1.Introduction

One of the urgent tasks of psychological and pedagogical science is the study of the conditions that ensure the development of independent thinking of schoolchildren in the course of education. On the one hand, this means that it is necessary to intensify research in the direction traditional for educational psychology — the formation of schoolchildren’s methods of independent problem solving. On the other hand, it follows from this, in our opinion, that it is necessary to conduct new research, in particular in the direction related to the formation of schoolchildren’s methods of independent production or formulation of tasks on various topics of subjects included in the school curriculum.

The provisions of the new FSES IEO contain indications of the need for elementary school students to achieve meta-subject results, which are, in fact, means and ways of implementing independent thinking, associated, in particular, with the ability to solve creative problems [5]. Such skills also include actions related to the independent compilation of new tasks by children, with the independent achievement of a creative goal.

In preliminary experiments with a small number of younger schoolchildren of different ages, on the material of this trial methodology, it was revealed that there are three ways to compose tasks.

The first method is characterized by the ability to formulate tasks formally. This means that children make up tasks of a non-problem type. One variant of such compilation is characterized by the fact that the answer is already presented in the condition of the formulated problem, it does not need to be searched for. For example: “Petya, Kolya and Vasya jumped high at competitions at school. Petya jumped higher than Kolya, and Kolya jumped higher than Vasya. Who jumped higher than Kolya? The second option is due to the fact that this question cannot be answered according to the condition of the task, For example: “Petya, Kolya and Vasya jumped high at competitions at school. Petya jumped higher than Kolya, and Kolya jumped higher than Vasya. Who is Petit?

The second method is characterized by meaningful formulation of tasks. This means that children make up problems in which an answer can be found by correlating the judgments given in the condition. For example: “Petya, Kolya and Vasya jumped high at competitions at school. Petya jumped higher than Kolya, and Kolya jumped higher than Vasya. Who jumped the highest? In this case, children usually make up one or two tasks to be solved.

The third way is characterized by productive tasking. This means that the children make up not one or two tasks, as in the previous case in the meaningful compilation of tasks, but three or five similar tasks.

2.Material and methods

The purpose of our study was to determine how these ways of composing problems are distributed among children in the second and third grades.

It was assumed that in the third grade, in comparison with the second grade, there will be more children who are meaningful and productive in constructing tasks, and fewer children who use the formal method.

A total of 212 students took part in four series of individual experiments that were conducted in the last quarter of the academic year:: 105 of them were in the second grade, 107 in the third. Among the students of the second grade, 27 people participated in the first series, 24 in the second, 29 in the third, and 25 in the fourth; Among the pupils of the third grade, 29 people participated in the first series, 25 in the second, 27 in the third, and 26 in the fourth.

To achieve this research goal, we have developed a methodology that includes plot-logical tasks of varying complexity. They are inferences built on plot material: their conditions contain information about the properties and relationships of people and things. Based on this information, it is required, correlating the content of these judgments (general and particular) in the condition of the problem, to find out the content of the given judgment (private). In other words, in such tasks it is necessary to draw a conclusion about the presence or absence of certain properties and relations in people and things presented in the condition. Similar problems are interesting for children and can serve as material for their independent compilation of similar problems (for more details on plot-logical problems, see our studies [1], [2], [3], [4]).

The experiments were carried out on the material of the tasks of the «Negation» technique related to the implementation of the reasoning, in which it was required, by correlating the data in the condition of the judgment task of different levels, to find out the content of the unknown (i.e. given) judgment. For example, the following task: “Petya and Nina had a dog each: someone had a Zhuchka, someone had a Polkan. Nina didn’t have a bug. Which of the guys had Polkan?”

To answer a problem question (i.e., to find an unknown quotient judgment), it is required to correlate the general judgment “Petya and Nina had a dog each: someone had a Bug, someone had a Polkan” and a private judgment “Nina did not have a Bug”. As a result, we can conclude (i.e. find another private judgment) — «Petya had Polkan.»

Four series of individual experiments were carried out:

— in the first series, tasks of the first degree of complexity were solved and compiled in the external plan,

— in the second series, tasks of the second degree of complexity were solved and compiled in the external plan,

– in the third series, tasks of the first degree of complexity were solved and compiled internally,

 — in the fourth series, tasks of the second degree of complexity were solved and compiled internally.

Thus, the series of experiments differed both in terms of the conditions for solving and compiling problems (i.e., externally or internally), and in their complexity, meaning the number of judgments that need to be compared in order to find a solution to problems).

2.1. The first series of experiments

In the experiments of the first series, the problems were solved and compiled externally, i.e., using cards with drawings. Some of them show girls and boys having different looks (that is, dressed differently or doing different things), while other cards show various kinds of objects found on the street, in the house, at school, etc.

First, the child was given a sheet of paper with text and was asked to read and solve a training problem: “Alik and Borya came to the store. Someone bought a pen, someone bought a pencil. Alik bought a pencil. What did Boris buy? If the child did not cope with such a task, then work with him ended.

If the child successfully solved the training task, then he was offered three main tasks of varying complexity, each of which was printed on a separate sheet of paper in large print.

First, it was necessary to solve the main task No. 1: “Sasha and Galya were reading: someone was reading a newspaper, someone was reading a magazine. Sasha didn’t read the newspaper. What did Galya read? (This is a task of the first degree of difficulty, since the conclusion is proposed to be made taking into account one judgment: «Sasha did not read the newspaper»).

If the child could not solve this problem, then work with him ended. If he successfully solved problem No. 1, then he was asked to solve the main problem No. 2: “Misha, Vova and Dima ate vegetables. Someone ate cucumbers, someone tomatoes, someone carrots. Misha ate carrots, Vova did not eat tomatoes. What did Dima eat?” (This is a task of the second degree of complexity, since the conclusion is proposed to be made taking into account two judgments: «Misha ate carrots» and «Vova did not eat tomatoes»).

If the child successfully solved problem No. 2, then he was asked to solve the main problem No. 3: “Natasha, Vera, Fedya and Tolya went to different cities. Some of the guys went to Orel, someone to Voronezh, someone to Ryazan, someone to Kursk. Natasha went to Orel, Vera went to Voronezh, Fedya did not go to Ryazan. Where did Tolya go? (This is a task of the third degree of complexity, since the conclusion is proposed to be made taking into account three judgments: «Natasha went to Orel», «Vera went to Voronezh» and «Fedya did not go to Ryazan»).

In any case, whether the child successfully or unsuccessfully solved the main task No.3, he (subject to the successful solution of the main task No. 2) was asked to further compose tasks of the first degree of complexity, i.e. tasks with two actors, as in the main task No.1.

“Now you will come up with problems yourself, where there were two guys who were doing something. You have already solved this problem. Come up with as many tasks as you want”.

Saying this, the experimenter pointed to a sheet with the conditions of the main task No.1 located on the table. Thus, the subjects were asked to come up with tasks of the first degree of complexity, similar to task No.1.

To write down the conditions of the new task, the child was given a separate sheet of paper. To make it easier for the child to come up with a plot basis for the task and it is easier to establish a connection of one or another person with one or another object, he received cards with drawings: some depicted girls and boys who had a different appearance (i.e., dressed differently or doing different things), and others — different kinds of objects found on the street, in the house, at school, etc. These cards could be moved and compared in different ways.

It is important to note that the child is not told how many tasks to complete, but only says: «Think up as many as you want.»

2.1.1. Groups of children

Five groups of children were identified according to the specifics of the task preparation. The children of the first group refused to compose tasks, saying «… I don’t know what to do…», «… I don’t know how…», etc.

The children of the second group acted formally. Their actions were characterized by the following. Sometimes they read problem No. 1 again, and sometimes they did not reread it (recall that the sheet with its conditions was located on the table to the left of the child).

As could be seen (especially when the children read the problem aloud), when reading the marked problem, they did not have a special consideration of its conditions — the problem was simply read as some plot text.

After that, they proposed tasks without first solving them. At the same time, different variants of the formal formulation of tasks were encountered.

First, unsolvable problems. For example, some of the children “composed” such tasks: “Vasya and Kolya ate porridge: someone buckwheat, someone rice. Vasya did not eat semolina. What did Kolya eat? or “Misha and Sergey painted: someone painted planes, someone drew tanks. Misha and Sergey drew different objects. What did Misha draw? As can be seen, in these problems there are no grounds for finding a solution, since the necessary data are not available in their conditions.

Secondly, non-problematic tasks. For example, some of the children suggested a task of this type: “Vova and Galya were picking berries: someone was picking raspberries, someone was strawberries. Vova picked raspberries, Galya picked strawberries. Who collected raspberries? As you can see, the solution process is not assumed here, since the answer to the question of the problem is already given in its condition.

Thirdly, tasks-copies. In these cases, the children suggested (without knowing their solution) correct, problematic, solvable tasks, since they exactly copied the main task No. 1, for example: “Katya and Masha did their homework: someone solved examples, someone wrote words. Katya did not solve the examples. What did Masha do?”

The children of the third group acted meaningfully, since they made up one or two (but not more) correct, solvable problems, since they were first convinced that the problem they proposed had a solution, for example:

1) “Igor and Vanya were playing chess. Someone won 3 times, someone 2 times. Vanya did not win 3 times. How many times has Igor won?”

 2) Marina and Galya drew animals. Someone drew bears, someone hares. Marina did not draw hares. Who did Galya draw?”

The actions of the children of the third group were characterized by the fact that before proposing new tasks, they first turned to the conditions of the main task No. 1: they read the conditions of this task several times, but not in its entirety, but in parts, in separate judgments and sentences. It can be assumed, based on observations of their actions, that they were trying to understand the «arrangement» of this task, to understand how it combines judgments of different types — general and particular.

Children of the fourth group acted productively, since they made up several (three — five) tasks to be solved. However, all tasks were built according to one scheme, one template, for example:

1) “Borya and Kostya were picking mushrooms: someone was picking russula, someone was white. Borya did not collect russula. What did Kostya collect?”

2) “Nina and Liza knitted: someone knitted a scarf, someone knitted a hat. Nina did not knit a scarf. What did Liza knit? ”

3) “Olya and Gena sculpted from plasticine: someone sculpted a hare, someone sculpted bear. Olya did not sculpt a hare. What did Gena sculpt? ”

The generality of the construction of these three tasks is manifested in a number of circumstances: a negative judgment always concerns the first of the actors and the first of the objects mentioned, the question always contains the name of the second actor (and not the first) and always refers to the object, not to the person).

2.2. The second series of experiments

In the second series of experiments (as in the first), the children were allowed to use the cards offered to them with images of children and objects when solving and compiling.

But only those children who were able to solve all the main problems (No. 1, No. 2 and No. 3, of the first, second and third degrees of complexity) were allowed to compose problems, since they were asked to compose problems not of the first (as in the first series), but the second degree of complexity, i.e. tasks with three actors, as in the main task No. 2.

The child was told: “Now you will come up with tasks yourself, where there were three guys who were doing something. You have already solved this problem. Come up with as many tasks as you want. Saying this, the experimenter pointed to the sheet with the conditions of the main task No. 2, located on the table.

Thus, the subjects were asked to come up with tasks of the second degree of complexity, similar to task No. 2. Just as in the first series, the child was given cards with images of children and objects, as well as children’s actions with objects. According to the nature and results of compiling tasks of the second degree of complexity, the children were divided into four groups.0

2.2.1. Groups of children

The first group included two subgroups of children who acted formally when compiling tasks. The first subgroup consisted of children who offered unsolvable problems. In some cases, the tasks lacked an object of comprehension that was missing in the condition, for example: “Petya, Misha and Vasya went in for sports: someone played football, someone played volleyball, someone played basketball. Petya played football, Misha did not play hockey. What did Vasya play?”

As you can see, in the first sentence (general proposition) there is no “hockey”, but in the private negative proposition it is present. In other cases, the tasks contained two negative judgments, for example: “Kolya, Natasha and Igor watched TV: some in the morning, some in the afternoon, some in the evening. Kolya didn’t watch TV in the morning, Natasha didn’t watch TV in the afternoon. When did Igor watch TV?”

The second subgroup consisted of children who offer non-problematic tasks without negative judgments. In this regard, the answer to the problem is contained in its condition, for example: “Vasya, Misha and Liza cut out figures: someone cut out circles, someone squares, someone triangles. Vasya cut out circles, Misha cut out squares, Lisa cut out triangles. What did Vasya cut out?”

The second group included children who act meaningfully when compiling tasks. They offered one or two correctly constructed problems of the second degree of complexity, which they themselves previously (that is, before formulating the final version of the condition) solved, for example: “Katya, Vera and Marina ate porridge. Someone ate rice, someone buckwheat, someone oatmeal. Katya ate rice porridge, Vera did not eat buckwheat. What kind of porridge did Marina have? ”

The third group included children who showed the productivity of the author’s thinking. They offered several (three — five) solvable, well-formed problems, where judgments were selected according to the same scheme, for example:

1) “Vera, Nadya and Galya painted animals: someone a fox, someone a wolf, someone a bear. Vera drew a fox, Nadia did not draw a wolf. Who drew the bear?”

2) “Dima, Oleg and Seva jumped high: someone took first place, someone second, someone third. Dima took first place, Oleg did not take second place. Who took third place? ”

3) “Katya, Masha and Lena embroidered: some with blue threads, some with red, some with green. Katya embroidered with blue thread. Masha did not embroider with red threads. Who embroidered with green threads? ”

The literal similarity of these three tasks is characterized by a number of features.

Firstly, the first of these characters is combined in a judgment with the first of the mentioned items — in the first task: «Vera drew a fox …», in the second task: «Dima took first place …», in the third task: «Katya was embroidered with blue threads … «.

Secondly, the second of the named characters in a negative judgment is combined with the second of the mentioned objects, — in the first task: «Nadya did not draw a wolf …», in the second task: «Oleg did not take second place …», in the third task: «Masha did not embroider with red threads … «.

Thirdly, the question is addressed to the character, not the object — in the first task: “Who drew the bear?”, in the second task: “Who took third place?”, in the third task: “Who embroidered with green threads?”.

Fourthly, the question contains the third of the mentioned “things of thought”, in the first task: “Who drew the bear?”, in the second task: “Who took third place?”, in the third task: “Who embroidered with green threads?”

2.3. The third series of experiments

In the third series of experiments (unlike the first two series), the children were not offered cards with images of characters and objects that were related to these characters according to the plot of the tasks, but they were required to solve and compose tasks only in terms of oral or written speech, without any reliance on drawings and images, that is, in the internal, mental plan.

At the same time (as in the first series), when compiling tasks, the child had the opportunity to refer to the sheet with the conditions of the main task No. 1, placed on the table to the left of the child.

First, the children were offered to solve one training and three main tasks, and then (those who managed to cope with the task of the second degree of complexity — No. 2) were asked to create new tasks of the first degree difficulties. The same groups of children were singled out according to the peculiarities of the task preparation.

2.4. The fourth series of experiments

In the fourth series of experiments (as well as in the third series), the tasks were solved and compiled internally, using oral and written speech. First, the children solved the training and main tasks, then (those children who were able to solve all the main tasks — the successful solution of task No. 3 was of fundamental importance here) were asked to compose tasks of the second degree of complexity (i.e. tasks with three characters and three objects).

At the same time (as in the second series), when compiling tasks, the child had the opportunity to refer to the sheet with the conditions of the main task No. 2, placed on the table to the left of the child.

The same groups of children were singled out according to the peculiarities of the composition of tasks (the fourth group, just as in the second and third series, included only fifth-graders who acted in an original way) and with the same characteristics of the tasks they proposed as in the second series (see above). ).

3. Results

            The tables show the number of students who formally, meaningfully and productively compiled logical problems in each of the four series of experiments.

Table 1

The results of the second-graders compiling plot-logical tasks in a formal, meaningful and productive way (in %)

Table 2

The results of the third-graders compiling plot-logical tasks in a formal, meaningful and productive way (in %)

Analysis of the data in tables 1 and 2 allows us to formulate a number of provisions.

First, in each class, the number of children who make up unsolvable tasks (i.e., acting formally) and solving tasks (i.e., acting meaningfully and productively) directly depends on the degree of their complexity. Thus, in the first and third series, the tasks consisted of a larger number of children than, respectively, in the second and fourth, although in the first-second and third-fourth series, the tasks were compiled under the same conditions (recall that in the first and third series there were tasks of the first degree of complexity, and in the second and fourth — of the second degree of complexity).

Secondly, in each class, the number of children who make up unsolvable and solvable problems directly depends on the conditions for compiling: externally or internally. So, in the first and second series, the tasks to be solved were more children than, respectively, in the third and fourth, although in the compared series the tasks were of the same degree of complexity — the first (in the first and third series) or the second (in the second and the fourth series), we recall that in the first and second series the tasks were compiled with the help of cards, and in the third and fourth — orally or in writing, but without cards.

Thirdly, it is of interest that the form of actions in the preparation of tasks to a greater extent affects the success of the author’s thinking, than their degree of difficulty. So, in each class, the total number of children who compose tasks meaningfully and productively in the second series (i.e., using cards, but of the second degree of complexity) is greater than the number of children compiling tasks meaningfully and productively in the third series (i.e. without cards, but the first degree of difficulty).

4.Conclusion

So, the conducted research confirmed his initial hypothesis: indeed, in the third grade there are fewer children who act formally when compiling tasks, and more children who prefer to use productive and meaningful ways.

The results obtained should be considered in the context of the design features of the experiments.

First, the experiments were carried out individually.

Secondly, only one type of plot-logical tasks was used — «Negation». The peculiarity of these tasks is due to the fact that when solving and compiling them, it is necessary to compare affirmative and negative judgments. This creates certain difficulties for children’s actions when comparing these tasks with tasks of the «Who has what» type. In the latter, only affirmative judgments are offered, for example: “Petya and Vasya bought school supplies. Someone bought pencils, someone bought pens. Vasya bought pens. What did Peter buy?”

Thirdly, the experiment included four series, differing in the conditions in which the children were asked to act: in the first series, tasks of the first degree of complexity were solved and compiled in the external plan, in the second — tasks of the second degree of complexity in the external plan, in the third — tasks of the first degree complexity in the internal plan, in the fourth — tasks of the second degree of complexity in the internal plan. This experimental design allowed to identify the relationship between the success of drawing up tasks with their complexity and the nature of actions (in the external or internal plan).

In general, it can be said, based on the data obtained in the study, that, in relation to plot-logical tasks, teaching children in the second and third grades is a period of relatively intensive formation, mainly of a meaningful way of composing tasks, their proactive production. The productive method during this period is formed less intensively, since in the second grade this method was implemented only when compiling problems in the first and second series (that is, when compiling problems only on the external plane). In the third grade, although this method was observed when compiling tasks in the third and fourth series, it was only in a few percent of the children.

In the future, it is planned to conduct a study of the features of compiling plot-logical problems with both first-grade and fourth-grade students. In this case, sufficient conditions will be created in order to characterize the age-related dynamics of mastering meaningful and productive ways of producing tasks in the primary grades as a whole.