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13PSYCHOLOGICAL SCIENCES
AGE DYNAMICS OF METHODS FOR SOLVING PROBLEMS IN PRIMARY SCHOOL
Zak A.
Leading Researcher, Psychological Institute RAE, Moscow, Russia
Abstract
The article examines the problem of age dynamics in the elementary school of a generalized way of solving problems. Two classes of students at the end of the second, third and fourth years of study in a group experiment solve spatial combinatorial problems in a visual-figurative form. It was shown that from the second grade to the fourth, the number of students who are able to solve search problems in a general, theoretical way increases significantly, and the number of students who are able to solve such problems in a particular, empirical way decreases less significantly.
Keywords: spatial-combinatorial problems, general and particular ways of solving problems, second graders, third graders, fourth graders.
1. Introduction
The new federal Standard for primary general education contains requirements for metasubject results of mastering the basic educational program of primary school [ 7 ]. At the same time, it is indicated that these metasubject results of mastering the basic educational program of primary general education should reflect the development of more complex types of cognitive actions by children than in preschool childhood, in particular, the formation of ways of solving problems of a creative and exploratory nature in younger schoolchildren. An insufficient level of formation of these methods will create serious difficulties for students in the future in assimilating knowledge and skills related to the content of the curriculum of the middle and senior classes of the school.
The purpose of our research was to characterize the ways of solving search problems by primary schoolchildren. In particular, it was necessary to establish how many children in the primary grades of the school solve problems in a generalized way. It was assumed, based on the data of previous studies [4], that the indicators characterizing the number of children solving problems in a generalized way in the fourth and second grades differ statistically significantly.
When developing a research methodology to determine the features of methods for solving search problems, we relied on those proposed by SL Rubinstein [6] and developed in detail by VV Davydov [1] and his followers [2], [3], [4] provisions on two approaches to understanding the conditions of problems and, accordingly, on two types of thinking in solving problems - theoretical and empirical. These types of thinking are realized in two different ways of solving problems - general (generalized), meaningful, theoretical and particular (non-generalized), formal, empirical.
According to the noted provisions, with one approach, essential and insignificant relations in the conditions of the problem do not differ, the solution is not entirely planned and is carried out by trial and error, a successful solution is either not realized at all, or only a specific composition of operations is realized in it. This approach is called empirical.
With another approach, essential relationships in the conditions of the problem are isolated, the solution is planned as a whole and carried out without trial and error, in a successful solution not only specific operations are recognized, but also its connection with essential relationships. This approach is called theoretical.
The first approach is used by children as early as preschool age. At the same time, the solution of the problem does not have an independent cognitive, theoretical part and is reduced mainly to practical actions. The second approach is mastered already in elementary school - on the material of typical assignments in mathematics and grammar. In this case, the solution to the problem includes a theoretical part (when the content of the problem is investigated with the help of special cognitive actions) and a practical part (when a specific result is actually achieved).
According to VV Davydov's research [1], the development of thinking in primary school age consists in changing the approach to solving problems: from solving problems in a non-generalized way, - empirically, children move to solving them in a generalized way, -theoretically. At the same time, the theoretical approach to solving problems (as a manifestation of theoretical, research thinking) includes the following basic cognitive actions. First, a meaningful analysis associated with the study of the conditions of problems, associated with the allocation of essential relationships in them. Secondly, meaningful reflection associated with the child's awareness of the method of action to solve the problem as associated with essential relationships. Third, meaningful planning associated with mental experimentation to develop a holistic program for performing the necessary practical actions to solve the problem.
The noted cognitive actions are interrelated, but the leading action, which determines the approach to solving the problem as a theoretical one, is a meaningful analysis as revealing essential relationships, in connection with which the solution method is realized and generalized, and based on which a holistic program of practical actions is developed. (for more details on cognitive actions that make up a theoretical approach to solving problems, see our papers [3], [4]).
2. Materials and methods
2.1. "Game of Five" methodology The well-known puzzle "Game of fifteen", which has undergone a certain modification, served as the initial model for the development of the methodology. This modification consisted in the fact that instead of fifteen pieces moving around a sixteen-square playing field, only five pieces were used that moved around a six-square playing field. As in the original "Game of
Fifteen" puzzle, our modification of this game had one free square and pieces that moved across the playing field (to an empty space) in any direction by the rook move, that is, horizontally and vertically.
So, in order to transform the original order of the pieces into the required order in six moves, you need to move the following pieces in sequence to the free space: 1, 2, 3, 5, 4 and 1 (see Fig. 1).
1 2 3 1 2 3 2 3 2 3 2 3 5 2 3 5 2 3 5
4 5 4 5 1 4 5 1 4 5 1 4 1 4 1 4
original after of 1st after of 2nd after of 3rd after of 4lh after of 5th required order move move move move move order
Fig 1. Solving the problem "Game offive" in six moves
An important feature of the "Game of Five" is the ability to develop equivalent problem situations on its basis. In this case, with different numbering of the tokens, the problems have the same number of moves and
an identical route of movement of the tokens in the process of converting the initial situation into the required one. For example, problem 1 is equivalent to problem 2 (both problems are solved in six steps).
1 2 3 2 3 5
4 5 1 4
Problem 1
4 5 2 5 2 3
1 3 4 1
Problem 2
Fig. 2. Equivalent problems
2.2. Preliminary experiments
In preliminary experiments, junior schoolchildren (grade 3) solved the problems of the "Game of Five" individually. Each child solved 8 eight-way equivalent problems in a visual-effective plan, that is, he moved cardboard chips by hand on a wooden board on which a six-cell field was marked. The optimal number of moves was not communicated to the children. This made it possible to establish on which problem the child can find the principle of solving all equivalent problems, i.e., the optimal (shortest) route for all problems to move the pieces in order to transform the initial situation into the required one in eight moves.
At the same time, it was believed that the method of solving problems would be general, meaningful if the child found this principle (that is, the shortest route) quickly, after solving one or two problems. If the child found the optimal route after a series of unsuccessful attempts, that is, only after solving five to six problems and for more than eight, the number of moves, then this method of solution was qualified as a private, formal, empirical, since it was found only after a lot of trial and error.
Thus, in these experiments, the result of solving the problem is not related to the method of obtaining it: the correct solution (obtaining the required position of the chips) can be provided by moving the chips both along the shortest route and in more than required number of moves.
2.3. Types of problems of the "Game offive" methodology
In our main experiments, an attempt was made to relate these points. For this purpose, it was necessary to build such a methodology (based on the material of the "game of five") so that the correct solution of the problem, ie, obtaining the required arrangement of chips, presupposes a theoretical solution to the problem, manifested in the abstraction of the essential relationship in the conditions of the problem.
And vice versa, an incorrect solution to the problem should indicate an empirical solution, i.e., the absence of significant dependencies in the condition of the problem, as a result of which the problem is solved in more than eight number of moves.
In addition, it was required to modify the version of the "Game of Five" methodology used in the preliminary experiments into a version that could correspond to the conditions of group work in the classroom.
In this case, the child solves problems not in a visual-effective form, as in an individual experiment, but mentally, in a visual-figurative form. This means that the solution to the problem is carried out not by moving the piece by hand across the playing field, but by mentally moving the number to a free cell of the playing field.
For the convenience of positioning on a sheet of paper, the playing fields were deployed along the length of the sheet (vertically) - see Fig. 3.
Fig. 3. Playing fields in vertical orientation
With this orientation of the playing fields on the sheet, two numbers could be moved one time either up or down (as in this example, numbers 1 and 4). After mentally moving the number, the resulting arrangement is recorded in the spaces specially left for this, not filled with numbers, on an intermediate playing field located between the initial (initial) and final (required) arrangement of numbers.
When developing the methodology on the material of the "Games of Five", it was taken into account that there are two types of routes for the movement of chips on the playing field: movement along the "big circle" and along the "small circle". In the first case, the pieces move along six squares of the field, so that the direction of movement sometimes changes after two moves (see Fig. 4).
Fig. 4. Moving chips in a "big circle"
In the given example, it can be seen that the numbers 2 and 3 remain in their places in all three moves, while the numbers 1, 4 and 5 move alternately to a free cell.
In the second case, the pieces move only along four (adjacent) squares, so that the direction of movement of the pieces changes after each move (Fig. 5).
Fig. 5. Moving chips in a "small circle"
In the given example, you can see that the numbers 4 and 5 all three moves remain in their places, and the numbers 1, 2, 3 move one after the other.
These features of the routes of movement of chips in the problems of the "game of five" were used in our methodology (see Form).
2.4. Characteristics of the diagnostic lesson The diagnostic lesson was carried out as follows. First, the organizer of the lesson (psychologist or teacher) depicts the condition of the problem on the blackboard (Fig. 6):
Fig. 6: First task on the chalkboard
Children are told: "The left position of the numbers (a) is the initial, and the right (b) is the final, required. It must be obtained in two steps. One action is to mentally move any number to an empty space up, down or to the side.
In this task, you need to do two such mental actions. First, mentally move down the number 8, because
it should not be at the top, but in the middle. Let's write down the result of this mental action like this, "- the teacher writes down the number 8 in the middle of the playing field, and the remaining numbers - 4, 1, 2 and 9 - are rewritten in the same places (Fig. 7).
(a) (b)
Fig. 7. Solving the first problem on the chalkboard
"With the second mental action we move the number 4 to the side. There is no need to record the result of this move, because it is already in the problem statement. This is how the solution of tasks for moving numbers in two steps is recorded."
The organizer of the lesson depicts the conditions of the second task, where the required location must be obtained from the initial one in three steps:
Fig. 8. Second task on the chalkboard
The solution to this problem is collectively consid- the third action has already been given in the required ered and the organizer writes down the results of the location: first and second actions on the board, since the result of
Fig. 9. Solving the second problem on the chalkboard
At the same time, the organizer of the lesson spe- After that, forms with three training (№№1,2,3)
cifically draws the attention of children to the fact that and eight main tasks (№№4, 5, 6, 7, 8, 9, 10, 11) are in one action only one number changes the place, and distributed, - Fig.10. the rest are rewritten without changes.
FORM
Training problems
№1
№2
№3
5
2 1
4 3
2 5
1
4 3
2 5
4 1
3
Main problems
№4
№5
№8
2 3
5 6
№10
7 8
9
5 6
2 7
6
8 1
№6
1 8
2 6
9
2 7
8 6
1
№7
l 8 6
2 9
№9
4 2
3
5 6
№11
7
5 8
6 9
4 2
6
3 5
5 7
6 8
9
Figure 10. Form with tasks
Children are invited to write their names at the top of the form and then the necessary explanations are given: "Look at the sheet. First (above) the conditions of three training problems are drawn: they are solved in two steps.
Further, the conditions of the main tasks 4, 5, 6 and 7 are drawn, they need to be solved in three steps. Then you need to solve basic problems 8, 9, 10 and 11, where you need to find four actions.
Solve your training tasks now. Write down the solution the way we did it on the board - put the numbers on the empty spaces. Remember that only one number moves mentally at a time. "
Walking through the class, the organizer of the lesson checks the solution of the training problems and helps the children correct mistakes in movements if they copy two numbers at once to free spaces, and not one.After checking the training tasks, the children are asked to solve the basic tasks.
The noted features of the routes of movement of chips in the problems of the "Game of Five" were used in our method in the following way. Thus, the three-way problem (No. 4 and 5) was solved on the basis of moving the numbers along the "small circle", and problems No. 6 and No. 7 - on the basis of moving along the
The data presented in the table reflect the peculiarities of the distribution in the second, third and fourth grades of children who solved the problems of the "Game of five" methodology in a general way (that is, correctly solved problems 1 - 11), in a particular way (that is, correctly solved only tasks 1 - 7) and did not cope with any of the main tasks (ie, who correctly solved only training tasks: 1-3).
Thus, the analysis of the data presented in the table shows that with age (from the second grade to the fourth grade), the number of students who solved problems in a general way increases and the number of students who solved problems in a private way and did not solve any of the main problems decreases.
4. Conclusion
So, the study made it possible to reveal the characteristics of ways of solving search problems by primary schoolchildren, in particular, the tasks of the "Game of five" methodology. It was shown how many children solving problems in generalized and non-generalized (private) ways (as well as how many children study in the second, third and fourth grades of primary school. It was also established how many children did not cope with the main tasks of the methodology "Game five "And, thus, did not have the opportunity to implement this or that way of solving problems.
Thus, the data obtained in the experimental study made it possible to characterize the age dynamics of mastering the generalized method of solving search
"big circle"; four-way problems No. 8 and No. 9 were solved by moving the numbers along the "small circle", and problems No. 10 and No. 11 - along the "big circle". Problems Nos. 1, 2 and 3 were two-way.
Thus, the correct solution of all problems presupposes a theoretical way of this solution for the following reasons:
1) the minimum number of moves is regulated;
2) when solving problems, it is forbidden to use drafts and correct written numbers;
3) only two tasks are built for each of the two types of route, which allows the child to discover the optimal route and carry out its transfer;
4) the types of route that underlie the solution of problems are constantly changing, every two tasks in order to exclude a random correct solution of problems and to ensure, in turn, their conscious solution, the necessary moment of which is the child's turning to his own way of action, i.e. that is, reflection.
3. Results
A total of 145 junior schoolchildren participated in the group survey according to this method at the end of the school year: 48 second graders, 46 third graders, 51 fourth graders. The data obtained in the survey are presented in the table.
Table
problems by primary school students and, consequently, the stages of the transition of children from solving problems by an empirical method to solving them by a theoretical method. It was shown that the majority of children begin to solve problems in a theoretical way after studying in the second, third and fourth grades of primary school. It is important to note that the data obtained reflect the distribution of the generalized method under certain experimental conditions: a group solution of the problem of the "Game of five" methodology was organized in a visual-figurative form.
In general, the results achieved in the study contain information that is important for developmental and educational psychology, since they expand the understanding of the peculiarities of the mental activity of younger schoolchildren.
A number of studies are planned in the future. In some works, we intend to organize an individual solution of problems of the "Game of Five" methodology in a substantive-effective form in the first, second, third and fourth grades of primary school. In other works, it is planned to organize a group solution of plot-logical problems. These works are necessary, since they will make it possible to clarify the distribution of the theoretical and empirical methods of solving problems for each year of schooling in primary school.
The purpose of future research will be to study ways of solving search problems of a different kind by younger schoolchildren, in comparison with this study,
Number of children in 2nd, 3rd and 4th grades, solved problems 1 - 11, 1 - 7 and 1 - 3 (in %)
Classes Problems
1 - 11 1 - 7 1 - 3
2nd grade 31,2* 52,1 16,7
3rd grade класс 43,5 45,6 10,9
4th gradegrade 52,9* 43,1 4,0
Note: *P<0.05.
in particular, the study of the features of ways of solving search tasks by younger schoolchildren in a sub-stantively-effective form is of serious scientific interest.
References
1. Davydov V.V. Lectures on general psychology. M.: Academy, 2008. 384 p. [in Russian].
2. Goncharov V.S. The psychology of cognitive development design. Kurgan: Publishing house KGU, 2005. 264 p. [in Russian].
3. Zak A.Z. The thinking of younger school students. St. Petersburg: Sodeystviye, 2004. 828 p. [in Russian].
4. Zak A.Z. Diagnostics of differences in the thinking of primary schoolchildren. Moscow: Genesis, 2007.159 p. [in Russian].
5. Maksimov L.K. Formation of mathematical thinking in younger schoolchildren. M.: MOPU, 1987.198p. [in Russian].
6. Rubinstein, S. L. Fundamentals of General Psychology. St. Petersburg: Peter, 2015.705 p. [in Russian].
7. Federal state educational standard of primary general education. 2nd ed. Moscow: Prosvechenie, 2011. 41 p. [in Russian].
ADOPTION OF REGULATIONS DEPENDING ON THE RESOURCE CHARACTERISTICS OF
MODERN YOUTH
Akimova M.
Russian State University for the Humanities, Professor, Doctor of Psychology
Persiyantseva S.
Russian State University for the Humanities; Associate Professor; Psychological Institute of Russian Academy of Education
Abstract
The article analyzes the normative approach. The issue of regional and educational differences in the adoption of standards is considered. Revealed the relationship between morality and the adoption of civic standards, civic values. The paper proposes methods of normative acceptance for assessing moral traits. To assess the basic life principles that guide modern youth. The set of rights and freedoms is considered as key civic values. Human equality before the law. Recognition of the value of human life, respect for national traditions and for the norms and rules of modern democracy. Truthfulness, patriotism, tolerance, justice, solidarity in a multinational country. The adoption of civic standards and civic values contributes to the well-being and prosperity of Russia, proceeding from responsibility for their country and realizing that they are part of the world community.
Keywords: moral traits, civic values, standards, socio-cultural environment.
A normative approach to the study of personality is developed in psychology as a concept of socialization - the unity of social adaptation and individualization. Group differences in attitude to standards reflect the heterogeneity of socialization conditions - 1) external sociocultural; 2) internal, ensuring the manifestation of personal selectivity, activity in the process of mastering group norms [1].
The adoption of standards is mediated by the experience of social interaction, regulatory acceptance. Normative acceptance determines the act of building the individuality of his mental appearance. Normative acceptance is often considered as a way of individual existence of a norm in the form of personality traits [3].
Three factors act in the process of human development: heredity, education, environment. We do not consider heredity in this article.
The educational system of the state is a powerful system of socialization of young people, which forms the intellectual, cultural and spiritual state of society. Thanks to the standardization of training programs, the national policy of the state is being built, leading to an assessment of the quality of life of its citizens. Educational, educational, professional institutions in the modern world have become centers for the transfer of accumulated knowledge, teaching methods. It is necessary
to systematically monitor the educational process, program and methodological material in order to timely make adjustments to it, "responding" to the "requests and requirements" of modern youth [4].
The student is at the epicenter of the organization of the process and activity, the personality of a person and his self-realization, the manifestation of his abilities. The formation and realization of personal potential as a person is possible only in the conditions of the development of a coordinated unity of his intellectual, spiritual, moral, aesthetic and physical sides. Humani-zation of educational processes maximally contributes to the development of individual human abilities.
The environment is essential to the formation of personality. The normative concept considers standards as given requirements of the social environment. Many common cultural traits serve the purpose of adapting an individual to his social community. This environment defines the desirable, favored, and useful traits. The higher the level of acceptance by a person of the approved traits, norms, rules of a given community, the more effective its adaptation in society will be.
These features include national character traits, national mentality, value structure, specificity of the motivational sphere, worldview, self-awareness, the nature of adaptation mechanisms, and much more.
