Good day, dear friends! Do you remember what grades you got in school? I remember. There are no triples in my certificate. But during any year of study there were triples, deuces, and even cola sometimes happened. So I think, who is Alexandra, my daughter, like? Excellent student, hangs on the honor roll! Apparently those additional exercises that we do with her are bearing fruit.
Lesson plan:
A very interesting exercise! Useful not only for children, but also for adults. This exercise is used as a test at the casting of radio hosts. Imagine, you come to the casting, and they say to you: “Come on, my friend, connect us a chicken with a pole.” In all seriousness, they say so!
The meaning is precisely in this, it is necessary to combine two absolutely unrelated concepts. Radio presenters need this in order to quickly and beautifully compose lead lines to songs during live broadcasts, for easy transitions from one topic to another.
Well, the kids are suitable for the development of creative, creative, quick thinking.
So how do you connect a chicken with a pole? Lots of options:
Do you want to work out? Good. Connect:
If in the previous exercise we connected, then in this we will break one long word into many short ones, consisting of letters big word. According to the rules, if a letter occurs once in a long word, then it cannot be repeated twice in short words.
For example, the word "switch" breaks down into:
I don't see any more options, do you?
You can break any long words, for example, “holiday”, “picture”, “towel”, “polar explorer”.
Solving puzzles helps to think outside the box, creatively. Teaches the child to analyze.
Rebuses may contain images, letters, numbers, commas, fractions, placed in a very different order. Let's try to solve some simple puzzles together.
Trained? Now try to solve the puzzle yourself.
You can share your answers in the comments. You will find many puzzles in children's magazines and.
Can an orange be turned into a spaniel and vice versa? "Easily!" anagram lovers will answer. You don't even need a magic wand.
An anagram is a literary device that consists in rearranging the letters or sounds of a certain word (or phrase), which results in another word or phrase.
Just as easily, a dream turns into a nose, a cat into a current, and a linden into a saw.
Well, shall we try? Let's make it so:
The more logic puzzles you solve, the stronger your thinking becomes. After all, it is not for nothing that they say that mathematics is gymnastics for the mind. Indeed, when solving some of them, you directly feel how the brain moves.
Let's start with the simpler ones:
And the next three problems Sashulya brought from the Mathematical Olympiad. These are tasks for the third grade.
“The gardener planted 8 seedlings. Of all but four, pear trees have grown. All but two pear trees grow pears. Pears from all fruit-bearing pear trees except one are not tasty. How many pear trees have tasty pears?”
“Vasya, Petya, Vanya wear ties of only one color: green, yellow and blue. Vasya said: "Petya does not like yellow." Petya said: "Vanya wears a blue tie." Vanya said: "You are both deceiving." Who prefers what color if Vanya never lies?
And now attention! A task of increased difficulty! "On the backfill," as they say. I couldn't solve it. I suffered for a long time, and then I looked at the answers. She is also from the Olympics.
“The traveler needs to cross the desert. The transition lasts six days. The traveler and the porter who will accompany him may take with him a supply of water and food for one person for four days each. How many porters will the traveler need to realize his plan? Enter the smallest number."
If you still fall asleep on any task, then contact me, I will help)
Matches are not toys for children! A tool for training thinking. For safety reasons, I suggest replacing matches with counting sticks.
These simple little sticks make very complex puzzles.
First, let's warm up:
Now more difficult:
Move three sticks so that the arrow flies in the opposite direction.
The fish also needs to be turned in the other direction, while shifting only three sticks.
After shifting only three sticks, remove the strawberry from the glass.
Remove two sticks to make two equilateral triangles.
The answers can be found at the end of the article.
And now let's work as Sherlock Holmes! Let us seek the truth and discover lies.
Show the child two pictures, on one of which depict a square and a triangle, and on the other a circle and a polygon.
And now offer cards with the following statements:
The task is to determine whether these statements are false or true for each picture with figures.
Such an exercise can be carried out not only with geometric shapes, but also with images of animals. For example, put a cat, a fox and a squirrel on the picture.
Statements can be as follows:
Pictures and statements to them can be selected independently.
We are surrounded by a variety of things. We use them. Sometimes we do not pay any attention to the instructions that are attached to these items. And it also happens that there are simply no instructions for some very necessary items. Let's fix this misunderstanding! We will write the instructions ourselves.
Take, for example, a comb. Yes, yes, the usual comb! That's what we got with Alexandra.
So, instructions for using the comb.
Try writing instructions for a pot, or slippers, or a glasses case. It will be interesting!
Stories can be composed in different ways, for example, based on a picture or on a given topic. By the way, this will help. And I suggest you try to compose a story based on the words that must be present in this story.
As always, an example.
Words are given: Olga Nikolaevna, poodle, sequins, turnip, salary, gray hair, castle, flood, maple, song.
Here's what happened to Sasha.
Olga Nikolaevna walked down the street. On a leash, she led her poodle Artemon, the poodle was all shiny. Yesterday he broke the lock on the locker, got to the box of glitter, and poured it all over himself. And Artemon gnawed through the pipe in the bathroom and made a real flood. When Olga Nikolaevna came home from work and saw all this, gray hair appeared in her hair. And now they were going for turnips, as turnips calm the nerves. And the turnip was expensive, worth half the salary. Before entering the store, Olga Nikolaevna tied the poodle to a maple tree and, singing a song, went inside.
Now try it yourself! Here are three sets of words:
We have already worked as detectives. Now I propose to work as a police officer. The fact is that the words in well-known proverbs and sayings violated the order. We will deal with violators of the order. Try to arrange the words the way they are supposed to stand.
I want to clarify. We don't do this on purpose. That is, it doesn’t happen that I say: “Come on, Alexandra, sit down at the table, let’s develop thinking!” No. All this in between times, if we go somewhere, we go, before going to bed instead of books. It is very interesting to do it, so you don’t have to force anyone.
Well, now the promised answers to matchstick puzzles!
About two triangles of five matches.
About two squares out of seven.
We get three squares.
Expand the arrow (watch the color of the sticks).
We turn the fish.
And about two equilateral triangles.
I recently found this video on the Internet. It has completely different exercises. We tried, until it turns out with difficulty. Well, let's practice. See if you can use it too.
Dare! Get busy! Develop with your children. Try these "golden" exercises. Show off your results in the comments!
Thank you for your attention!
And I look forward to visiting again! Here you are always welcome!
Annotation.
The article highlights the psychological and pedagogical aspect of development problems logical thinking students primary school. Influence of innovative pedagogical technologies on the learning process of younger students. Conclusions of experimental work on the development of logical thinking.
Keywords:
research, innovative technologies, indicators of the development of logical thinking
Target of this work is to study the development of logical thinking of younger students in mathematics lessons.
The object of the study is
Subject of study: development of logical thinking of younger schoolchildren in mathematics lessons.
Hypothesis- It is assumed that the process of developing logical thinking in younger students will be more effective if:
On the extracurricular activities in mathematics at primary school innovative technologies will be applied;
innovative technologies will be the main tool for learning new material, consolidating what has been learned and testing knowledge.
Base of experiment: 3rd and 4th grades of secondary secondary school No. 13 of the city of Almetyevsk, Republic of Tatarstan.
Introduction
The relevance of research. The development of logical thinking in younger students is a necessary stage in their psychological development, as well as their most comfortable adaptation in modern society. Thus, the relevance of this study lies in the need to improve various techniques teaching younger schoolchildren aimed at developing their logical thinking. Such well-known psychologists as V. Krutetsky, N. Lukin, A. Luria, J. Piaget, S. Rubinshtein, D Feldshtein and others. The research of these scientists formed the basis of the psychological and pedagogical concepts of developmental education (V. Davydov, L. Zankov, E. Kabanova-Meller, N. Pospelov), the central idea of which is the development of the student's mental abilities as a subject of educational activity. The question of applicability and expediency the use of innovative technologies for the development of logical thinking in primary school students is still open. And this is connected, first of all, with the growth and improvement of the scientific and technical base used in the pedagogical industry. A significant contribution to the development of the methodology and theory of the concept of pedagogical innovative technology was made by modern teachers: V. Bespalko, G. Burgin, V. Zhuravlev, V. Zagvyazinsky, G. Klarin, B. Likhachev, V. Monakhov, P. Pidkasisty, G. Selevko , N. Yusufbekov.
Theoretical foundations for the development of logical thinking with the help of innovative technologies
Psychological and pedagogical aspect of the problems of development of logical thinking of primary school students
The problem of logical thinking of students in pedagogy was studied by the classics of pedagogy (Y. Comenius, I. Pestalozzi, K. Ushinsky), but its study began especially intensively in the 50s of the 20th century, which was served by the publication methodical writing"The development of logical thinking in the process of teaching in elementary school", compiled by the Institute of Teaching Methods of the Academy of Pedagogical Sciences of the RSFSR. In this document, the following tasks were formulated for pedagogical science and practice: a) to develop the logical thinking of students in the process of teaching them general subjects, b) to explain to students the meaning and essence of logical knowledge and skills, c) to determine ways and means of implementing the above tasks. Already in elementary school, children must master the elements of logical actions of comparison, classification, generalization. school age thinking undergoes significant changes. It becomes abstract and generalized. Researchers such as P. Galperin and V. Davydov also noted the facts of confusion by children of size and quantity (the younger student is shown 4 small circles and 2 large ones and they ask where is more, the child points to 2 large ones) Other scientists (L. Vygotsky and A. Luria ) noted that speech appears for a child of primary school age as a glass through which something is visible, but the glass itself (the word) is not visible. Many foreign and domestic scientists dealt with the problem of developing the logical thinking of students. Scientists I. Lerner, I. Nikolskaya, N. Partiev, N. Podgoretskaya, A. Stolyar, N. Talyzina, theoretically and experimentally proved that the school does not provide elementary school graduates with the necessary level of logical literacy. logical thinking of younger schoolchildren is quite acute in front of the tasks of elementary school. And before giving a definition of "logical thinking", it is necessary to answer the questions, what is "logic" and "thinking" in particular. For convenience, a content analysis of definitions was compiled. At primary school age, it is thinking that becomes the dominant function. Depending on the extent to which the thought process is based on perception, representation or concept, there are three main types of thinking: objective-effective (visual-effective); visual-figurative; abstract (verbal-logical).
Age features of younger students
If we talk about the features of the cognitive and educational activities of a younger student, then we can distinguish the following components: perception; memory; reproduction; attention (switching); imagination; thinking (comparison, abstraction, generalization); speech.
Reproduction is a difficult activity for a younger student, requiring goal setting, the inclusion of thinking processes, and self-control.
The elementary schoolchildren are also imperfect in such an important property of attention as switching. Children more easily abstract the properties of objects than connections and relationships. Generalization in primary school characterized by awareness of only some of the signs, since the student cannot yet penetrate into the essence of the subject. And finally, the inference is made by him on the basis of knowledge of general theoretical concepts. Deductive inference is more difficult for a younger student than inductive one. At primary school age, children become aware of their own mental operations, which helps them to exercise self-control in the process of cognition. In the process of learning, the qualities of the mind also develop: independence, flexibility, criticality.
G. Zukerma distinguishes four groups of junior schoolchildren who are included in educational activities in different ways: "breakthrough group", "breakthrough group reserve", "hard-working" and "not showing themselves".
The Influence of Innovative Pedagogical Technologies on the Learning Process of Primary School Students
The scientific innovations that drive progress cover all areas of human knowledge. There are socio-economic, organizational and managerial, technical and technological innovations. One of the varieties of social innovations are pedagogical innovations.
Pedagogical innovation is an innovation in the field of pedagogy, a purposeful progressive change that introduces stable elements (innovations) into the educational environment that improve the characteristics of both its individual components and the educational system itself as a whole.
At the moment, a variety of pedagogical innovations are used in school education. It depends, first of all, on the traditions and statute of the institution. Nevertheless, the following most characteristic innovative technologies can be distinguished: information and communication technologies in subject education; personality-oriented technologies in teaching the subject; information and analytical support of the educational process and quality management of schoolchildren's education; monitoring of intellectual development; educational technologies as the leading mechanism for the formation a modern student; didactic technologies as a condition for the development of the educational process; psychological and pedagogical support for the introduction of innovative technologies in the educational process of the school.
There is another classification of pedagogical innovative technologies that is used in teaching children. Such innovative learning technologies include: interactive learning technologies, project-based learning technology and computer technology.
Pedagogical conditions for the development of logical thinking of younger students
Our teaching staff has formed pedagogical conditions development of logical thinking using innovative technologies.
Practicing the organization and conduct of non-standard lessons, we can conclude that it is these lessons that increase the effectiveness of learning, develop activity, independence, personal initiative and creative abilities of students.
The use of innovative technologies in teaching mathematics is explained by the need to solve the problem of finding ways and means of activating the cognitive interest of students, developing their creative abilities, and stimulating mental activity. A feature of the educational process with the use of computer tools is that the center of activity is the student, who, based on his individual abilities and interests, builds the process of cognition. A “subject-subjective” relationship develops between the teacher and the student. The teacher often acts as an assistant, consultant, encouraging original discoveries, stimulating activity, initiative and independence.
The results of the diagnostic stage to determine the level of development of logical thinking in younger students
Criteria, indicators, levels of development of logical thinking of primary school students were identified using computer tools.
Determined the level of ability to apply logical actions in practice.
Within the framework of theoretical and activity criteria, to determine the ability of primary school students to understand the educational task and to determine the level of development of the ability of younger students to plan their actions, the method "Logical tasks" was used.
Analyzing the work obtained in the course of the ascertaining experiment, it should be noted that the children expressed uncertainty in the ability to solve problems. This was expressed by the fact that the children constantly asked whether they had solved this or that problem correctly. The rest of the children actively participated in the testing with expressed interest and confidence in their actions.
To determine the level of development of the ability to plan their actions, the test "Logical tasks" was taken.
Based on the test results, a table was compiled that reflects the ability of the class to plan their actions. On average, the level of development of planning their actions in two cases is satisfactory.
As part of a practical criterion to determine the level of application of simple logical actions in practice, the “Think!” methodology was used, which offers 5 tasks of a mathematical and everyday nature. This technique reflects a number of indicators: the use of simple logical operations in mathematics; application of logical skills in everyday life; ability to solve problems that require logical actions
According to the test results, it can be seen that younger students have sufficiently developed logical thinking, but not everyone can apply logical actions in practice. Most of the class is at the lower level, which indicates the inability to solve such problems.
Based on the analysis of the test, a table was compiled in which the result of the answers was placed in percentage terms.
The general results of the initial level of logical thinking were as follows: students have little command of logical actions, are unable to single out a learning task and apply their knowledge in practice. However, they show a desire to develop their logical skills, middle-level students kept within the task, most of the tasks were solved correctly. Children of this level can single out a learning task, try to plan their actions, but cannot put into practice general logical operations. Expressed interest in further development. A high level of logical thinking implies full possession and application of the basic logical actions that are characteristic of primary school children. That is, children of this level easily single out a learning task, plan their actions, applying their knowledge in practice. They also strive to further develop their abilities. As a rule, these students have an interest in exact sciences such as mathematics, physics and computer science.
Comparative results of the level of development of logical thinking of younger students.
Based on the results of the ascertaining experiment, it can be concluded that the logical thinking of students is below the average level and needs to be improved and corrective work. Therefore, tasks were developed for the implementation of psychological and pedagogical conditions for the development of logical thinking of younger students.
Extra-curricular activities were developed aimed primarily at developing the basic skills of educational activities. Namely: highlight and hold the learning task; independently find and assimilate common ways of solving problems; adequately assess and control themselves and their activities; own reflection and self-regulation of activity; use the laws of logical thinking; own and use different forms generalizations, including theoretical ones.
To implement the first pedagogical condition, namely, the use of innovative technologies in extracurricular activities, lesson notes were developed for children in the third and fourth grades.
To implement the second pedagogical condition - the use of ICT when studying new material, consolidating what has been learned and testing knowledge, the computer game complex "World of Informatics" was used. From it were selected tasks aimed at the development of logical thinking.
The result of such techniques as "Magic Squares", "Logical tasks" showed that children began to master logical operations better and apply them in practice. Most of the children in the class showed high level knowledge in the lessons of mathematics and the Russian language; increased their intellectual level and learned to identify learning tasks; learned to plan and organize their activities.
As experience shows, at school age one of effective ways The development of thinking is the solution of non-standard logical problems by schoolchildren. Mathematics has a unique developmental effect. Like no other subject, mathematics provides real prerequisites for the development of logical thinking.
“She puts the mind in order”, i.e. forms the best tricks mental activity and qualities of the mind, but not only. Its study contributes to the development of memory, speech, imagination, emotions; forms perseverance, patience, creative potential of the individual. The main purpose of doing mathematics is to give the child a sense of self-confidence, based on the fact that the world is ordered and therefore comprehensible, and therefore predictable for a person. What can you teach a child when teaching mathematics? Reflect, explain the results obtained, compare. Guess, check. Are they correct; observe, summarize and draw conclusions.
In principle, in mathematics textbooks, a line is quite clearly traced towards the development of students' cognitive interests: they contain exercises aimed at developing attention, observation, memory, as well as developmental tasks, tasks of a logical nature, tasks requiring the application of knowledge in new conditions. Such tasks should be included in classes in a certain system through the use of the method of inductive reasoning, to lead students to the goal. It is necessary to teach children to notice patterns, similarities and differences starting from simple exercises, gradually complicating them.
It must be remembered that mathematics is one of the most difficult subjects, but the inclusion of didactic games and exercises allows you to change the types of activities in the lesson more often, and this creates conditions for increasing the emotional attitude to the content. educational material ensures its accessibility and awareness.
A well-known domestic teacher V. Sukhomlinsky devoted a significant place to the issue of teaching younger schoolchildren to logical problems in his works. The essence of his reasoning is reduced to the study and analysis of the process of solving logical problems by children, while he empirically revealed the peculiarities of children's thinking. He writes about work in this direction in his book “I give my heart to children”: There are thousands of tasks in the world around us. They were invented by the people, they live in folk art as riddle stories.
Here is one of the tasks that the children solved at Sukhomlinsky's school: From one bank to another it is necessary to transport a wolf, a goat and a cabbage. At the same time, you can neither transport nor leave a wolf and a goat, a goat and cabbage together on the shore. You can transport only a wolf with cabbage or each passenger separately. You can make as many flights as you like. How to transport a wolf, a goat and a cabbage so that everything goes well?
In the work on the development of logical thinking, it is also necessary to use a system of non-traditional tasks, exercises, games. They are aimed at the development of almost all mental operations. They can be successfully used in the classroom, recommended to use their parents during classes with children. Moreover, non-traditional tasks, exercises, games are not currently in short supply. A huge number of printed materials, video products, all kinds of games - all this is possible, selectively taking into account age and psychological characteristics students to use in the classroom, extracurricular activities and, accordingly, in the family.
But the development of logical thinking is impossible in principle without knowledge of the characteristics of the psychology of primary school age. All this is necessary for the child to successfully complete the lower grades, successfully study in the middle school, i.e. it is necessary to help him in the development of his mental processes, the formation of mental functions that contribute to:
formation of the ability to self-regulation;
the formation of theoretical thinking;
an interest is formed in the content of educational activities, the acquisition of knowledge.
attention becomes arbitrary;
there is an awareness of one's personal relationship to the world;
"memory becomes thinking";
"perception becomes thinking";
the content of the internal position of children changes;
the nature of self-esteem changes;
character develops;
Considering all this, it is necessary to start learning logical actions from the formation
relevant elementary skills.
As tasks that develop logical thinking in mathematics lessons, these are tasks for:
Isolation of features of objects
Recognition of objects by given features
Formation of the ability to highlight the essential features of objects
Comparison of two or more items
Classification of objects and phenomena.
Exercises aimed at developing the ability to divide objects into classes according to a given basis
Geometric lotto.
8. The development of logical thinking is facilitated by tasks that can be called "Mistakes - invisible."
9. Logical tasks.
Most elements of the development of logical thinking have a game meaning, but children should not be taught to expect games or fairy tales at every lesson, since the game should not be an end in itself, but must necessarily be subordinated to those specific educational and educational tasks that are solved on class and outside of class.
The systematic use in mathematics lessons and extracurricular activities of special tasks and tasks aimed at developing logical thinking expands the mathematical horizons of younger students and allows them to more confidently navigate the simplest laws of the reality around them and more actively use mathematical knowledge in Everyday life.
The development of thinking also affects the upbringing of the child, develop positive features character, the need to develop their good qualities, efficiency, activity planning, self-control and conviction, love for the subject, interest, desire to learn and know a lot. All this is essential for the future life of the child. Sufficient preparedness of mental activity relieves psychological overload in learning, preserves the health of the child.
Tasks, exercises, tasks for the development of logical thinking
I. Selection of features of objects:
1. What are the signs of a triangle, square, pentagon.
2. What digits does the number consist of: 27?
3. Name some three signs of this figure.
4. What number do the numbers start with: 14,18,25,46,37,56?
5. What shape does the figure have?
6. Specify signs of numbers: 2,24,241
II. Recognition of objects by given features
1. Which object has the following features at the same time:
a) has 4 sides and 4 corners;
b) has 3 sides and 3 corners.
2. How many vertices does the figure have, how many segments does it consist of? how
what is the name of this figure?
3. What numbers are missing in the following examples?
a) 12+12:2=18
b) 12+12:3=16
c) 12+12: …=…
III. Formation of the ability to highlight the essential features of objects
1.Triangle (corners, sides, drawing, plywood, cardboard, area)
Answer: (Angles, sides).
2.Cube (corners, drawing, stone, side)
Answer: (corners, side)
IV. Comparison of two or more items
1. How are the numbers similar?
a) 7 and 71 b) 77 and 17 c) 31 and 38 d) 24 and 624 e) 3 and 13 e) 84 and 754
2. What is the difference between a triangle and a quadrilateral?
3. Find common features in the following numbers:
a) 5 and 15 b) 12 and 21 c) 20 and 10 d) 333 and 444 e) 8 and 18 f) 536 and 36
4. Read the numbers of each pair. How are they similar and how are they different?
a) 5 and 50 b) 17 and 170 c) 201 and 2010 d) 6 and 600 e) 42 and 420 f) 13 and 31
V. Classification of objects and phenomena.
1. A set of squares is given - black and white, large and small.
Divide the squares into the following groups:
a) large and white squares;
b) small and black squares;
c) large and black squares;
d) small and white squares.
2. Circles are given: large and small, black and white. They are divided into 2 groups:
On what basis are the circles divided?
a) by color
b) in size
c) by color and size (correct answer).
VI . Exercises aimed at developing the ability to divide objects into classes according to a given basis
1. Divide the following numbers into 2 groups:
1,2,3,4,5,6,7,8,9,10.
Even numbers______________
Odd numbers____________
To which group do you attribute the numbers: 16,31,42,18,37?
2. Divide the following numbers into 2 groups:
2,13,3,43,6,55,18,7,9,31
single digits ____________
double figures______________
3. Name the groups of numbers in one word:
a) 2,4,6,8 is ________________
b) 1,3,5,7,9 is ______________
4. Schoolchildren are given a set of cards.
Tasks: Divide the cards into the following groups:
a) in form
b) by the number of items
VII . Geometric lotto.
Here work with children continues, their knowledge, shapes, sizes and colors of objects are consolidated.
Great observation is required from students by logical chains that need to be continued to the right and left, if possible. To complete the task, you need to establish a pattern in the notation of numbers:
Answers
……5 7 9…… (1 3 5 7 9 11 13)
…..5 6 9 10….. (1 2 5 6 9 10 13 14)
…..21 17 13….. (29 25 21 17 13 9 51)
6 12 18………. (6 12 18 24 30 36..)
…..6 12 24…… (36 12 24 48 96…)
0 1 4 5 8 9…….. (014589 12 13 16 17)
0 1 4 9 16……… (0149 16 25 36 49..)
Interesting game"Extra number".
Numbers are given: 1,10,6 Which of them is superfluous?
Extra can be 1 (odd)
Extra may be 10 (two-digit)
Extra may be 6 (1 and 10 used 1)
Given numbers: 6,18,81 What is the odd number?
Comparison can be carried out on even, odd, unambiguous, double-valued, the participation of the numbers 1 and 8 in writing. But in addition, they can be compared by the presence of identical divisors.
You can also compare mathematical expressions:
3+4
1+6
What common?
At first glance, there is nothing in common, except for the sign of the actions, but the first terms are less than the second, the first terms are odd, and the second are even. Yes, the amount is the same.
VIII . The development of logical thinking is facilitated by tasks that can be called "Invisible Errors".
Several mathematical expressions containing an obvious error are written on the board. The task of the students, without erasing or correcting anything, is to make the mistake invisible. Children can give different variants bug fixes.
Tasks and options for correcting errors:
10 < 10 8=7 6+3=10
10 < 100 15-8=7 6+3=10-1
10 < 10+1 8=7+1 1+6+3=10
12-10 < 10
Presented tasks, games, exercises are of great interest to children. But it is he who should underlie the education of a younger student. Interest supports a high level of cognitive activity, which in turn contributes to the development of the child's intellectual abilities.
Logical tasks allow you to continue classes with children to master such concepts as left, right, above, below, more, less, wider, narrower, closer, further, etc.
IX .Logical tasks.
Examples of logical tasks related to mathematics that contribute to the development of logical thinking:
1. Five knots were tied on the rope. How many parts did these knots divide the rope into?
2. To cut the board into several pieces, the student made six marks on it. How many pieces will the student cut the board into?
3. Two sons and two fathers are walking down the street. Only three people. Could it be?
4. The thermometer shows three degrees of frost. How many degrees will two such thermometers show?
5. Alyosha spends 5 minutes on the way to school. How many minutes will he spend if he goes alone with his sister?
6. Kolya is taller than Andrei, but shorter than Serezha. Who is taller Andrey or Seryozha?
7. In a rectangular room, 8 chairs should be arranged like this. Each wall should have 3 chairs.
Complex intellectual games for the development of logical thinking of children Game thinking training is useful to all students, especially those who experience noticeable difficulties in performing various kinds educational work: understanding and comprehension of new material, its memorization and assimilation, establishing links between various phenomena, expressing one's thoughts in speech. The complex of intellectual games allows you to develop and improve thinking. The games use tasks based on simple, well-known material.
Games:
1. "Drawing up proposals."
Children are offered three words that are not related in meaning, for example: “pencil”, “triangle”, “student”.
Exercise: make up as many sentences as possible that would necessarily include all these three words. The time allotted is approximately 10 minutes. This game develops the ability to establish connections between objects and phenomena, think creatively, create new integral images from destroyed objects.
2. "Search for common properties."
Children are offered two words that are little related to each other. In 10 minutes, they must write as many common features as possible for these objects.
For example, "bucket", " balloon". The one with the longest list of common features wins the game. This work is essential. So that children learn to discover the connections between objects, and also learn very clearly what the essential and non-essential features of objects are.
3. "What is superfluous?"
Children are offered any three words:
Exercise: of the proposed three words, only those two that have somewhat similar properties should be left, and one word is “superfluous”, it does not have this common feature, so it should be excluded.
Example: six, eighteen, eighty-one.
4.Thisa game develops the ability to describe properties, compare according to certain parameters, establish relationships, and also move from one relationship to another. The game forms an attitude towards what is absolutely possible. different ways unions and dismemberments of a certain group, and therefore should not be limited to any one solution. There can be many solutions. This game,
therefore, teaches to think creatively.
5. "Search for an item (numbers, etc.) that have similar properties.”
The word is written on the board. For example: "square". Time to complete this task
limited to 5-10 minutes.
Exercise: it is necessary to write as many objects (something) as possible that are an analogue of a given word and indicate by what property it is similar to the named one. This game teaches to single out a wide variety of properties in an object, as well as to operate separately with each of them, forms the ability to classify phenomena (forms, etc.) according to their characteristics.
6. "Search for objects with opposite properties."
Take the word "circle" for example.
Task for children : Write as many words as possible that are opposite in features to what is written on the board.
This game forms the ability to study properties, introduces such a category as the opposite, which is very important for the development of the child's intellectual abilities.
Ministry of Education and Science of the KChR, Zelenchuksky district
MOU "Secondary School N. Arkhyz"
The development of logical thinking in younger students
Nizhny Arkhyz
I. Significance of the development of logical thinking in children.
II. Types of exercises for the development of logical thinking.
a) Choose two words
b) "What's wrong?"
c) What do they have in common?
d) "Choose the words"
III. Intersubject communications.
IV. The development of verbal-logical memory.
a) Tasks for determining the truth and falsity of judgments;
b) Tasks with linking words.
V. "Mathematics is the gymnastics of the mind."
a) Development of cognitive interests;
b) Logical tasks in mathematics lessons;
c) "Compare and draw a conclusion";
d) Logical tasks of three levels;
e) Finding patterns;
e) "Continue the row";
g) Non-standard tasks.
VI. And what is the result?
The development of logical thinking in children is one of the important tasks of primary education. The ability to think logically, to make conclusions without visual support, to compare judgments according to certain rules - necessary condition successful assimilation of educational material.
Thinking should be developed from the first days of a child's life: at home, in kindergarten and school.
In parallel with the development of thinking, the child also develops speech, which organizes and clarifies the thought, allows you to express it in a generalized way, separating the important from the secondary.
The development of thinking affects the upbringing of a person. The child develops positive character traits and the need to develop good qualities in himself, efficiency, the ability to think and reach the truth on his own, plan activities, as well as self-control and conviction, love and interest in the subject, the desire to learn and know a lot.
Sufficient preparedness of mental activity relieves psychological stress in learning, prevents poor progress, and preserves health.
No one will argue with the fact that every teacher must develop the logical thinking of students. This is stated in the explanatory notes to the curricula, they write about this in methodical literature for teachers. However, the teacher does not always know how to do this. Often this leads to the fact that the development of logical thinking is largely spontaneous, so the majority of students, even in high school, do not master the initial methods of logical thinking, and these methods must be taught to younger students.
First of all, from lesson to lesson, it is necessary to develop the child's ability to analyze and synthesize. The sharpness of the analytical mind allows you to understand complex issues. The ability to synthesize helps to simultaneously keep in sight difficult situations, find causal relationships between phenomena, master a long chain of inferences, discover connections between single factors and general patterns. The critical orientation of the mind warns against hasty generalizations and decisions. It is important to develop productive thinking in a child, that is, the ability to create new ideas, the ability to establish connections between facts and groups of facts, to compare a new fact with a previously known one.
The psychologist noted the intensive development of the intellect of children at primary school age. The development of thinking leads, in turn, to a qualitative restructuring of perception and memory, their transformation into regulated, arbitrary processes.
A child, starting to study at school, must have a sufficiently developed concrete thinking. To form him scientific concept, it is necessary to teach him a differential approach to the features of objects. It must be shown that there are essential features, without which an object cannot be brought under this concept. The criterion for mastering a particular concept is the ability to operate with it. If students in grades 1-2 distinguish, first of all, the most visual external signs characterizing the action of the object (what it does) or its purpose (what it is for), then by the third grade, schoolchildren already rely more on knowledge, ideas that have developed in the learning process.
The following exercises contribute to this:
Select two words that are most significant for the word in front of the brackets:
Reading (eyes , notebook, book, pencil, glasses)
Garden (plant, dog, fence, shovel , Earth)
Forest (sheet, trees, apple tree, hunter, bush)
What is superfluous?
ONUAI
135А48
"What do they have in common?"
.
Ask your child how one word can describe what you read.
1. Perch, crucian - ...
2. Cucumber tomato - …
3. Wardrobe, sofa - …
4. June July - …
5. Elephant, ant -…
A more complex version of the exercise contains only two words for which you need to find a common concept.
"Find what the following words have in common: a) bread and butter (food)
b) nose and eyes (parts of the face, sense organs)
c) apple and strawberry (fruits)
d) clock and thermometer (measuring instruments)
e) whale and lion (animals)
f) echo and mirror (reflection)"
An exercise. "Choose the words."
1) "Pick up as many words as possible that can be attributed to the group of wild animals (pets, fish, flowers, weather phenomena, seasons, tools, etc.)".
2) Another version of the same task.
Connect with arrows the words that fit the meaning:
ball furniture
poplar flower
cupboard insects
plate wood
coat clothes
ant tableware
pike toy
rose fish"
Such tasks develop the child's ability to distinguish generic and species concepts, form inductive speech thinking.
Working on the development of logical thinking, I rely on my faith in the potential of children. Some guys can think quickly, are capable of improvisation, others are slow. We often rush the student with the answer, get angry if he hesitates. We demand speed of reaction from the child, but we often achieve that the student either gets used to expressing hasty, but unfounded judgments, or withdraws into himself.
Already in elementary school, when constructing the content of education, it is necessary to provide a system of necessary logical methods of thinking. And although logical techniques were formed in the study of mathematics, they can later be widely used as cognitive ready-made means in mastering the material of other academic subjects. Therefore, when selecting logical techniques that should be formed in the study of a certain subject, one should take into account interdisciplinary connections.
Taking into account subject relations, I use the following tasks:
1. Find an unknown number:
Herring Ice
Soloist List
72350 ?
Answer: 3
In the words of the first column, the first two and the last two letters are excluded. This means that in the number it is necessary to exclude the first two and last two digits, respectively. We get the number 3.
2. Find an unknown number:
Aircraft Scrap
Starling Ditch
350291 ?
Answer: 20
Children notice that in the words plane and starling, two extreme letters are excluded, and the rest are read in reverse order. Therefore, eliminating the two extreme digits and rearranging the rest, we get the number 20.
3. Find an unknown number:
Machine 12
Tier 6
School?
Answer: 10
Analyzing words and numbers, we notice that in the word the car- 6 letters, and the number is 2 times more, in a word shooting gallery- 3 letters, the number is 2 times larger, in a word school- 5 letters, the number is 2 times more - 10.
4. Find an unknown number:
Wood + earth = 11
Tourist X sport = ?
Answer: 30
In the word wood- 6 letters, in a word Earth- 5 letters, adding these numbers, we get the number 11. In the word tourist- 6 letters, in a word sport- 5 letters, multiplying these numbers, we get the number 30.
In connection with the relative predominance of the activity of the first signal system, visual-figurative memory is more developed in younger students. Children better remember specific information, faces, objects, facts than definitions and explanations. They often memorize verbatim. This is explained by. That mechanical memory is well developed among them and the younger schoolchild still does not know how to differentiate the tasks of memorization (what needs to be remembered verbatim and what in general terms), the child still has a poor command of speech, it is easier for him to memorize everything than to reproduce in his own words. Children still do not know how to organize semantic memorization: they do not know how to break the material into semantic groups, highlight strong points for memorization, and draw up a logical plan of the text.
Under the influence of learning, memory in children at primary school age develops in two directions:
Increasing role and specific gravity verbal-logical memorization (compared to visual-figurative);
The ability to consciously control one's memory and regulate its manifestation (memorization, reproduction, recall) is formed.
The development of verbal-logical memory occurs as a result of the development of logical thinking.
Tasks for determining the truth or falsity of judgments
1. There are two drawings on the board. One depicts a monkey, a cat, a squirrel, the other a snake, a bear, a mouse. Children are given cards on which various statements are written:
All the animals in the picture can climb trees.
All the animals in the picture have fur.
None of the animals in this picture can fly.
Some of the animals in the picture have paws.
Some of the animals shown in the picture live in burrows.
All the animals in this picture have claws.
Some of the animals in the picture hibernate.
In this picture, there is not a single animal without a mustache.
All animals drawn in the picture are mammals.
None of the animals in the picture lay eggs.
Students need to determine for which picture the statement is true, and for which it is false.
You can invite the children on their own sheets opposite each statement to indicate the number of the picture for which this statement is true.
This task can be made more difficult by inviting the children, looking at these pictures, to come up with their own true and false statements, using the words: all, some, none.
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I use special tasks and tasks in mathematics lessons aimed at developing the cognitive abilities and abilities of children. Non-standard tasks require heightened attention to the analysis of the condition and the construction of a chain of interrelated logical reasoning.
I will give examples of such tasks, the answer to which must be logically substantiated:
1. There are 5 pencils in the box, 2 blue and 3 red. How many pencils must be taken from the box without looking into it so that there is at least one red pencil among them?
2. The loaf was cut into 3 parts. How many incisions were made?
3. The bagel was cut into 4 parts. How many incisions were made?
4. Four boys bought 6 notebooks. Each boy received at least one notebook. Could any boy buy three notebooks?
I introduce non-standard tasks already in the first grade. The use of such tasks expands the mathematical horizons of younger students, contributes to mathematical development and improves the quality of mathematical preparedness.
The use of the classification method in mathematics lessons allows you to expand the methods of work available in practice, contributes to the formation of positive motives in educational activities, since such work contains elements of the game and elements of search activity, which increases the activity of students and ensures independent work. For example:
Divide into two groups:
8 – 6 8 – 5 7 – 2 1 + 7 2 + 5
8 – 4 7 – 3 6 – 2 4 + 3 3 + 5
Write down all the numbers written with two different digits:
22, 56, 80, 66, 74, 47, 88, 31, 94, 44
But especially effective for the development of logical thinking of students are tasks in which the basis for classification is chosen by the children themselves.
The system of work on the development of logical thinking of students is aimed at the formation of mental actions of children. They learn to identify mathematical patterns and relationships, make feasible generalizations, and learn to draw conclusions. The use of reference diagrams and tables in mathematics lessons contributes to a better assimilation of the material, encourages children to think more actively.
As a result of systematic work on the development of logical thinking, the educational activity of students is activated, the quality of their knowledge is noticeably improved.
In conclusion, I would like to advise teachers working on the development of logical thinking in younger students not to forget that it is necessary to take into account the level of ability of the children in your class. Difficulties must be overcome.
List of used literature.
1., Sideleva in primary school: Psychological and pedagogical practice. Teaching aid. – M.: TsGL, 2003. – 208 p.
2. Kostromina to overcome difficulties in teaching children: Psychodiagnostic tables. Psychodiagnostic methods. corrective exercises. - M.: Os - 89, 2001. - 272 p.
3. Artemov A. K., Istomina basics of teaching mathematics in primary school: A manual for students of the faculty of training teachers of primary classes of the correspondence department. - M.: Institute practical psychology, Voronezh: NPO "MODEK", 1996. – 224 p.
4. Vinokurov's abilities of children: Grade 2. – M.: Rosmen-Press, 2002. – 79 p.
5., Parishioners: Textbook for students of secondary pedagogical educational institutions./ Ed. . - M .: Publishing Center "Academy", 1999. - 464 p.
6., Kostenkova activities with children:
Materials for independent work of students on the course "Psychological - pedagogical diagnostics and counseling". – M.: V. Sekachev, 2001. – 80 s.
8. Istomina. Grade 2: A textbook for a four-year elementary school. - Smolensk: Association XXI century, 2000. - 176 p.
In order to develop and improve the logical thinking of younger students, it is necessary to create pedagogical conditions conducive to this.
Primary school education should be aimed at the teacher helping each student reveal your abilities. This is real when the teacher takes into account the individuality of each. In addition, the disclosure of the potential of the younger student contributes to diverse educational environment.
Consider pedagogical conditions, contributing to the formation of the student's logical thinking:
“The success of the full-fledged formation of the logical thinking of a younger student depends on how comprehensively and systematically this is taught.”
Primary school is the best period for purposeful work on the active development of logical thinking. To help make this period productive and productive, all kinds of didactic games, exercises, tasks and assignments aimed at:
Exercises and games for logic
The means of developing the logical thinking of a younger student must be selected taking into account the goals, as well as focusing on individual characteristics and child preferences
It is useful to use non-standard tasks, exercises, games for the development of mental operations both in the classroom and during homework with children. Today they are not in short supply, as developed a large number of printing, video and multimedia products, various games. All these means can be used, selecting taking into account the goals, as well as focusing on the individual characteristics and preferences of the child.
Watch a video with an example of a tablet game aimed at developing the logical thinking of younger students
Exercises and games for logical thinking
In reading lessons:
In Russian language lessons:
In the lessons of natural history:
In math class:
"Advice. To enrich the educational process, as well as for homework, use logical problems and riddles, puzzles, rebuses and charades, numerous examples of which you can easily find in different teaching aids and also on the Internet.
Tasks that activate the brain
There are many tasks that activate the brain
Tasks for developing the ability to analyze and synthesize
"Cut out the necessary shapes from the various ones proposed in order to get a house, a ship and a fish."
How many sides, angles and vertices does a triangle have?
“Nikita and Yegor jumped long. On the first attempt, Nikita jumped 25 cm further than Yegor. From the second, Yegor improved his result by 30 cm, and Nikita jumped in the same way as from the first. Who jumped further on the second attempt: Nikita or Yegor? How much? Guess!"
What number comes before the number 7? What number comes after the number 7? Behind the number 8?
Tasks for the ability to classify:
"What common?":
1) Borsch, pasta, cutlet, compote.
2) Pig, cow, horse, goat.
3) Italy, France, Russia, Belarus.
4) Chair, desk, wardrobe, stool.
"What's extra?"- a game that allows you to find common and unequal properties of objects, compare them, and also combine them into groups according to the main feature, that is, classify.
"What unites?"- a game that forms such logic operations as comparison, generalization, classification according to a variable attribute.
For example: take three pictures with images of animals: a cow, a sheep and a wolf. Question: "What unites a cow and a sheep and distinguishes them from a wolf?".
The task of developing the ability to compare:
“Natasha had several stickers. She gave 2 stickers to a friend and she has 5 stickers left. How many stickers did Natasha have?
Tasks for the search for essential features:
"Name the attribute of the object." For example, a book - what is it? What material is it made from? What size is it? What is its thickness? What is its name? What subjects does it apply to?
Useful games: "Who lives in the forest?", "Who flies in the sky?", "Edible - inedible."
Tasks for comparison:
Color comparison.
a) blue b) yellow c) white d) pink.
Form comparison. You need to name more items:
a) square b) round c) triangular d) oval.
Let's compare 2 things:
a) a pear and a banana b) a raspberry and a strawberry c) a sled and a cart d) a car and a train.
Compare seasons:
Conversation with students about the features of the seasons. Reading poems, fairy tales, riddles, proverbs, sayings about the seasons. Drawing on the theme of the seasons.
Non-standard logical problems
One of the most effective ways to develop logical thinking in elementary school is to solve non-standard problems.
“Did you know that mathematics has a unique developmental effect? It stimulates the development of logical thinking, most the best way forming methods of mental work, expanding the intellectual abilities of the child. Children learn to reason, notice patterns, apply knowledge in various fields, be more attentive, observant.
In addition to mathematical problems, the brain of younger students is developed puzzle, different types tasks with chopsticks and matches(laying out a figure from a certain number matches, transferring one of them in order to get another picture, connecting several points with one line without taking off the hand).
Problems with matches
Comprehensive development of thinking is also provided puzzle games: "Rubik's Cube", "Rubik's Snake", "Fifteen" and many others.
Well-developed logical thinking will help the child in learning, making the assimilation of knowledge easier, more enjoyable and more interesting.
The games, exercises and tasks proposed in this article are aimed at developing the logical thinking of younger students. If these tasks are gradually complicated, then the result will be better every day. And flexible, plastic thinking and quick reaction will help the child in his studies, making the assimilation of knowledge easier, more pleasant and more interesting.
