- Introduction
In accordance with the new Federal State Educational Standard of Primary General Education [5], part of the main educational program of elementary school should be a special program for the formation of universal educational activities based on typical tasks related to the content of academic subjects.
At the same time, it can be assumed that tasks based on non-educational material should also be part of this program, since in this case the actions being formed are mastered in a general form without connection with any specific subject material of primary school disciplines.
The purpose of the study was to establish the nature of the influence of a series of 30 developmental lessons (during the academic year) on the formation of cognitive universal learning activities in second graders related to the construction of reasoning.
It was assumed that the second-graders participating in developmental activities, where it is proposed to solve plot-logical problems on non-educational material, will have universal actions for constructing reasoning at a higher level than those of second-graders not participating in developing classes.
The objectives of the study were, firstly, to build a program of developmental classes, secondly, related to the selection of types of plot-logical tasks, and secondly, to develop and test a diagnostic technique to determine the formation of a universal action for building reasoning, thirdly, in conducting 30 lessons on solving plot-logical problems (at the rate of one lesson per week), fourthly, in organizing the initial and final diagnostics of the formation of a universal action for building reasoning.
2.Materials and methods
The content of developing classes included seven types of plot-logical tasks with conditional names: “Closer, more to the left”, “Relatives”, “More than …”, Just like …”, “Coincidences”, “Older , younger”, “Either one or the other” [ 1 ], [ 2 ], [ 3 ], [ 4 ].
2.1. Options for constructing «Closer, more to the left tasks
The construction of the tasks “” is based on the correlation of judgments about the spatial relations of the objects mentioned in the condition.
In the first version of the construction of tasks, the spatial relation «above — below» is used, for example:
“With blue and red pencils they wrote two words:
SEA
LAKE
The blue word is above the red one. With what pencil did you write the word LAKE?”
In the second variant, the relation “to the left — to the right” is given, for example:
“With yellow and brown pencils they wrote two words:
COW HORSE
The yellow word is to the left of the brown one. What word was written in brown pencil?
In the third option, the relation «closer — farther» is given, for example:
“Three words were written in black, blue and orange pencils:
NUMBER LETTER NUMBER
The black word is further from the word NUMBER than the blue one. What word is black?”
In the fourth option, it is required to determine which question is suitable for these components of the task condition, for example:
“Two words were written with a pen and pencil:
SISTER BROTHER
A word written in pencil is to the left of a word written in pen.
Which question can be answered according to the condition of the problem: (1) What color is the pencil? (2) How long is the handle? (3) What word is written with a pen?”
In the fifth option, it is required to determine what information is missing in the condition in order to be able to answer the question of the problem, for example:
“Two words were written in red and yellow paints:
BEETLE SOM
[ … ].What paint is used to write the word BEETLE?”
What do you need to know to answer this question? (1) The catfish was small. (2) The beetle crawled fast. (3) The red word is to the left of the yellow one.
2.2. Options for constructing «Relatives» tasks
The reasoning in the tasks » Relatives » is based on the correlation of kinship judgments mentioned in the condition.
In the first variant, affirmative judgments are used in the condition of the problem and the question, for example: “Alexander is the son of Boris. Who can be Boris Alexander?”
In the second option, a negative judgment is used in the condition of the problem, and an affirmative one in the question, for example: “Mikhail is not Larisa’s brother, but her relative. Who can Larisa be to Mikhail — a grandmother, a sister, or cannot she be his relative?”
In the third option, an affirmative judgment is used in the condition of the problem, and a negative one in the question, for example: “Konstantin is Nina’s uncle. Who can’t Nina Konstantin be — a daughter, mother or niece?
In the fourth option, the question becomes unknown, for example: “Vladimir is Nikolai’s grandfather. [ … ].Nikolai is Igor’s friend.
Which question can be answered according to the condition of the problem: (1) Who is the brother of Nicholas? (2) Who is Vladimir’s friend? (3) Who is Nicholas Vladimir?”
In the fifth variant, one of the components of the condition is unknown, for example: “Gennady works together with Viktor. Who can be Viktor Gennady?
What do you need to know to answer this question? (1) Gennady is older than Victor. (2) Victor is taller than Gennady. (3) Gennady brother of Victor.
2.3. Options for constructing « More than…» tasks
The basis of reasoning in the tasks «More than…» is the correlation of judgments about the degree of manifestation of the properties of the characters.
In the first variant, affirmative judgments are used in the condition of the problem and the question, for example: “Misha and Kolya crossed the river. Misha swam faster than Kolya. Which boy swam slower?”
In the second option, a negative judgment is used in the condition of the problem, and an affirmative one in the question, for example: “Vova and Zina wrote letters. Vova did not write as beautifully as Zina. Which of the guys wrote letters more beautifully?”
In the third variant, an affirmative judgment is used in the condition of the problem, and a negative judgment is used in the question, for example: “Lyuba and Natasha washed the dishes. Natasha washed cleaner than Lyuba. Which of the girls did not wash dishes as well as Natasha?”
In the fourth option, it is required to determine which question is suitable for these components of the task condition, for example: “Vova and Galya were jumping. Galya jumped higher than Vova.”
“Which question can be answered according to the condition of the problem: (1) How many jumps did Galya make? (2) How high did Vova jump? (3) Who jumped below Gali?”
In the fifth option, it is required to determine what information is missing in the condition to answer the question of the problem, for example: “Seva and Igor rode bicycles. [ … ].Which of the boys was driving faster?”
What do you need to know to answer this question?
(1) The boys were driving along the highway. (2) Igor had a new bicycle. (3) Seva was driving slower than Igor.”
2.4. Options for constructing « Just like …» tasks Reasoning in problems of the type «Just like …» is based on the analysis and generalization of methods for transforming a sequence of objects.
In the first variant, affirmative judgments are used, for example: “Alik and Borya made up words from cubes with letters. First, Alik composed the word BAD. Then he rearranged the letters and got the word DAB. Borya first composed the word TAB, and then rearranged the letters in it in the same way as Alik. What happened to Boris?”
In the second option, a negative judgment is used in the condition of the problem, and an affirmative one in the question, for example: “Katya had cubes with numbers, Lenya had letters. Katya first put the cubes like this — 7 2 1 4, then she rearranged them and it turned out — 4 2 1 7. Lenya first arranged the cubes like this — TON, and then rearranged them differently from Katya. What could have happened to Leni?
In the third variant, an affirmative judgment is used in the condition of the problem, and a negative one in the question, for example: “Egor and Nina arranged cubes with numbers. Egor first arranged the cubes like this — 12 43 65 27, then rearranged them and it turned out like this — 43 12 65 27. At first, Nina’s cubes were like this — 72 56 81 39. And then she rearranged them in the same way as Egor. What could not happen with Nina?”
In the fourth option, it is required to determine which question is suitable for these components of the problem statement, for example: “Zhenya and Masha arranged cubes with letters. Zhenya first arranged it like this — STOP, then rearranged them and it turned out — POST. Masha made the same permutation in the word PAL.
What question can be answered according to the condition of this problem? 1) What color were the cubes? 2) What size were the cubes? 3) What happened to Masha after the rearrangement?”
In the fifth option, it is required to determine what information is missing in the condition so that it is possible to answer the question of the problem, for example: “Yura and Anya arranged cubes with letters. Yura first composed the word AIST, then rearranged the letters and it turned out — ATIS. Anya rearranged her cubes in the same way as Yura. [ … ].What did she get?”
What do you need to know to answer this question? 1) Anya had four cubes. 2) Yura rearranged three letters. 3) First, Anya put the cubes like this — CON.
2.5. Options for constructing « Coincidence « tasks
The basis of reasoning in tasks of the «Coincidence» type is the correlation of judgments about the place of letters in the compared words.
In the first variant, affirmative judgments are used, for example: “The words were written on the board with colored crayons:
SEA SON CONE
The blue and white words have the same first letter, while the white and red words have the same second letter. What is the blue word?”
In the second option, a negative judgment is used in the condition of the problem, for example: “One word was written on Wednesday, another on Monday, the third on Friday:
LOG BAG LOVE
Words written on Monday and Wednesday have the same third letter, while words written on Wednesday and Friday have the same first letter. On what days was the word «LOVE» not written?
In the third option, it is required to determine which question is suitable for these components of the task condition, for example: “The words were written on the board with colored crayons:
CASE FACE CLOD
The blue and white words have the same first letter, while the white and red words have the same second letter.
What question can be answered according to the condition of this task? 1) Who wrote the word FACE? 2) Who wrote with blue chalk? 3) What color is the word CASE?”
In the fourth option, it is required to determine what information is missing in the condition in order to be able to answer the question of the problem, for example: “On the blackboard they wrote the words with colored crayons:
BOOT SEFT COSY
The white and green words have the same fourth letter. What word is green? What do you need to know to answer this question? 1) The word Eaves is not white. 2) The green word is not Eaves. 3) The green and red words have the same second letter.
2.6. Options for constructing « Older, younger » tasks
The basis of reasoning in problems of the type «Older, younger» is the correlation of judgments about the relationship of the characters of the problem by age.
In the first version, the entire composition of the components of the task is present — the necessary judgments and the question — for example: “Klava and Lena lived in the same house. In many years, Klava will be a little older than Lena is now. Which of the girls is younger?”
In the second option, it is required to determine what information is missing in the condition in order to be able to answer the question of the task, for example: “Lenya and Petya lived on the same street. [ … ]. Several years will pass. Which of the guys is younger?”
What do you need to know to answer this question? 1) Lenya and Petya lived in different houses. 2) Petya is older than Lenya. 3) Lenya lived on the second floor.
In the third option, it is required to determine which question is suitable for these components of the problem statement, for example: “Borya and Yura built a house. Many years ago, Borya was a little younger than Yura is now. What question can be answered according to the condition of this task?”
1) How old was Yuri? 2) Where was the house built? 3) Which of the guys is older?
2.7. Options for constructing « Either one or the other » tasks
The basis of reasoning in tasks of this type «Either one or the other» is the correlation of judgments about features that are mutually exclusive.
In the first variant, affirmative judgments are used in the condition and question of the tasks, for example: “Three cats — gray, white, black — were sitting: one in the room, one in the corridor, one in the bedroom. In the morning they fed either a black cat, or sitting in the bedroom, in the evening — either sitting in the bedroom, or white. Where was the gray cat?”
In the second variant, affirmative judgments are used in the condition of the problems, and negative ones are used in the question, for example: “Katya, Masha and Nadia are friends. Some of them studied at a music school, someone at a sports school, someone at an art school. Fours were received either by Katya, or someone at a music school, fives — either by someone at a music school, or by Nadia. Who didn’t go to music school?” .
In the third option, it is required to determine which question is suitable for these components of the problem statement, for example: “There were three trees: pine, spruce and linden. On one of them there were three birds, on the other — five, on the third — six. First, they drew either a pine tree, or five birds, then either six birds, or a pine tree.
What question can be answered according to the condition of this task? 1) How many birds were sitting on the spruce? 2) How many birds are on the linden? 3) How many birds are on the pine tree?
In the fourth option, it is required to determine what information is missing in the condition in order to be able to answer the question of the problem, for example: “Egor and Yura are translators. Some of them read newspapers, some magazines, some in Czech, some in Polish. In the morning, either newspapers were translated or from Czech.[ … ]. Who read magazines?”
What do you need to know to answer this question?
1) Egor translated during the day. 2) During the day, either Yura translated, or someone from Czech. 3) Yura read in the morning.
2.8. The content of developing classes
On the basis of the considered seven types of plot-logical tasks, a program of 30 lessons was developed, which were held outside school hours.
Lesson 1. Tasks «Closer, to the left», options 1, 2, 3.
Lesson 2. Tasks «Relatives», options 1, 2, 3.
Lesson 3. Tasks «More than …», options 1, 2, 3.
Lesson 4. Tasks «The same as …», options 1, 2, 3.
Lesson 5. Tasks «Coincidence», options 1, 2, 3.
Lesson 6. Tasks «Older, younger», options 1, 2, 3.
Lesson 7. Tasks “Either one or the other”, options 1, 2, 3.
Lesson 8. Tasks «Closer, more to the left», options 2, 3, 4.
Lesson 9. Tasks «Relatives», options 2, 3, 4.
Lesson 10. Tasks «More than …», options 2, 3, 4.
Lesson 11. Tasks «Just like …», options 2, 3, 4.
Lesson 12. Tasks «Coincidence», options 2, 3, 4.
Lesson 13. Tasks «Older, younger», options 2, 3, 4.
Lesson 14. Tasks «Either one or the other», options 2, 3, 4.
Lesson 15. Tasks “Closer, more to the left”, options 1, 2, 3, 5.
Lesson 16. Tasks “Relatives”, options 1, 2, 3, 5.
Lesson 17. Tasks “More than …”, options 1,2,3, 5.
Lesson 18. Tasks «Just like …», options 1, 2, 3, 5.
Lesson 19. Tasks «Coincidences», options 1, 2, 3, 5.
Lesson 20 Tasks «Older, younger», options 1, 2, 3, 5.
Lesson 21. Tasks “Either one or the other”, options 1, 2, 3, 5.
Lesson 22. Tasks «Closer, more to the left», options 2, 3, 4, 5.
Lesson 23. Tasks «Relatives», options 2, 3, 4, 5.
Lesson 24. Tasks «More than …», options 2, 3, 4, 5.
Lesson 25. Tasks «Just like …», options 2, 3, 4, 5.
Lesson 26. Tasks «Coincidence», options 2, 3, 4, 5.
Lesson 27. Tasks «Closer, more to the left», options 1, 2, 3, 4, 5.
Lesson 28. Tasks «Either one or the other», options 1, 2, 3, 4.
Lesson 29. Tasks «More than …», options 1, 2, 3, 4, 5.
Lesson 30. Tasks «Just like …», options 1, 2, 3, 4, 5.
2.9. Characteristics of the diagnostics of the construction of reasoning
To diagnose the formation of the universal action of constructing reasoning, the technique «Similarity, difference» was developed and tested, which includes 9 tasks, the construction of which is based on the correlation of judgments about the similarity and difference in the properties of characters.
- Sveta, Anya and Galya planted vegetables in the beds: two – beets, one –turnips. Sveta and Gali, Sveta and Anya had different vegetables. Who planted turnips?
- a) no one knows who, b) Sveta, c) Galya, d) Anya, e) Marina
- Vera, Anya, Olya and Galya cooked porridge: three — semolina, one — rice. Gali and Anya, Anya and Vera had different cereals. What kind of porridge did Olya cook?
- a) barley, b) it is not known which, c) semolina, d) buckwheat
- Misha, Borya and Yura repaired toys: two – a car, one – a plane. Sasha and Yura had different toys. Who repaired the plane?
- a) Misha, b) Borya, c) Sasha, d) no one knows who, e) Yura
- Asya, Nina and Yulia milked animals: two – a cow, one is a goat. Asya and Yulia, Yulia and Nina had different animals. Who hasn’t milked a cow?
- a) no one knows who, b) Yulia, c) Nina, d) Asya, e) Ira
- Borya, Misha, Sasha and Vasya made shelves for the closet: three are large shelves, one is small. Boris and Misha had different regiments, while Sasha and Vasya did not have different regiments. What shelves did Sasha make?
- a) large, b) it is not known which, c) small, d) wooden
- Vera, Anya, Yulia and Katya were preparing dinner: three of them cooked meat, one fish. Katya and Yulia, Yulia and Vera cooked different things. What didn’t Anya cook?
- a) it is not known what, b) meat, c) poultry, d) fish, e) crayfish
- Lyova, Klim and Igor read newspapers: two – for the second nick, one for Wednesday. Petya and Sasha read the newspaper for Thursday. Igor and Lyova, Lyova and Klim read different newspapers. Who read the newspaper for Wednesday?
- a) Petya, b) no one knows who, c) Lyova, d) Igor, e) Klim
- Roma, Borya, Kolya and Petya drank milk: three from tea shek, one from a glass. Nicholas and Mikhail did not drink juice from cups and glasses. Petya and Roma, Roma and Borya had different dishes. Why didn’t Kolya drink milk?
- a) from a glass, b) from a cup, c) from a glass, d) it is not known from what
- Dima, Ilya and Yura bought shoes: two – boots, one – boots. Roma and Borya bought sandals. Dima and Yura had different shoes. What did Ilya buy?
- a) boots, b) it is not known what, c) boots, d) shoes
3.Results
At the first stage of the study, at the beginning of the school year (the first week of September), frontal experiments were carried out with second-grade students, the control group (46 people) and the experimental group (49 people), using the diagnostic technique “Resemblance , difference».
The results of the survey showed approximately the same level of formation of the action of constructing reasoning in children of the control and experimental groups: all 9 tasks of the method were correctly solved by 10.9% and 10.2% of the subjects, respectively.
At the second stage, 30 lessons were conducted with the experimental group after school hours. At each lesson, the children solved 12-14 plot-logical problems of different variants of each of the seven types indicated above.
At the third stage, at the end of the academic year (the last week of May), frontal experiments were again carried out with the subjects of the control and experimental groups on the material of the diagnostic technique «Similarity, Difference».
The results of the survey showed approximately the same level of formation of the action of constructing reasoning in children of the control and experimental groups: all 9 tasks of the method were correctly solved by 10.9% and 10.2% of the subjects, respectively.
At the second stage, 30 lessons were conducted with the experimental group after school hours. At each lesson, the children solved 12-14 plot-logical problems of different variants of each of the seven types indicated above.
At the third stage, at the end of the academic year (the last week of May), frontal experiments were again carried out with the subjects of the control and experimental groups on the material of the diagnostic technique «Similarity, Difference».
The results of the survey showed a statistically significant difference in the level of formation of the action of constructing reasoning in children of the control and experimental groups: all 9 tasks of the method were correctly solved, respectively, by 21.7% and 42.8% of the subjects (the difference between the noted indicators is statistically significant at p < 0.05).
- Conclusion
The data obtained indicate that conducting 30 developmental lessons with second-graders on the material of plot-logical tasks of various types creates favorable conditions for the formation in children of the universal action of constructing reasoning.
This fact suggests that the inclusion in a special program for the formation of universal educational activities (the main educational program of elementary school) tasks that are not related to the content of academic subjects creates conditions for expanding the possibilities of primary education in the formation of
universal learning activities related, in particular, to the construction of reasoning.
In the future, it is planned to conduct 30 lessons, tested in this study, with children studying in the third and fourth grades of primary school.
References
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3. Zak A. Z. (2007).Diagnosis of differences in the thinking of younger schoolchildren. Moscow: Genesis [in Russian].
4. Zak A. Z. (2007). Intelligence. The book for the teacher. Moscow: Intellect-center[in Russian].
5. Federal State Educational Standard of Primary General Education / Bulletin of Education of Russia. 2010. No. 2. pp.10 – 38. [In Russian].