How to carry out the Kravtsova labyrinth technique. Formation of spatial thinking in children of primary school age during mathematics lessons. Qualitative and quantitative analysis

"Labyrinth" technique

The material is an image of clearings with branched paths and houses at their ends, as well as “letters” conditionally indicating the path to one of the houses placed under the clearing (see Appendix to the “Labyrinth” method). Introductory tasks consist of two tasks - task "A" and task "B". The solution to each problem is checked by an experimenter. The main tasks follow. The pictures for problems 1-2 show only branched paths and houses at the end of them; on all the others, each section of the path is marked with a landmark, and in tasks 3-4 landmarks of the same content are given in different sequences; in problems 5-6, each branch is marked with two identical landmarks. In problems 7-10, two identical landmarks are given in different sequences and placed not on sections of the path, but at branching points. On the “letters” for tasks 1-2 there is a broken line showing the direction of the path along which the search should be carried out. In the “letters” for tasks 3-6, in a certain sequence from bottom to top, images of those objects that you need to walk past are given. In the “letters” for problems 7-10, both the turns of the path (broken line) and the necessary landmarks are depicted.

To find the right path, the child must take into account in tasks 1-2 the directions of turns, in tasks 3-4 - the nature of landmarks and their sequence, in tasks 5-6 - combinations of landmarks in a certain sequence, in tasks 7-10 - both landmarks and directions turns.

Control experiment

After mathematics and design lessons, I conducted a control experiment. In the control experiment, the same set of techniques was used as in the ascertaining experiment.

Students of class 2 "A" showed the following results:

Method "Walk through the labyrinth". ( A.L. Wenger)

Target: To identify spatial orientation, the level of development of spatial thinking, the technique is aimed at developing fine motor skills of the hand, coordination of vision and hand movements.

After carrying out this technique, the following results were obtained:

8 students (40%) - high level

3 students (15%) - low level

Methodology D.B. Elkonin "Graphic dictation".

Target: The technique is designed to study orientation in space. With its help, the ability to listen carefully and accurately follow the instructions of an adult, correctly reproduce the given direction of a line, and independently act as directed by an adult is determined.

The results obtained and their analysis:

After carrying out the “Graphic Dictation” technique, the following results were obtained:

Analysis: From the table it can be seen that:

6 students (30%) - high level

12 students (60%) - average level

The results can be presented in the form of a diagram:

"House" technique. (N.I. Gutkina)

Target: to identify the features of the development of voluntary attention, spatial perception and spatial thinking, sensorimotor coordination and fine motor skills of the hand, the child’s ability to focus his work on a model, the ability to accurately copy it. The test also allows you to identify (in general outline) intelligence of child development, the ability of children to reproduce a model; identify spatial orientation associated with drawing:

1. Place geometric shapes on a sheet of paper in the indicated manner, drawing them or using ready-made ones;

2. Without reference points, reproduce the direction of the drawing using the sample. In case of difficulty - additional exercises in which you need:

A) distinguish the sides of the sheet;

B) draw straight lines from the middle of the sheet along various directions;

B) trace the outline of the drawing;

D) reproduce a drawing of greater complexity than the one proposed in the main task.

The results obtained and their analysis:

When performing the tasks of the "House" Method, the subjects made the following mistakes:

A) some details of the drawing were missing;

B) in some drawings proportionality was not observed: an increase in individual details of the drawing while maintaining a relatively arbitrary size of the entire drawing;

C) incorrect representation of the elements of the picture; the right and left parts of the fence are assessed separately;

D) deviation of lines from a given direction;

D) gaps between lines at junctions;

E) lines climbing on top of one another;

The results of this technique are presented in the table:

Analysis: From the table it can be seen that:

9 students (45%) - high level

9 students (45%) - intermediate level

2 students (10%) - low level

The results can be presented in the form of a diagram:

Thus, during the preliminary experiment, students of class 2 "A" showed the following results:

38% - high level of development of spatial thinking,

50% of children have an average level of development of spatial thinking,

12% - low level of development of spatial thinking.

The diagnostic results can be presented in the form of a diagram:

Thus, after the lessons in mathematics and design, the level of development of spatial thinking increased significantly. This suggests that the lessons we conducted in grade 2 significantly improved the development of this type of thinking in second-graders, which was the basis for proving the correct hypothesis we put forward.

Goal: To identify spatial orientation, the level of development of spatial thinking, the technique is aimed at developing fine motor skills of the hand, coordination of vision and hand movements.

Diagnostic results:

4 students (16.7%) - high level

6 students (25%) - low level

2) Methodology D.B. Elkonin "Graphic dictation".

Purpose: the technique is intended to study orientation in space. With its help, the ability to listen carefully and accurately follow the instructions of an adult, correctly reproduce the given direction of a line, and independently act as directed by an adult is determined.

Table No. 3. “Results”

3 students (12.5%) - high level

19 students (79.2%) - intermediate level

2 students (8.3%) - low level

The results can be presented in the form of a diagram:

3) “House” technique. (N.I. Gutkina)

Goal: to identify the features of the development of voluntary attention, spatial perception and spatial thinking, sensorimotor coordination and fine motor skills of the hand, the child’s ability to focus his work on a model, the ability to accurately copy it. The test also allows you to identify (in general terms) the child’s developmental intelligence, the children’s ability to reproduce a model; identify spatial orientation associated with drawing:

1. Place geometric shapes on a sheet of paper in the indicated manner, drawing them or using ready-made ones;

2. Without reference points, reproduce the direction of the drawing using the sample. In case of difficulty - additional exercises in which you need:

A) distinguish the sides of the sheet;

B) draw straight lines from the middle of the sheet in different directions;

B) trace the outline of the drawing;

D) reproduce a drawing of greater complexity than the one proposed in the main task.

The results obtained and their analysis:

When performing the tasks of the "House" Method, the subjects made the following mistakes:

A) some details of the drawing were missing;

B) in some drawings proportionality was not observed: an increase in individual details of the drawing while maintaining a relatively arbitrary size of the entire drawing;

C) incorrect representation of the elements of the picture; the right and left parts of the fence are assessed separately;

D) deviation of lines from a given direction;

D) gaps between lines at junctions;

E) lines climbing one on top of another.

The results of this technique are presented in Table No. 4.

Table No. 4. “Results”

Analysis: the table shows that:

7 students (29.2%) - high level

14 students (58.3%) - intermediate level

3 students (12.5%) - low level

The results can be presented in the form of a diagram:

After the formative experiment, students of grade 2 “D” showed the following results:

38% - high level of development of spatial thinking,

50% of children have an average level of development of spatial thinking,

12% - low level of development of spatial thinking.

The diagnostic results can be presented in the form of a diagram:

Thus, after the formative experiment, the level of development of spatial thinking increased significantly. This suggests that the lessons we conducted in grade 2 significantly improved the development of this type of thinking in second-graders, which was the basis for proving the correct hypothesis we put forward. If in a stated experiment

no one had a high level of development of spatial thinking, then after the formative experiment they had the highest level

38% of students. 50% of students began to have an average level, and 12% - a low level.

Conclusion

Among the numerous problems in psychology, the problem of developing the thinking of younger schoolchildren is undoubtedly one of the intensively studied ones. Interest in her is by no means accidental. The problem of thinking development is reflected in the works of both domestic and foreign psychologists and teachers. There are several points of view on the definition of the concept of spatial thinking. After analyzing the psychological and pedagogical literature on this topic, we established a basic definition for the study. This is the definition of I.S. Yakimanskaya.

In its structure, spatial thinking is a multi-level formation, which includes elements of different content and levels of development. This work is based on the structure of T.V. Andryushina, based on which a set of methods was selected for studying spatial thinking in primary schoolchildren.

Currently, as one of the main criteria for the mathematical development of a person, many psychologists and teachers consider the level of development of spatial thinking, which is characterized by the ability to operate with spatial images. Recently, there has been a decrease in students’ geometric preparedness. This is manifested primarily in the low level of development of spatial thinking. And since the figurative components of thinking develop more intensively at primary school age, it is advisable to develop spatial thinking in students primary classes.

The development of spatial thinking occurs in the process of a child mastering the knowledge accumulated by humanity and is one of the essential characteristics of the ontogenesis of the child’s psyche. A high level of development of spatial thinking is a necessary condition for the successful mastery of a variety of general education and special education courses. technical disciplines at all stages of training, thereby emphasizing the relevance of this research topic. Spatial thinking is an essential component in preparing for practical activities in many specialties.

To improve geometric knowledge and develop spatial thinking among students in grade 2 “D”, integrated lessons were conducted on the course of S.I. Volkova and O.L. Pchyolkina “Mathematics and design”. In the lessons developed, children needed not only mathematical knowledge, but also design skills. The development of spatial thinking during integrated mathematics and labor training lessons, as the study showed, is very important and actual problem. While researching this problem, we carried out and tested a set of exercises and games aimed at developing this type of thinking, and selected methods for diagnosing spatial thinking in relation to primary school age.

In the practical part of the work, the level of development of spatial thinking among students in grade 2 “D” was studied. The results of the primary study showed that the level of development of this type of thinking among students is weak.

The conducted formative experiment, as shown by the results of the control experiment, significantly increased the level of development of spatial thinking in primary schoolchildren. In the classroom, the process of developing spatial thinking among students has reached a higher level. This suggests that the integrated lessons we conducted in mathematics and labor training contribute to the development of spatial thinking in second-graders, which was the basis for proving the correctness of our hypothesis.

As a result of all the work carried out, we can conclude that children have become better oriented in space, have accumulated a wider stock of spatial ideas, expanded their stock of verbal knowledge and terminology, and have acquired the ability to establish relationships between objects, words, images and the subject of reality; began to mentally operate with ideas, using them as a support in the assimilation of knowledge.

Practical significance The research is that the developed system of lessons can help to increase the level of development of spatial thinking of primary schoolchildren in the process of studying geometric concepts and representations. These techniques can be recommended to teachers in mathematics lessons. This work can be continued in 3rd and 4th grades.

Thus, the development of spatial thinking needs to be given more attention than is provided in textbooks primary school. It is necessary to develop methods for developing spatial thinking in younger schoolchildren, which will include exercises presented in a certain system, and also based on the material that is in the textbook, it is necessary to organize the work of children so that it contributes to the development of spatial thinking.

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The material is an image of clearings with branched paths and houses at their ends, as well as “letters” conditionally indicating the path to one of the houses placed under the clearing (see Appendix to the “Labyrinth” method).

Introductory tasks consist of two tasks - task "A" and task "B". The solution to each problem is checked by an experimenter. The main tasks follow. The pictures for problems 1-2 show only branched paths and houses at the end of them; on all the others, each section of the path is marked with a landmark, and in tasks 3-4 landmarks of the same content are given in different sequences; in problems 5-6, each branch is marked with two identical landmarks. In problems 7-10, two identical landmarks are given in different sequences and placed not on sections of the path, but at branching points. On the “letters” for tasks 1-2 there is a broken line showing the direction of the path along which the search should be conducted. In the “letters” for tasks 3-6, in a certain sequence from bottom to top, images of those objects that you need to walk past are given. In the “letters” for problems 7-10, both the turns of the path (broken line) and the necessary landmarks are depicted.

To find the right path, the child must take into account in tasks 1-2 the directions of turns, in tasks 3-4 - the nature of landmarks and their sequence, in tasks 5-6 - combinations of landmarks in a certain sequence, in tasks 7-10 - both landmarks and directions turns.

Instructions

Children are first given two introductory problems, then tasks 1-10 in order.

Instructions are given after the children have opened the first sheet of the notebook with the introductory task.

“In front of you is a clearing, paths and houses are drawn on it at the end of each of them. You need to correctly find one house and cross it out. To find this house, you need to look at the letter. (The experimenter points to the bottom of the page where it is placed.) "The letter says that you need to go past the grass, past the Christmas tree, and then past the fungus, then you will find the right house. Find this house, and I will see if you made a mistake."

The examiner looks at how the child solved the problem and, if necessary, explains and corrects errors.

Moving on to the second task, the examiner invites the children to turn over the piece of paper and says:

“There are also two houses here, and again you need to find the house. But the letter here is different: it shows how to go and where to turn. You need to again go straight from the grass, and then turn to the side.”

At these words, the inspector runs his hand over the drawing in the “letter.” The solution to the problem is checked again, errors are explained and corrected.

Then comes the solution of the main problems. Brief additional instructions are given for each of them.

For tasks 1-2:

“The letter shows how to go, which way to turn. Start moving from the grass. Find the desired house and cross it out.”

To task 3:

“Look at the letter. You have to go from the grass, past the flower, then past the fungus, then past the birch tree, then the Christmas tree. Find the right house and cross it out.”

To task 4:

“Look at the letter. You need to go from the grass, first past the birch tree, then past the fungus, past the Christmas tree, then the chair. Mark the house.”

For tasks 5-6:

“Be very careful. Look at the letter, find the right house and cross it out.”

For problems 7-10:

“Look at the letter, it shows how you should walk, what object to turn near and in which direction. Be careful, find the right house and cross it out.”

Evaluation of results

When evaluating the results, it is necessary to take into account the number of the selected house and the number of the task (see the rating scale). The score (in points) is indicated at the intersection of their coordinates. The number of the selected house and the rating are entered into the protocol (see the protocol for the “Labyrinth” method). All scores are summed up. The maximum number of points is 44.

Grading scale

cove

Task No.

Interpretation of the results obtained

38-44 points - children with a detailed correlation of two parameters simultaneously. They have fairly complete and dissected spatial representations.

31-38 - children with incomplete orientation to two parameters (usually solve the first 6 problems correctly). When taking into account two parameters at the same time, they constantly slide towards one. This is due to insufficient stability and mobility in the development of spatial concepts.

24-31 points - children with clear completeness of orientation to only one sign. They can construct and use spatial representations of the simplest structure.

18-24 - these children are characterized by incomplete orientation even to one sign. They divide the task into stages, but by the end of the work they lose their bearings. They are just beginning to develop a method of visual-figurative orientation in space.

Less than 18 points - children with inadequate forms of orientation. They try to find the right house, but their choice is random. This is due to the lack of development of the ability to relate the diagram to the real situation, i.e. underdevelopment of visual-figurative thinking.

Appendix to the “Labyrinth” method

Introductory tasks

Problems 1-2

a) clearing, b) first letter, c) second letter

Problems 5-6

a) clearing, b) first letter, c) second letter

a) clearing, b) first letter, c) second letter

Problems 9-10

a) clearing, b) first letter, c) second letter

Key to problems 1-6 (house numbers)

Key to problems 9-10 (house numbers)

Protocol to the "Labyrinth" technique

baby name

Sum

Notes

The technique is aimed at identifying the level of development of visual-schematic thinking (the ability to use diagrams and conventional images when navigating the situation). The assessment is made in “raw” points without conversion to a normalized scale.

The material is a set of sheets that depict clearings with branched paths and houses at their ends, as well as “letters” conditionally indicating the path to one of the houses.

The first two sheets (A and B) correspond to introductory problems.

Children are first given two introductory problems, then, in order, tasks 1-10 (sheets 1-10).

Instructions are given after the children have opened the first sheet of the notebook with the introductory task. “In front of you is a clearing, paths and houses are drawn on it at the end of each of them. You need to find one house correctly and cross it out. To find this house, you need to look at the letter. (The inspector points to the bottom of the page where it is placed.) The letter says that you need to go from the grass, past the Christmas tree, and then past the fungus, then you will find the right house. Everyone find this house, and I’ll see if you made a mistake.”

The examiner looks at how each child solved the problem and, if necessary, explains and corrects errors.

Moving on to the second introductory task, the examiner invites the children to turn over the piece of paper and says: “There are also two houses here, and again we need to find the right house. But the letter here is different: it shows how to go and where to turn. You need to walk straight away from the grass again, then turn to the side.” With these words, the inspector runs through the drawing in the “letter”. The solution to the problem is checked again and errors are corrected.

Then comes the solution of the main problems. Brief additional instructions are given for each of them.

For tasks 1-2: “The letter shows how to walk, which way to turn, start moving away from the grass. Find the house you need and cross it out.”

For task 4: “Look at the letter. You need to walk away from the grass, first past the fungus, then past the berries (cherries), the tree (oak), then the flower. Mark the house."

For problems 7-10: “Look at the letter, it shows how to walk, what object to turn around and in which direction. Be careful, find the right house and cross it out.”

Problem 7	Problem 8
Problem 9	Problem 10

Evaluation of results

When processing the results for each of problems 1-6, 1 point is awarded for each correct turn. Since problems 1-6 require four turns, the maximum number of points for each problem is 4. In problems 7-10, 2 points are awarded for each correct turn; in problems 7-8 (two rotations) the maximum number of points is 4; in problems 9, 10 (three turns) - 6 points.

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