first intermediate conclusion (held in the internal plan) and one directly presented judgment (of the two judgments that remained uncompared), respectively: «Dima is as strong as Yegor» and «Dima is weaker than Yegor», — the second intermediate conclusion is made, respectively: “Misha is as strong as Yegor” and “Misha is weaker than Yegor”.

The third is drawn on the material of the second intermediate conclusion (held in the internal plane) and the last (remaining uncompared) directly presented judgment, respectively: “Egor was as strong as Kolya” and “Egor is weaker than Kolya”, — the third intermediate the conclusion that serves as the desired answer to the entire problem, respectively: «Misha is as strong as Kolya» and «Misha is weaker than Kolya.»

Thus, the analysis of the structure of problems shows that the successful solution of problems with two and, moreover, three comparisons of relational judgments involves the implementation of controlled logical actions to compare the proposed judgments with judgments generated in the process of thinking. Therefore, the successful solution of tasks by schoolchildren with three and, even more so, with four relational judgments indicates, respectively, an average and high level of formation of cognitive competence associated with mastering the logical action of constructing reasoning.

2.3. Problems with attributive judgments

When including tasks with attributive judgments in the diagnostic methodology, it should be taken into account that one type of such tasks contains only affirmative judgments in the conditions, and the other type contains only negative judgments.

For example, the following task is of the first type: Dasha, Valya and Sveta learned the words: someone — English verbs, someone — English prepositions, someone — German prepositions. Dasha learned English words. Valya taught verbs. What words did Sveta teach?”

For example, the following task belongs to the second type: “Dasha, Valya and Sveta learned words: someone — English verbs, someone — English prepositions, someone — German prepositions. Dasha did not learn English words. Valya did not learn verbs. What words did Sveta teach?”

To control the level of complexity of tasks with positive and negative attributive judgments, the number of subjects and predicates in the conditions should be taken into account.

The first level includes tasks in which the large premise contains three subject judgments, for example: “Dasha, Valya and Sveta learned the words …”: and three predicates corresponding to them, for example: “… someone — English verbs, someone — German verbs, someone — German prepositions … «.

The second level includes tasks in which the large premise contains four subjects of judgments, for example: “Dasha, Valya, Sveta and Nina learned the words …”: and the four predicates corresponding to them, for example: “… someone — English verbs”. , someone — German verbs, someone — German prepositions, someone — Polish dialects … «.

Each of the marked levels includes tasks of three degrees of complexity, depending on the number of simple and complex judgments in the conditions of tasks in a smaller premise.

2.4.1. Tasks of the first degree of complexity with 3 subjects

Problems of the first degree of complexity with three subjects and predicates and with affirmative judgments include those problems in which the minor premise contains two simple affirmative judgments, for example: “Dasha, Valya and Sveta learned the words: someone — English verbs, someone — English prepositions, someone — German prepositions. Dasha learned verbs. Valya learned German words. What words did Sveta teach?”

In this problem, simple judgments include «Dasha learned verbs» and  “Valya learned German words». Their simplicity is determined by the possibility, on the basis of each of these judgments, to do a direct conclusion of a certain content: the judgment “Dasha learned verbs” unequivocally indicates that “Dasha learned English words”, since only verbs were related to English words .

The simplicity of the sentence “Valya learned German words»” is defined similarly: it unambiguously indicates that only prepositions refer to German words.

Problems of the first degree of complexity with three subjects and predicates and with negative judgments also include such problems that have two simple negative judgments in a smaller premise, for example: “Dasha, Valya and Sveta learned the words: someone — English verbs, someone — English prepositions, someone — German prepositions. Dasha did not study prepositions. Valya did not study English words. What words did Sveta teach?”

In this problem, simple judgments include » Dasha did not study prepositions » and » Valya did not study English words «. Their simplicity is determined by the possibility, on the basis of each of these judgments, to draw a direct conclusion that has a specific content: the judgment “Dasha did not study prepositions” clearly indicates that “Dasha learned verbs”  because verbs refer to English words.

The simplicity of the sentence “Valya did not study English words” is defined in the same way: this judgment unambiguously indicates that  “Valya learned German words” and, hence prepositions, since only prepositions were German.

2.4.2. Tasks of the second degree of complexity with 3 subjects

Tasks of the second degree of complexity with three subjects and predicates and with affirmative judgments include such tasks in which the smaller premise contains one complex judgment and one simple one, for example:

“Dasha, Valya and Sveta learned the words: someone — English verbs, someone — English prepositions, someone — German prepositions. Dasha learned English words. Valya taught verbs. What did Sveta teach?

In this problem, simple judgments include the judgment “Valya taught verbs”, since this judgment allows us to make an unambiguous conclusion that “Valya taught English verbs”, since the  verbs were only in English.

Complex judgments include the judgment “Dasha learned English words”, since this judgment does not immediately allow us to make an unambiguous conclusion that it was “Dasha taught” — “English verbs” or “English prepositions”.

An unambiguous conclusion based on a complex judgment can only be made by comparing it with the conclusion from a simple judgment: «Valya learned English verbs.» As a result of the comparison, the conclusion is made: «Dasha learned English prepositions.»

Tasks of the second degree of complexity with three subjects and predicates and with negative judgments include those tasks in which the smaller premise contains one complex judgment and one simple one, for example: «Dasha, Valya and Sveta learned the words: someone — English verbs, someone — English prepositions, someone — German prepositions. Dasha did not learn verbs. Valya did not learn English words. What words did Sveta teach?»

In this problem, simple judgments include the judgment » Valya did not learn English words». Its simplicity is determined by the ability to draw a direct conclusion with a specific content based on this judgment: the judgment “Valya is not English words” clearly indicates that “Valya learned German words” and, consequently, German verbs, since only prepositions were German words.

Complex judgments include the judgment “Dasha did not learn verbs”, since this judgment does not immediately allow us to make an unambiguous conclusion that it was “Dasha taught” — “German prepositions” or “English prepositions”.

An unambiguous conclusion based on a complex judgment can only be made by comparing it with the conclusion from a simple judgment «Valya did not learn English prepositions.» As a result of the comparison, the conclusion is: «Dasha learned English prepositions.»

2.4.3. Tasks of the third degree of complexity with three subject

Tasks of the third degree of complexity with three subject and predicate and affirmative judgments include those tasks in which the smaller premise contains two complex judgments and one simple one, for example: «Dasha learned English prepositions.» Tasks of the third degree of complexity with three subject and predicate and affirmative judgments include tasks in which the smaller premise contains two complex judgments and one simple one, for example: “Dasha, Valya and Sveta learned the words: someone — English verbs, someone — English prepositions, someone — German prepositions. Someone learned English words, someone — English prepositions, someone — German prepositions. Dasha learned English words. Galya taught prepositions. Sveta taught German words. What did Dasha teach?

In this task, simple judgments include the judgment “Sveta learned German words”, since this judgment allows us to make an unambiguous conclusion that “Sveta learned German prepositions”, since only squares were drawn in blue.

Complex judgments include the judgments “Dasha learned English words” and “Valya taught prepositions”, since these judgments do not allow us to draw an immediate unambiguous conclusion about what exactly “Dasha taught”, “English verbs” or “English prepositions”, and what exactly «memorized by Valya», — «English prepositions» or «German prepositions».

An unambiguous conclusion based on one or another complex judgment can only be made by comparing it with the conclusion from a simple judgment «Sveta taught German words» — «Sveta taught German prepositions.»

Tasks of the third degree of complexity with three subjects and predicates and with negative judgments include tasks in which the smaller premise contains two complex judgments and one simple one, for example: “Daria, Vera and Sasha sang. Someone — cheerful folk songs, someone — sad folk songs, someone — sad pop songs. Daria did not sing sad songs. Vera did not sing cheerful songs. Sasha did not sing folk songs. What did Daria sing?”

In this task, simple judgments include the judgment “Sasha did not sing folk songs”, since this judgment allows us to draw an unambiguous conclusion that “Sasha sang sad pop songs”, because only pop songs were sad.

Complex judgments include the judgments “Daria did not sing sad songs” and “Vera did not sing cheerful songs ”, since these judgments do not immediately allow us to make an unambiguous conclusion about what exactly “Daria sang” — “cheerful folk songs” or “sad folk songs” and what exactly “Vera sang sad songs” – “ folk songs” or “pop songs”.

An unambiguous conclusion based on one or another complex judgment can only be made by comparing it with the conclusion from a simple judgment » Sasha sang sad pop songs» — » Sasha sang sad pop songs». Include the following analysis of permissions: » Vera sang sad folk songs»

2.4.4. Tasks of the first degree of complexity with four subjects

Tasks of the first degree of complexity with four subjects and predicates and with affirmative judgments include those problems in which the smaller premise contains three simple judgments, for example: “Dasha, Valya, Sveta and Tanya learned words. Someone — English verbs, someone English prepositions, someone German prepositions, someone Arabic dialects. Dasha learned verbs. Valya learned German words. Sveta taught adverbs. What did Tanya study?”

In this task, simple judgments include «Dasha learned verbs», «Valya learned German words», and «Sveta learned adverbs». Their simplicity is determined by the possibility, on the basis of each of these judgments, to draw a direct conclusion with specific content: from the judgment “Dasha learned verbs”, it unequivocally follows that “Dasha learned English verbs”, because the verbs were only English; from the judgment “Valya learned German words” it unequivocally follows that “Valya learned German prepositions”, since only prepositions were German; from the sentence “Sveta taught adverbs” it unambiguously follows that “Sveta taught Arabic adverbs”, because adverbs were only Arabic.

Tasks of the first degree of complexity with four subjects and predicates and with negative judgments include those problems in which the minor premise contains three simple judgments, for example: “Dasha, Valya, Sveta and Tanya learned words: some English verbs, some English prepositions, some German prepositions, some Arabic dialects. Dasha did not learn prepositions and verbs. Valya did not learn English and Arabic words. Sveta did not learn English and German words. What did Tanya study?”

In this task, simple judgments include “Dasha did not learn prepositions and verbs”, “Valya did not learn English and Arabic words”, “Sveta did not learn English and German words”. Their simplicity is determined by the possibility, on the basis of each of these judgments, to draw a direct conclusion of a specific content.

So, from the judgment “Dasha did not learn prepositions and verbs”, it unequivocally follows that “Dasha taught adverbs”, since only three types of words were taught — verbs, prepositions and adverbs; from the judgment “Valya did not learn English and Arabic words” it unequivocally follows that “Valya did not learn German prepositions”, therefore, words were taught only in three languages — English, German and Arabic; from the judgment “Sveta did not learn English and German words” it unequivocally follows that “Sveta learned Arabic dialects”, because only the dialects were Arabic.

2.4.5. Tasks of the stcond degree of complexity with four subjects

Tasks of the second degree of complexity with four subjects and predicates and with affirmative judgments include those tasks in which the smaller premise contains one complex judgment and two simple ones, for example: “Dasha, Valya, Sveta and Tanya learned foreign words: some English verbs, some English prepositions, some German prepositions, some Arabic dialects. Dasha learned English words. Valya taught verbs. Sveta taught Arabic words. What did Tanya study?”

In this task, simple judgments include «Valya learned verbs» and «Sveta learned Arabic words.» Their simplicity is determined by the ability, on the basis of each of these judgments, to draw a direct conclusion with a specific content: the judgment “Valya verbs” unambiguously indicates that “Valya English verbs”, because verbs were studied only in English; the statement “Sveta learned Arabic words” unambiguously indicates that «Sveta taught Arabic dialects», because only the dialects were Arabic.

Complex judgments include the judgment “Dasha learned English words”, since this judgment does not immediately allow us to make an unambiguous conclusion that it was “Dasha taught” — “English verbs” or “English prepositions”.
An unambiguous conclusion based on this complex judgment can only be made by comparing it with the conclusion from the simple judgment «Valya learned verbs» — «Valya learned English verbs».

Tasks of the second degree of complexity with four subjects and predicates and with negative judgments include those tasks in which the smaller premise contains one complex judgment and two simple ones, for example: “Dasha, Valya, Sveta and Tanya learned foreign words: some English verbs, some English prepositions, some German prepositions, some Arabic dialects. Dasha did not learn German and Arabic words. Valya did not study prepositions and adverbs. Sveta did not learn English and German words. What did Tanya study?”

In this task, simple judgments include «Valya did not learn prepositions and adverbs» and «Sveta did not learn English and German words.» Their simplicity is determined by the ability, on the basis of each of these judgments, to draw a direct conclusion with a specific content: the judgment “Valya did not learn prepositions and adverbs” clearly indicates that “Valya learned English verbs”, because they learned three types of words: glavgols, prepositions and adverbs; the judgment «Sveta is not English and German words» unequivocally indicates that «Sveta learned Arabic» because she learned words in only three languages: English, German and Arabic.

Complex judgments include the judgment «Dasha did not learn German and Arabic words», since this judgment does not immediately allow us to make an unambiguous conclusion that it was «Dasha taught» — «English verbs» or «English prepositions». An unambiguous conclusion based on this complex judgment can only be made by comparing it with the conclusion from the simple judgment «Valya learned English verbs» — «Dasha learned English prepositions.»

2.4.6. Tasks of the third degree of complexity with four subjects

Tasks of the third degree of complexity with four subject and predicate and affirmative judgments include those tasks in which the minor premise contains two complex judgments and two simple ones, for example: “Dasha, Valya, Sveta and Tanya learned foreign words: some English verbs, some English prepositions, some German prepositions, some Arabic dialects. Dasha learned English words. Valya taught prepositions. Tanya learned German words. Sveta taught Arabic words. What did Dasha study?”

In this task, simple judgments include the judgments “Tanya learned German words” and “Sveta learned Arabic words”, since these judgments allow us to make an unambiguous conclusion that, respectively, “Tanya learned German prepositions”, because only prepositions were German. , and «Sveta taught Arabic dialects», because the dialects were only Arabic.

Complex judgments include the judgments “Dasha learned English words” and “Valya taught prepositions”, since these judgments do not allow us to draw an immediate unambiguous conclusion that it was “Dasha taught” — “English verbs” or “English prepositions” and that in particular , “Valya taught”, — “English prepositions” or “German prepositions”.

An unambiguous conclusion based on one or another complex judgment can only be made by comparing it with the conclusion from a simple judgment «Tanya learned German words» — «Tanya learned German prepositions.» As a result of such a comparison, the conclusion is made: «Valya learned English prepositions.» When comparing this conclusion with the judgment «Dasha learned English words», the conclusion is made: «Dasha learned English verbs».

Tasks of the third degree of complexity with four subjects and predicates and negative judgments include those tasks in which the smaller premise contains two complex judgments and two simple ones, for example: “Dasha, Valya, Sveta and Tanya learned foreign words: some English verbs, some English prepositions, some German prepositions, some Arabic dialects. Dasha did not learn German and Arabic words. Valya did not learn verbs and adverbs. Tanya did not learn English and Arabic words. Sveta taught German and English words. What did Dasha study?”

In this task, simple judgments include the judgments “Tanya did not learn German and Arabic words” and “Svet learned German and English words”, since these judgments allow us to make an unambiguous conclusion that, respectively, “Tanya learned German prepositions”, because prepositions there were only German, and «Sveta Arabic dialects», because only Arabic dialects were taught. Complex judgments include the judgments “Tanya did not learn English and Arabic words” and “Valya did not learn verbs and adverbs”, since these judgments do not allow us to immediately draw an unambiguous conclusion that it was “Dasha taught” — “English verbs” or “English prepositions» and what specifically «Valya taught» — «English prepositions» or «German prepositions».

An unambiguous conclusion based on this or that complex judgment can be made only when compared with the conclusion from a simple proposition «Tanya did not learn English and Arabic words» — «Tanya learned German prepositions.» As a result of such a comparison, the conclusion is made: «Valya learned German prepositions.» When comparing this conclusion with the judgment “Dasha did not learn German and Arabic words”, the conclusion is made: “Dasha learned English verbs”.

2.4.7. Types of questions in tasks

In the considered problems with a different number of characters, different questions can be formulated.

In one case, a question addressed to the object of discussion is possible, for example: «What did Dasha teach» or «What did Vera sing?»

In the second case, a question is possible addressed to the person who taught or sang, for example: «Who taught the verbs?» or «Who sang folk songs?»

In both cases, you can ask in the affirmative and negative form: «What didn’t Valya teach?» or «Who didn’t sing pop songs?»

2.5. «Reasoning» technique

Consideration of a number of examples of plot-logical problems with statements of various kinds and of varying complexity made it possible to build the «Reasoning» technique. With its help, it is possible to determine the possibilities of schoolchildren in the implementation of consistent conclusions.

The «Reasoning» method includes 12 problems of various types and complexity, placed on one sheet, which each student of the group received.

According to the complexity of the 12 tasks of the methodology, they are divided into three groups according to complexity: tasks 1 — 4 with three subjects and predicates in the condition refer to tasks of the first degree of complexity, tasks 4 — 8 — with four subjects and predicates in the condition refer to tasks of the second degree of complexity, tasks 9 — 12 — with five subjects and predicates in the condition refer to tasks of the third degree of complexity.                                                     FORM

1. Misha ran faster than Gena. Gena ran faster than Dima. Who was ahead, Masha or Dasha?

Decision. 1. Misha is not ahead of Dima. 2. Dima was not ahead of Misha. 3. Misha and Dima ran equally fast. 4. It is impossible to know who is ahead of whom.

2. Vera, Nadia and Lena moved into houses of different colors with different windows. Someone had a red house with square windows, someone had a blue house with square windows, someone had a blue house with round windows. Vera had a red house. Nadia had a house with round windows. What kind of house did Lena have?

Decision. 1. Lena had a red house with square windows. 2. Lena had a blue house with square windows.3. It is impossible to find out what kind of house Lena had. 4. Lena had a blue house with round windows. 5. Lena had a red house with round windows.

3. Vova jumped higher than Gena. Vova jumped lower than Dima. Who jumped higher, Vova or Dima?

Decision. 1. Vova did not jump as high as Dima. 2. Dima did not jump as high as Vova. 3. Vova jumped as high as Dima. 4. It is impossible to know who jumped higher — Vova or Dima.

4. Masha, Galya, Katya and Vera memorized foreign words: some Spanish verbs, some Spanish prepositions, some Polish prepositions, some Czech dialects. Masha did not remember prepositions and adverbs. Galya did not memorize Spanish and Czech words. Katya did not remember Spanish and Polish words. What did Vera remember?

Decision. 1. Vera memorized Polish prepositions. 2. Vera memorized Spanish prepositions. 3. It is impossible to know what Vera remembered. 4. Vera memorized Czech dialects. 5. Faith memorized Spanish verbs. 6. Vera memorized Spanish dialects. 7. Vera memorized Polish verbs.

5. Alla spoke louder than Vali. Valya spoke louder than Gena. Gena spoke louder than Zhanna. Who spoke louder — Alla or Zhanna?

Decision. 1. Alla did not speak as loudly as Zhanna. 2. Jeanne did not speak as loudly as Alla. 3. Alla spoke as loudly as Zhanna. 4. It is impossible to know who spoke louder — Alla or Zhanna.

6. Natasha, Rita and Zoya knitted winter things: someone a green scarf, someone a green hat, someone a red hat. Natasha knitted with green threads. Rita knitted a scarf. What did Zoya knit?

Decision. 1. Zoya knitted a green scarf. 2. Zoya knitted a green hat. 3. It is impossible to find out what Zoya knitted. 4. Zoya knitted a red hat. 5. Zoya knitted a red scarf.

7. Somov studied better than Alov. Somov studied worse than Bykov. Bykov studied worse than Volkov. Who studied better, Somov or Volkov?

Decision. 1. Somov did not study as well as Volkov. 2. Volkov did not study as well as Somov. 3. Somov studied as well as Volkov. 4. It is impossible to know who studied better, Somov or Volkov.

8. Alik, Borya, Vova and Gena knew foreign words: someone hundred Spanish words, someone hundred German words, someone two hundred German words, someone three hundred Czech words. Alik did not know two hundred or three hundred words written in the same language. Borya did not know German and Czech words. Vova did not know a hundred or two hundred words written in the same language. How many and what words did Gena know?

Decision.1. Gena knew a hundred Spanish words. 2. Gena knew a hundred Czech words. 3. It is impossible to find out how many and what words of the cash gene. 4. Gena knew three hundred Spanish words. 5. Gena knew three hundred Czech words.

9. Zina dived deeper than Sveta. Sveta dived deeper than Ira. Ira dived deeper than Lena. Lena dived deeper than Vera. Who dived deeper, Zina or Vera?

Decision. 1. Zina did not dive as deep as Vera. Vera did not dive as deep as Zina. 3. Zina dived as deep as Vera. 4. It is impossible to know who dived deeper, Zina or Vera.

10. Alla, Nadya and Lyuba sewed dresses of different colors for the dolls: someone — green with polka dots, someone — green with stripes, someone — blue with stripes. Alla’s dresses were green. Nadia’s dresses were polka dots. Luba’s dresses were blue. What dresses did Alla have?

Decision. 1. Alla’s dresses were green with polka dots. 2. Alla’s dresses were green with stripes. 3. It is impossible to find out what dresses Alla had. 4. Alla’s dresses were blue with stripes. 5. Alla’s dresses were blue with polka dots.

11. Grisha is more active than Oleg. Grisha is more passive than Petya. Petya is more passive than Pasha. Roma is more active than Pasha. Who is more active, Oleg or Roma?

Decision. 1. Oleg is not as active as Roma. 2. Roma is not as active as Oleg. 3. Oleg is as active as Roma. 4. It is impossible to know who is more active — Oleg or Roma.

12. Grisha, Gena, Kolya and Nikita went to sports sections at different times: someone went to football clubs for two months, someone went to volleyball for two months, someone went to handball for three months, someone went to basketball for four months.Grisha did not go to the section for three or four months.Gena did not go to the football section.Nikita did not go to the section for two or four months.Kolya did not go to the section for four months.Which section did Grisha go to and for how many months?

Decision. 1. Grisha went to the football section for two months. 2. Grisha went to the volleyball section for two months. 3. It is impossible to find out how much time and which section Grisha went to. 4. Grisha went to the volleyball section for three months. 5. Grisha went to the basketball section for four months.
3. Results.

53 fifth-graders and 49 sixth-graders took part in the group diagnostic sessions, which were held at the end of the academic year. Each of the marked contingents of subjects is divided into three groups. The first group includes students who correctly solved problems 1 — 4 and incorrectly the remaining problems from 5 to 12. The second group includes students who correctly solved problems 1 — 8 and incorrectly — problems 9 — 12. The third group includes students who correctly solved all problems , — from 1 to 12.

The results of solving the problems of the method «Reasoning» are presented in the table.

Table

The number of students in grades 5 and 6 who correctly solved problems 1-4, problems 1-8 and problems 1-12.

 Note: *p<0.05.

The data presented in the table indicate the following.

Firstly, during the sixth grade, the number of students who correctly solved the first four tasks of the methodology, in which reasoning was associated with the correlation of judgments concerning three subjects and predicates, significantly decreased: from 75.5% at the end of the fifth grade to 59 .3% at the end of sixth grade. Mathematical processing using Fisher’s test showed that the difference between 75.5% and 59.3% is statistically significant (at p<0.05).

This fact also means that during the sixth grade, the total number of students who successfully solved problems with four and five subjects and predicates in the condition (i.e. problems from fifth to eighth and from ninth to twelfth) also increased significantly: with 24.5% to 40.7% (the difference between these indicators is also, of course, statistically significant (at p<0.05).

It is also important to note the fact that during the sixth grade the number of students who correctly solved all problems increased more than the number of students who correctly solved problems with three and four subjects and predicates in the condition, respectively: from 5.6% to 14 .2% and from 18.9% to 26.5% (in the first case, the increase is 8.6%, in the second case, 7.6%).

The data obtained allow us to note that the result of the sixth year of schooling is a decrease in the number of students who successfully cope with tasks of only the first degree of complexity (with three subjects and predicates in the condition) and an increase in the number of students who successfully cope with tasks of the second and third degrees of complexity (respectively , with four and five subjects and predicates in the condition).

4. Conclusion.

The study was devoted to the study of the features of the development of logical thinking in schoolchildren of the fifth and sixth grades. For this purpose, group experiments were carried out using the author’s technique «Reasoning», in which the students of the marked classes solved twelve logical problems built on the material of attributive and relational judgments. At the same time, the tasks were divided by complexity into three groups: the first group consisted of tasks with three subjects and predicates in conditions (tasks 1–4), the second group, with four subjects and predicates (tasks 5–8), the third group, with five subjects and predicates (tasks 9–12).

As a result of these experiments, it was shown for the first time that 40% of students during their studies in the sixth grade master the solution of problems of the second and third groups (from the fifth problem to the eighth and from the ninth problem to the twelfth).

In the future, it is planned to conduct group experiments on the material of the tasks of the «Reasoning» method with students of the seventh, eighth and ninth grades. It is necessary to know what part of the schoolchildren for the year of study in the seventh, eighth and ninth grade masters the solution of complex logical problems (with four and five subjects and predicates in the conditions). The results of these studies will make it possible to establish the contribution of training in each of the marked classes to the development of logical thinking in adolescence.