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11PSYCHOLOGICAL SCIENCES
FEATURES OF THE CHANGE IN THE FORMATION OF METASUBJECT COMPETENCIES
WHEN TEACHING IN THE FIFTH GRADE
Zak A.
Leading Researcher, Psychological Institute RAE, Moscow, Russia
Abstract
The experimental work presented in the article is aimed at clarifying the features of changes in the formation of meaningful reflection, holistic planning and a general way of solving problems in the process of teaching fifth grade children. As a result of the study, a fact was established that characterizes the more intensive formation of holistic planning than the formation of meaningful thinking and a general way of solving problems.
Keywords: children 10-11 years old, holistic planning, meaningful reflection, general way of solving problems.
1. Introduction
According to the provisions of the new Federal State Education Standard (for secondary school) during the period of study in the middle grades of school, children should develop cognitive metasubject competencies associated, in particular, with the development and implementation, firstly, of effective ways of solving educational and cognitive tasks and problems of a search nature, and secondly , initial and developed forms of cognitive reflection and related skills to control their actions, determine and correct their methods, thirdly, the ability to plan ways to achieve goals.
In understanding the effectiveness of the methods of solving problems, in the interpretation of the forms of cognitive reflection and the ability to determine and correct the methods of solving problems, in the interpretation of the characteristics of the formation of planning skills, we relied on the provisions on two types of cognitive activity, developed in dialectical logic [4] and implemented in psychological research [ 1], [ 3].
According to these ideas, a person's cognition of the surrounding world can be aimed at reflecting the internal connections of objects and phenomena (theoretical, meaningful, reasonable, holistic knowledge) and at reflecting their external connections (empirical, formal, rational, partial knowledge). In the first case, cognitive activity is effective, since its result is an understanding of the reasons for changing the objects of cognition. In the second case, cognitive activity is ineffective - its result is only a description and ordering of the observed features of the change in cognized objects.
Based on these ideas about the two types of cognition, it was accepted [3] that the development of a method for solving problems in one case involves the allocation of essential relationships in their conditions, in the other case there is no connection with essential relationships. When identifying essential relations, the methods of solution are characterized as meaningful, generalized, since they provide the solution to all problems of a certain class; in the absence of identification of essential relations, the methods of solution are characterized as formal, private, since they provide the solution of only individual problems of a certain class.
It was also believed that cognitive reflection and the ability to determine and correct methods of action
in solving problems can be associated with a person's appeal only to the external features of methods of action or with an appeal to the foundations of methods of action. In the first case, cognitive reflection is qualified as formal, external, since the object of treatment is the observed features of the mode of action. In the second case, cognitive reflection is qualified as meaningful, internal, since the object of treatment in this case is the hidden, internal characteristics of the mode of action.
In considering the characteristics of planning, two types of programming actions for solving problems were distinguished. In one case, the development of the plan may be aimed at developing the required sequence of actions in general. In this case, all the necessary actions are planned before the start of the decision. In another case, the drawing up of the plan is carried out in parts: subsequent actions are planned after the implementation of the previous ones. In the first case, planning will be holistic, meaningful, in the second - partial, formal.
1.1.Types of methods for solving problems
The formation of cognitive metasubject competence associated with the development of ways of solving problems by schoolchildren in the course of learning presupposes their mastery of the mental action of analysis, which is associated with an analysis of the conditions for achieving the required result. In some cases, such analysis is implemented as a formal analysis, only breaking down the proposed conditions into separate data - this is typical for a non-general, empirical way of solving problems [ 1], [ 3].
In other cases, the analysis of conditions is associated not only with the selection of data and their relations, but also, most importantly, with the clarification of their role in a successful decision: which of them is essential and necessary, and which is insignificant and accidental. This is a meaningful, clarifying analysis, which serves as a condition for a generalized, meaningful way of solving problems.
The mastery of generalized ways to achieve the required result is characterized by the ability to carry out a meaningful analysis of the proposed conditions associated with the selection of essential data relations. As a result, all problems of this class are successfully
solved. The fact of unsuccessful solution of one or several of them indicates the absence of meaningful analysis and, consequently, the presence of a non-generalized way of solving the proposed problems.
Based on ideas about the originality of different approaches to the analysis of the conditions of 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 the nature of a method of action (generalized or non-generalized, particular) upon reaching the required result.
First, the subject needs to propose not one, but several problems to solve; secondly, these problems should have a common principle of construction and solution; thirdly, their conditions should differ in external, directly observable features.
1.2. Types of reflexia in solving problems
Mastering the initial forms of cognitive reflection in the course of teaching is a condition for the formation of schoolchildren's ability to control and correct their actions. Depending on the purpose for which reflection, control and correction are carried out, two levels of their implementation are distinguished, which is manifested in the student's consideration of the methods of his actions [ 1], [ 3].
If such a consideration is carried out in order to find out what specific operations need to be performed in order to obtain the required result, then it is believed that here the student is guided only by the external characteristics of his actions.
This characterizes the formal level of implementation of the actions under consideration, since it reflects the dependence of the methods of action on random and single conditions for achieving the required result. In this case, the student, focusing on the external similarity of the features of their conditions when successfully solving problems that have an objectively general principle of construction, can group them formally, and, focusing on the external difference of these features, he can generally abandon the grouping of tasks, considering them to be different.
If the consideration of methods of action is carried out in order to find out why a given action is performed in this way and not otherwise, to understand the reasons for its successful implementation in solving various problems, then the student comprehends the method of his actions, relying on its hidden, not directly observable characteristics, and can, therefore, generalize actions meaningfully.
This level of comprehension is associated with the implementation of meaningful reflexive actions, since the connection between the method of actions and the essential conditions for their implementation is revealed. In this case, the focus on the internal, essential unity of tasks that have a common principle of construction allows them to be grouped meaningfully.
To determine the type of reflexive actions in solving problems, a special experimental situation has been developed. In its first part, it is proposed to solve several problems, which, firstly, belong not to one, but to two classes - this means that some problems are solved on the basis of one principle, and some on the basis of
another, and, in - second, the conditions of the tasks differ in external features.
In the second part of this experimental situation, it was proposed to group the problems. The nature of the grouping determined the presence or absence of the implementation of meaningful reflexive actions. If the basis of the grouping was taken as a significant commonality of methods for solving problems, then, when solving, meaningful reflexive actions were carried out, and if the grouping was based on the external similarity of the conditions of the tasks, then, when solving, formal reflexive actions were carried out.
Thus, the formation of reflexive actions is characterized by the student's ability to reveal an essential commonality of the methods of his actions when solving problems of the same kind and to highlight the fundamental difference in the methods implemented when solving problems of various kinds.
1.3. Types of planning actions to solve problems
The formation of the ability to plan ways to achieve the goal is associated with the development of actions in the internal plan, which are the conditions for building a program of steps to achieve the required result. When solving problems, planning is carried out in different ways [ 1], [ 3].
In one case, the achievement of the goal is planned for individual links, which are not linked into a single system. The desired result is obtained, therefore, by trial and error, when planning operations alternate with the implementation of individual actions to achieve the goal. This is formal, partial planning, typical for the implementation of a non-generalized way of solving problems.
In another case, subsequent actions to obtain the required result are planned simultaneously with the previous ones, and the previous actions are planned taking into account the possible options for performing the subsequent ones. This is contentious, holistic planning, characteristic of a generalized way of solving problems.
In accordance with the above concepts, a special two-part experimental situation was developed. In its first part, the subject is asked to master some simple action, in the second part it is required to solve several problems to build a sequence of these actions.
The selection of tasks in the second part should meet a number of requirements: first, the sequence of executive actions should gradually increase from the first task to the last; secondly, there should be at least two tasks with the same number of executive actions; thirdly, tasks should not have a common principle of solution, so that it is necessary to experiment mentally each time, re-developing an ever-increasing sequence of actions.
2. Materials and methods
Based on the outlined ideas about the types of cognitive metasubject competencies, reflecting the methods of solving search problems, cognitive reflection and planning, the "Permutations" technique was developed. This technique is designed to determine the levels of formation of the noted competencies in schoolchildren.
A group diagnostic lesson based on the tasks of the "Permutations" methodology was conducted with 53
fifth-graders at the beginning of the academic year (September) and at the end (May). It was organized as follows.
2.1. "Permutations" technique First, the class organizer distributes answer sheets to the children, on which they indicate their last name.
Then the organizer draws the playing fields on the blackboard, putting down numbers on the left, and letters on the bottom (Fig. 1):
Fig. 2. Condition of Problem 1.
Then the organizer says: "In this problem, you need to mentally swap some two figures so that the same figures are in the same cells as the same numbers.
Who can tell which pieces can be swapped? "
After evaluating the options for the exchange of figures proposed by the students, the organizer shows on the board on the right side how to write down the solution of problems in one action (Fig. 3).
Fig. 1. Playing fields.
The names of the cells of the playing field (its notation) are explained to children: "In both squares, each cell has a name consisting of a letter and a number. The bottom two cells are called A1 and B1, and the top two are called A2 and B2 "
Further, the cells of both playing fields are filled with objects. In the playing field on the left, the initial arrangement of objects is placed - a pair of identical figures. These objects will move. In the playing field on the right - the final arrangement of objects - a pair of identical numbers - these objects will not move (Fig. 2).
Fig. 3. Solution of the problem 1
At the same time, the meaning of the found solution is explained:"If the circle from A1 is interchanged with the triangle from B2, then the same numbers will be in the same cells, where the same numbers: two circles will be in the upper cells, where there are eights, and two triangles will be in the lower chambers - there are fives. Here the solution should be written as follows: A1 - B2.
And if the circle from A2 swaps places with the triangle from B1, then the triangles will be where the eights are, and the circles will be where the fives, and the solution is written as follows: A2 - B1."
Next, the blackboard depicts the condition of the problem in two steps (Fig. 4):
A B C
Fig. 4. Condition of the task in two steps
In this task, you need to find two actions so that the same figures are in the same cells where the numbers are the same ".
After discussing the options for the first and second actions proposed by the children, the organizer writes down one of the solutions, for example: 1) A2-C2, 2) B2-C1 (Fig. 4) and explains its meaning: "First, with the first action, - you can swap the circle and triangle in the corner upper cells, - A2 and C2. Then the circles will be in the place of fives, and the triangle will be in cell C2. Then, by the second action, this triangle can be swapped with the square from B1. Then the triangles will be where the nines are, and the squares will be where the sevens ... ".
Then the organizer points out: "If a problem has several solutions, like this one, then you need to write only one option ...".
Further, students are given sheets with conditions for 12 problems (Fig. 5).
Opinions about tasks Several 4th grade students solved these problems and exchanged views.
Tanya said: "Problems 3, 4 and 5 are similar." Kolya disagreed: "Problems 3, 4 and 5 are different."
Vika: "I think that tasks 3 and 4 are similar, but task 5 is different from them".
Katya: "I think that tasks 3 and 5 are similar, but task 4 is different from them".
Nina: "I am sure that tasks 4 and 5 are similar, but task 3 is different from them". Which student is right?
Task 2
3 2 1
o A A
o □ O
□ □ A
M
2 a.
7 8 7
5 5 8
7 5 8
a b c
3 □ □ A
2 O A A
1 O □ O
a b c
№7 2 a.
7 5 8
7 8 7
5 5 8
3 2 1
+ □ A A
O A O +
+ O □ □
abed
□ □ + O
A O □ +
+ A A o
abed
JVg 9 2 a-
■TS» 11 3 a.
n n o
□ □ A
o A A
a 5 b
8 6 7 6
9 7 9 9
8 8 6 7
№ 8 2 a.
Task 3
3 2
5 5 H
7 5 8
7 8 7
A O □ 0
□ A A A
□ O O □
abed
№ 10
5 9 7 9 3 + O □ O
7 5 8 7 2 A □ A +
8 5 8 9 1 □ O + A
a b c d
№ 12 3 a.
6 7 6
5 5 6 5
7 1 6 7
4 1 6 5
7 6 7 S
5 6 4 4
Fig. 5. Worksheet with tasks
Then the organizer characterizes the arrangement of the tasks on the form: "Look at the task sheet. In the first task, you first need to solve problems No. 1 and 2, and then problems No. 3, 4 and 5. After that, you need to read the students' opinions about these three problems and on the sheet with answers, select and mark the name of the student whose opinion is the most correct for you ... In the second task, you need to solve three problems in two steps. In the third task, you need to solve 4 problems: two in 2 actions and two in three actions. "
The organizer then characterizes the content of the answer sheet: "Look at the answer sheet. Above, it is reminded that each cell is designated by a letter and a number, for example: A2, B3 or B1, and that the action to exchange figures is recorded as it was when solving problems on the board, the names of two cells are indicated, for example, A1 - A2 or B3 - C1.
Then there is room to record one action to solve problem 1 and two actions to solve problems 2, 3, 4, and 5. Next, you need to select and mark the opinion of the student whose opinion about tasks 3, 4 and 5 is the most correct for each of you.
In the second task, you need to write down two actions to solve problems 6, 7 and 8.
In the third task, you need to write down two actions to solve problems 9 and 10 and three actions to solve problems 11 and 12 ".
At the end of the instruction, the children are explained: "Solve the problems in a row, starting with the first:
- do not copy the task conditions,
- look for and write down only one solution;
- you cannot make any notes on the sheet with the conditions of the problems, as well as on the table and any pieces of paper.
Solve problems only mentally, in your mind, as examples for addition in oral counting. Act carefully and independently. "
2.2. Purpose of tasks of the "Permutations" technique
When processing the results of solving problems, the following provisions were used as grounds.
Task 1 is intended to determine the level of mastering the initial forms of cognitive reflection when solving problems in a visual-figurative form. Children need to solve three problems (two are built according to the same principle, one according to another) and choose one opinion about them from the five proposed.
If, having correctly solved three problems, the child chooses the 1st, 2nd, 3rd or 5th opinion, then in this case it was considered that formal reflection took place in the solution.
If, having correctly solved the three problems, the child chooses the 4th opinion, then in this case it was considered that there was meaningful reflection in the solution.
In the absence of the correct solution to all three of these problems, it was believed that the choice of the 4th opinion does not indicate the presence of both formal and, moreover, meaningful reflection.
Task 2 is intended to determine the level of mastering the methods of solving search problems when solving problems in a visual-figurative form. Children need to solve three problems (built on a single principle).
If the child solved all three problems correctly, then in this case it was believed that the solution was based on the selection of essential relations underlying a single principle of the solution, which means that the solution was carried out in a general way.
If the child did not solve three problems, but solved correctly any two or one of the three problems, then in this case it was considered that the solution was not based on the selection of essential relations underlying the single principle of the solution, - this means that the solution was carried out in a private way.
In the absence of a solution to at least one problem, it was assumed that there was no solution, i.e. was not found at all.
Task 3 is intended to determine the level of development of the ability to act "in the mind" as a starting point for the formation in children of the ability to plan, control and evaluate educational actions. Children need to solve four problems, operating with a significant number of elements of conditions in a mental plan.
If all the tasks are solved incorrectly, then there is a manifestation of a zero level of development of the ability to act "in the mind." In this case, it was believed that there was a lack of planning.
If any one task is correctly solved, then the first level of development of this ability is manifested.
If any two tasks are solved correctly, then this is a manifestation of the second level of development of this ability. The first and second levels were qualified as the implementation of partial planning. If any three tasks are correctly solved, then this is a manifestation of the third level of development of this ability.
If the four tasks are solved correctly, then this is a manifestation of the fourth level of development of this ability. The third and fourth levels were quaoified as the implementation of holistic planning. 3. Results
As noted, 53 fifth-graders participated in the study. The results of solving the problems of the "Permutations" methodology at the beginning and end of the academic year are presented in Table.
Table
Results of solving problems of the "Permutations" methodology by fifth-graders at the beginning (September)
Time of Diagnostics General way of solution Meaningful reflection Holistic planning
September 49,1 9,4 11,3
May 60,1 22,6 26,2
The data presented in table indicate the following.
As a result of the year of study, the number of children who showed the ability to apply the general method (by 11.0%), meaningful reflection (by 13.2%) and holistic planning (by 14.9%) in solving problems increased.
These data allow us to assert that, (similar to what takes place when teaching children in primary school [2]), in the first year of schooling in the middle grades, the number of children who use holistic planning in solving problems also increases more intensively than the number of children, who use meaningful reflection in solving problems and, especially, the number of children who use the general method in solving problems.
It is also important to note that the number of children who solve problems in a general way is noticeably greater than the total number of children who use meaningful reflection and holistic planning in solving problems, respectively: 60.1% and 48.8%.
This fact allows us to assume that in the future, when teaching in middle grades (sixth, seventh, eighth and ninth), the number of children using meaningful reflection and holistic planning in solving problems will increase at a faster pace than the number of children using when solving problems, the general method.
4. Conclusion
The conducted research really made it possible to establish new and important facts characterizing the features of the formation of basic cognitive metasubject competences during one year of study in the fifth grade.
It was shown, firstly, that in the fifth grade, just as it was in the primary grades, these competencies are formed in children with different intensity.
In particular, the most intensively formed competence associated with the implementation in solving the
problems of holistic planning, which is associated with the development of a general program of all actions necessary to obtain the desired result.
Less intensively, the competence associated with the fulfillment of meaningful reflection when solving problems is formed, when the student is aware of the reasons for his actions, and not their external features.
The least intensively formed competence is associated with solving problems in a general way, which is based on an analysis aimed at identifying essential relationships in the context of tasks.
In further research, it is planned to establish, in particular in experiments with students of the sixth grade, whether the unevenness of the formation of the above-mentioned metasubject competencies, noted in the fifth grade, remains and whether holistic planning is really most intensively formed in the period of younger adolescence, less intensively - meaningful reflection and the least intensive there is a formation of a general way of solving problems.
References
1. Davydov V.V. Lectures on general psychology. Moskow, Academy, 2008. 384 p. [in Russian].
2. Zak A.Z. Conditions of Formation of Cognitive Meta-Subject Results in Younger Schoolchildren [El-ektronnyi resurs]. [Psychological-Educational Studies], 2018. Vol. 10, no. 2, pp. 11-20 doi: 10.17759/ psy-edu.2018100202. [in Russian].
3. Zak A.Z. Development and diagnostics of thinking in adolescents and high school students. Moskow; Obninsk: IG-SOCIN, 2010.350 p. [in Russian].
4. Ilyenkov E.V. Dialectical logic: essays on history and theory. Moskow, Science, 1984.427 p. [in Russian].
