1.Untroduction.

The development of the skills of semantic reading of texts of different styles and genres in schoolchildren is an essential prerequisite for successful education in the middle classes, since the transition to the main school is associated with a significant increase in the amount of information that the student must receive and assimilate from written sources (primarily from a variety of textbooks).

It is important to note that the achievement of meta-subject results by schoolchildren reflects the formation of meta-subject competencies associated, in particular, with the construction of reasoning and the development of ways to solve search problems. These competencies underlie the development of semantic reading skills, which is characterized by a clear distinction in any text between form and content, main and secondary, complete and incomplete, authorial and borrowed, known and new.

Meta-subject results are achieved by schoolchildren in the course of mastering various academic disciplines both in primary and secondary schools. In assessing the achievement of meta-subject results and related competencies, we proceeded from considering them as new formations of educational activity, which is the leading activity in primary school age.

The activity approach in assessing the formation of the noted meta-subject competencies suggests that schoolchildren need to be offered tasks, the condition for the successful completion of which in some cases is the child’s mastering the methods of solving problems, in others — the construction of consistent reasoning.

When diagnosing cognitive meta-subject competence associated with the development of methods for solving problems of a search nature, we proceeded from the fact that this development involves the formation of a mental action of analysis aimed at analyzing the conditions of the proposed problems.

In some cases, such an analysis is implemented as a formal analysis that only divides the conditions of the problems into separate data — this is typical for a non-generalized, empirical method of solving problems of a search nature.

In other cases, the analysis of conditions is connected not only with the selection of data and their relationships, but also, most importantly, with the clarification of their role in a successful solution: what is essential and necessary, and what is insignificant and accidental. This is a meaningful, clarifying analysis, which acts as a condition for a generalized, theoretical method for solving search problems (see, for example, [1], [2], [3]).

The mastery of generalized methods for solving problems of an exploratory nature is characterized by the ability to carry out a meaningful analysis of their conditions, associated with the identification of significant data relationships. As a result, all the problems of the proposed class are successfully solved. The fact of unsuccessful solution of one or several problems of the proposed class indicates the absence of meaningful analysis and, therefore, the presence of a non-generalized way of solving problems.

2. Materials and methods

Based on these ideas about the originality of different approaches to the analysis of the conditions of search problems belonging to the same class, and the different ways of solving them associated with these approaches, requirements were developed for an experimental situation designed to determine which (generalized or non-generalized) mode of action took place. regarding the proposed search problems.

First, the subject must be offered to solve not one, but several problems.

Secondly, these problems must have a common principle of construction and solution.

Thirdly, their conditions must differ in external, directly observable features.

2.1. The «Exchanges» technique

In accordance with the noted requirements, the «Exchanges» technique was developed, which included 8 gradually becoming more complex spatial-combinatorial tasks, solved in a visual-figurative plan. Tasks 1 and 2 are required to be solved in two actions, tasks 3 and 4 — in three actions, tasks 5 and 6 — in four actions, tasks 7 and 8 — in five actions.

A diagnostic lesson in order to determine the characteristics of the formation of cognitive meta-subject competence associated with the development of a general method for solving problems is carried out as follows.

 First, students are given blank sheets of paper to write down the solution of problems, the conditions of which are placed on a special form, which is given after familiarization with the rules for solving problems.

After the children sign the blank sheets, the condition of the problem is displayed on the board:

                                   MM _ _ _ 7 4

                                   D D           7 4

Then the organizer of the lesson says: “The same letters must be arranged in one action so that they stand in the same places where the same numbers are. One action is a mutual exchange of places of any two letters. In this problem, the solution is to exchange the places of the letters «M» and «D».

The following is written on the board:

• M D

                                                 M D

After that, the organizer of the lesson depicts on the board the conditions of the second task, where the letters, like numbers, must be arranged in two actions:

                                       T T R R _ _ _ 4 2 7 9

                                       V VN N          4 2 7 9

The solution to this problem is collectively analyzed (first the letters T and V are changed, and then R and N) and it is written on the board:

                                       1) Т V R R,          2) Т V RN

                                            T V N N               Т V R N

At the same time, the organizer of the lesson  pecifically draws the attention of the children to the  fact that only two letters change places in one action,  and the remaining letters are simply rewritten.

Then a form with training and basic tasks is distributed.

Form

Training tasks

1. V V _ _ _ 3 5 (1 action)

     NN          3 5

2. R R S S _ _ _ 6 8 3 5 (2 actions)

    T T HH          6 8 3 5

Main tasks

1. M T N S _ _ _ 7 5 5 7 (2 actions)

M T N S          6 1 1 6

2. K S R M B _ _ _ 8 5 4 5 8 (2 actions)

K S R M V          2 3 4 3 2

3. B P R M V H_ _ _ 2 7 1 1 7 2 (3 steps)

B P R M V H         8 4 5 5 4 8

4. V N K F X F S _ _ _ 9 5 3 8 3 5 9 (3 actions)

V N K F X F S          6 2 7 8 7 2 6

5. R H N S V D P W _ _ _ 3 2 1 5 5 1 2 3 (4 actions)

R G N S V D P W          4 8 7 6 6 7 8 4

6. B D L R W G K M T _ _ _ 1 2 3 9 4 9 3 2 1 (4 steps)

D L R W G K M T              7 5 4 8 4 8 4 5 7

7. L W N G P R V K S M _ _ _ 2 1 3 5 7 7 5 3 1 2 (5 actions)

L  S  N G P R V K S M          8 9 6 0 4 4 0 6 9 8

8. B T F X D N W H R Z _ _ _ 0 3 2 5 9 9 5 2 3 0 (5 actions)

B T F X D N W H R Z           1 7 4 8 6 6 8 4 7 1

                                                  *                     *               *

After handing out the forms, the children are given the necessary explanations: “Look at the sheet. First (above), the conditions of the 1st and 2nd training tasks are drawn, and then the main tasks that need to be solved in a row for a different number of actions: the 1st and 2nd tasks are solved in two actions, the 3rd and 4th — for three, 5th and 6th — for four, 7th and 8th — for five actions.

Now solve the training problems. Write the solution as we did on the board. Remember: in one action, only two letters change places”.

Passing through the classroom, the class organizer checks the solution of the training problems and points out errors, if any.

After checking, the children solve the main problems. At the end of the work, students hand over forms and sheets with solutions.

The solution of the main problems is easier to check based on the principle of their construction, since in each problem there can be many specific options for the correct solution. So, in the first action, letters can be interchanged, occupying in the sequence both extreme places and middle ones.

All eight tasks of the presented series are based on the mirror ratio of numbers: the same are, in the top row and in the bottom row, the first number on the left and the first on the right, the second on the left and the second on the right, the third on the left and the third on the right, the fourth on the left and fourth from the right, etc.

Thus, when solving, it is necessary to change the letters located, firstly, in different rows (upper and lower) and, secondly, mirrored. This means that you need to change the first letter of the top row and the last letter of the bottom row, or, conversely, the first letter of the bottom row and the last letter of the top row; the second letter of the top row and the penultimate one of the bottom row, or, conversely, the second letter of the bottom row and the penultimate one of the top row, etc.

As a result, when solving problems of this kind correctly, identical letters should be placed in the same row (upper or lower), and different letters in different rows (upper and lower).

The solved problems are evaluated on the basis of the following considerations.

If all tasks are solved correctly, then this indicates the construction of a general method for solving all the proposed search problems.

If the initial tasks (in two and three actions) are solved correctly, and the remaining four are incorrect, then, then, successful actions in tasks 1–4 were not based on the construction of a general way to solve them.

The same conclusion (i.e., about the absence of constructing a general method for solving all the proposed problems) can be drawn even if tasks in 4 actions (i.e., tasks 5 and 6) are successfully solved, and tasks in five actions (tasks 7 and 8) are solved incorrectly.

49 fifth grade students participated in group experiments using the «Exchanges» method. The results of the experiments indicate that 48.9% of the subjects solved all the problems correctly and, therefore, built a general method for solving all the proposed search problems.

2.1. The «Inference» technique

In the diagnosis of cognitive meta-subject competence associated with the mastering of the ability to build a reasoning and to make conclusions consequently following from the proposed judgments, we proceeded from the that into the methodology it is reasonable to included verbal-logical questions.

Thus, in logical science (see, for example, [5]), among simple judgments, attributive (ie, judgments of properties) and relational (ie, judgments of a relation) are singled out.

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

Among the relational judgments, 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 B is equal to B, then C is equal to B), for example: “… if Vasya had the same height as Zhenya, then Zhenya had such the same height as Vasya … «.

In the second case, when the previous and subsequent members of the relation are interchanged, it changes to the opposite (if B is less than B, therefore, C is greater than B), for example: «… if Vasya is higher than Vova, then Vova is lower than Vasya …».

Thus, when diagnosing the development of cognitive meta-subject competence associated with mastering the logical action of constructing reasoning, one should use verbal-logical tasks composed of relational judgments of both types.

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, problems 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 problems with relational symmetric judgments, in each pair of problems of the same degree of complexity, first degree, second and third, the combination of judgments must be different. For example, there are two options: (1): “Grisha is as brave as Zhenya. Zhenya is as brave as Vova. Which of the schoolchildren is more courageous — Grisha or Vova? (2) “Grisha is as brave as Zhenya. Grisha is as brave as Vova. Which of the schoolchildren is more courageous — Grisha or Vova?”

In the first case, in both judgments of the problem, there is the second character in the order of mention in the problem, in the second case, the first one.

In a similar way, two options for combining judgments are implemented in problems with relational asymmetric judgments.

There are two types of problems with attributive judgments. Firstly, tasks with affirmative judgments, for example: “Dasha, Valya and Sveta sculpted from plasticine: someone — a big hare, someone — a big fox, someone — a small fox. Dasha sculpted a large animal, Valya sculpted a fox. Who did Sveta sculpt?”

Secondly, tasks with negative judgments, for example: “Dasha, Valya and Sveta sculpted from plasticine: someone — a big hare, someone — a big fox, someone — a small fox. Dasha did not sculpt a large animal, Valya did not sculpt a fox. Who did Sveta sculpt?”

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 subjects of judgments, for example: “Dasha, Valya and Sveta sculpted from plasticine …”, and three predicates corresponding to them, for example: “… someone is a big hare, someone then — a big fox, someone — a small fox … «.

The second level includes tasks in which the large premise contains four subjects of judgments, for example: “Dasha, Valya, Nina and Sveta sculpted from plasticine …” and four predicates corresponding to them, for example: “… someone is a big hare , someone — a big fox, someone — a small fox, someone a medium-sized wolf … «.

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.

In problems with affirmative and negative attributive judgments of the first, second and third degree of complexity with three subjects and three predicates in a large premise and problems of the first, second and third degree of complexity with four subjects and four predicates in a large There are two possible formulations of the question in the premise.

The first version of the wording of the question is characterized by the fact that the predicate of the judgment is the desired one, and the subject of the judgment is known, for example: “What did Dasha sculpt?”.

The second version of the wording of the question is characterized by the fact that the subject of the judgment is the desired one, and the predicate of the judgment is known, for example: “Who sculpted the big hare?”.

Moreover, each version of the wording of the question can contain not only an affirmation, as in the above examples, but also a negation, for example, respectively: “What didn’t Dasha sculpt?” and «Who hasn’t sculpted big animals?».

On the basis of the analysis of the content of different variants of verbal-logical tasks with relational and attributive judgments, the method «Inference» was developed for conducting group surveys of students in order to assess the formation of cognitive meta-subject competence associated with mastering the logical action of constructing reasoning.

The tasks of the «Inference» technique are given on the form to each student.

Form

1.Klava walked faster than Valya. Valya walked faster than Dina. Which of the girls walked faster — Klava, Valya or Dina?”

Answers: 1. Klava did not go as fast as Dina. 2. Dina did not walk as fast as Klava. 3. Klava walked as fast as Dina. 4. It is impossible to say which of the girls walked faster.

2. Zina, Anya and Nina lived on different floors in different houses: someone on the third floor of a tall building, someone on the third floor of a low building, someone on the fifth floor of a low building. Zina lived in a high house. Anya lived on the fifth floor. Where did Nina live?”

Answers: 1. Nastya lived on the third floor of a tall building. 2. Nastya lived on the third floor of a low building. 3. It is not known where Nastya lived. 4. Nastya lived on the fifth floor of a low building. 5. Nastya lived on the fifth floor of a tall building.

3. Artem screamed more than Vova. Artyom shouted more quietly than Yegor. Which of the boys screamed more, Artyom or Yegor?”

Answers: 1. Artem did not shout as much as Yegor. 2. Igor did not shout as much as Artem. 3. Artem screamed as much as Yegor. 4. It is impossible to say which of the schoolchildren shouted more — Artem or Yegor.

4. Grisha, Lena, Katya and Kolya solved problems: someone added three-digit numbers, someone added two-digit numbers, someone multiplied two-digit numbers, someone divided single-digit numbers. Grisha did not solve problems with two-digit and one-digit numbers. Lena did not solve addition and division problems. Katya did not solve addition and multiplication problems. What tasks did Kolya solve?

Answers: 1. Kolya solved problems on the multiplication of two-digit numbers. 2. Kolya solved problems involving the addition of two-digit numbers. 3. It is not known what problems Kolya solved. 4. Kolya solved problems involving the division of single-digit numbers. 5. Kolya solved problems for adding three-digit numbers. 6. Kolya solved problems on the addition of single-digit numbers. 7. Kolya solved problems on the multiplication of three-digit numbers. 5. Anya remembers prose more easily than Vera. Anya remembers prose more easily than Kolya. Kolya memorizes prose more easily than Zhenya. Which of the guys remembers easier — Anya or Zhenya?”

Answers: 1. Anya does not memorize prose as easily as Zhenya. 2. Zhenya does not memorize prose as easily as Anya. 3. Anya remembers prose as easily as Zhenya. 4. It is impossible to say which of the girls remembers prose more easily — Anya or Zhenya.

6. Nastya, Raya and Nadia were preparing pies: someone with egg and rice, someone with egg and cabbage, someone with meat and cabbage. Nastya cooked pies with eggs. Raya was making rice pies. What pies did Nadia cook?”

Answers: 1. Nadia cooked pies with egg and rice. 2. Nadia cooked pies with eggs and cabbage. 3. It is not known what pies Nadya cooked. 4. Nadia cooked pies with meat and cabbage. 5. Nadia cooked pies with meat and carrots.

7. Alik was farther from the forest than Borya. Alik was closer to the forest than Misha. Misha was closer to the forest than Sanya. Which of the boys was farther from the forest, Alik or Sanya?”

Answers: 1. Alik was not as far from the forest as Sanya. 2. Vanya was not as far from the forest as Alik. 3. Alik was as far from the forest as Sanya. 4. It is impossible to say which of the boys was further from the forest — Alik or Sanya.

8. Seva, Misha, Tolya and Vitya were traveling: some went by plane to the north, some went by plane to the east, some went by train to the east, some went by helicopter to the south. Seva did not use the train or helicopter. Misha did not go east and south. Tolya did not use the plane and the train. On what and where did Vitya travel?”

Answers: 1. Vitya went by plane to the north. 2. Vitya went by plane to the east. 3. It is not known on what and where Vitya went. 4. Vitya went south on a bicycle. 5. Vitya rode a bicycle to the north.

9. Nina lived higher than Kolya. Kolya lived higher than Igor. Igor lived higher than Lera. Lera lived higher than Misha. Which of the guys lived higher, Nina or Misha?”

Answers: 1. Nina did not live as high as Misha. 2. Misha did not live as high as Nina. 3. Nina lived as high as Misha. 4. It is impossible to say which of the guys lived higher — Nina or Misha.

10. Alik, Kostya and Lesha made beds for vegetables: someone — long beds for radishes, someone — long beds for cabbage, someone — short beds for cabbage. Alik made long beds. Kostya made beds for cabbage. Lesha made short beds. What beds did Alik make?”

Answers: 1. Alik made long beds for radishes. 2. Alik made long beds for cabbage. 3. It is not known what beds Alik did. 4. Alik made short beds for cabbage. 5. Alik made short beds for radishes.

11. Masha is more fun than Olya. Masha is sadder than Katya. Katya is sadder than Polya. Rimma is happier than Paul. Which of the schoolgirls is more fun — Olya or Rimma?”

Answers: 1. Olya is not as cheerful as Katya. 2. Katya is not as cheerful as Olya. 3. Olya is as cheerful as Katya. 4. It is impossible to say which of the girls is more fun — Olya or Rimma.

12. Masha, Galya, Katya and Natasha learned to play musical instruments: someone — five years on the domra, someone — five years on the piano, someone — six years on the piano, someone — seven years on the clarinet . Masha did not study for six and seven years. Galya did not learn to play the domra and clarinet. Natasha did not study for five and seven years. Katya did not study for six and seven years. What musical instrument and for how many years did Masha study?”

Answers: 1. Masha studied domra for five years. 2. Masha studied piano for five years. 3. It is not known what musical instrument and for how many years Masha studied. 4. Masha studied piano for six years. 5. Masha studied clarinet for seven years.

3. Results

The survey, which was conducted using the «Inference» technique, involved 56 students in the fifth grade and 54 students in the sixth grade. The survey results are presented in the table.

Table

                          Note: *p < 0.05.

The data presented in the table testify to the differences between fifth-graders and sixth-graders in the success of solving the problems of the «Inference» methodology.

Thus, only the first two tasks (the simplest ones) were successfully solved in the fifth grade — 14.3% of children, in the sixth grade a little less — 9.3%. The remaining 10 problems were solved incorrectly by some students of both classes, and some students did not solve some problems at all, most often these were problems from the eighth to the eleventh.

All problems in the fifth grade were successfully solved by 23.2% of the students, and in the sixth grade it was much more — 38.9%. This fact testifies to the percentage of fifth-graders and sixth-graders who have the ability to successfully perform logical actions for constructing reasoning — it should be noted that the difference in the noted indicators is statistically significant              (at p < 0.05).

The remaining tasks (from the third to the eleventh) were successfully solved in the fifth grade by 62.5% of the students, in the sixth grade — by 51.8%.

 It is clear that if all the tasks (including the last one, the twelfth, the most difficult one) were successfully solved by more students in the sixth grade than in the fifth grade, then, therefore, the rest of the tasks are both the simplest (the first two) and more complex ( from the third to the eleventh) – on the contrary, in the sixth grade fewer students decided than in the fifth grade.

4.Conclusion

In the study, two methods were developed and tested in surveys of students of younger adolescence.

One of them, the «Exchanges» technique, was built on the material of spatial-combinatorial tasks of a search nature of non-educational content. This technique is intended to determine the achievement of a meta-subject result associated with the development of generalized methods for solving problems of a search nature based on a meaningful analysis of their conditions. Such an analysis, as shown by our studies [2,3], is associated with the identification of significant relationships in the conditions of problems.

This technique was tested in a group survey with 49 fifth grade students. The results showed that all the proposed tasks were solved correctly and, therefore, almost half of the students (48.9%) built a common way to solve them.

Another technique, “Inference”, was built on the material of 12 gradually becoming more complex plot-logical tasks of non-educational content. This technique was intended to determine the achievement of a meta-subject result associated with mastering the logical actions of constructing reasoning. As our studies have shown [2,3], such logical actions underlie the ability to draw conclusions that follow consistently from the proposed judgments.

This methodology was tested in group surveys with a total of 110 fifth and sixth grade students. It was shown that in the fifth grade logical actions of constructing reasoning were fully mastered (in relation to the proposed 12 tasks) by 23.2% of students, in the sixth grade — 38.9%.

The study made it possible to establish a number of new facts.

Firstly, it was shown that almost half of the fifth graders are able to generalize the method of solving search problems of a spatially combinatorial nature of non-educational content.

Secondly, the results of the surveys showed that in the fifth and sixth grades, a smaller part of the students — respectively, one fifth and one third — are able to perform logical actions of constructing reasoning on the material of plot-logical problems of non-educational content.

Thirdly, it turned out that the ability to generalize the method of solving search problems of a spatially combinatorial nature among schoolchildren of the same age (fifth graders) is formed to a greater extent than the ability to perform logical actions for constructing reasoning.

The noted facts significantly expand the ideas of developmental and educational psychology. about the intellectual capabilities of children of younger adolescence.

In further research, it is planned to conduct surveys of sixth-graders and seventh-graders on the material of the «Exchanges» methodology and seventh-graders on the material of the «Inference» methodology. This is necessary to obtain important data on the nature of the relationship between the achievement of meta-subject results associated with the development of generalized methods for solving search problems and logical actions for constructing reasoning, with the age of children.