 Introduction.
The Federal State Educational Standard for Primary General Education [4] prescribes that the primary school educational program should include a special program for improving educational learning within the framework of mastering academic subjects.
We believe that such a program should also include children completing nonacademic tasks. This will make it possible to form a generalized educational system that is not limited by the framework of a specific primary school subject.
Our research was aimed at determining to what extent the 28 lessons we developed (September – May) of the noncurricular program “Plots” will contribute to secondgraders in improving the CLA necessary for the implementation of consistent reasoning.
The study was based on the assumption that secondgraders who mastered the content of classes in the “Plots” program would be able to solve diagnostic problems related to reasoning significantly more successfully than their peers who did not attend these classes.
The study was aimed at solving the following problems:
– assessment of the effectiveness of classes in the “Plots” program;
– checking the compliance of the diagnostic technique with the purposes of determining the formation of actions to carry out reasoning;
– organizing and conducting twentyeight additional weekly lessons;
– performing initial and final diagnostics to determine the characteristics of actions associated with the execution of reasoning.
 Materials and methods.
The «Plots» program includes 6 types of logic problems with simple plots. Practice has shown that such problems are interesting for children (some of the problems were taken from our Intellektika program [1]).
2.1. Characteristics of problems of the first type.
Tasks of this type are associated with judgments characterizing the relationships of objects in space, and have 3 plot and 2 structural modifications (find the question and find the missing part of the conditions).
In the 1st modification, the plots in the tasks are based on the relationship between the locations of objects, expressed by the prepositions “above — below”.
For example: “Using a green and yellow pen, we drew word pairs in a notebook:
WIDE FIELD
BLONDE BRAID
The green pair of words appeared above the yellow pair of words. What color is Blonde Braid? I
n the 2nd modification, plots are based on the relationship between the locations of objects “near — far”.
For example: “Three numbers were painted on a sheet of plywood using brown, blue and red paint:
136 247 895
The brown number is further away from 895 than the blue number. Which number is brown?
In the 3rd modification, plots are based on the relationship between the locations of objects “from left – to right”.
For example: “Using red and white chalk, two figures were drawn on the blackboard:
The red piece is to the left of the white one. What figure is drawn with white chalk?”
In the 1st structural modification, you need to find a question that corresponds to the content proposed in the problem.
For example: “We drew two prepositions with hard and soft pencils:
BETWEEN ABOUT
The preposition drawn with a hard pencil is to the left of the preposition drawn with a soft pencil.
You need to choose a question that has an answer in the content of the problem:
 Soft colored pencil?
 Is the hard pencil long?
 What preposition is drawn with a soft pencil?
In the 2nd structural modification, it is necessary to establish what knowledge is missing in the proposed content of the task to answer the question posed in the task.
For example: “We used green and blue felttip pens to write the names on the boxes of writing instruments:
PENS PENCILS
What color is the name of the HANDLE?”
What must be known to answer the question posed?
 The pens were ballpoint pens.
 The pencils were colored.
 The green name is to the left of the blue one.”
2.2. Characteristics of problems of the second type.
Tasks of this type are associated with judgments characterizing the characteristics of the actions of subjects mentioned in the task conditions. Problems of this type are offered to children in 3 plot and 2 structural modifications (find the question and find the missing part of the conditions).
In the 1st modification, judgments in the question and conditions of the proposed problems are characterized in logic as affirmative.
For example: “Masha and Katya were running along the road. Masha ran faster than Katya. Which of the girls ran less quickly?”
In the 2nd modification, the conditions in the tasks include judgments of a negative nature, and the question includes judgments of an affirmative nature.
For example: “Kolya and Vasya were drawing geometric figures. Kolya did not draw as neatly as Vasya. Who drew the figures more accurately?”
In the 3rd modification, the conditions in the tasks include affirmative judgments, and the question includes negative judgments.
For example: “Petya and Misha were throwing a spear. Petya rushed further than Misha. Who threw a spear not as far as Petya?”
In the 1st structural modification, you need to find a question that corresponds to the content proposed in the problem.
For example: “Petya and Misha were diving. Petya dived further than Misha.”
You need to choose a question that has an answer in the content of the problem:
 How many dives did Misha make?
 How far did Petaya dive?
 Who dived closer to Petya??”
In the 2nd structural modification, it is necessary to establish what knowledge is missing in the proposed content of the task to answer the question posed in the task.
For example: “Borya and Vanya folded paper figures. Who folded the most figures? What must be known to answer the question posed?
 The figures were large.
 The paper was colored.
 Vanya folded fewer figures than Borya.”
2.3. Characteristics of problems of the third type.
Tasks of this type are associated with judgments reflecting ways of changing the order of objects. Problems of this type are offered in 3 plot and 2 structural modifications (find the question and find the missing part of the conditions).
In the 1st modification, judgments in the question and conditions of the proposed problems are characterized in logic as affirmative.
For example: “Vova and Gena played words using cubes with letters printed on them. Rearranging the cubes, Vova received the word TON for the first time, and NOT the second time. Gena got PAL the first time, and the second time, rearranging the cubes the way Vova did, he got a different word. How did Vova rearrange the cubes the second time?”
In the 2nd modification, the conditions in the tasks include judgments of a negative nature, and the question includes judgments of an affirmative nature.
For example: “Dima was bought cubes with twodigit numbers printed on them, and Zhenya was bought cubes with singledigit numbers printed on them. The first time Dima arranged the cubes this way — 22 33 44 55, and the second time he arranged them differently — 66 33 44 22. Zhenya the first time arranged the cubes this way — 6 8 7 9, but the second time he arranged them differently, like Dima. What arrangement of cubes did Zhenya get?”
In the 3rd modification, the conditions in the tasks include affirmative judgments, and the question includes negative judgments.
“The girls, Gala and Lena, were given cubes with syllables printed on them. For the first time, Galya arranged the cubes in this way — VA DO KU LO, and the second time she arranged them differently — DO VA KU LO. The first time Galya arranged the cubes in this way — BI SA TE KO, and the second time she made the same rearrangement that Galya did. What arrangement of cubes cannot Lena achieve?”
In the 1st structural modification, you need to find a question that corresponds to the content proposed in the problem.
For example: “Petya and Misha had cubes with numbers. The first time Petya arranged the cubes this way — 8 2 4 6, and the second time he arranged them differently — 8 4 2 6. Misha arranged the cubes this way for the first time — 5 1 3 9, and then changed the arrangement of the numbers in the same way as Petya did.
You need to choose a question that has an answer in the content of the problem:
 How many cubes did each boy have?
 Who had the colored cubes?
 How did Misha change the arrangement of the cubes?”
In the 2nd structural modification, it is necessary to establish what knowledge is missing in the proposed content of the task to answer the question posed in the task.
For example: “Fedya and Sasha rearranged cubes with threedigit numbers. The first time Fedya arranged the cubes this way — 123,654,798, and the second time he placed them differently — 798,654,123. Sasha changed the arrangement of the numbers in the same way as Petya did. What rearrangement of the cubes did Sasha make?”
What must be known to answer the question posed?
 The cubes were large.
 The cubes were colored.
 Sasha arranged the cubes for the first time like this: 378,614,952.”
2.4. Characteristics of problems of the fourth type. Tasks of this type are associated with judgments characterizing the features of the arrangement of letters in the comparison of proposed words. Problems of this type are offered to children in 2 plot and 2 structural modifications (find the question and find the missing part of the conditions).
In the 1st modification, judgments in the question and conditions of the proposed problems are characterized in logic as affirmative.
For example: “The names of three cities were written on the poster in different colors: KAZAN KALUGA VORKUTA Blue and orange names have the same initial letter, orange and green have the same last letter. What name is on the blue paint?”
2nd modification of the conditions in the tasks include judgments of a negative nature.
For example: “In their travel diary in the Ryazan region, tourists entered the names of three villages, one of which they visited on Thursday, another on Tuesday, and the third on Wednesday:
TARANKA DOLUNOVO BOKOVOL
The names of villages visited on Thursday and Tuesday have the same consonant, the names of villages visited on Tuesday and Wednesday have the same vowel. On what day did you visit the village of DOLUNOVO?”
In the 1st structural modification, you need to find a question that corresponds to the content proposed in the problem.
For example: “On different pages of the book we found three numbers: 521 627 387 The numbers found on the ninth and tenth pages have the same second digit, and the numbers found on the tenth and twelfth pages have the same third digit.
You need to choose a question that has an answer in the content of the problem:
 What book were the pages in?
 What was the book about?
 On what page was the number 627 found?”
In the 2nd structural modification, it is necessary to establish what knowledge is missing in the proposed content of the task to answer the question posed in the task.
For example: “The names of three geometric shapes were written on the poster in different colors:
BALL CUBE CONE
The green and red names have the same number of letters. The name of which figure is green?
What must be known to answer the question posed?
 The name «CONE» is not green.
 The name of the red color is not «CONE».
 The names of green and yellow have the same first letter.”
2.5. Characteristics of tasks of the fifth type.
Tasks of this type are associated with judgments reflecting differences in age of the characters mentioned in the plots. Problems of this type are offered in 1 plot and 2 structural modifications (find the question and find the missing part of the conditions).
In the plot modification, problems contain all the judgments necessary for solution.
For example: “Vasya and Oleg were born in different years: some earlier, some later. They go to the same school. When a large number of years have passed, Vasya will be a small number of years older than Oleg is currently. Which student is younger, Vasya or Oleg?”
In the 1st structural modification, you need to find a question that corresponds to the content proposed in the problem.
For example: “Anna and Vera lived in different cities and corresponded. A large number of years ago, Anna was a small number of years younger than Vera is now.
You need to choose a question that has an answer in the content of the problem:
 In what cities did your friends live?
 What did they write letters about?
 Which one is older?
In the 2nd structural modification, it is necessary to establish what knowledge is missing in the proposed content of the task to answer the question posed in the task.
For example: “Tractor drivers Vladimir and Nikolai were born in the same village at different times. Which tractor driver is younger?
What must be known to answer the question posed?
 They worked on tractors of different models.
 Vladimir is older than Nikolai.
 Nikolai worked better than Vladimir.
2.6. Characteristics of tasks of the sixth type.
Tasks of this type are associated with judgments reflecting features that contradict each other. Problems of this type are offered in 2 plot and 2 structural modifications (find the question and find the missing part of the conditions).
In the 1st plot modification, the content and question of the task contain affirmative judgments. For example: “Three dogs — a poodle, a bulldog, a greyhound — lived on different floors of the house: one on the first, one on the second, one on the third. On Monday we walked either the greyhound or the dog from the first floor. On Tuesday we walked either with the dog from the first floor or with the poodle. What floor did the bulldog live on?”
In the 2nd plot modification, affirmative judgments are used in the content of the task, and the question contains negative judgments.
For example: “Misha, Kolya and Seva attended different sports sections. Some played football, some played handball, some played volleyball. At the competition, the first place was taken either by Misha or the one who played football, the second place was taken either by the one who played football or Kolya. Which of the guys didn’t play football?”
In the 1st structural modification, you need to find a question that corresponds to the content proposed in the problem.
For example: “There were three houses: red, green and yellow. One house had three floors, one had four, and one had two floors. On Monday they repaired either a red house or a house with three floors, on Tuesday they repaired either a house with three floors or a yellow house.
You need to choose a question that has an answer in the content of the problem:
1.What was repaired in the houses?
 In what month were the houses renovated?
 What color was the house with three floors?
In the 2nd structural modification, it is necessary to establish what knowledge is missing in the proposed content of the task to answer the question posed in the task.
For example: “Katya and Lena lived in different villages. Some lived in Bakovka, others in Zhukovka. In some villages there were many inhabitants, in others there were few. On Monday we went to visit either Bakovka or a village where there are few inhabitants. In what village did Katya live?
What must be known to answer the question posed?
 Bakovka was surrounded by forest.
 There was a bell tower in Zhukovka.
 On Tuesday we went to visit either a village where there are few inhabitants, or to the village where Katya lived.
2.7. Characteristics of the stages of the experimental work under consideration.
At the first stage, which began in September (first half), group diagnostic classes were organized with thirdgrade students included in the control (52 people) and experimental (54 people). The problems of the author’s “Miscellaneous” methodology were proposed, the solution of which involves performing actions related to the construction of consistent reasoning.
At the second stage of the work under discussion, 28 group lessons were organized with students making up the experimental group. The classes were after school hours (afternoon) and were held once a week for one hour. In the abovementioned classes, schoolchildren were asked to solve 12–14 search problems of noneducational content of a plotlogical nature (of various modifications), which were included in the author’s task. program «Stories».
At the third stage of work, in the second half of May, schoolchildren from the control and experimental groups again solved problems of the author’s “Miscellaneous” methodology, the solution of which involves performing actions related to the construction of consistent reasoning.
2.8. Determining the maturity of the methods of performing reasoning.
In order to conduct a group diagnostic lesson to assess the mastery of actions to build a consistent reasoning, the author’s “Miscellaneous” methodology was used, including tasks, modifications of which were presented in our works [2, 3]. This technique includes nine tasks. Their solution involves making a correlation of judgments that reflect the coincidence and discrepancy of the objects with which the characters included in the content of the tasks act.
 Nikolai, Boris and Alexey planted fruit trees in the garden. Two of them planted apple trees, one planted pears. Nikolai and Boris and Boris and Alexey planted different trees. Which one of them planted pears?
 a) it is impossible to answer the question of the problem, b) Nikolai, c) Boris, d) Alexey.
 Vitya, Gena, Dima and Egor solved arithmetic problems: three schoolchildren had examples on compounding, one on subtraction. Vitya and Gena, Gena and Dima performed different arithmetic operations. What examples did Egor solve?
 a) “for addition”, b) it is impossible to answer the question of the problem, c) “for subtraction”, d) “by division.”
 Katya, Lena and Marina bought fruit: two had oranges, one had bananas. Katya and Lena and Lena and Marina bought different fruits. Who had bananas?
 a) at Marina’s, b) at Katya’s, c) at Lena’s, d) it is impossible to answer the question of the problem.
 Kolya, Sasha and Vova read books. Two boys read about space, one — about seas and oceans. Sasha and Kolya and Kolya and Vova were reading different books. Who hasn’t read about space?
 a) Sasha, b) Kolya, c) it is impossible to answer the question of the problem, d) Vova.
 Lisa, Nina, Olya and Ira baked four pies: three pies were with meat, one pie was with cabbage. Lisa and Olya baked different pies, and Ira and Nina baked identical pies. What kind of pie did Ira bake?
 a) it is impossible to answer the question of the problem, b) with cabbage, c) with meat, d) with carrots.
 Igor, Kostya. Seva and Vanya were repairing pieces of furniture. Three of them were repairing stools, one was repairing a sofa. Kostya and Seva, Seva and Igor were repairing various items. What items did Seva not repair?
 a) stools, b) sofa, c) it is impossible to answer the question of the problem, d) an armchair.
 Anya, Vika and Dasha draw geometric shapes. Two girls draw pentagons, one draws triangles. Natasha and Marina draw octagons. Galya and Dasha, Dasha and Vika draw different figures. Which girl draws triangles?
 a) Anya, b) Dasha, c) Vika, d) it is impossible to answer the question of the problem.
 Gena, Fedya, Misha and Dima trained in jumping: three jumped high, one long jumped. Sasha and Masha did not train in long and high jumps. Fedya and Misha, Misha and Gena performed different jumps. What jumps did Fedya not perform?
 a) high jumps, b) it is impossible to answer the question of the problem, c) long jumps, d) diving.
 Marina, Katya and Natasha sculpted animals from plasticine: two girls — bears, one — hares. Valya and Olya sculpted wolves. Marina and Natasha sculpted different animals. What animals did Katya sculpt? a) bears, b) hares, c) it is impossible to answer the question of the problem, d) wolves.
 Results.
The results of the study related to determining the effectiveness of forming reasoning actions among thirdgraders in extracurricular activities together with classes according to the school curriculum (experimental group) and in classes only according to the school curriculum (control group) are presented in the table.
Table.
Successful completion of diagnostic tasks of the “Miscellaneous” methodology by students in the control (C) and experimental (E) groups in September (beginning of the school year) and May (end of the school year).
Groups Diagnostic periods September May Group K 11 (21.1%) 17 (32.7%)* Group E 10 (18.5%) 26 (48.1%)* Note: * p<0.05.
Groups

Diagnostic periods


September  May  
Group С

11 (21,1%)

17 (32,7%)*

Group E

10 (18,5%) 
26 (48,1%)* 
Note: * р<0,05.
The data presented in the table indicate how the success of students in the control and experimental groups in performing diagnostic plotlogical tasks of the “Miscellaneous” methodology, which are associated with the construction of reasoning, changes from the beginning of the school year to its end.
In particular, in the control group, the increase in the number of schoolchildren who managed to solve all the problems of the noted methodology in May compared to September was 11.6%, and in the experimental group the increase was 32.7%. Thus, the number of children who solved all problems in the experimental group increased more significantly than in the control group — by 21.1%. As a result, such children in the experimental group in May became 48.1%, and in the control group — 32.7% — the difference in these indicators, as mathematical processing showed, is statistically significant (at p < 0.05).
The results obtained in the study indicate that the initial hypothesis was confirmed: indeed, classes in the author’s program “Plots” and the school curriculum contribute to the formation of universal educational actions related to the construction of consistent reasoning to a greater extent than classes in the school curriculum alone.
 Conclusion.
The data obtained as a result of this study allow us to note the effectiveness of extracurricular weekly classes for the formation of universal educational actions in thirdgraders related to the performance of consistent reasoning.
However, it should be noted that the results obtained in the study have certain limitations.
Thus, the average result of children in the control and experimental groups in September is 19.8%. If this result were equal to 15.0% or 10.0%, then the effectiveness of extracurricular extracurricular activities throughout the school year would be significantly lower.
In addition, limitations are associated, on the one hand, with the sample size of schoolchildren participating in the study, and on the other hand, with the characteristics of additional classes: with the methodology of their implementation, with their duration and the content of noneducational tasks solved during them, as well as with their number in week.
It is important to note that the use of the “Plots” program in elementary school opens up new intellectual opportunities for younger schoolchildren, in particular, for third graders.
The results of experimental work indicate the serious influence of regular classes both on children’s mastery of the actions of constructing reasoning, and in general on the formation of cognitive actions in younger schoolchildren.
The data obtained in this study expand and clarify the ideas of educational and developmental psychology about the possibilities of intellectual development of children at primary school age. This will create conditions for improving learning in the primary grades of school on the basis of activities that contribute to the formation of universal educational actions related to the construction of reasoning.
In the course of further work, it is planned to find out how effective classes in the “Plots” program will be for second and fourth grade students.
So, the study showed the possibility of improving the actions of constructing reasoning in elementary school, in particular, among schoolchildren studying in the third grade.
References
1. Zak A.Z. Intelligence. 3rd grade. Notebook for the development of thinking abilities. M.: Intellect Center, 2019. 96 pp.2. Zak A.Z. Characteristics of solving logical problems by junior schoolchildren // Alley of Science. – 2018. – No. 5 (21). pp. 535 – 547.
3. Zak A.Z. Methods for solving search problems by junior schoolchildren // Alley of Science, 2019, No. 2 (29). C.858 – 867.
4. Federal state educational standards for primary and basic general education. M.: Vako Publishing House, 2022. 160 p.