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CHARACTERISTICS OF WAYS TO SOLVE PROBLEMS BY PRIMARY SCHOOL STUDENTS
Zak A.
Leading Researcher, Psychological Institute RAE, Moscow, Russia
Abstract
The article describes the content of the study of the features of the methods of solving problems by pupils of the 3rd and 4th grades of primary school. As a result of individual experiments according to the author's methodology "Alternation", the theoretical and empirical methods of solving problems are characterized. It is shown that teaching in the fourth grade significantly contributes to the development of the theoretical method of solving problems by children.
Keywords: students of grades 3 and 4, search problems, theoretical and empirical methods of solving problems.
1. Introduction
According to the provisions of the new FSES of primary general education [6], the mastering of the basic educational program by children in the primary grades of school should lead not only to the achievement of subject educational results based on the assimilation of the content of the programs of specific academic disciplines, but also to the achievement of meta-subject results, reflecting, in particular, cognitive competencies.
The subject of our research was the cognitive competence associated with the development of methods for solving problems of a search nature. The purpose of the study was to develop a methodology to determine the formation of the named cognitive competence in primary school graduates.
1.1. Methodological basis
In understanding the characteristics of methods for solving problems of a search nature, we relied on the concept of two types of cognitive activity, developed in the dialectical theory of knowledge (see, for example, [5]) and implemented in the works of V.V. Davydov (see, for example, [1 ]).
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 knowledge) and at reflecting their external connections (empirical, formal, rational knowledge).
In the first case, cognitive activity is effective, since its result is an understanding of the reasons for changing the objects of knowledge. In the second case, cognitive activity is ineffective, since its result is only
a description and ordering of the observed features of changes in cognizable objects.
Based on these ideas about the two types of cognition, it was accepted (see, for example, [1], [2], [3], [4]) that the development by a person of ways to solve problems of a search nature in one case involves the allocation of essential relations in conditions for achieving the required result, otherwise such development is not related to the disclosure of material relations. In the first case, the methods used can be characterized as meaningful, in the second case - as formal.
Achievement of a cognitive meta-subject result associated with the development by schoolchildren in the course of training of methods for solving problems of a search nature presupposes the formation of the mental action of analysis, which is associated with the analysis of conditions for obtaining the required result.
In some cases, such analysis is implemented as a formal analysis, only dividing the proposed conditions into separate data - this is typical for a non-generalized, empirical method for solving search problems (see, for example, [1], [2], [3], [4]) .
In other cases, the analysis of conditions is associated not only with the selection of data and their relationships, but also, most importantly, with the clarification of their role in a successful decision: which of them is essential and necessary, and which is inessential and accidental. This is a meaningful, clarifying analysis, which serves as a condition for a generalized, meaningful way of solving search problems.
The development 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 more of them indicates the absence of meaningful analysis and, therefore, the presence of a non-generalized way to solve the proposed problems.
2. Materials and methods
2.1. Description of the method
On the basis of ideas about the originality of different approaches to the analysis of the conditions of the proposed problems belonging to the same class, and the different ways of solving them associated with these approaches, requirements for an experimental situation were developed, designed to determine the nature (generalized or non-generalized) of the method of action in achieving the required result.
First, the subject needs to propose to solve not one, but several problems. Secondly, these problems should have a general solution principle. Thirdly, their conditions must differ in external, directly observable features.
Compliance with the noted requirements makes it possible to determine when children use meaningful analysis when solving problems of the same type and when children use formal analysis. As a result, it will be possible to characterize the formation of the cognitive metasubject competence associated with the development of methods for solving search problems.
In accordance with the specified requirements, the "Alternation" technique was developed. The meaning of the tasks of this technique is to find a way to move an imaginary character ("goose") from one cell of the playing field to another according to the given rules and in the required number of steps (Fig. 1).
The movement of the "goose" along the cells of the playing field is subject to the following rules. The "goose" can move to adjacent cells either straight (i.e. horizontally or vertically) or obliquely (i.e. diagonally). Moreover, he can take no more than two identical steps in a row. This means that after two steps straight, he takes a step obliquely and after two steps obliquely - a step straight.
Thus, the "goose" can alternate steps straight and obliquely in different ways: a straight step - an oblique step, a straight step - two oblique steps, two straight steps - an oblique step, two straight steps - two oblique steps. Four options for alternating steps will be, if you first take steps obliquely: an oblique step - a straight step, an oblique step - two straight steps, two oblique steps - a straight step, two oblique steps - two straight steps.
Here's how, for example, such a multi-step problem: how can a "goose" get from cell A9 to cell H1 (Fig.) in 10 steps? Solution: first, the "goose" took two steps obliquely A9 - B8 - C7, then two straight steps C7 - C6 - C5, a step obliquely C5 - D4, a straight step D4 - E4, an oblique step E4 - E3, a straight step E3 -G3 and two steps obliquely G3 - H2 - K1.
On the basis of the rules for moving the "goose", tasks of three types were developed: multivariate, single-variant and unsolvable
In multivariate problems, the solution has several successful sequences of steps. For example, a problem where you need to get from B2 to D2 in three steps has six successful solutions: 1) B2 - C2 - D3 - E2; 2) B2 -C3 - D2 - E2; 3) B2 - C3 - D3 - E2; 4) B2 - C2 - D1 -E2; 5) B2 - C1 - D2 - E2; 6) B2 - C1 - D1 - E2.
In single-variant problems, the solution has only one successful sequence of steps. For example, the problem where you need to get from A4 to E9 in five steps is solved as follows: A4 - B5 - C6 - C7 - D8 -E9.
Figure. Solving a multi-pass problem.
In unsolvable problems, there is no satisfactory solution provided that the rules and the required number of steps are observed. For example, a problem where you need to get from cell A1 to cell D4 in three moves. The fact is that the most probable sequences of three steps are completed in cells B4 or G3. And to get into the G4 cell you need to take the fourth step.
2.2 Individual experiments
2.2.1. Experiment design
To test the "Alternation" methodology, individual experiments were organized with fourth grade students. The meaning of the experiments was to reveal the possibilities of the methodology in differentiating children according to the method of solving problems.
The first task was training, so that the children tried to use the rules for moving the "goose". For this, a multivariate task in three actions was proposed: B1 -D4, which has three options for a successful solution: 1) B1 - C2 - D3 - D4; 2) B1 - C2 - C3 - D4; 3) B1 -B2 - C3 - D4.
The second, third, fourth and fifth tasks were the main ones. They were proposed to determine the type of analysis of the conditions of problems - theoretical, meaningful, associated with the allocation of essential relations, or formal, empirical, when essential relations are not distinguished. As the main ones, we used single-variant problems, which, with the external difference in their specific conditions, had a general principle solutions.
Each problem had to be solved in eight steps: in the first problem it was required to find a path from A1 to G9, in the second - from K2 to A8, in the third -from K9 to A3, in the fourth - from B9 to H1.
The tasks differ in terms of the external features of the conditions (different initial and final cells) so that the specific steps of the "goose" in the method of solving the previous task are not used in the next one.
The general principle for solving all problems is that in each problem a sequence of eight moves includes six moves obliquely and two steps straight: the
first two steps and the last two steps must be performed obliquely.
2.2.2. The interaction of the experimenter and the subject
A total of 104 pupils participated in individual experiments using the "Alternation" method: 51 of them were in the third grade, 53 in the fourth grade. The experiment with each student proceeded as follows.
At the beginning the child is offered a sheet of paper on which a square cellular playing field has been drawn (Fig.).
Then the experimenter said: "Today we will solve interesting problems. Here, a square of cells is drawn on the sheet. Each cell in it has its own name from a letter and a number. For example, this cell - (the experimenter points to the lower left corner) - is called A1. In this corner - (the lower right corner is indicated) -there will be a cell K1. Here there will be a cell A9, -(the upper left corner is indicated), and here - K9, - (the upper right corner is indicated). Now I will point to different cells of the square, and you will speak their names. "
Along with this test option, the experimenter uses another: he names different cells, and the student shows them on the playing field. After it becomes clear that the child confidently operates with the names of the cells of the playing field, he is told: "A magic" goose "walks along the cells of this square. He steps only into adjacent cells: up, to the side or down. And he never jumps over the cage. For example, from cell B3, he can go straight to cell B2, or B4, or A3, or C3 in one step.
In addition, the "goose" walks into adjacent cells and obliquely. For example, from cell B3, he can obliquely enter cell C4, or C2, or A4, or A2 in one step.
The main rule of steps is that he can take no more than two identical steps in a row. If he took two steps straight, then then he should take a step obliquely. For example, if he went from A1 to A2 and then to A3, then after that, he must make the third step obliquely - either to B4 or to B2.
Table 2
And if the "goose" took two steps in a row obliquely, then then he must take a step straight. For example, if from A1 he first went to B2 and then to A3, then he must take the third step directly: to cell A4 or to cell B3.
Of course, the "goose" can alternate one step at a time: a straight step - an oblique step - a straight step -an oblique step, for example: A1 - A2 - B3 - C3 - D4
- E4.
He can also alternate one step and two steps, for example: a straight step - two oblique steps (A1 - A2 - B3
- C4) or an oblique step - two straight steps (A1 - B2 -B3 - B4). But the main thing is that you cannot take three identical steps in a row.
Now let's practice our "goose" steps. How can he get from cell A1 to K9? ... What can be the first step? ... What is the second step? ... "In the course of a joint discussion, the children suggest different steps of the" goose "on the way to the specified goal, and the experimenter recalls the basic rule of its movements -" no more than two identical steps in a row ".
Then the experimenter says: "Let's solve this problem. From cell B3, the "goose" took three steps and entered cell E2. Name the cells he walked through.
It is true that at first he could take a step into the C3 cell, then into D3 and, then, into E2. Write down this solution using the names of these cells ", - the child independently writes down the solution of three moves as follows: 1) C3, 2) D3, 3) E2.
Then the experimenter proposed to solve a control training problem, where in three moves it was required to find a way from cell C1 to cell E4.
The number of "theorists" and '
After solving this problem, the subject was asked to solve four basic single-variant problems. Each problem required eight moves. This was given 20 minutes.
3. Results
3.1 Quantitative characteristics of problem solving
Experiments with subjects made it possible to establish the following indicators for solving four main problems. It turned out that some of the students in the third and fourth grades solved problems using theoretical, meaningful analysis and found a general principle for their solution. They can be conventionally called "theorists". At the same time, observations of the actions of children in this group allowed us to distinguish two subgroups. The first subgroup, T-1, included the "theoreticians" who discovered the general principle of solution based on the first problem. The second subgroup, T-2, included the "theoreticians" who discovered the general principle of solution based on the second problem.
The rest of the students in both grades were unable to perform theoretical analysis in solving basic problems and find a general solution principle. They can be conventionally called "empiricists". Observations of the actions of the "empiricists" made it possible to distinguish three subgroups of the subjects. The first subgroup, E-1, is "empiricists" who have solved two problems correctly. The second subgroup, E-2, is "empiricists" who have solved one problem correctly. The third subgroup, E-3, are "empiricists" who have not solved a single main problem.
The experiments carried out allowed us to establish the number of pupils in grades 3 and 4 who coped with the four main tasks (see tables 1 and 2).
Table 1
Classes Student groups
Theorists Empiricists
The third (51 students) 27 (52,9%) 24 (47,1%)
The fourth (53 students) 32 (60,4%) 21 (39,6%)
Classes Subgroups of students
T-1 T-2 E-1 E-2 E-3
The third (51 students) 10 (37,1%) 17 (62,9%) 4 (16,6%) 14 (58,4%) 6 (25,0%)
The fourth (53 students) 14 (43,7%) 18 (56,6%) 6 (28,6%) 10 (47,6%) 5 (23,8%)
Analysis of the data presented in tables 1 and 2 allows us to note the following.
Thus, a comparison of data on the success of solving problems in the third and fourth grades indicates that, firstly, the number of "theorists" increases with age: 52.9% in the third grade and 50.4% in the fourth grade, and, accordingly, the number of "empiricists" is decreasing: 47.1% in the third grade and 39.6% in the fourth grade.
Secondly, with age, the ratio of subgroups in the group of "theorists" and in the group of "empiricists"
changes. Thus, in the group of "theorists" the number of children who discovered the general principle of solving from the first problem increases: in the third grade - 37.1%, in the fourth grade - 43.7% and, accordingly, the number of children who discovered the general principle of solving from the second problem decreases: in the third grade - 62.9%, in the fourth grade - 56.6%.
In the group of "empiricists", the number of children who have solved some two problems (subgroup E-1) is increasing: from 16.6% in the third grade to 28.6%
in the fourth grade, the number of children who have solved only one problem is decreasing (subgroup E-2): from 58.4% in the third grade to 47.6% in the fourth grade, and the number of children who did not solve any problem also decreases (subgroup E-3): from 25.0% to 23.8%.
Thus, the data in Tables 1 and 2 show the positive impact of teaching in the fourth grade on the ability of children to solve problems in a theoretical way based on a meaningful analysis of their conditions.
3.2. Qualitative characteristics of problem solving
3.2.1. Training problems
Along with the above-mentioned productive characteristics of problem solving, the data of observations of the process of solving problems by children of the above five groups are of serious importance: T-1, T-2, E-1, E-2 and E-3.
Differences between the indicated groups of subjects took place already when solving the training problem. Thus, the subjects of groups T-1 and T-2 not only used one solution, but also themselves proposed two more options for successfully solving this problem. Most often these were, firstly, the option when the first two moves were obliquely, and the third move was straight (i.e. C1 - D2 - E3 - E4), and, secondly, the options when the first move was straight, and the second and third - obliquely (i.e., C1 - C2 - D3 - E4). To the experimenter's question about whether other options for successfully solving this problem are still possible, the subjects easily found the third variant of the sequence of three moves (from C1 to E4): in this case, moves of different types simply alternated (i.e., the first move was oblique, the second straight, the third obliquely: C1 - D2 - D3 - E4).
The tested groups E-1, as well as the "theoreticians", could independently find two options for solving the training problem. However, unlike the "theoreticians", they found slightly different options. So, usually, as the first option, they found a sequence of three moves, in which moves of different types alternated as follows: obliquely, straight, obliquely (C1 - D2 - D3 -E4). As a second option, they proposed such a sequence of three moves, when the first move was straight and the other two were obliquely (i.e. C1 - C2 - D3 - E4). At the same time, the experimenter's question about whether there were still options for the successful solution of this problem, the subjects of the E-1 group most often found it difficult to answer and usually did not find the third option, when the sequence of three moves included oblique steps as the first two steps, and - step straight (i.e. C1 - D2 - E3 - E4).
The subjects of the E-2 group, in contrast to the subjects of the E-1 group, could not independently find any two variants of a successful sequence of three moves in the training problem. Most often, they offered such a variant, which was associated with a sequence of three moves, in which moves of different types alternated as follows: obliquely - straight ahead - obliquely (i.e. C1 - D2 - D3 - E4). To the experimenter's question about whether there were still options for successfully solving this problem, the subjects of this group could with great difficulty find only one more option: usually this option was associated with a sequence of three
moves, in which the first move was direct, and the other two were obliquely (i.e. C1 - C2 - D3 - E4).
The subjects of the E-3 group, just like the subjects of the previous group (i.e., the E-2 group), were able to independently find only one variant of the sequence of three moves in the training task and, in the same way as in the subjects of the E- group. 2, this variation was most often associated with a sequence of three moves, where different types of steps alternated as follows: C1 - D2 - D3 - E4. When asked by the experimenter whether there were still options for successfully solving this problem, the subjects of this group could not find any more option.
3.2.2. Main problems
Significant differences in procedural characteristics between the groups of subjects T-1, T-2, E-1, E-2, E-3 were observed when solving four main problems, each of which, as noted, had one variant of a successful solution associated with the sequence of eight moves, where 1 and 2, 4 and 5, 7 and 8 moves obliquely, and 3 and 6 straight.
Let us consider these differences using the example of the procedural characteristics of solving problem 1 by subjects of different groups. The subjects of the T-1 group were characterized by the following behavioral features.
Determination of the location of the initial and final cells was carried out by the subjects of this group clearly and quickly. At the same time, they, as a rule, first touched cell A1 with the handle, then cell G9. Then, active movements of gaze were observed from cell A1 to cell G9 for some time. This indicated, in our opinion, that the children tried to remember the extreme points of the desired route.
Then, one part of the children of the T-1 group performed three trial attempts to solve, and the other part of the children of the same group performed four trial attempts. For those children who limited themselves to three attempts, of which the third was successful, it was characteristic that the first attempt was completed. This means that a path has been presented from the starting cell to the ending cell. However, due to the fact that not eight, but nine moves were made, this attempt was unsuccessful.
The second attempt was then, as a rule, incomplete. This means that the children usually performed four or five moves, after which it became clear to them that it would be impossible to keep within eight moves.
The third attempt, like the first, was complete: here the children demonstrated a sequence of eight moves, with the help of which one can get from cell A1 to cell G9.
Those children who had a successful fourth test attempt have some differences from the previous part of the children of the T-1 group. They were expressed in the fact that their second trial attempt was completed and also unsuccessful, since it included nine moves. The third attempt was incomplete, like the second attempt in the subjects of the first part of the T-1 group. The behavior of the subjects of the T-2 group in the process of solving task 1 differed from the behavior of the subjects of the T-1 group.
Thus, the determination of the location of the initial and final cells was performed by the subjects of the
T-2 group less clearly and less quickly than it was in the subjects of the T-1 group. Having fixed the location of these cells first by touching them with a pen and then with their gaze, the subjects of the T-2 group, like the subjects of the T-1 group, (although not as long as the subjects of the T-1 group) measured the distance from A1 to G9 with their gaze.
Then one part of the children of the T-2 group (the first subgroup T-2) performed four trial attempts at the solution before the fifth attempt was successful. Another part of the children (the second subgroup T-2) performed five trial attempts of the solution before the sixth attempt was successful. The unsuccessful nature of the attempts that preceded the one where the problem was solved correctly was associated with the fact that the children, in order to get from A1 to G9, performed not eight, but nine moves.
It should be noted that an attempt immediately preceding the final (successful) one was always incomplete: during its implementation, usually four or five moves were performed. And all the initial trial attempts (first, second and third) in the first subgroup T-2 and (first - fourth) in the second subgroup T-2 were completed.
The behavior of the subjects of the E-1 group in the process of solving the first main problem differed from the behavior of the "theoreticians". As noted earlier, the subjects of the E-1 group could not, in contrast to the subjects of the T-1 and T-2 groups, solve all the main tasks successfully: they successfully solved only two of the four main tasks - the first and fourth or the first and third or second and fourth. Thus, in some cases, the subjects of the E-1 group coped with the first task without solving, then the second, in other cases, on the contrary, they could not cope with the first task, but then correctly solved the second task.
It should be noted that the successful solution of any problem - the first, second, third or fourth - occurred in the subjects of the E-1 group in a random manner. This follows from the data of observation of the problem solving process, according to which the behavior of the subjects of this group did not differ in situations of successful and unsuccessful solution of the same problem.
The total number of trial attempts in the subjects of the E-1 group, regardless of whether the solution was successful or unsuccessful, reached seven to eight. All attempts were completed, i.e. children each time "walked" the path from the initial cell to the final one. It is important to note that the initial attempts, usually from the first to the fifth, had a straight step as the first move (or even the first two moves), although sometimes an oblique step was encountered as the first move. The last three or four attempts had, as a rule, an oblique step as the first move.
It should be noted that in the test attempts of subjects E-1 there were a variety of options for the ratio of steps of different types: alternating steps one by one (obliquely - straight - obliquely - straight or, conversely, straight - obliquely - straight - obliquely), alternating steps two and one (straight - straight -obliquely - obliquely), alternating steps two and two
(obliquely - obliquely - straight - straight or straight -straight - obliquely - obliquely).
Thus, the analysis of the process of solving task 1 by the subjects of the E-1 group shows significant differences in the actions of the subjects of this group from the actions of the subjects of the T-1 and T-2 groups, who successfully solved all four main tasks.
Observations of the actions of the subjects of the E-2 and E-3 groups in solving problem 1 show their significant similarity with the actions of the subjects of the E-1 group. As well as the subjects of the E-1 group, the subjects of the E-2 and E-3 groups carried out a significant number of trial attempts - seven, eight, and sometimes even nine, all attempts were completed, as the first move and often the first two moves, a straight step was used, the ratios of steps of different types were very diverse: obliquely - straight - obliquely, straight -obliquely, straight - obliquely - obliquely,
In general, consideration of the features of the actions of the tested groups E-1, E-2 and E-3 shows a significant commonality of the behavior of these children in the course of solving problem 1 and the fundamental difference between such behavior and the behavior of the tested groups T-1 and T-2 when solving the same problem.
Observations of the behavior of children show that the differences noted above remain in the solution of the other three main tasks.
4. Conclusion
Concluding the consideration of the results of the development and testing of the "Alternation" methodology, designed to determine the formation of cognitive competence associated with the development of methods for solving problems, the following should be noted.
First, the approbation of the developed methodology showed that its application makes it possible to distinguish between children solving problems in different ways: effective, associated with a meaningful analysis of the conditions of the problems and ineffective, associated with their formal analysis.
Secondly, observations of the actions of students who carry out meaningful analysis in solving problems made it possible to identify two groups of children: those who single out the general principle of solution when analyzing the content of the first problem and when analyzing the content of the second problem.
Third, observations of the actions of students who carry out formal analysis in solving problems made it possible to identify three groups of children: those who solved two problems, solved one problem and did not solve a single problem.
These provisions give reason to believe that the "Alternation" methodology developed in the study will effectively determine the formation of cognitive competence in younger schoolchildren (in particular, primary school graduates), associated with the development of ways by children to solve search problems.
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ПРАКТИКООРИЕНТИРОВАННАЯ МОДЕЛЬ КОММУНИКАТИВНОЙ КОМПЕТЕНТНОСТИ В КОНТЕКСТЕ АРТ-ТЕРАПЕВТИЧЕСКОЙ ПОМОЩИ ДЕТЯМ ДОШКОЛЬНОГО ВОЗРАСТА С ОБЩИМ НЕДОРАЗВИТИЕ РЕЧИ
Кириллова М.К.
Удмуртский государственный университет доцент кафедры коррекционной педагогики и специальной психологии
кандидат психологических наук Новгородова Ю. О.
Удмуртский государственный университет старший преподаватель кафедры психологии развития и дифференциальной психологии
PRACTICE-ORIENTED MODEL OF COMMUNICATIVE COMPETENCE IN THE CONTEXT OF ART-THERAPEUTIC CARE FOR PRESCHOOL CHILDREN WITH GENERAL SPEECH
UNDERDEVELOPMENT
Kirillova M.
Udmurt State University Associate Professor of the Department of Correctional Pedagogy and
Special Psychology Candidate of Psychological Sciences Novgorodova Y.
Udmurt State University Senior lecturer of the Department developmental psychology and differential psychology
Аннотация
В статье освещается проблема развития коммуникативной компетентности детей с нарушениями речи. Авторы эксплицируют понятие коммуникативной компетентности ребенка, а также дают определение структурно-содержательных характеристик коммуникативной компетентности старших дошкольников с общим недоразвитием речи (ОНР) III уровня. Согласно предлагаемой практикоориентированной модели, интегрирующей функцией для всех компонентов коммуникативной компетентности является опытный компонент. Коммуникативно-компетентностный опыт как опытный компонент любой компетентности активно формируется в ходе преобразования обучающимся внешнего мира и самого себя. Потому необходимым для интенсивного формирования коммуникативно-компетентностного опыта ребенка является инициация коммуникативных процессов в условиях преобразующей деятельности, к которой, в первую очередь, относится творчество. Эффективное формирование коммуникативно-компетент-ностного опыта дошкольников с ОНР в специально организованной коррекционной работе обеспечивается учетом специфики нарушений развития детей, созданием благоприятного эмоционального фона в условиях арт-терапевтического пространства, стимулирующего коммуникативную деятельность; применении различных художественных материалов для инициации преобразующей деятельности.
Abstract
The article highlights the problem of developing the communicative competence of children with speech disorders. The authors explicate the concept of a child's communicative competence, as well as define the structural and content characteristics of the communicative competence of older preschoolers with general speech underdevelopment of level III. According to the proposed practice-oriented model, the integrating function for all components of communicative competence is the experienced component. Communicative competence experience as an experienced component of any competence is actively formed during the transformation of the external world and
