1.Introduction

The new Federal State Educational Standard of Primary General Education   [8 ] formulates the requirements for modern education in elementary school. According to these requirements, training in the basic educational program (BEP) should ensure the achievement of meta-subject educational results. In this case, children will have the opportunity to critically evaluate a variety of information and make informed judgments.

Of particular importance for the creation of such opportunities is the development by children of cognitive universal actions, in particular, the logical actions of constructing reasoning. These actions, according to the ideas of a number researchers, are a fundamental characteristic of critical thinking [10 ],  [9 ], [7 ], [ 6]. At the same time, scientists believe that critical thinking is associated with reflection.

Considering the features of critical thinking and reflection, it is important to note the following.

First, relying on the provisions of dialectical logic about rational and rational cognition, we accepted that critical thinking as a cognitive process associated with the substantiation of statements that characterize, in particular, the solution of a problem, can be based on essential relations in its content and on non-essential ones. In the first case, critical thinking is connected, therefore, with the substantiation of statements on the basis of a meaningful analysis of the conditions of the problem, in the second case, on the basis of their formal analysis.

Secondly, based on the works of V.V. Davydov [ 1] and his collaborators            [ 2], [5 ] reflection as a cognitive process aimed at analyzing a person’s own actions when solving problems can be associated with the necessary characteristics of the conditions for performing actions and with random characteristics. In the first case, reflection will be internal, in the second — external.

2.Materials and methods.

2.1. Brief summary of the study

The purpose of the study is to characterize the connection between the formation of reflection (as the development of internal reflection by children) and the development of critical thinking (as the transition from its formal level to the content one). The study involved 111 third-graders (62 — the control group, 49 — the experimental group, which was engaged in the «Intellectika Plus» program in 18 classes from January to May.

It should be noted that the program «Intellectika plus» is a modification of the program «Intellectika» for grade 3 [3, 4  ].

The noted modification of the program » Intellectika » is associated with the inclusion of tasks in the lesson material, in solving which the child needs to change the activity position (i.e., the position of the person solving the problem) to the reflexive position (i.e., the position of the person checking the solution of the problem).

The research hypothesis is that the formation of internal reflection in the classes under the program «Intellectika Plus» contributes to the development of critical thinking as a transition from its formal level to the content one.

The study included three stages. Stage 1 (January): students of both groups solve diagnostic tasks to determine the type of reflection and the level of formation of critical thinking. Stage 2 (January — May): the experimental group masters the         «Intellectika Plus» program in 18 extracurricular activities. Stage 3 (May): re-diagnosis of reflection and critical thinking.

2.2. Features of the “Intellectika Plus” program

It is important to note the originality of the problematic material of the program «Intellectika Plus» and features of group classes.

The program is based on the material of search tasks of non-educational content of four types: plot-logical, comparative, spatial-combinatorial, route. In each genus contains six types of tasks. Problems of each type are proposed to be solved in several structural variants: a problem with a complete condition and a question (“find an answer”), with an incomplete condition and a question (“find a part of the condition”), with a complete condition and without a question (“find a question”).

The “Intellectika Plus” program is designed for 18 classes. At each lesson, one of 18 types of problems of non-educational content was solved: 6 types of logical problems (for the formation of actions related to reasoning), 6 types of spatial problems (for the formation of actions necessary to combine judgments in the process of deploying critical thinking), 6 types of route problems associated with the movement of imaginary characters around the playing field based on the proposed rules (for the formation of actions for planning a sequence of judgments, substantiation or refutation as forms of critical thinking). Within each lesson, students were asked to solve only one type of problem.

2.3. Problems of a logical nature

The six types of logical problems have a number of characteristic features.

No. 1, for example: “Gena, Oleg and Dima ran across the field. Gena ran slower than Oleg. Oleg ran slower than Dima. Which boy ran the slowest?”

No. 2, for example: “The names Misha, Masha and Pasha were written in red, yellow and black pencils. The red and black names have the same 1st letter, while the black and yellow names have the same 2nd letter. Whose name was written in yellow pencil?”

No. 3, for example: “Egor and Vasya differed in age. When many years pass, Yegor will be several years older than Vasya is now. Which of the guys is younger?”

No. 4, for example: “Fedya, Alik and Tolya sent telegrams: two to                      St. Petersburg, one to Samara. Fedya and Alik, Alik and Tolya sent telegrams to different cities. To which city did Fedya send the telegram?”

No. 5, for example: “Three geometric shapes were drawn with pink, purple and brown paint: a square, an oval, a rhombus. The pink shape is drawn on the forest side of purple, and the brown shape is drawn on the right side of purple. What color is the oval drawn in?”

No. 6, for example: “Dasha and Nina played cubes with letters on them. The first to play was Dasha, who folded the BAG, and then rearranged the cubes and it turned out GAB. Nina folded the MAP, and then rearranged the cubes following Dasha’s example. What happened to Nina?”

2.4. Spatial issues

Six types of spatial problems have this content.

Type 1, for example: “What is possible to change the order of numbers                  | 4 |    | 8 | using two actions to become such an order | 8 | 4 |    |?”

Rule: one action is to move some number to an unoccupied place.

Answer: (1) | 4 |   | 8 | — |   |4 | 8 | (2) |   | 4 | 8 | —| 8 |4 |   |.

Type 2, for example: “What is possible to change the order of numbers                        | 5 | 5 | 7 |  | with the help of two actions to become such an order of letters                           | G | K |  | K | ?”

Rule: 1) one action is to move some number to an unoccupied place; 2) you need identical numbers to be in the same places where there are identical letters.

Answer: | 5 | 5 | 7 |    | — |   | 5 | 7 | 5 | — | 7 | 5 |   |5 |.

Type 3, for example: “What is possible to change the order of numbers                  | 8 |   | 4 |   | 2 | using two actions to become such an order |    | 8 | 4 | 2 |   |?”

Rule: one action is to move some number to an unoccupied place.

Answer: (1). | 8 |   | 4 |   | 2 | — | 8 |   | 4 |   | 2 |   | (2). |   | 8 | 4 |   | 2 |   | —             |   | 8 | 4 | 2 |   |.

Type 4, for example: “What is possible to change the order of numbers                  | 2 | 2 |   |4 |   | with the help of two actions to become such an order of letters                      |   |   | C | D |   | C |?”

Rule: 1) one action is to move some number to an unoccupied place; 2) you need identical numbers to be in the same places where there are identical letters.

Answer: | 2 | 2 |   |4 |   | — |   | 2 |   | 4 | 2 | — |   |   | 2 |4 | 2 |.

Type 5, for example: “What is the possibility of changing the order of the numbers: 9 2 5 using two actions to become the order 5 9 2?”

Rule: for one action, a simultaneous permutation of any two digits is taken.

Answer: 9 2 5 — 5 2 9 — 5 9 2.

Type 6, for example: “What is the possibility of changing the order of the numbers 7 7 5 3 with the help of two actions so that the letters become I K M M ?”

Answer: 7 7 5 3 — 3 7 5 7 — 3 5 7 7.

2.5. Route problems

Six types of problems that involve movements of fictional game participants on the playing field based on conditional rules are characterized by the following content.

                     1          2         3             4          5

                     6          7         8             9         10

                          11        12       13         14        15

                          16         17        18        19        20

                          21         22        23        24       25

                                    Fig. Field for the game.

Type 1, for example: «What 2 steps did the ant take from 11 to 18?»

Rules: 1) «Ant», — the first invented participant in the game «Moving by the rules», — moves by numbers; 2) the characteristics of his movements: (a) he walks straight, i.e. to the neighboring number vertically (for example: from the number 13 to the number 8 or 18) or horizontally (for example: from 13 to 14 or 12); b) walks obliquely, i.e. diagonally (for example, from 13 to 7, or 9, or 19, or 17); 3) the ant cannot take two identical steps (two straight steps or two oblique steps) in a row.

Solution: 11 — 12 — 18.

Type 2, for example: «What two jumps did the grasshopper make to get from 11 to 5?»

Rules: 1) «Grasshopper», — the second invented participant in the game, — moves through the numbers; 2) characteristics of his movements: (a) he jumps straight, i.e. over a number vertically (for example: from 13 to 3 or to 23) or horizontally (for example: from 13 to 11 or 15); b) jumps obliquely, i.e. diagonally, for example: from 13 to 5 or 1, or 21, or 25; 3) a grasshopper cannot make two identical jumps (two straight or two oblique) in a row.

Solution: 11 — 13 — 5.

Type 3, for example: «What two moves must an ant and a grasshopper make to get from 7 to 20?»

Rules: 1) the ant and the grasshopper move in turn, 2) the ant only steps straight, 3) the grasshopper only jumps obliquely — for example: ant: 12 — 7, grasshopper: 7 — 19, ant: 19 — 18, grasshopper: 18 — 10.

Solution: 7 — 8 — 20.

Type 4, for example: «What two moves must an ant and a grasshopper make to get from 8 to 19?»

Rules: 1) the ant and the grasshopper move in turn, 2) the ant steps only obliquely, 3) the grasshopper only jumps straight, for example: ant: 8 — 14, grasshopper: 14 — 4 ant: 4 — 10, grasshopper: 10 — 20.

Solution: 8–7–19.

Type 5, for example: «What three moves must an ant and a grasshopper make to get from 20 to 3?»

Rules: 1) the ant and the grasshopper move in turn, 2) the ant steps straight or obliquely, 3) the grasshopper jumps straight or obliquely, for example: ant: 7 — 12, grasshopper: 12 — 14, ant: 14 — 18.

Solution: 20–19–7–3.

Type 6, for example: «What are the three moves that a grasshopper and an ant must make to get from 2 to 25?»

Rules: 1) the grasshopper and the ant take turns walking, 2) the grasshopper jumps straight or obliquely, 3) the ant steps straight or obliquely, for example: grasshopper: 17 — 9, ant: 9 — 10, grasshopper: 10 — 20.

Solution: 2-12-13-25.

2.6. Features of classes under the program «Intellectika Plus»

Each lesson in the program consists of three parts. In the first part, the teacher, together with the students, analyzes the solution of the sample problem, i.e. tasks typical of the type that is mastered in this lesson. Such a discussion is necessary so that children understand what needs to be found in problems of this type and how this can be done. Children are given the means of analyzing problems and ways to manage the search for a solution and control their actions (this contributes to the development of internal reflection of actions to solve a problem).

 In the second part, children independently solve 12-15 tasks of this type. Here, favorable conditions are created for the use of tools for analyzing the conditions of the problem and methods for finding a solution presented in the first part.

In the third part, the teacher and students check the solved problems. Wrong decisions and their reasons are analyzed, which is useful for all children, both for those who made a mistake and for those who decided correctly: the methods of analyzing conditions and analyzing problem solving are once again explained to children. This creates favorable conditions for children to master cognitive actions of various kinds and internal reflection of actions to solve problems.

2.7. Diagnostics of reflection and critical thinking

Before and after 18 sessions with children from both groups, a group diagnostic session was conducted on the material of two tasks: “Exchanges” and “Conclusions.

2.7.1. Task «Exchanges»

This task is intended to determine the type of reflection in solving problems. The construction of this task was based on the above-mentioned provisions on two types of reflection. In accordance with these provisions, we have developed a two-part experimental situation [2  ].

In its first part, it was proposed to solve three problems of two classes (the first and third problems were constructed and solved on the basis of one principle, the second problem — on the basis of another principle). In the second part, with the correct solution of all problems, it was proposed to group them.

If the grouping was based on random characteristics of the conditions of action in solving problems, then it was assumed that in this case external reflection was carried out. If their necessary characteristics (a single principle of their construction and solution) were taken as the basis of the grouping, then this testified to the implementation of internal reflection.

The task «Exchanges» includes tasks in which it is required, according to certain rules, to change places of letters.

Explaining the characteristics of the tasks of the «Exchanges» task, the teacher said: «Let’s consider a task in two actions, where you need to convert the arrangement of letters P L B in two actions to the arrangement B P L. One action is the exchange of places of any two letters.»

After discussing with the children possible approaches to getting an answer, the teacher writes down the solution to this problem on the board:1) B L P, 2) B L P and explains: “The letters P and B are reversed with the first action, the letters L and P with the second action.”

After the teacher’s explanations, it is proposed to solve two training and three main tasks in two actions.

Training tasks

1. D V F — V F D
2.         R N K — K R N

Main goals

1) W G L M — G W M L

2) R S P H — P C R S

3) W T F B — T W B F

                                                        *   *   *

Next, you had to choose one of five opinions about these tasks:

1) all the main tasks are similar;

2) all the main tasks are different;

3) the main tasks 1 and 2 are similar, but the 3rd differs from them;

4) the main tasks of the 1st and 3rd are similar, and the 2nd differs from them;

5) the main tasks 2 and 3 are similar, but the 1st is different from them.

Then it was required to briefly explain the reasons for the choice.

2.7.2. Task «Conclusions»

The task «Conclusions» is intended to determine the level of formation of critical thinking. The task includes logical tasks constructed in different ways.

In some tasks, the question «Who …?» The correct answer is the name of one of the characters in the story. For example: “Alik, Borya and Vova solved examples: someone for addition, someone for subtraction, someone for multiplication. Alik solved addition problems. Borya didn’t solve multiplication problems. Who solved the examples for subtraction?” Answer: Borya.

In other problems, the correct answer is a statement characterizing the absence of a solution. For example: “Alik, Borya and Vova solved examples: someone for addition, someone for subtraction, someone for multiplication. Alik did not solve addition problems. Borya didn’t solve multiplication problems. Who solved the examples for subtraction?” Answer: the problem has no solution.

In each problem, you need to choose an answer from several proposed ones, among which there are correct and incorrect ones. The “Conclusions” task included 8 tasks, in half of which the correct answer is “the task has no solution”. If the student solved correctly all the tasks of the “Conclusions” task, then this testified to the formation (in relation to these tasks) of the meaningful level of critical thinking. If not all tasks were solved correctly, especially those where it is impossible to find out the name of the character of the plot, then this testified to the lack of formation (in relation to these tasks) of the meaningful level of critical thinking and the manifestation of its formal level.

3. Results.

The results of the students’ tasks «Exchanges» and «Conclusions» are presented in the table.

Table

The number of children in the control and experimental groups who successfully solved the tasks of the tasks «Exchanges» and «Conclusions» in January and May (in %).

Note: * p < 0.05.

The data given in the table make it possible to note the following.

First, among the subjects of the control and experimental groups, according to the results of completing the “Exchanges” task in January, there were, respectively, 11.3% and 10.2% of children who performed internal reflection when solving problems, in May — respectively: 19.4% and 38.8% (the difference between these results is statistically significant: at p < 0.05).

Secondly, among the subjects of the control and experimental groups, according to the results of solving the task “Conclusions”, in January there were, respectively, 20.9% and 20.4% of children who showed a meaningful level of critical thinking when solving problems, in May — respectively: 29.0% and 48.9% (the difference between these results is statistically significant: at p < 0.05).

Thirdly, a comparison of the results of performing both tasks in the control and experimental groups indicates that the proportion of children with internal reflection among children with a meaningful level of critical thinking has increased: in January, respectively: 53.8% and 50.0%, in May: 66.7% and 75.0%.

4. Conclusion.

4.1. Experiment conditions

It should be noted that the result obtained in the study is due to the peculiarities of the «Intellectika Plus» program: non-educational content and the search nature of the tasks solved by children, differentiation of tasks by nature: logical, spatial-combinatorial and route.

It is also important that 18 one-hour lessons were organized, held weekly for five months.

At the same time, each lesson included three periods: preliminary discussion, independent problem solving, and final discussion.

The preliminary discussion is intended to familiarize students with the methods of analyzing the conditions of problems and ways to find solutions. Such a discussion contributes to the formation of cognitive actions in children to solve problems. The final discussion is aimed at teaching children how to control their own mental activity when solving problems.

It should be mentioned that the subjects were ordinary students in ordinary classes in ordinary schools.

4.2. Scientific value of research An analysis of the results of the study allows us to state that new knowledge has been obtained about the conditions for the formation of internal reflection in third-graders and the transition of children’s critical thinking from its formal level of implementation to the content one.

This knowledge expands and refines the ideas of developmental and pedagogical psychology about the possibilities of intellectual development of children during their education in the primary grades of the school.

5.Summary

The data obtained allow us to reasonably assert that classes under the program «Intellectika Plus» significantly contribute to the formation of actions of internal reflection in third-graders and the development of critical thinking as a transition from its formal level to the content one. In addition, these activities significantly increase the proportion of children with internal reflection among children with a meaningful level of critical thinking.

In general, the study showed that the formation of reflection in younger students (in particular, third-graders) reveals and enhances its connection with critical thinking, significantly contributing to its development.