PSYCHOLOGICAL SCIENCES

FEATURES OF THE DYNAMICS OF COGNITIVE REFLECTION IN PRIMARY SCHOOL

Zak A.

Leading Researcher, Psychological Institute RAE, Moscow, Russia

Abstract

The article analyzes the dynamics of cognitive reflection among students of the first and second grades. The content of individual experiments, which involved 49 first-graders and 51 second-graders. It was shown that by the end of the second grade, the number of students with meaningful reflection and differentiated formal reflection increases, while those with undifferentiated formal reflection decreases.

Keywords: cognitive reflection, first-graders, second-graders, the subject form of action, the task of moving pseudo-chess figures.

1. Introduction

Features of the development of cognitive reflection in primary grades is one of the important problems of educational psychology. The purpose of this study was to determine the nature of the distribution of types of cognitive reflection in the first and second years of primary school.

The activity approach to the study of cognitive actions suggests that children need to be offered tasks, the condition for the successful completion of which is the child's cognitive reflection.

Cognitive reflection, associated with the child's awareness of the way of his actions, presupposes its consideration [2]. Depending on the purpose for which it is carried out and what it is supposed to establish, it is advisable to distinguish between two types of awareness of the mode of action, or two types of reflection as a person's turning to their own actions.

So, if the consideration of the mode of action is carried out in order to find out what operations need to be performed and what needs to be done specifically in order to obtain the required result, then in this case the child is aware in his actions only of their visual characteristics.

This level of consideration of the method of action is characterized by awareness of its features, given in direct perception, and is a manifestation of formal cognitive reflection, since it reflects the dependence of the method of action on random and individual conditions for its implementation.

In this case, with the successful solution of problems that have an objectively general principle of construction, the child, when focusing on the external similarity of the features of the conditions of the tasks, can group them formally, and when focusing on the external difference of these features, he can generally refuse grouping, considering the tasks to be different.

If, however, the consideration of the method of action is carried out in order to find out why the given action is performed exactly like this and what is in this action the reason for its successful implementation in different conditions (when solving different but related tasks), then the child realizes the method of his actions, relying on his hidden, not directly observable characteristics, and can, therefore, generalize actions meaningfully. This level of consideration of the method of

action is a manifestation of internal, or meaningful cognitive reflection, since it reflects the dependence of the method on the necessary and essential conditions.

In this case, with the successful solution of tasks that have a general principle of construction, the child, when orienting towards the internal, essential unity of these tasks, can group them meaningfully. Therefore, the understanding of the proposed tasks as belonging to the same type, which is based on the generalization of the method for their solution, can serve as an indicator of the awareness of the connection between the method and essential relations, i.e. an indicator of the implementation of meaningful cognitive reflection. 2. Materials and methods 2.1. Characteristics of constructing an experimental situation

To determine the type of reflection in solving problems, a general scheme for constructing an experimental situation was developed [3, 4, 5, 6], a modification of which was used in works on non-educational [7] and educational material [1, 8]. In its first part, the subject was asked to solve several problems, which, firstly, should belong not to one, but to two classes (or subclasses) - this means that some problems are solved on the basis of one principle, and some with the use of another, and, secondly, the conditions of the problems should differ in external, directly perceived features.

In the second part, in case of successful solution of problems, they need to be grouped. By the nature of the grouping, the presence or absence of meaningful, internal reflection in solving them was determined.

If the basis of the grouping was taken as an essential commonality of methods for solving problems, then, in the process of solving them, meaningful cognitive reflection was carried out, and if the external similarity of the features of their conditions was taken as the basis, then, consequently, meaningful cognitive reflection, - as an understanding of the connection of actions with essential relations and generalization on their basis of the method of solution, - was absent. This means that formal reflection has taken place.

Thus, the mastery of the initial forms of cognitive reflection is characterized by the child's ability to sub-stantively generalize the method of action in solving problems, i.e. to reveal the essential commonality of the methods of their actions when solving problems of the

same kind and to highlight the fundamental difference between the implemented methods when solving problems of various kinds. In this case, the child relies on knowledge of the grounds for his actions, on the knowledge of why he acted in one way or another in solving problems.

2.2. Research methodology To carry out the research, the technique "Jumping figures" was developed. It included three tasks for moving volumetric geometric figures made of wood across the playing cell field: a cylinder, a cone and a tetrahe-dral prism ("bar") according to certain rules. The study involved a total of 100 children: 49 first graders and 51 second graders. The research was carried out in the second half of the school year.

The experiments were carried out individually as follows. In the first part of the experiment, the child learned the rules and methods of moving around the cellular playing field for each of the three volumetric geometric figures used in solving problems - a cylinder,

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Fig. 1. The playing field.

Then they gave him a top hat and said: "This is a jump. Her jump is equal in length to two different steps new chess piece. She can walk across the cell field di- in one direction - straight and obliquely or obliquely rectly into the adjacent cell and obliquely. She can also and straight "(Fig. 2, - a, b, c, d).

a cone and a prism (the children were told that these were new chess pieces). In the second part of the experiment, the child solved the proposed problems. In the third part, the experimenter said: "You have solved three problems. Many children solved these problems. Some children said that all tasks are similar, others - all tasks are different. Children of another group said that tasks 2 and 3 were similar, but task 1 was different from them. Children of the other group said that tasks 1 and 3 were similar, but task 2 was different from them. Children of the third group said that tasks 1 and 2 were similar, but task 3 was different from them. Who do you think said correctly? "

Let's consider in detail the content of each part of the experiment. At the very beginning of the first part of the experiment, the child was given a playing cell field of the same size as a chessboard: 8 cells horizontally and 8 cells vertically (each cell had the shape of a square with a side of 3 cm, - Fig. 1.

Fig. 2. Displacement of the cylinder

Then the child tried to walk and jump with a cylinder from different cells of the playing field. In conclusion, learning how to move the cylinder was offered a control task, where it was required to show all its possible jumps from some central cell of the field, for example, from cell E5 (it should be noted that the children

did not master the names of the cells of the playing field).

After the child mastered the steps and jumps of the cylinder, he was asked to learn how to move the cone (Fig. 3). One of his steps was moving obliquely to an adjacent cell (see the second step in option "a", the first step in option "b", the third step in option "c").

Fig. 3. Displacement of the cone

The other two steps were associated with moving the cone straight to the adjacent cell (see the first and third steps in option "a", the second and third in option "b", the first and second in option "c").

The child was shown at first how the cone steps and jumps, and then they were asked to make them a series of jumps. In conclusion, the child was given a control task: they indicated one of the central cells of

the field (for example, D4) and asked to perform all possible jumps from this cage with a cone. After successfully completing this task, he was presented with a prism.

The prism steps into the neighboring cell only obliquely and its jump is equal to three such steps (Fig. 4, options "a" and "b").

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Fig. 4 Displacement of the prism

The child was first shown how a prism walks and jumps, then they were offered to independently perform individual jumps with it from different cells of the playing field. After all, the child had to complete the control task - to show all possible jumps of the prism from some central cell of the playing field, for example, from cell E4. The first part of the experiment ended with the mastery of prism jumping.

It should be noted that when mastering the methods of moving figures, children differed in the following characteristics.

First, there were differences in the speed of the control jumps: some acted slowly, others quickly.

Secondly, there were differences in the form of jumps: some children made jumps in a straight line from the initial jump cage to the last cage found (see

Fig. 5); others "jumped" in a different way: they repeated the contour of movement of the given figure in steps (see Fig. 2 and 3).

Thirdly, there were differences in the number of cells included in the jump contour: some of the children, moving the figures, counted the cells out loud, others counted the cells not in terms of external speech (not aloud), but in terms of internal speech (silently, "to themselves") , - this could be judged by the characteristic nods of the head; in a third of the children, cell counting was completely absent (both in terms of external and internal speech).

Fourth, there were procedural differences in the movement of figures when performing jumps: a number of children moved figures directly across the playing field, a number of children moved figures over the playing field from the initial jump cell to the final one.

Fig. 5. Jump "in a straight line"

2.3. Children's actions in part 1 of the experiment

Analysis of the protocols of experiments showed certain connections between the noted features of the movements of figures in control tasks. For children who acted without errors, the following was characteristic: they acted relatively quickly, made jumps in a straight line from a given initial jump cell to the last cell found, did not count the cells included in the jump contour, neither in terms of external speech, nor in terms of internal speech, the figures above the playing field were transferred (and not moved along the surface of the playing field).

Children, who made few mistakes in the control tasks, acted at different speeds: the majority - quickly, the smaller part - slowly. At the same time, both children made jumps in a straight line from the given initial jump cell to the last cell found, counted the cells in terms of internal speech and transferred figures over the playing field (and did not move them along the surface of the playing field).

Children, who made many mistakes in the control tasks, acted slowly, made jumps, repeating the contour of the movement of this figure in steps and moved the figures along the surface of the playing field.

Consideration of the noted differences in the assimilation of the movements of figures by children of different ages showed that by the end of the second grade, the number of children of the three groups noted

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Fig. 6. Problem for cylinder jumping

After successfully solving the first problem (inde- and the cardboard circle - its location indicated the

pendently or with help), it was proposed to solve the point where the cone should get through two jumps

second problem, where you need to make two jumps in from cell C2 - was located in cell E8 (Fig. 7). a cone. To do this, the experimenter placed it in cell C2,

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changed as follows. The number of children who jumped slowly, reproducing the contour of the figure's steps, decreased; carrying out the moves of the figures touching the playing field; who counted the cells of the playing field in terms of internal speech and, especially, in terms of external speech, both simultaneously with the movement of the figure, and before its movement; performing jumping figures with a small number of errors and, especially, with a large number. And, accordingly, the number of children who jumped relatively quickly, in a straight line, in the absence of cell counting (in terms of external and internal speech) and who jumped without the figure touching the playing field, increased.

As a result, the number of children who acted without errors or with a small number of errors increased, and the number of children who made many mistakes when performing control tasks to assess the degree of mastering the jumps of the three proposed figures: a cylinder, a cone and a prism decreased.

2.4. Children's actions in part 2 of the experiment

In the second part of the experiment, the children solved problems. In the first one it was necessary to hit B3 with two jumps from cell D3. For this, the experimenter placed a cylinder in B3 and a cardboard circle in D3 (Fig. 6).

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Fig. 7. Problem for jumping cone

After successfully solving the second problem (independently or with the help), the child was asked to solve the third problem, in which it was required to

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make two jumps with a prism. For this, it was placed in cell A4, and the cardboard circle was placed in cell G4

(Fig. 8).

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Fig. 8. Problem for jumping prism

According to the peculiarities of solving problems, the children differed in the following characteristics. First, there were differences in indicative actions when solving problems. Some children had an independent preparatory stage before completing both required actions to solve problems, within which a general orientation (with the help of perceptual actions) in the content of the proposed task was carried out. Other children did not have such a stage of general orientation in the task: they developed orientation in the content of the task before performing each of the two jumps: however, before the first jump, orientation was carried out more often than before the second. It is important to note that one part of the children of this group spent a long time looking for the first move only in the first problem, another part - only in the second problem, the third part - in the first and second problems.

Secondly, there were differences in the independence of problem solving. In some cases, children were able to independently (without the help of the experimenter) figure out their mistakes and solve problems correctly. In other cases, the children were able to solve the problem only with the help of the experimenter, since they could not find the first jump on their own. At the same time, one part of the children needed help when solving only the first problem, another part -when solving only the second problem, the third part -when solving the first and second problems.

Thirdly, similarly to the actions at the previous stage of the experiment (on mastering the rules for moving figures), there were differences in the form of jumps of figures: one children did both jumps of figures in a straight line, first from the given initial cell of both jumps to the found last cell of the first jump, then from the found last cell of the first jump to this last cell of the second jump; other children did both jumps, repeating the contour of the movement of this figure in steps.

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Fourthly, just as when learning the rules for moving figures, there were procedural differences in the performance of jumps: some children moved figures directly across the playing field, others performed jumps, transferring figures over the playing field from the initial cell of the first jump to its final cell and from this cell to the final cell of the second jump.

Analysis of the protocols of experiments, which reflected the noted characteristics of problem solving, showed certain connections between these characteristics and the success of solving problems. For children who successfully solved the problems, independence of behavior is characteristic, as well as the presence of orienting actions: either in relation to the entire task (before completing both jumps), or in relation to each of the two jumps separately. At the same time, they did both jumps in a straight line: first from the given initial cell of both jumps to the found last cell of the first jump, then from the found last cell of the first jump to this last cell of the second jump. In addition, it is important to note that none of the children who successfully solved all the problems touched the surface of the playing field while moving the figures.

Children who solved problems unsuccessfully needed the experimenter's help, which usually boiled down to prompting the correct first jump either when only the first problem was solved incorrectly, or when only the second problem was solved incorrectly, or when both of these problems were solved incorrectly. At the same time, the children of this group are characterized by the performance of both jumps with a detailed reproduction of the contour of the steps of the corresponding figure and the movement of figures on the surface of the playing field.

Analysis of the protocols for solving problems by pupils of the first and second grades made it possible to reveal that by the end of training in the second grade, the number of students who solved the problems on their own increases and the number of students who need the help of an experimenter decreases.

The second part of the experiment ended with the solution of the third problem.

2.5. Children's actions in part 3 of the experiment

In the last, third part of the experiment, as mentioned above, the child was asked to evaluate 5 opinions about the tasks, thus expressing his own: (1) "... all tasks are similar ..."; (2) "... all tasks are different ..."; (3)"... the first task differs from the other two ..."; (4)"... the second task differs from the other two ..."; (5)"... the third task differs from the other two ...".

Based on the above ideas about the two types of cognitive reflection, the child's opinion about tasks was

interpreted as a reflection of the peculiarities of understanding their objective content.

If the child believed that all tasks are similar, pointing out such features of their conditions, for example: in all tasks it is required to find two jumps, all tasks are related to the movement of figures across the playing field, in all tasks, after two jumps, you need to get into the cage , where there is a carton circle, etc., then in these (and similar) cases it was assumed that the child solved problems on the basis of a situational understanding of their subject content, since he judged tasks based only on external features their conditions (opinion No. 1).

If the child thought that all tasks are different, pointing out the following features of their conditions: in all tasks, different volumetric geometric figures are used, all figures walk and jump in different ways, etc., then in these (and similar) cases (just as in the previous case), it was assumed that the child solved problems on the basis of a situational understanding of their subject content, since he judged the problems by the external features of their conditions: the characteristics of the movements of the figures, their apparent differences, the location places of jumps on the playing field (opinion No. 2).

Along with the children who considered the tasks to be different or similar (for different reasons given above), there were children who believed that among the proposed tasks there is one that does not fit the other two.

One part of the children in this group believed that the third task did not fit the other two, because "... in it the figure jumps straight ...", and in the first and second tasks "... the figures jump with a turn..." (opinion No.

3).

Another part of the children of the group under discussion believed that the first problem did not fit the other two, because "... in it the figure jumps close ...", and in the second and third problems ". the figures jump far ..." (opinion No. 5).

Qualifying the opinions of these groups of children, it should be said that they reflect the diversity of children's situational understanding of the subject content of the tasks they have solved. So, pointing out the

difference between the third task from the first two or the first task from the second and third, children are actually guided by the external features of the conditions of the tasks that they knew even before solving the problems (at the stage of mastering the methods of moving figures), in particular, on the features jumping figures. This understanding testifies to the implementation of formal reflection when solving problems of moving volumetric geometric figures.

Some of the children who participated in the experiments indicated that the second task was different from the first and third. These children believed that the second task was not suitable, because the movement of the figure in it had a different shape. In particular, the children noted that in the second task all jumps "... are done along one line., go in one direction.", and in the first and third tasks, the figures ". walk straight and back., back and forth.". In this case, it was assumed that the children substantively generalize the methods of solving the first and third problems, and highlight the intrinsic kinship of these tasks (opinion No. 4).

The validity of such an opinion of children about the tasks corresponds to our intention when constructing these tasks: the first and third tasks refer to the so-called "mirror" tasks, since in them the second jump is, as it were, a mirror (symmetric) reflection of the first jump. In the second problem, there is no such symmetry of two jumps: the second jump is a continuation of the first in the same direction.

Thus, based on an understanding of the characteristics of formal and content-based cognitive reflection, it can be argued that the children of this group carried out meaningful cognitive reflection when solving problems.

3. Results

The distribution of subjects who expressed different opinions about the solved problems - No. 1 (all tasks are similar), No. 2 (all tasks are different), No. 3 (the first task differs from the other two), No. 4 (the second task differs from the two others), No. 5 (the third task differs from the other two), - is presented in the table.

Table

Number of children who expressed opinions

Classes Number students Opinions about tasks

№1 №2 №3 №4 №5

1 49 30,6 28,6 10,2 18,4 12,2

2 51 19,6 23,5 15,7 27,4 13,8

The data presented in the table reflect the peculiarities of the distribution of the types of cognitive reflection in the first and second grades of primary school. First, it should be noted that by the end of the second year of education, the number of children who have carried out the content of cognitive reflection in solving problems increases (by 9.0%): from 18.4% to 27.4%. Secondly, there are changes in the distribution

of children who carried out formal cognitive reflection in solving problems.

On the one hand, there was a decrease in the number of children who considered all tasks to be similar and all tasks to be different. In the first case, the decrease was 11.0% (from 30.6% to 19.6%), in the second case - 5.1% (from 28.6% to 23.5%).

On the other hand, there was an increase in the number of children who believed that the first task did

not fit the other two and that the third task did not fit the rest. In the first case, the increase was 4.5% (from 10.2% to 15.7%), in the second case - 1.6% (from 12.2% to 13.8%).

4. Conclusion

Thus, the analysis of the data in the table under consideration allows us to outline some trends in the dynamics of the distribution of the types of cognitive reflection over the course of two years of primary school education.

The first tendency is associated with an increase in the number of children who carry out content reflection when solving problems. The second tendency is associated with a multidirectional change in the number of children performing formal cognitive reflection: the number of children giving a common, undifferentiated description of three tasks ("all are similar" or "all different") decreases, and the number of children giving a differentiated description of tasks (one task does not fit to the other two) increases. True, this increase in total is less than the noted decrease, respectively: 6.1% and 16.1%.

So, the study made it possible to identify a number of characteristics of the age dynamics of cognitive reflection in the first half of primary school (first - second grades). In further research, it is planned to determine the characteristics of the age dynamics of cognitive reflection in the second half of primary school (third -fourth grades).

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