1.Introduction

The general meaning of this study was to develop such an important direction in solving the fundamental psychological and pedagogical problem «Training and Development» as establishing the characteristics of the formation of metasubject intellectual actions, – cognitive competencies, – among schoolchildren during the period of study in the fifth and sixth grades of basic school.

According to the provisions of the new Federal State Educational Standard for Secondary Schools [8], the mastering of curricula by children in the fifth-sixth grades of secondary school should lead not only to the assimilation of knowledge, skills and abilities in specific school disciplines, but also to the mastery of cognitive competencies of various kinds by students.

These competencies are associated with children’s mastering the skills of constructing inferences of varying complexity, with mastering the ability to choose and implement effective approaches in developing methods for solving search problems on educational and non-educational material, with schoolchildren mastering the skills of planning ways to solve problems, with mastering cognitive reflection and control skills their actions in order to correct them.

1.1.Types of knowledge

It should be noted that — in understanding the effectiveness of methods for solving search problems, in interpreting cognitive reflection, in understanding the characteristics of the formation of planning skills and in assessing the actions of constructing inferences of varying complexity — we relied on the provisions on two types of cognition developed in dialectical logic [4 ] and implemented in the studies of V.V. Davydov [2], [3] and his collaborators (see, for example, [1], [5], [6], [7]).

According to these provisions, a person who cognizes the surrounding reality can be aimed both at reflecting the internal connections and relations of objects and phenomena, thereby realizing theoretical, meaningful, reasonable knowledge, and at reflecting their external connections and relations, thus realizing way, empirical, formal, rational knowledge.

The first case is characterized by the effectiveness of cognitive activity, because its result is associated with the identification of the causes underlying the changes in the object being cognized, which is the basis for the development of the corresponding pattern.

The second case is characterized by insufficient efficiency of cognitive activity, because its result is associated only with the description and classification of externally presented characteristics of objects of knowledge. This approach is associated with the impossibility of revealing the reasons for the change of a cognizable object and reliably characterizing the patterns of its existence in the past, present and future.

1.2. Cognitive competencies of schoolchildren

Based on the above provisions on the content and methods of different types of cognition, an understanding of the features of cognitive competencies was developed [5], [6]. In accordance with this understanding, the development of methods for solving problems in one case is associated with the allocation of significant data relationships contained in their conditions, in the other case, the disclosure of significant data relationships that are objectively contained in the conditions of the problems being solved does not occur. The development of a solution method, associated with the allocation of significant relations, is implemented as a meaningful action, the result of which is a general method of solving problems, and the development of a solution method, not associated with the allocation of essential relations, is implemented as a formal action, the result of which is a particular method of solving problems.

Based on the above provisions on the two types of cognitive activity, we assumed that cognitive reflection can be associated with a person’s appeal in one case to the foundations of these methods and with understanding the features of their development as related to significant relationships in the conditions of the proposed tasks. In another case, cognitive reflection may be associated with a person’s appeal only to the external features of these methods without comprehending their objectively existing connections with significant relationships in the conditions of the problems being solved. In the first case, cognitive reflection is realized as a meaningful action, and in the second case, as a formal action.

When analyzing the features of planning, two approaches were considered in developing a program of action in a situation of problem solving. Within the framework of one approach, the solution of search problems includes two stages — research and execution. At the first stage, the conditions of the proposed problem are analyzed, associated with the identification of data and their relationships in the conditions, and the preparation of a plan for solving the problem. The content of planning at this stage is the determination of the sequence of all actions required for a successful solution of the problem, the development of a program for the implementation of previous and subsequent actions to solve the problem in the entire volume. It is important to emphasize that all the required actions in this case are planned before the implementation of the solution to the proposed problem.

Within the framework of another approach, the research stage associated with the analysis of the conditions of the proposed problem and the planning of its solution as a whole is absent. Drawing up a plan with this approach is carried out in parts, each of which may include one or more required actions. In this case, subsequent actions are planned only after the previous ones have been completed.

Planning, implemented on the basis of the first approach, is carried out as a meaningful action, since the action program for solving the problem is developed based on the analysis of the entire amount of data contained in the condition of the proposed problem. Planning, implemented on the basis of the second approach, is carried out as a formal action, since the program of actions to solve the problem is developed and implemented in parts, in separate links, without comprehending the content of previous and subsequent actions and their relationships within the entire set of actions to solve the proposed problem.

When developing criteria and indicators for the formation of skills in constructing reasoning when making inferences, the fact was taken as a basis that in one case the derivation of a conclusion is associated with the selection of true relations based on the correlation of all judgments that make up the task, and in the other case, deriving a conclusion from the proposed judgments is associated with highlighting false relationships, since only a part of the proposed ones correlates.

Highlighting the true relations of the proposed judgments leads to favorable conditions for demonstrating a consistently realized inference, and highlighting the false relations of judgments leads to contradictions in the execution of the inference. In the first case, the construction of reasoning is implemented as a meaningful action, in the second case, as a formal action.

1.3. Study Characteristics

The purpose of the study was to determine the characteristics of the cognitive competencies of students in the fifth and sixth grades of the basic school. At the same time, it was based on the assumption that cognitive competencies — associated with the mastery of schoolchildren’s ability to build logical reasoning, with the mastery of effective ways to solve problems of a search nature, with the mastery of the ability to independently plan ways to achieve the goal and with the development of the initial forms of cognitive reflection — are formed in schoolchildren during the specified period of study with different intensities: the most intensively is the ability to build logical reasoning, less intensively is the ability to implement effective ways to solve problems of a search nature, even less intensively is the ability to exercise cognitive reflection and control of one’s actions, the least intensively is the ability to plan an achievement goals.

2. Materials and methods

2.1. Diagnostics of the method of solving problems

Determination of the characteristics of ways to solve search problems in schoolchildren of grades 5-6, in order to assess the formation of the corresponding cognitive competence, was carried out using the «Exchanges — 1» methodology. The content of the methodology consisted of eight spatial-combinatorial tasks, the solution of which was required to be carried out in a visual-figurative form, in a mental plan. Tasks from the first to the eighth gradually became more difficult: to solve the first and second tasks, it was required to perform two actions, the third and fourth — three actions, the fifth and sixth — four actions, the seventh and eighth — five actions.

At the beginning of the diagnostic lesson, children receive sheets where they should write down the solution of problems. After the distribution of the indicated sheets and forms on the blackboard, a variant of the problem of the “Exchanges — 1” methodology is presented:

MM _ _ _ 8 5

T T           8 5

Further, the children are told: “You need to do one action with the same letters, so that as a result these letters are arranged in the same way as the same numbers. For one action, we take one mutual exchange of their places of any two letters. In this problem, you need to swap the letters M and T”.

The following is the solution:

• T M

    T M

Then the second task is drawn on the board. It requires that the same letters in two actions end up in the same places where the same numbers are located:

C C H H _  _ _ 7 2 4 9

K K G G           7 2 4 9

After a joint discussion with the children of the solution to this problem — which consists in the fact that in the first action the letters H and K are interchanged, and in the second action — C and G — this solution is written on the board:

                                                1) C K H H        2) C K G H

                                                    C K G G             C K G H

Then, after answering the students’ questions, the teacher distributes forms with tasks: two training and eight main ones.

FORM

Training tasks

1. LL _ _ _ 36 (1 action)

                                             RR          36

2. B B A A _ _ _ 5 4 7 6 (2 actions)

                                    P  P O O          5 4 7 6

Main goals

1. W B R T _ _ _ 4 8 8 4 (2 actions)

    W B R T          7 2 2 7

2. K W R M B _ _ _ 7 4 9 4 7 (2 actions)

    K W R M B          1 8 9 8 1

3. V K N P R S _ _ _ 8 3 2 2 3 8 (3 actions)

    V K N P R S          7 1 6 6 1 7

4. G P T N V R F _ _ _ 8 4 2 7 2 4 8 (3 actions)

    G P T N W R F         5 1 6 7 6 1 5

5. L B S R M W X H _ _ _ 4 7 8 9 9 8 7 4 (4 actions)

    L B S R M W X H          2 3 6 1 1 6 3 2

6. R P K V C F W G S _ _ _ 5 4 3 7 8 7 3 4 5 (4 actions)

    R P K V C F W G S          6 2 9 1 8 1 9 2 6

7. N M W B K R S T F W _ _ _ 1 9 2 8 7 7 8 2 9 1 (5 actions)

    N M W B K R S T F W          3 6 5 4 0 0 4 5 6 3

8. P L T V S B M X D R _ _ _ 8 2 7 1 3 3 1 7 2 8 (5 actions)

    P L T W S B M X D R         5 6 9 0 4 4 0 9 6 5

The children are told: “At the top of the sheet with tasks are the conditions of two training tasks. The conditions of the main tasks are given below. Near each task, it is indicated how many actions it needs to be solved: tasks 1 and 2 — in two actions, tasks 3 and 4 — three, tasks 5 and 6 — four, tasks 7 and 8 — in five actions.

First you need to solve two problems at the very top of the sheet — training. Write down your actions in the same way as it was on the board. Above all, do not forget that only two letters exchange their places in one action”.

Further, moving from one student to another, the teacher tells each student whether he solved the problem correctly or not. In the latter case, he explains what the mistake was.

Then the children are offered to move on to solving the main problems. Since all tasks are built on the basis of the same principle — the letters of the upper row are interchanged with the letters of the lower row — the correct solution of all tasks allows us to assert that there has been a development of a general method for solving these search problems, which is associated with a meaningful analysis of the conditions of the problem. In the case when the first two or four main problems had the correct solution, and more complex problems had the wrong solution, this means that in the first four problems the general solution method was not applied. The same assessment will be in the case when tasks from the first to the fifth or to the sixth are successfully solved, but problems 7 and 8 are not successfully solved.

2.2. Reflection Diagnostics

Determining the characteristics of reflection of methods for solving problems in schoolchildren of grades 5 — 6, in order to assess the formation of the corresponding cognitive competence, was carried out using the “Anagram” technique.

At the beginning of the lesson, the psychologist distributes forms with the conditions of the tasks and says: “There are six letter combinations on the form. In each, you need to rearrange the letters in places so that meaningful words are obtained”.

1. A, C, O, K → ____________
2. W, A, K, A → ____________
3. A, K, Y, R → ____________
4. D, A, B, O → ____________
5. E, R, O, M → ____________
6. B, O, N, E → ____________

Opinions

1. All six tasks are similar.
2. All six tasks are different.
3. Tasks 1, 2, 3 and tasks 4, 5, 6 are similar.
4. Tasks 1, 3, 5 and tasks 2, 4, 6 are similar.
5. Tasks 1, 2, tasks 3, 4 and tasks 5, 6 are similar.

Further, the psychologist says: “There are six tasks on the form. Each contains a meaningless word. In it, you need to rearrange the letters in places so that you get a meaningful word. After solving these six problems, choose one of the five opinions about these problems that you think is the most correct, and circle its number. Write why you chose this opinion about the tasks”.

The proposed tasks are constructed in such a way that in the first, third and fifth tasks the anagram is converted into a word by mutual exchange of places of the first and fourth, second and third letters (i.e. by reading the proposed letter combination from right to left), and in the second, fourth and sixth tasks the way of converting anagrams is different — by interchanging the places of the first and third, second and fourth letters (that is, by rearranging two syllables in places).

If the children, having correctly solved all six tasks, chose the fourth opinion about the tasks, then this indicates that in solving them they carried out meaningful reflection, generalizing the methods for solving the first, third and fifth tasks as built on the same principle, and the second , fourth, sixth tasks as constructed according to a different principle (for example: “… in the first, third and fifth tasks you need to read the other way around, and in others you need to rearrange the syllables …”).

Any other opinion about the task, – the first one (for example “… in all words the letters are interchanged …”), the second (for example: “… letters are different everywhere …”), the third (for example: «… in the first, second and third tasks there is the letter A, and in the fourth, fifth, sixth — the letter O …», the fifth (for example: «… in the first and second tasks the same letter is K, in the third and fourth tasks the same the letter — A, in the fifth and sixth tasks the same letter — O … «), – associated with the generalization of tasks according to the external features of their conditions, indicates the absence of meaningful reflection in their solution.

2.3. Planning Diagnostics

Determination of the characteristics of problem solving planning among schoolchildren of grades 5 — 6, in order to assess the formation of the corresponding cognitive competence, was carried out using the «Exchanges — 2» methodology.

At the beginning of the lesson, the psychologist depicts the condition of the problem on the board:

S R P — R S P

Then he says: “The letters on the left must be changed in one step so that they are arranged as on the right. 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 «S» and «R».

The following is the solution:

1) R S P

After that, the conditions of the second task are displayed, where the required location must be obtained from the initial one in two actions:

VNLK — NVKL

The solution to this problem is collectively analyzed (first the letters B and H change, and then L and K) and it is written on the board:

VNLK — NVKL

                                             1) NVLK, 2) NVKL

At the same time, the attention of the children is specially drawn to the fact that only two letters change places in one action, and the rest are rewritten without changes.

It is further explained that in the first action (and, accordingly, in the second one), the other two letters can also be changed, first L and K, and then V and N:

1) VNKL, 2) NVKL

After that, the children are given forms with training and basic tasks.

FORM

Training tasks

1.NKP — KNP (one action).

2. R K M TV — — — K R V T M (two actions).

Main tasks

1. M G V W C N K — M V G C W K N (3 actions).
2. P L G W R S D — G W P L D S R (3 actions).
3. L B N T — N T B L (3 actions).
4. S R K V — K V S R (3 actions).
5. T N L P M — M T N L P (4 actions).
6. R D V K W — D V K W R (4 actions).
7. N P R S T V — R S T V P N (5 actions).
8. K L B S G V — V S K L B G (5 actions).

Further, the psychologist explains the content of the form (points to two training tasks, four main tasks in 3 actions, two in 4 actions and two in 5 actions) and suggests solving training problems.

Then he checks the solution of these problems, considering that the most common mistake is moving (mentally) in one action only one letter, not two.

After correcting the errors, it is proposed to solve the main tasks. The lesson organizer indicates that the main problems have several options for the correct solution and that only one solution should be indicated.

If the child coped with tasks where it is required to find two and three mutual exchanges of letters in places (i.e. with the main tasks 1 — 4), and did not cope with more complex tasks (Nos. 5 — 8), then this indicates that that in solving them, he carried out formal, partial planning, outlining the subsequent action after the previous one was completed.

If the child successfully solved problems with only two, three, four, and, moreover, five exchanges (i.e., with problems 7–8), then this indicates that, when solving them, he carried out meaningful planning, which is associated with preliminary programming the entire sequence of required actions.

2.4. Diagnosis of actions of reasoning

Determining the characteristics of the logical actions of constructing reasoning among schoolchildren of grades 5 — 6, in order to assess the formation of the corresponding cognitive competence, was carried out using the “Plots” methodology, which includes 10 logical tasks of varying complexity.

1. Two boys played checkers: one won three times, the other two times. How many times did Igor win if Oleg didn’t win three times?
2. Three girls Lisa, Natasha and Masha went to different schools and different classes: someone went to a sports school in the 3rd grade, someone went to a music school in the 2nd grade, someone went to a sports school in the 2nd grade. In what school and in what class did each girl study, if Masha, like Natasha, studied in the 2nd grade, and Masha and Liza studied at a sports school?
3. Misha runs faster than Kolya. Misha runs slower than Alyosha. Who runs the slowest?
4. Misha, Gena and Seryozha sculpted from plasticine: someone — a cat, someone — an elephant, someone — a dog. Who sculpted what, if Gena did not sculpt an elephant, Seryozha did not sculpt an elephant and a dog?
5. Five days in April there was different weather: April 2, 6, 8.14 and 19. On one day it was cold and dry, on the other it was cold and rainy, on the third it was warm and dry, on the fourth it was warm and rainy, On the fifth day it snowed unexpectedly. On the 2nd and 6th of April it was warm, on the 2nd and 19th it was rainy, on the 19th and 14th it was cold. What was the weather like on each of the five days?
6. In a year, Nikolai will be 2 years older than Andrei was three years ago. Which of the guys is older?
7. A pencil is thicker than a pen and longer than a marker. A pencil is thinner than a felt-tip pen and shorter than a pen. Which object is the thinnest of all and which is the shortest of all?
8. Misha and Sasha Rogov, Misha and Sasha Belov and Misha Serov were standing on the stairs. Who stood on the next step below with Misha Belov, if both Rogovs stood across the step and both Belovs stood across the step, and three Mishas stood on the neighboring steps?
9. Guys — travelers went on a hike at the same time: Borya and Gena — from Yalta to Baku, Sasha and Vasya — from Baku to Yalta. After 4 days, Sasha was closer to Yalta than Gena to Baku, and Borya was further from Yalta than Vasya from Baku, Gena walked faster than Bori. Who walked the slowest?
10. Misha runs faster than Viti, jumps higher than Kolya and dives better than Oleg. Misha jumps lower than Vitya, dives worse than Kolya and runs slower than Oleg. Who runs the slowest, who jumps the lowest, and who dives the worst?

The tasks of this technique, taking into account the number of characters in the conditions, the number of relationships between them and, accordingly, the number of judgments that need to be correlated in the process of inference, are divided by complexity into four groups.

Firstly, tasks 1 and 2 are the easiest, training (with two characters), and secondly, tasks 3 and 4 are simple (their solution requires a correlation of two judgments), tasks 5 to 8 are more complex (their solution requires correlation of three judgments) and problems 9 and 10 are the most difficult (their solution requires correlation of four judgments).

If the student coped only with tasks 1-4 (incorrectly solving the remaining tasks), then this indicates that when solving them, he carried out the formal action of constructing reasoning.

If the student coped with tasks 1 — 8 and, moreover, with tasks 9 and 10, then this indicates that in solving them he carried out a meaningful action of constructing reasoning.

3. Results

Experiments according to the methods presented above were carried out at the end of the academic year in a group form. The first series involved 127 students of the 5th grade, in the second series — 119 students of the 6th grade. The results of processing the obtained data are presented in the table.

Table

The distribution of children among students in grades 5 and 6 who, when solving problems of research methods, carried out a meaningful construction of reasoning, a meaningful development of a method for solving problems, meaningful planning and meaningful reflection (in %).

3. Results

Experiments according to the methods presented above were carried out at the end of the academic year in a group form. The first series involved 127 students of the 5th grade, in the second series — 119 students of the 6th grade. The results of processing the obtained data are presented in the table.

Table

The distribution of children among students in grades 5 and 6 who, when solving problems of research methods, carried out a meaningful construction of reasoning, a meaningful development of a method for solving problems, meaningful planning and meaningful reflection (in %).

Note: * — p < 0.05.

The data given in the table testify to the following characteristics of the formation of cognitive competencies during the period of schoolchildren’s education in grades 5 — 6 of the basic school.

Firstly, as a result of teaching in the fifth grade, the most formed competence is associated with the meaningful development of ways to solve problems of a search nature, in particular with the choice of a general method — 62.9, the competence associated with the development of a meaningful approach to constructing reasoning — 56.7%, to an even lesser extent — the competence associated with the implementation of meaningful planning — 27.5%, and to the least extent — the competence associated with the implementation of the tasks of meaningful reflection of the mode of action — 24.4%.

Secondly, in the sixth grade, compared with the fifth grade, the competence associated with a meaningful approach to the construction of reasoning is most intensively formed, – the number of children with such competence increases by 13.0%; less intensively, – the competence associated with meaningful reflection, – the number of children with such competence increases by 10.9%, even less, – the competence associated with the meaningful development of ways to solve problems of a search nature, – the number of children with such competence increases by 8.5% and least intensively, – the competence associated with holistic planning, – the number of children with such competence increases by 6.1%.

Presumably, as we see it as an emerging trend (since to substantiate this assumption, more large-scale surveys with the participation of schoolchildren from different regions of Russia are required), it can be argued that a more intensive (relative to other competencies) formation in the sixth grade of competence related to content reasoning is based on the fact that biology, computer science, geography and social science are studied in this class, a significant part of the content of which consists in presenting theoretical material, for the assimilation of which it is necessary to make inferences and draw conclusions.

4.Conclusion

Thus, the conducted study confirmed the initial hypothesis that cognitive competencies associated with schoolchildren’s mastery of the ability to build logical reasoning and draw conclusions; with the development, selection and implementation of effective ways to solve problems of a search nature, educational and cognitive tasks; with the mastery of schoolchildren’s ability to independently plan ways to achieve the goal; with their mastering the initial forms of cognitive reflection and the skills associated with it to exercise control over their actions by students, to determine and correct their methods, are formed in schoolchildren during the specified period of study with different intensity.

The ability to build logical reasoning is formed most intensively in the period under review, less intensively — the ability to implement effective ways to solve search problems, even less intensively — the ability to exercise cognitive reflection and control of one’s actions, and least intensively — the ability to plan the achievement of a goal.

So, in the study, data were obtained that testify to the peculiarities of mastering by schoolchildren in the fifth and sixth grades of cognitive competencies related to: schoolchildren mastering the skills of constructing inferences of varying complexity; with mastering the ability to choose and implement successful approaches in the development of methods for solving search problems on educational and non-educational material; with the development of cognitive reflection and skills of control over their actions, associated with the ability to exercise control in order to correct them; with the mastery of schoolchildren’s ability to independently plan ways to achieve the goal.

The established facts make it possible to more concretely present the dynamics of the development of these cognitive competencies during the period of schoolchildren’s education in the fifth and sixth grades. In particular, the features of the formation of the studied competencies in the sixth grade in relation to the fifth grade were determined. The experimental data show that in the noted period, the competence associated with the meaningful construction of reasoning is most intensively formed, less intensively — the competence associated with internal reflection, even less intensively — the competence associated with the general way of solving search problems, and the least intensively — the competence associated with with holistic planning.

In addition, the data obtained indicate that the cognitive competence associated with mastering the ability to choose and implement successful approaches to the development of methods for solving search problems on educational and non-educational material is formed in a larger number of children in the fifth and sixth grades of basic school, and the competence associated with children’s mastering the skills of constructing inferences of varying complexity, formed in a larger number of children only in the sixth grade. The remaining two competencies studied in the study were formed in a smaller number of children in the fifth and sixth grades.

In general, the results of the study create important prerequisites for the development of further research to study the features of the formation of cognitive competencies among schoolchildren of the other grades of the basic school, from the seventh to the eleventh.