1. Introduction.

In recent decades, the number of various messages in the media has been constantly increasing. The current situation requires the functioning of critical thinking to analyze the degree of objectivity of the statements contained in these messages. Such an analysis is associated with the implementation of logical actions aimed at analyzing these statements and correlating them according to the rules of logic. With the help of such actions, a person has the opportunity to substantiate or refute the proposed statements.

If the noted analysis ends with a correct conclusion, then critical thinking is characterized as evidential [11], since it is realized as scientific thinking based on understanding the essence of the matter, on identifying patterns of change in the objects under consideration [13].

If the analysis ends with an incorrect conclusion, then critical thinking is characterized as unsubstantiated [10], since it is realized as everyday, everyday thinking based on inaccurate, random and superficial information about the objects under consideration [9].

The need for an experimental examination of critical thinking in primary school students is based on the need for constant updating and deepening of curricula in middle school, especially in the natural sciences [17].

Mastering the basic principles and provisions of the noted disciplines involves, in particular, an analysis of approaches to achieving the desired result in matters of qualitative focus. In this case, the proposed special cases are considered in order to justify the legitimacy of using general patterns to the identified special cases. Correlating the individual and the general in order to draw a conclusion about the individual, the particular, based on the general, is one of the fundamental functions of critical thinking.

1.1. Research into the potential of critical thinking in primary school. students.

Evidence-based critical thinking is studied by psychologists in various contexts [7].

Thus, in one direction of research, the importance of improving critical thinking was discussed. In particular, the possibility of planning critical thinking training using appropriate educational materials was considered [19], it was indicated that in order to improve the critical thinking of primary school students, the teacher should encourage them to reason [22], it was emphasized that the ability of critical thinking in primary school students affects their success in the future and that the basis for improving critical thinking is the creative method [21].

In another direction, researchers studied the features of the conditions for improving critical thinking when mastering educational materials related to language. The first study considers a three-stage approach to the development of critical thinking based on linguistic realities [8], the second study considers CLIL as a condition for improving critical thinking in language learning [12], and the third study analyzes the possibilities of foreign language lessons for developing critical thinking skills in the 4th grade [23].

The third direction studied the possibilities of developing critical thinking using the material of academic disciplines not related to language. In one study, examining the features of studying fractions in the 4th grade mathematics course showed that students could not make the correct conclusion and give a reasoned explanation of the ways to achieve the required result in the proposed tasks [17], in another study, the problems of improving students’ critical thinking are solved by using ICT in biology lessons when studying topics related to health [16], the third study analyzes the conditions for developing critical thinking when studying the school subject «Technology» [24], and the fourth study solves the problems of developing critical thinking when studying problems of morality and ethics [16].

The fourth direction studied the influence of the content of various types of teaching aids on the development of critical thinking. One study analyzed science textbooks for primary schools and showed that these textbooks do not have the conditions for improving a number of critical thinking skills [14], another study examined how children analyze information provided in word problems in mathematics [25], and a third study, when working with third-graders, found that a planned choice of the studied content contributes to the development of critical thinking [15].

1.2. Brief summary of the work.

As shown by the consideration of the content of the presented works, the researchers analyze the conditions for the functioning of critical thinking activity, mainly on school material.

Our preliminary group experiments demonstrated the possibility of studying critical thinking activity on extracurricular material of an entertaining nature. In these experimental classes, failing students were more confident, active and successful than in the framework of educational activities. It can be assumed that this fact is due to the fact that the use of academic knowledge was not required to achieve success on extracurricular material.

Our work is aimed at analyzing the conditions for the development of critical thinking activity in primary school students when solving extracurricular problems. In doing so, we relied on the activity-based approach proposed in Russian psychology by S. L. Rubinstein [6], A. N. Leontiev [4], V. V. Davydov [2].

The fundamental principle of the activity-based approach states that in order to improve an action, it must be part of the activity for the implementation of which its implementation is required. Based on this principle, we believe that the construction of reasoning for the implementation of a consistent conclusion is the type of thinking activity that requires the implementation of critical thinking actions.

This experimental work was aimed at identifying the possibilities of improving evidential critical thinking in third-graders. We assumed that school classes and a series of extracurricular additional classes developed by us under the conditional name «Derivation 1» to a greater extent ensure the formation of evidential thinking activity of a critical orientation than school classes alone. In making this assumption, we relied on the results of the above-mentioned preliminary experiments.

The study in question included three stages. The first stage (the initial period of the school year, September) was a group diagnostics of the level of development of critical thinking in schoolchildren of the control group (59 people) and the experimental (research) group (62 people). The children were offered a series of tasks based on the transitivity of a binary relation. The second stage (during the school year, from September to May), the 62 students took part in 30 extracurricular additional classes of the «Derivation — 1» series. The third stage (the end of the school year), children from both groups again took part in group diagnostics.

2.2. Materials and methods.

2.1. Characteristics of the classes that make up the «Derivation 1» series.

The «Derivation 1» series of classes was developed to organize 30 additional lessons with 10 types of original logical problems based on plots of an extracurricular nature.

 The entire series of 30 additional lessons is divided into three periods: No. 1 – 10, No. 11 – 20, No. 21 – 30. In the first period, thinking activity is associated with choosing a solution from the given options, in the lessons of the second period (No. 11 – 20) – with choosing a question, in the lessons of the third period (No. 21 – 30) – with choosing the missing fragment of the problem conditions. Thus, the noted diversity of thinking activity allows students to create favorable conditions for improving critical thinking.

In lessons №№1, 11 and 21, students work on problems like “Who did what?”, in particular: “Anton, Kolya and Oleg wrote stories: someone about traveling, someone about sports, someone about animals. Kolya did not write about sports, but Anton wrote about animals. Who wrote stories about sports?”

In lessons №№2, 12 and 22, students work on problems like “Earlier, later”, in particular: “Alla and Vera were drawing birds. They started working at the same time and drew at the same speed. Alla drew more birds than Vera. Did Alla or Vera finish drawing earlier?”

In lessons №№3, 13, 23, the following tasks are worked on: “Similarities, differences”, in particular: “Fedya, Vasya, Yura received parcels: two boys from Tula, one from Ufa. Vasya received a parcel from Ufa. Where did Fedya receive the parcel from?” I

In lessons №№4, 14, 24, the following tasks are worked on: “Coincidences”, in particular: “On the wall of the house in different places – at the top, in the middle and at the bottom – the names of friends are indicated: TOLYA, VASYA, TANYA. The second letter of two names – at the top and in the middle – matches, the first letter of the names located in the middle of the wall and at the bottom matches. Which name is indicated in the middle of the wall?”

In lessons №№5, 15, 25, the following tasks are worked on: “Just like…”, in particular: “Vova and Dima were playing with cubes that had numbers on them. Vova got the number 451 from three cubes. After rearranging them, he got the number 154. Dima got the number 238 and then swapped them like Vova. What number did Dima get?”

In lessons №№6, 16, 26, the tasks of the “Combination” type are worked on, in particular: “Lyuda, Valya and Zina brought a doll each. One doll was in a white dress with long sleeves, another in a white dress with short sleeves, and the third in a green dress with long sleeves. The color of the dresses of Lyuda and Valya’s dolls matched, and the length of the sleeves of Valya and Zina’s dolls matched. Whose doll is wearing a white dress with long sleeves?”

In lessons №№7, 17, 27, the tasks of the “Older, younger” type are worked on, in particular: “Vitya and Oleg are cousins. When many years have passed, Vitya will be several years older than Oleg is now. Is Vitya younger than Oleg or is Oleg younger than Vitya?

In lessons №№8, 18, 28, the following tasks are worked on: «Closer, higher», in particular: «Two names were written with yellow and green markers:

KATYA

MASHA

The green name is below the yellow one. Is the name MASHA green or yellow?»

In lessons №№9, 19, 29, the following tasks are worked on: «Slower, faster», in particular: «Vova and Gena are tourists and set off on a hike at the same time: Vova from Tula to Ufa, Gena from Ufa to Tula. Three days later, Vova was closer to Tula than Gena was to Ufa. Which tourist walked faster?»

In lessons №№10, 20, 30, the following problems of the “Either one or the other” type are worked on, in particular: “The dogs – a bulldog, a shepherd, a greyhound – were in the garden: by the pond, by the barn, by the fence. First, they trained either the shepherd or the dog by the pond, then – either the dog by the pond, or the greyhound. Was the bulldog by the pond, by the fence, or by the barn?”

When solving problems in the 1st period, it was suggested to choose an answer from the given options. For example, the problem “Who did what?”: “Anton, Kolya, and Yura were making up stories: someone about traveling, someone about sports, someone about animals. Kolya did not make up stories about sports, but Anton made up stories about animals. Who made up stories about sports?” Solutions: 1) Anton, 2) Kolya, 3) It is not clear who, 4) Yura.

When solving problems in the 2nd period, it was proposed to choose a question from the given options, in particular, in such a problem: «Anna and Varya were drawing birds. They started working at the same time and drew at the same speed. Anna drew more birds than Varya.» Which question is suitable for this problem: 1) «What birds were required to be drawn?» 2) «How many drawings were needed?» 3) Which of the girls finished drawing earlier?» 4) «At what time did the girls start drawing?»

When solving problems in the 3rd period, it was proposed to choose the missing fragment from the given options, in particular, in such a problem of the «Similarity, Difference» type: «Fedya, Vasya and Yura received parcels: two boys — from Tula, one — from Ufa. Vasya received a parcel from Ufa. Where did Fedya receive the parcel from?» What knowledge is missing to answer: 1) Yura received a parcel from Tula. 2) Vasya received a parcel from Tula. 3) Yura received a parcel from Ufa. 4) Vasya did not receive a parcel from Ufa.

In each lesson, children were given twelve similar problems, distinguished by important features. In the conditions and questions from the first to the fourth problems, affirmative formulations of judgments were used. In problems from the fifth to the eighth, the conditions contained affirmative formulations, and the questions contained negative formulations. In problems from the ninth to the twelfth, the conditions contained negative formulations, and the questions contained affirmative formulations.

To ensure variety of thinking activities, the first and second, fifth and sixth, ninth and tenth problems required finding an answer, while the third and fourth, seventh and eighth, eleventh and twelfth required evaluating the solution found. In any lesson, problems 1, 2, 3, 4 are the least complex (find a conclusion from 2 judgments), 5–8 and 9–12 are more complex, with three and four judgments, respectively. It is important to note that lessons 1–10 are associated with choosing a solution: one of them was formulated negatively, for example, as follows: “The problem question cannot be answered” or “It is not clear who”, “It is not clear what”. At the same time, for some problems, the negative solution was correct, for others, it was incorrect.

2.2. Organization of additional lessons.

Each lesson according to the “Derivation 1” program is conducted in three stages. In the first (15 minutes), the teacher and children consider the features of solving a problem of the type that corresponds to this lesson. Schoolchildren need to know what to look for in the problems of the proposed type and how to do it. Children are introduced to the techniques of analyzing the content of problems and the possibilities of monitoring and evaluating their actions.

At the second stage (30 minutes), schoolchildren solve 12 problems as part of independent work. In this case, the knowledge gained in the first stage is used.

At the third stage (15 minutes), the teacher and schoolchildren evaluate the results of independent work, paying special attention to incorrect solutions. In this case, the teacher again shows how to analyze problems and how to control their own actions.

2.3. Determining the development of critical thinking.

Before the start of 30 additional lessons (in September) and upon their completion (in May), a group lesson was held to determine the development of critical thinking. The subjects of the control and experimental groups solved logical problems included in the author’s assignment «Relativity» related to the use of the property of transitivity of a binary relation: A> B, B> C, therefore, A> C.

Each schoolchild received a form with 12 logical problems.

FORM

1.Kolya is more confident than Galya. Galya is more confident than Alla. Who is the most confident?

2. Vitya is weaker than Kolya. Kolya is weaker than Dima. Who is the strongest?
3. Igor is more successful than Oleg. Igor is less successful than Sasha. Who is the most successful?
4. Nadya has more books than Valya. Nadya has fewer books than Olya. Who has the fewest books?
5. Lida is bigger than Galya. Galya is bigger than Olya. Who is the biggest?
6. Vitya is bigger than Misha. Miga is bigger than Vova. Who is the biggest?
7. A goat is lighter than an ant. A goat is heavier than a giraffe. Who is the lightest?
8. A dog is smaller than a fly. A dog is bigger than a cow. Who is the biggest?
9. Egorov is 5 years older than Bokov. Egorov is 68 years younger than Kotov. Who is the youngest?
10. Katya was driving a little faster than Anya. Katya was driving much slower than Varya. Who was driving the slowest?
11. Galya listens to music more often than Nadya and draws animals better than Vika. Galya listens to music less often than Vika and draws animals worse than Nadya. Who listens to music the least? Who draws animals the worst?
12. Egor jumps higher than Kolya and swims further than Vova. Egor jumps lower than Vova and swims closer to Kolya. Who jumps the highest? Who swims the farthest?

* * *

After handing out the forms, the students were told: “There are 12 problems printed on each sheet. Problems 1, 2, 3 and 4 are the easiest. You should read them, think about the solution and find the answer. In it you need to indicate the name of the one who is the most confident, the strongest, the most successful and who has the fewest books.

Problems 5 and 6 contain artificial words that replace such well-known words as higher, smarter, braver. When solving these problems, you need to mentally substitute well-known words for the artificial words.

Problems 7 and 8 are fairy tales. They say something unusual about well-known animals. To solve these problems correctly, you need to take into account only what is written in the conditions.

Problems 11 and 12 require answering two questions.

Be attentive and independent when solving the problems.»

The 12 logical problems placed on the Form differ in the number of judgments contained in their conditions. To solve problems 1–4, two judgments are analyzed and compared. To solve problems 5–10, you also need to consider two judgments. However, unlike problems 1–4, problems 5–10 contain additional data that should be ignored when searching for a solution. Problems 11 and 12 are significantly more difficult than the previous ones, since their solution requires analyzing and correlating four judgments.

The noted characteristics of the 12 problems allow us to classify problems 1–4 as the first level of complexity, problems 5–10 as the second level, and problems 11–12 as the third level of complexity.

3. Results.

Table. The number of students in the control (C) and experimental (E) groups (proportional to the total number of students in each group) who correctly solved problems 1–4, 5–10, 11, and 12 of the “Relativity” assignment in September and May (in %).

Note: *p<0.05; ** p<0.01.

The table data show that in each group in May, compared to September, there were more students who correctly solved problems of each of the three difficulty levels.

First, the success rate of actions in relation to problems of the first difficulty level in the control group increased by 6.7% (from 79.7% to 86.4%), and in the experimental group the increase was more noticeable – by 14.5% (from 77.4% to 91.9%).

The latter indicator shows that in the experimental group almost all students coped with problems of the first difficulty level as a result of a year of classes according to the “Derivation 1” program.

Second, the success rate of actions in relation to problems of the second difficulty level in the control group increased by 20.3% (from 40.7% to 61.0%), in the experimental group the increase was much more significant: by 43.5% (from 37.1% to 80.6%). An important fact is that the difference in the success rates of actions in relation to problems of the second complexity level in the control and experimental groups — 61.0% and 80.6% — is statistically significant (at p < 0.01).

Thirdly, the success rate of actions in relation to problems of the third complexity level in the control group increased by 5.1% (from 1.7% to 6.8%), in the experimental group the increase was significantly more significant (more than three times): by 17.8% (from 1.6% to 19.4%). An important fact is that the difference in the success rates of actions in relation to problems of the third complexity level in the control and experimental groups — 6.8% and 19.4% — is statistically significant (at p < 0.05).

Thus, the noted increase in the success of solving problems of three levels of complexity in the experimental group indicate a significant influence of mastering the content of additional lessons on the material of the tasks «Derivation 1» in unity with mastering the content of school lessons on the success of children’s actions in relation to the problems of the «Relativity» methodology, which are solved using the property of transitivity of a binary relation.

In general, the considered data of the experimental work indicate the peculiarities of improving evidential critical thinking in third-graders throughout the school year. The results characterizing the increase in the success of actions in relation to the tasks of the «Relativity» task in May (relative to September) show that some lessons of educational content make a significantly smaller contribution to the improvement of evidential critical thinking than lessons of educational content in unity with lessons of non-educational content of the «Derivation 1» program.

The conducted research confirms the initial hypothesis that lessons on the program «Derivation 1», related to solving 10 types of original logical problems, built on plots not related to the educational content, really contribute to the improvement of critical thinking in third-graders.

4. Discussion.

4.1. Experimental conditions.

The results of the study are related to the characteristics of the logical problems included in the program «Derivation 1». In particular, students need to solve ten types of problems. In this case, any type of problem is offered in structural versions related to finding a solution, choosing a question from the given options, choosing a part of the condition from the proposed options. In addition, students complete tasks not only to find a solution, but also to check it.

At the same time, as part of independent work, students solve problems of varying complexity, using affirmative and negative statements, as well as problems where the correct answer is: «The problem has no solution.» The characteristics of additional lessons are also of great importance for the results of the study. Thus, over the course of 9 months (from September to May), children mastered the material of 30 lessons (one per week). Each lesson included three periods: preliminary discussion (approximately 15 minutes); independent work (approximately 30 minutes); final discussion (approximately 15 minutes).

4.2. Scientific significance of the study.

The study allowed us to obtain new knowledge about the conditions for improving critical thinking in third-graders. This knowledge expands and clarifies the ideas of developmental and educational psychology about the possibilities of developing children’s mental abilities during primary school education.

The results of our study serve as an additional argument in favor of the position of L. S. Vygotsky [1] in his polemics with J. Piaget [5]. Considering the problem of the relationship between learning and development, L. S. Vygotsky argued: «… Only that learning in childhood is good that runs ahead of development and leads development behind itself…»

Our study shows that learning with the help of a teacher (i.e., within the zone of proximal development) contributes to a significantly more intensive (in relation to the control group) improvement of critical thinking actions.

4.3. Limitations of the study.

The data obtained in the work should be considered taking into account a number of limitations, one of which is related to the composition of children in the control and experimental groups.

Thus, the results of children’s actions in relation to the logical problems of the «Relativity» task in September were expressed in the fact that 40.7% of students in the control group coped with the problems of the second level of complexity, and 37.1% in the experimental group. If not so many students in both groups solved these problems, for example, 20% or 15% in groups, then the success of additional lessons would be much less.

Another limitation is related to the composition of teachers. The experience of teaching in elementary grades of teachers in the control and experimental groups was, on average, 15 — 20 years. If additional lessons were conducted by teachers with less experience, for example, 3 — 5 years, then the improvement of critical thinking of students in the experimental group would be less effective.

4.4. Problems of further research.

The results of the work carried out allowed us to formulate a number of problems for further study.

It is planned to carry out similar work with fourth-graders for a more complete and more accurate characterization of the influence of the «Derivation 1» program on the improvement of critical thinking in younger students.

It is necessary to determine the optimal composition of logical problems included in the program «Derivation 1» for schoolchildren of different ages: 10 — 12 years.

It is necessary to characterize the effectiveness of independently composing logical problems for the formation of critical thinking.

5. Conclusions.

The study examined the conditions for improving critical thinking in third-graders. It was found that as a result of mastering the content of school lessons in unity with mastering the content of the program «Derivation 1», the improvement of evidential critical thinking occurs significantly more intensively than as a result of mastering the content of school lessons alone.