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CREATIVE THINKING STRATEGIES FOR PRIMARY SCHOOL STUDENTS A.Z. Zak, Leading Researcher
Psychological Institute of Russian Academy of Education (Russia, Moscow)
DOI:10.24412/2500-1000-2024-9-3-33-40
Abstract. The article presents a study aimed at studying the characteristics of creative actions in situations of problem-writing by children studying in primary school (grades 3 and 4). Based on individual experiments, four strategies of creative thinking of children were identified and characterized when independently composing problems similar to those solved: formal, content, productive, original.
Keywords: creative actions, primary school students, problem-writing, individual experiments, four strategies of creative thinking.
1. Introduction.
The Federal State Educational Standard of Primary General Education contains provisions that one of the important indicators of mastering the basic educational program of primary school is the achievement by students of subject results related to the mastery of the content of academic disciplines in junior grades.
At the same time, various meta-subject results reflecting the formation of children's cognitive and regulatory universal educational actions are of great importance in this context.
Meta-subject results are associated, in particular, with mastering the ability to accept and maintain the goals and objectives of educational activities, with the formation of the ability to plan, control and evaluate educational activities, with the mastery of the initial forms of cognitive and personal reflection.
An important role in the intellectual development of schoolchildren is played by meta-subject results associated with their mastery of creative and exploratory problem solving methods [4].
We believe that children's independent creation of new problems is also a creative problem and requires the use of creative thinking techniques.
In this regard, the aim of our study was to examine the methods used by primary school students, in particular third- and fourth-graders, in their creative activities when composing new problems.
At the same time, an important direction in the study of children's creative actions is to clarify the issue of how different methods of composing problems are distributed among third- and fourth-graders.
2. Materials and methods
A total of 57 students (29 third-graders and 28 fourth-graders) participated in the study, with whom individual experiments were conducted. Each child was asked to first solve problems and then compose similar ones.
2.1. Route problems "with rules".
The methodology of these experiments included route problems "with rules", where it is necessary to find out how an imaginary character moves along a cellular playing field (for more details on problems of this kind, see our works [1, 2, 3].
It should be noted that in route problems "without rules", an imaginary character can move along any cells of the playing field, performing any number of actions. In contrast, in route problems "with rules", the search for a solution is determined by the proposed rule for moving along the cells of the playing field and the required number of actions.
In two series of experiments in our study, such route problems were used, in which it was required to find out how the "Rooster" (an imaginary character), moving along the cells of the playing field, can get from one point to another in the required number of actions.
In this case, movement along the cells of the playing field was carried out according to a rule that provides for the alternation of ele-
mentary movements - steps. One step is a Another step is to move to the adjacent cell move to an adjacent cell, for example, diagonally, i.e. diagonally (see Fig. 1 for ex-straight, i.e. i.e. vertically or horizontally. amples of the "Rooster"'s movements).
Fig. 1. Playing field 1
For example, from cell 1 to cell 9 the following route of movement of the "Rooster" is possible. The first step can be made straight, - to cell 2, the second step should be diagonally, -for example, to cell 6, the third step should again be straight, - for example, to cell 5, the fourth step should again be diagonally - to cell 9.
Thus, the rule of movement of the imaginary character ("Rooster") in problems of this type is that a step to an adjacent cell directly alternates with a step to an adjacent cell diagonally and, conversely, a step diagonally al-
ternates with a step straight. This rule means, therefore, that the "rooster" cannot take two identical steps in a row, i.e. it cannot take two steps straight in a row or two steps diagonally in a row.
As noted, two series of experiments were conducted with problems of this kind. In each of them, such problems had to be solved first, and then composed.
2.2. Contents of the experiments.
First, a training problem was solved. For this, the child was asked to familiarize himself with a playing field of 25 cells (Fig. 2).
5 4 3 2 1
A B C D E Fig. 2. Playing field 2
In the experiments of the first series, children were asked to solve and compose problems of this type in the external plane. This means that the role of an imaginary character ("Rooster") was played by a cube that could be moved along the cells of the playing field, and the starting and ending points of the movements were indicated by cardboard circles. The playing field was drawn on a sepa-
rate sheet of paper (each cell was 4 cm by 4 cm in size).
First, the child was told that each cell on the playing field had a name that was formed from a combination of a letter and a number. Thus, the cell in the lower left corner was called A1, in the lower right corner - E1, in the upper left corner - A5, in the upper right corner - E5.
Then the experimenter pointed to different cells to make sure that the child was familiar with the names of the cells in different places on the playing field.
Next, the child was told that a "magic rooster" walked along the cells of this playing field. He has a rule: he cannot jump on the cells, but can only step into the neighboring cell, either straight (for example, from cell A1 to cell A2 or to cell B1), or diagonally (for example, from cell A1 to cell B2).
Then (to make sure that the child understood the rules of the "Rooster's" movements), he was asked to show with the help of a cube how the "Rooster" can, observing the rule of alternating steps, get from cell A5 to cell E1.
El
Problem №1 required finding two steps that the "Rooster" took to get from A1 to B3, respectively, in problem №2 - three steps from B3 to D5, in problem №3 - four steps from D1 to B4.
The solution of the noted problems in the first series was carried out, as noted, in the external plan. In this regard, the child was asked to mark the starting and ending points of the "Rooster's" movements on the playing field with cardboard circles, and to use the movements of the cube to find the route of the "Rooster's" movements.
At the third stage of the experiment, if the subject coped with problems № 1 and № 2 (regardless of whether he coped with problem № 3), he was asked to compose problems of the first degree of complexity (i.e. such where, as in problem № 1, it was necessary to find two steps).
After completing this task, the child was offered a training task: "How can the "Rooster" get from cell A3 to cell A2 in two steps?" If the child experienced difficulties or made a mistake, he was given the necessary help.
At the second stage of the experiment (after completing the training task), the child was asked to solve three main problems in a row:
№ 1 ("What two steps did the "Rooster" take from A1 to B3?"), - Fig. 3;
№2 ("What three steps did the "Rooster" take from C3 to E5?"), — Fig. 4;
№3 ("What four steps did the "Rooster" take from E1 to B4?"), — Fig. 5.
B4
At the same time, to the left of the child on the table there was a sheet of paper with a playing field, where cells A1 and B3 were covered with cardboard circles, i.e. the condition of the sample problem was presented.
To compose problems, he was given several more sheets of paper with the same playing field as before, many cardboard circles and a cube.
The child was told: "Now you will come up with problems yourself where you need to find two steps of the "Rooster". You have already solved such a problem. Come up with as many problems as you want."
While saying this, the experimenter pointed to the playing field on the table with the conditions of problem No.1 (where there were cardboard circles in cells A1 and B3). Thus, the subjects were asked to come up with
Al
B3
Fig. 3. Problem №1
C3
E5
Fig. 4. Problem №2
Fig. 5. Problem №3
problems of the first degree of complexity, similar to problem № 1.
One of the sheets of paper with the playing field was placed directly in front of the child and he was told: "Think about between which cells the "Rooster" made two steps and place circles in these cells. This will create a problem where you need to find two steps." 2.2.1. The first group of subjects When composing problems, the children acted differently.
The first group implemented a formal approach in their actions when composing problems. As a result, they got problems that could not be solved by performing only two actions, two steps of the "Rooster".
These children simply placed circles in the cells of the initial and final points of the "Rooster's" movements, without checking how many steps actually needed to be taken in accordance with the regulations of the "Rooster's" movements in order to get from the initial point to the final point.
As a rule, these children composed problems of the second, rather than the first degree of complexity (i.e., such that the "Rooster" had to take three steps, not two, as was suggested to the subjects). Thus, they composed a problem that could not be solved in two steps (Fig. 6).
CI
D4
Fig. 6. Problem of the second degree of complexity
The following actions were typical for the children of this group.
Having looked at the conditions of problem #1, located on the playing field to the left of them, they, as one could see, noted (sometimes even out loud) that both cells with cardboard circles were located diagonally.
Then they placed cardboard circles in cells B1 and G4, also located diagonally, on their playing field. After that, they said that the problem had been invented. Thus, it can be considered that they were guided only by the external features of the sample problem, without finding out the features of its construction.
When composing such problems, the children, as one could observe, did not solve them themselves, but simply first put one circle in the initial cell (for example, in C1), and the second circle in the final cell (for example, in D4) and reported that the problem was ready.
2.2.2. The second group of subjects The subjects of the second group acted meaningfully - they composed one or two correct problems that had a solution in two steps of the "Rooster". For example, the following problem was composed (Fig. 7):
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C2
Fig. 7. Correct problem in two steps
Unlike the children in the previous group, they did not simply look at the conditions of problem No.1, but, as you could see, studied it, recalling their solution: sometimes they simply said: "...first straight, then diagonally...", sometimes they moved the cube straight from B1 to B2, and then diagonally -from B2 to C3.
Then they turned to their playing field, placed a cardboard circle in some cell, for example, A2 and moved the cube first to cell A3
and then to cell B4. Then they placed the circle in B4.
When the experimenter asked them to tell the conditions of this problem, they usually said: "We need to find out what two steps the "rooster" took from A2 to B4."
After that, the experimenter put aside the playing field with the conditions of the first problem and asked the child if he wanted to compose more problems. If the child agreed, he was offered to take another game board.
When composing the second problem, the children acted in the same way as when composing the first. As a result, they marked the beginning and end of the two steps of the "Rooster" with circles.
2.2.3. The third group of subjects The children of the third group also composed solvable problems, but not one or two (like the children of the second group), but three to five. Thus, they acted productively.
At the same time, when starting to compose problems, just like the children of the second group, they first considered the conditions of the sample problem (problem № 1), highlighting two steps of the "Rooster" there, and then offered the first problem.
The children of this group composed several (three to five) identical problems (i.e., such where the "Rooster" made the same steps). This could be judged by observing how these children moved the cube, composing problems.
If in the first task there was a diagonal step and then a straight step, then in the remaining tasks exactly the same steps were performed. In addition, the distance from the initial cell to the final cell in all tasks was also the same (see Fig. 8, 9, 10 and 11, 12, 13).
Some children in this group (subgroup A) moved a cube from cell B1 to cell B2 and then to cell C3 and placed cardboard circles in cells B1 and C3 (Fig. 8).
B1
C3
Fig. 8. The first composed task (subgroup A)
Next, taking the second playing field, they looked at the conditions of the first composed problem and after that they moved the cube
from cell C1 to cell C2 and then to cell D3 and placed cardboard circles in cells C1 and D3 (Fig. 9).
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D3
Fig. 9. The second composed problem (subgroup A)
Then they took the third playing field and D2 - E3, acted in the same way as when composing the (Fig. 10). second problem: they combined cells D1 -
placing circles in D1 and E3
CI
D3
Fig. 10. The third composed problem (subgroup A)
Thus, the children of this subgroup obtained the second and third problems (and sometimes the fourth and fifth) simply by shifting the cardboard circles, which denoted the initial and final cells of the two steps of the "rooster", by one cell to the side, to the right. In all the problems composed, the dis-
tance between the initial and final cells was the same.
The other children in this group (subgroup B) moved the cube from cell B1 to cell C2 and then to cell D2 and placed cardboard circles in cells B1 and D2 (Fig. 11).
B1
D2
Fig. 11. The first composed problem (subgroup B)
Then, taking the second playing field, they looked at the conditions of the first composed problem and after that moved the cube from
cell B2 to cell C3 and then to cell D3 and placed cardboard circles in cells B2 and D3 (Fig. 12).
- Психомогицеские nayHU -
B2
D3
Fig. 12. The second composed problem (subgroup B).
Then they took the third playing field and acted in the same way as when composing the second problem: they combined the cells B3 -
C3 - D4, placing the circles in B3 and D4 (Fig. 13).
BE
D4
Fig. 13. The third composed problem (subgroup B)
Thus, the children of subgroup B (unlike the children of subgroup A) obtained the second and third problems (and sometimes the fourth and fifth) by shifting the circles denoting the initial and final cells of the two steps of the "rooster" one cell up. At the same time (as with the children of subgroup A), in all the composed problems the distance between the initial and final cells was the same.
As a result, the children of both subgroups of the third group acted productively, composed several problems, but constructed in the same way.
2.2.4. The fourth group of subjects The children of the fourth group, like the children of the third group, offered several (three to five) problems, but these problems were constructed differently: the initial and
final cells in these problems were at different distances.
The children of this group thus created a variety of problems and, therefore, in our opinion, demonstrated not only productivity, but also originality of creative thinking when composing problems.
The children of this group were characterized by the following actions.
When composing the first problem, they acted in the same way as the children of the third group: first, they considered the condition of the sample problem (problem № 1), highlighting two steps there, and then offered the first problem, where the "Rooster" moved, as in the sample problem, in the vertical direction, for example (Fig. 14).
B1
C3
Fig. 14. The first problem composed (fourth group)
Next, taking the second playing field, they, unlike the children of the third group, looked not only at the condition of the first problem they had composed, but also, as could be observed, compared this condition with the con-
dition of problem № 1 (i.e. the sample problem) they had solved at the second stage.
As a result, the second problem they had created was not the same as the first one - in it, the "Rooster" moved a short distance between the initial and final cells (Fig. 15).
CI
C2
Fig. 15. The second composed problem (fourth group)
When composing the third problem, they, taking the third playing field, compared the conditions of three problems - problem № 1 and two previously composed problems. As a result, the third task differed from the first
task in the direction of movement and from the second task in the distance between the initial and final cells - in it, the "Rooster" moved in the horizontal direction (Fig. 16).
- Психомогицеские nayHU -
B1
B2
Fig. 16. The third composed task (fourth group)
3. Results.
As noted, 29 third-graders and 28 fourth-graders participated in the individual experi-
ments described above. The number of subjects in the four groups described above is presented in the table.
Table. The number of third- and fourth-graders who acted formally, meaningfully, produc-
tively, and originally when composing tasks.
Classes Methods of creating tasks
Formal Meaningful Productive Original
3 2 (6,8%) 8 (27,6%) 15 (51,8%) 4 (13,8%)
4 2 (7,2%) 2 (7,2%) 17 (60,7%) 7 (25,0%)
The analysis of the data presented in the table allows us to formulate a number of provisions.
Firstly, in the third and fourth grades, the minimum number of subjects formally composed problems. In each of the specified classes, there were two such students: in the third grade - 6.8%, in the fourth grade - 7.2%. Thus, based on the data discussed, we can conclude that the formal composition of problems is not associated with the age of the subjects.
Secondly, in the third grade, eight people composed problems meaningfully - 27.6%, in the fourth grade - only two people - 7.1%. These data indicate that with age, the number of schoolchildren composing only one or two solvable problems, i.e. acting meaningfully, decreases.
Thirdly, among the third grade students, 15 people (more than half of all third graders -51.8%) acted productively when composing problems - among the fourth grade students, these subjects made up 60.7% (17 people). Thus, the data under consideration allow us to conclude that with age, the number of schoolchildren composing problems productively increases.
Fourthly, in the third grade, 4 people (13.8%) composed problems originally, in the fourth grade - 7 people (25.0%).
Just as with the subjects who composed the problems productively, in this case it can be stated (based on the data under consideration) that with age the number of subjects who composed the problems in an original way increases.
Combining the data on the subjects who composed the problems productively and originally in the third grade - 65.6% (51.8% and 13.8%) and in the fourth grade - 85.7% (60.7% and 25.0%) allowed us to establish the following fact. With age, there is a significant increase in the number of children who act in the most complex ways when composing the problems - productively and originally (the differences between the indicators of 65.6% and 85.7% are statistically significant - at p < 0.05).
4. Conclusion.
The conducted research was aimed at studying the characteristics of the creative actions of younger schoolchildren (in particular, third-graders and fourth-graders) when composing new problems.
In individual experiments, students solved and composed problems related to the movement of an imaginary character ("Rooster") across a playing field according to the rules regulating these movements.
As a result of the experiments, it was shown that primary school students composed problems in different ways.
Some children act formally, composing problems that cannot be solved in a specified number of actions. Other children act meaningfully, offering one or two solvable problems. The third group of children act productively, composing three to five solvable problems, but constructed in the same way, according to the same template. The fourth group of children acted originally: just like the children of the previous group, they com-
posed three to five problems, but constructed differently.
Processing the results obtained in the experiments made it possible to establish that with age (in the fourth grade compared to the third grade), the number of schoolchildren capable of composing problems productively and originally increases. At the same time, accordingly, the number of schoolchildren composing only one or two solvable problems (i.e. acting meaningfully) decreases.
The noted facts for the first time demonstrate the capabilities of primary school stu-
References
1. Zak A.Z. Differences in the mental activity of younger students. - Moscow: MPSI, 2000. -192 p.
2. Zak A.Z. Thinking of a younger student. - St. Petersburg: Assistance, 2004. - 828 p.
3. Zak A.Z. Diagnostics of differences in the thinking of younger students. - Moscow: Genesis, 2007. - 160 p.
4. Federal state educational standard of primary general education // Bulletin of education of Russia. - 2010. - № 2. - P. 10-38.
СТРАТЕГИИ ТВОРЧЕСКОГО МЫШЛЕНИЯ МЛАДШИХ ШКОЛЬНИКОВ
А.З. Зак, ведущий научный сотрудник Психологический институт РАО (Россия, г. Москва)
Аннотация. В статье представлено исследование, направленное на изучение характеристик творческих действий в ситуациях сочинения задач детей, обучающихся в начальной школе (3, 4 классы). На основании проведения индивидуальных экспериментов были выделены и охарактеризованы четыре стратегии творческого мышления детей при самостоятельном составлении задач, аналогичных решенным: формальная, содержательная, продуктивная, оригинальная.
Ключевые слова: творческие действия, младшие школьники, сочинение задач, индивидуальные эксперименты, четыре стратегии творческого мышления.
dents in producing new problems. Knowledge of these facts enriches the ideas of developmental and educational psychology about the development of creative abilities in children of primary school age.
In further studies, it is necessary to determine how schoolchildren with different methods of composing problems are distributed among first - and second-graders, as well as among younger adolescents studying in the fifth and sixth grades.
