The development of thinking in young schoolchildren: the first step to great success! Development of visual-effective and visual-figurative thinking of younger students
Primary school age is characterized by intense intellectual development. During this period, there is an intellectualization of all mental processes and the child's awareness of his own changes that occur in the course of educational activities. The most significant changes are taking place, as L.S. Vygotsky, in the sphere of thinking. The development of thinking becomes the dominant function in the development of the personality of younger schoolchildren, which determines the work of all other functions of consciousness.
The peculiarity of the figurative thinking of a younger student is its visually effective character. Forming imaginative thinking of students means educating the need for knowledge, enriching children with a system of knowledge, skills, and modern ways of understanding the world around them. Now, more than ever, our country needs people who can think figuratively. The monotonous, patterned repetition of the same actions turns the train back to study. Children are spared the joy of discovery and may gradually lose the ability to be creative. The main goal is to develop in the child the ability to manage the processes of creativity: fantasizing, understanding patterns, solving complex problem situations.
The selection of individual elements of the image allows the child to combine the details of different images, invent new, fantastic objects or ideas.
As a result, the "serving thinking" functions are intellectualized and become arbitrary. The thinking of a younger student is characterized active search connections and relations between different events, phenomena, things, objects. It differs markedly from the thinking of preschoolers. Preschoolers are characterized by involuntariness, low controllability, they often think about what interests them.
And younger students, who, as a result of studying at school, need to regularly complete assignments, are given the opportunity to learn how to control their thinking, to think when they need to, and not when they like it. When studying at primary school children develop awareness, critical thinking. This is due to the fact that the class discusses ways to solve problems, considers solutions, children learn to substantiate, prove, and tell their judgments.
In the primary grades, a child can already mentally compare individual facts, combine them into a coherent picture, and even form abstract knowledge for himself, remote from direct sources.
Younger schoolchildren are regularly placed in situations where they need to reason, compare different conclusions, hence the third type of thinking - verbal-logical, higher than the visual-effective and visual-figurative thinking of children up to school age.
J. Piaget established that the thinking of a child at the age of six or seven is characterized by "centring" or the perception of the world of things and their properties from the only possible position for the child to actually occupy. It is difficult for a child to imagine that his vision of the world does not coincide with how other people perceive this world. So, if you ask a child to look at a layout that shows three mountains of different heights that obscure each other, and then offer to find a picture that shows the mountains as the child sees them, then he can easily cope with this task. But if you ask a child to choose a drawing that depicts mountains, as they are seen by a person looking from the opposite point, then the child chooses a drawing that reflects his own vision. At this age, it is difficult for a child to imagine that there may be a different point of view, that one can see in different ways.
In elementary school, such methods of logical thinking are formed as comparison associated with the allocation of common and different, analysis associated with the allocation and verbal designation of different properties and features, generalization associated with abstraction from non-essential features and association on the basis of essential ones. As they study at school, the thinking of children becomes more arbitrary, more programmable, i.e. verbal-logical.
The most important condition for the formation of figurative thinking of primary school students is the visibility of learning (layouts, illustrations, drawings, technical means).
Taking into account the peculiarities of students' thinking is an important prerequisite for the successful organization of the educational process at all stages. school studies especially when working with younger students. After all, the next development of the student depends on how optimally their thinking develops. This is how figurative thinking, creative imagination, the development of intelligence and logical thinking of younger students are formed.
Hello, friends! Do you want a follow up question? So tell me, what is thinking? Answers like, “well, it’s like that ... how is it there ... when thoughts are different ...” are not accepted)
I specifically tested my friends here (since I started the blog, I have been constantly testing them while they endure) and got the following results. Only one person out of ten more or less clearly answered this question. And that, because he studied at pedagogical university and wrote a dissertation on related topics.
Therefore, there is a proposal, before talking about the development of thinking in primary school age, to figure out what it is. To know what to develop.
Lesson plan:
What it is?
Let's start with the definition, there are many of them, I chose the simplest.
Thinking is a cognitive activity of a person. Thought is the result of this activity.
Thinking is what distinguishes man from animals. This is the same mental function as memory, attention, imagination.
Thinking is such a complex concept that it even has its own structure. It has several forms and types. A person thinks in different ways and with the help of the brain performing various mental operations. Understandably? I don't know about you, but I don't. Need to figure it out. For clarity, here is a diagram.
Where does it come from?
When a baby is born, he does not have thinking. But he has an innate ability to it. And this ability is gradually developing.
When the baby is a year old, he already thinks. In its own way, primitive, but still thinks. So calling little kids "silly" is a big mistake.
Magic transformations
Thinking in its development goes through certain stages. It causes certain associations for me. For example, with computer game. Until you pass the first level, you do not rise to the second, until you overcome the second, then the third does not shine for you.
There is a more beautiful association, with a butterfly. After all, she, too, was once a caterpillar, then turned into a chrysalis, and only then spread her wings.
Likewise, thinking in children gradually passes from one of its types to another.
Types of thinking in children
So, to put it briefly, without delving into the jungle of psychology, then the following types of it are distinguished:
- visual and effective;
- visual-figurative;
- verbal-logical.
Let's look at examples to make it clearer.
Visual and effective
When the baby is about a year old, he already shows thinking. Even if he doesn't speak yet. He thinks in action. For example, he takes a toy out of the box, strings rings on a pyramid, climbs onto a chair, and taps a metallophone with a hammer. He thinks when he performs these actions.
Visual-figurative
When the baby grows up, masters speech, then there is a shift in thinking towards the visual-figurative. When working with children (drawing, designing, games), new tasks are set before them, and in order to solve them, the kids have to imagine something. That is, to call the desired images.
The kid is already able to think not only about what he is doing at this particular moment, but to get ahead of his actions with his thoughts. That is, he will first say: “I’ll go and put the doll to sleep,” and only then will he go and put it down.
Visual-figurative thinking is the foundation necessary for building logical, verbal thinking.
Verbal-logical
What happens next? And then actions and images give way to concepts expressed in words. To solve any problem, any visual support is no longer required. Thinking reaches a new level and becomes verbal-logical.
For example, in order to solve the problem about how the gardener picked apples, the student does not need to see or touch the fruit and talk to the gardener. No action required. Visual-effective thinking is not involved. But it is quite possible to evoke the image of apples and even the gardener himself.
But what about, for example, solving problems for speed? Try to conjure up an image of speed in your head. Does not work. In the best case, you get the image of a car that quickly rushes along the road. But this is not an image of speed, this is an image of a car.
However, when we hear the word "speed", then we all understand what is at stake. It turns out that speed is a concept that is common to all of us and expressed in a word. Concepts are concrete, but images are vague and individual for each person.
What happens in elementary school?
When the kids go to school, their imaginative thinking reaches quite high level development. But he still has room to grow. So at school they do not forget about it and widely use the principle of visibility in teaching.
When solving problems, students imagine the situation and act in this situation.
In general, psychologists distinguish two stages in the development of thinking:
- 1 - 2 classes. Children still think like preschoolers. The assimilation of the material in the lessons takes place in a visual-effective and visual-figurative plan.
- 3 - 4 classes. By the third grade, the formation of verbal-logical thinking begins.
And one of the main tasks primary education- the development of logical thinking in children. It is necessary to teach the child to think logically and to do without visual, that is, visible to the eye, support.
Development of logical thinking
How is it being developed? With the help of performance, tasks, as well as with the help of, for example, chess or checkers.
And elementary school is the right time for its development. In contrast, for example, from, which is better developed in the preschool period or from perception, which is of great importance in early childhood. However, thanks to the development of thinking, both memory and perception, and all other mental functions become more mature.
Children are taught to make connections between various items or phenomena, compare, analyze, draw conclusions. Students learn to separate the important from the insignificant, create their own conclusions, seek confirmation of their assumptions or refute them. Isn't this what we, dear friends, do every day of our adult lives?
So logic is necessary not only for successful study at school. It is necessary for a successful life in this difficult world.
It influences the development positive traits character, efficiency, self-control, the ability to independently establish the truth and plan their actions. Find a way out in difficult, non-standard situations.
And how great it is if a son or daughter gets into the class of a teacher who knows exactly how to help his students develop thinking. But even in this case, our help, friends, will not be superfluous. Fortunately, the literature on this topic is more than enough.
There are also TV shows. Do you remember "ABVGDeyka"? Turns out it still exists! Only now, instead of Iriska, the girl Shpilka, the constant clown Klepa and the excellent student Gosha Pyaterkin are there. I'm sure you'll enjoy watching it with your kids.
Let's work with our little schoolchildren in addition, we will develop. Don't forget the best time to do this is right now!
After all, we really need, it is simply necessary that our children grow up and become successful and sane people who are able to cope with any possible problems.
On this, perhaps, everything.
Thank you for your attention and waiting for your comments!
See you soon!
Always yours, Evgenia Klimkovich!
Intensive development of the intellect occurs in primary school age.
Going to school makes a huge difference in a child's life. The whole way of his life changes drastically, his social status in a team, family. From now on, teaching becomes the main, leading activity, the most important duty is the duty to learn, to acquire knowledge. And teaching is a serious work that requires organization, discipline, strong-willed efforts of the child. The student is included in a new team for him, in which he will live, study, develop for 11 years.
The main activity, his first and most important duty is teaching - the acquisition of new knowledge, skills, the accumulation of systematic information about the world, nature and society.
Younger students tend to understand literally the figurative meaning of words, filling them with specific images. Students solve this or that mental problem more easily if they rely on specific objects, ideas or actions. Given the figurative thinking, the teacher accepts a large number of visual aids, reveals the content of abstract concepts and the figurative meaning of words in a number of specific examples. And primary schoolchildren remember not what is most significant in terms of educational tasks, but what made the greatest impression on them: what is interesting, emotionally colored, unexpected and new.
Visual-figurative thinking also involves speech, which helps to name a sign, to compare signs. Only on the basis of the development of visual-effective and visual-figurative thinking, formal-logical thinking begins to take shape at this age.
The thinking of children of this age differs significantly from the thinking of preschoolers: so if the thinking of a preschooler is characterized by such a quality as involuntariness, low controllability both in setting a mental task and in solving it, they more often and easily think about what is more interesting to them, what they captivates, then younger students as a result of studying at school, when it is necessary to regularly complete tasks in without fail learn to control your thinking.
Teachers know that the thinking of children of the same age is quite different; there are such children for whom it is difficult to think practically and operate with images, and to reason, and those for whom it is easy to do all this.
The good development of visual-figurative thinking in a child can be judged by how he solves the tasks corresponding to this type of thinking.
If the child successfully solves easy problems intended for the application of this type of thinking, but finds it difficult to solve more complex problems, in particular because he cannot imagine the whole solution as a whole, since the ability to plan is not sufficiently developed, then in this case it is considered that he has the second level of development in the corresponding kind of thinking.
It happens that a child successfully solves both easy and complex tasks within the framework of the corresponding type of thinking and can even help other children in solving easy tasks, explaining the reasons for the mistakes they make, and can also come up with easy tasks himself, in this case it is considered that he has the third level of development of the corresponding type of thinking.
So, the development of visual-figurative thinking in children of the same age is quite different. Therefore, the task of teachers, psychologists is to differentiated approach to the development of thinking in younger students.
figurative thinking junior schoolboy
The development of thinking in primary school age has a special role.
By the time of entering school, a child of 6-7 years old should already have formed visual-active thinking, which is the necessary basic education for the development of visual-figurative thinking, which forms the basis of successful education in elementary school. In addition, children of this age should have elements of logical thinking. Thus, at this age the child develops different types thinking, contributing to the successful mastery of the curriculum.
With the beginning of learning, thinking moves to the center mental development child and becomes decisive in the system of other mental functions, which, under his influence, are intellectualized and acquire an arbitrary character.
The thinking of a child of primary school age is at a turning point in development. During this period, a transition is made from visual-figurative to verbal-logical, conceptual thinking, which gives the child’s mental activity a dual character: concrete thinking, associated with reality and direct observation, already obeys logical principles, but abstract, formal-logical reasoning for children is still not available .
The features of the mental activity of a younger schoolchild in the first two years of study are in many respects similar to the features of thinking of a preschooler. The younger schoolchild has a clearly expressed concrete-figurative nature of thinking. So, when solving mental problems, children rely on real objects or their image. Conclusions, generalizations are made on the basis of certain facts. All this is manifested in the assimilation of educational material.
When some problems arise, the child tries to solve them, really trying on and trying, but he can already solve problems, as they say, in his mind. He imagines a real situation and, as it were, acts in it in his imagination. Such thinking, in which the solution of the problem occurs as a result of internal actions with images, is called visual-figurative. Figurative thinking is the main type of thinking in primary school age. Of course, a younger student can think logically, but it should be remembered that this age is sensitive to learning based on visualization.
The thinking of a child at the beginning of schooling is characterized by egocentrism, a special mental position due to the lack of knowledge necessary to correctly solve certain problem situations. So, the child himself does not discover in his personal experience knowledge about the preservation of such properties of objects as length, volume, weight, etc. The lack of systematic knowledge, insufficient development of concepts lead to the fact that the logic of perception dominates in the child's thinking. For example, it is difficult for a child to evaluate the same amount of water, sand, plasticine, etc. as equal (the same) when before his eyes there is a change in their configuration in accordance with the shape of the vessel where they are placed. The child becomes dependent on what he sees at each new moment of changing objects. However, in the primary grades, a child can already mentally compare individual facts, combine them into a coherent picture, and even form abstract knowledge for himself, remote from direct sources.
By the 3rd grade, thinking passes into a qualitatively new stage, requiring the teacher to demonstrate the connections that exist between the individual elements of the information being assimilated. By the 3rd grade, children master the generic relationships between the individual features of concepts, i.e. classification, an analytical-synthetic type of activity is formed, the action of modeling is mastered. This means that formal-logical thinking begins to take shape.
As a result of studying at school, in conditions when it is necessary to regularly complete tasks without fail, children learn to control their thinking, to think when necessary.
In many ways, the formation of such arbitrary, controlled thinking is facilitated by the instructions of the teacher in the lesson, encouraging children to think.
When communicating in primary school, children develop conscious critical thinking. This is due to the fact that the class discusses ways to solve problems, considers various solutions, the teacher constantly requires students to substantiate, tell, prove the correctness of their judgment, i.e. requires children to solve problems on their own.
The ability to plan one's actions is also actively formed in younger students in the process of schooling; study encourages children to first trace the plan for solving the problem, and only then proceed to its practical solution.
The younger student regularly and without fail enters the system when he needs to reason, compare different judgments, and carry out conclusions.
Therefore, at primary school age, the third type of thinking begins to develop intensively: verbal - logical abstract thinking, in contrast to the visual - effective and visual - figurative thinking of preschool children.
The development of thinking largely depends on the level of development of thought processes. Analysis starts as partial and gradually becomes complex and systemic. Synthesis develops from simple, summing up, to a broader and more complex one. Analysis for younger students is an easier process and develops faster than synthesis, although both processes are closely related (the deeper the analysis, the more complete the synthesis). Comparison at primary school age comes from non-systematic, focused on external signs to planned, systematic. When comparing familiar objects, children more easily notice similarities, and when comparing new ones, differences.
| Introduction |
| Chapter I. Development of thinking in integrated lessons of mathematics and labor training. |
| Clause 1.1. Characterization of thinking as a mental process. |
| Clause 1.2. Features of the development of visual-effective and visual-figurative thinking of children of primary school age. |
| Clause 1.3. Studying the experience of teachers and methods of work on the development of visual-effective and visual-figurative thinking of younger students. |
| Chapter II. Methodological and mathematical foundations for the formation of visual-effective and visual-figurative thinking of younger schoolchildren. |
| Clause 2.1. Geometric figures on the plane. |
| Clause 2.2. The development of visual-effective and visual-figurative thinking in the study of geometric material. |
| Chapter III. Experimental work on the development of visual-effective and visual-figurative thinking of younger students in integrated lessons of mathematics and labor training. |
| Clause 3.1. Diagnosis of the level of development of visual-effective and visual-figurative thinking of younger students in the process of conducting integrated lessons in mathematics and labor training in grade 2 (1-4) |
| Clause 3.2. Features of the use of integrated lessons in mathematics and labor training in the development of visual-effective and visual-figurative thinking of younger students. |
| Clause 3.3. Processing and analysis of experimental materials. |
| Conclusion |
| List of used literature |
| Appendix |
Introduction.
Creation new system elementary education follows not only from the new socio-economic conditions of life in our society, but is also determined by the great contradictions in the system public education, which have developed and are clearly manifested in last years. here are some of them:
Long time there was an authoritarian system of education and upbringing in schools with a strict management style, using coercive teaching methods, ignoring the needs and interests of schoolchildren, cannot create favorable conditions for the introduction of ideas for reorienting education with the assimilation of ZUNs to the development of the child's personality: his creative abilities, independence of thinking and feelings of personal responsibility.
2. The teacher's need for new technologies and the developments that pedagogical science gave.
Long years the attention of researchers was focused on the study of learning problems, which yielded many interesting results. Previously, the main direction in the development of didactics and methodology followed the path of improving individual components of the learning process, methods and organizational forms of learning. And only in recent times teachers turned to the personality of the child, began to develop the problem of motivation in learning, ways of forming needs.
3. The need for the introduction of new academic subjects (especially subjects of the aesthetic cycle) and limited scope curriculum and learning time for children.
4. One of the contradictions is the fact that modern society stimulates the development of selfish needs (social, biological) in a person. And these qualities contribute little to the development of a spiritual personality.
It is impossible to resolve these contradictions without a qualitative restructuring of the entire system of primary education. The social demands placed on the school dictate the search for new forms of education for the teacher. One of these urgent problems is the problem of integration of education in primary school.
A number of approaches have been outlined to the question of the integration of education in primary school: from conducting a lesson by two teachers of different subjects or combining two subjects into one lesson and conducting it by one teacher to creating integrated courses. About the need to teach children to see the connections of everything that exists in nature and in Everyday life, the teacher feels, knows and, therefore, integration in learning is the imperative of today.
As a basis for the integration of learning, it is necessary to take, as one of the components, the deepening, expansion, clarification of general concepts, which are the object of study of various sciences.
The integration of education has the goal: in elementary school to lay the foundations for a holistic view of nature and society and to form an attitude towards the laws of their development.
Thus, integration is a process of rapprochement, connection of sciences, occurring along with processes of differentiation. integration improves and helps to overcome the shortcomings of the subject system and is aimed at deepening the relationship between subjects.
The task of integration is to help teachers to integrate separate parts different subjects into a single whole with the same goals and functions of learning.
An integrated course helps children combine the knowledge they gain into single system.
The integrated learning process contributes to the fact that knowledge acquires the qualities of a system, skills become generalized, complex, all types of thinking develop: visual-effective, visual-figurative, logical. The personality becomes comprehensively developed.
The methodological basis of an integrated approach to learning is the establishment of intra-subject and inter-subject relationships in the assimilation of sciences and understanding the patterns of everything existing world. And this is possible under the condition of repeated return to the concepts on different lessons, their deepening and enrichment.
Therefore, any lesson can be taken as the basis for integration, the content of which will include that group of concepts that relates to a given academic subject, but in an integrated lesson knowledge, analysis results, concepts from the point of view of other sciences, other scientific subjects. In elementary school, many concepts are cross-cutting and are considered in the lessons of mathematics, the Russian language, reading, fine arts, labor education, etc.
Therefore, at present it is necessary to develop a system of integrated lessons, the psychological and creative basis of which will be the establishment of links between concepts that are common, cross-cutting in a number of subjects. The purpose of educational preparation in elementary school is the formation of personality. Each subject develops both general and special qualities of the individual. Mathematics develops intelligence. Since the main thing in the activity of a teacher is the development of thinking, the theme of our thesis is relevant and important.
Chapter I. Psychological and pedagogical foundations of development
visual-effective and visual-figurative
thinking of younger students.
clause 1.1. Characterization of thinking as a psychological process.
Objects and phenomena of reality have such properties and relations that can be known directly, with the help of sensations and perceptions (colors, sounds, shapes, placement and movement of bodies in visible space), and such properties and relations that can be known only indirectly and through generalization. , i.e., through thinking.
Thinking is a mediated and generalized reflection of reality, a type of mental activity, which consists in knowing the essence of things and phenomena, regular connections and relationships between them.
The first feature of thinking is its indirect character. What a person cannot cognize directly, directly, he cognizes indirectly, indirectly: some properties through others, the unknown through the known. Thinking is always based on the data of sensory experience - sensations, perceptions, ideas, and on previously acquired theoretical knowledge. indirect knowledge is indirect knowledge.
The second feature of thinking is its generalization. Generalization as knowledge of the general and essential in the objects of reality is possible because all the properties of these objects are connected with each other. The general exists and manifests itself only in the individual, the concrete.
People express generalizations through speech, language. Verbal designation refers not only to a single object, but also to whole group similar objects. Generalization is also inherent in images (representations and even perceptions). But there it is always limited by visibility. The word allows you to generalize without limit. Philosophical concepts matter, movement, law, essence, phenomenon, quality, quantity, etc. - the broadest generalizations expressed by the word.
Thinking is the highest level of human cognition of reality. Sensual basis of thinking are sensations, perceptions and representations. Through the sense organs - these are the only channels of communication between the body and the outside world - information enters the brain. The content of information is processed by the brain. The most complex (logical) form of information processing is the activity of thinking. Solving the mental tasks that life puts before a person, he reflects, draws conclusions and thereby cognizes the essence of things and phenomena, discovers the laws of their connection, and then transforms the world on this basis.
Our knowledge of the surrounding reality begins with sensations and perception and moves on to thinking.
The function of thinking is to expand the boundaries of knowledge by going beyond the limits of sensory perception. Thinking allows, with the help of inference, to reveal what is not given directly in perception.
The task of thinking is to reveal the relationships between objects, to identify connections and separate them from random coincidences. Thinking operates with concepts and assumes the functions of generalization and planning.
Thinking is the most generalized and mediated form of mental reflection, establishing connections and relationships between cognizable objects.
Thinking is the highest form of active reflection of objective reality, consisting in a purposeful, mediated and generalized reflection by the subject of essential connections and relations of reality, in creative creation new ideas, forecasting events and actions (speaking the language of philosophy); higher function nervous activity(speaking the language of physiology); a conceptual (in the system of the language of psychology) form of mental reflection, peculiar only to man, establishing connections and relationships between cognizable phenomena with the help of concepts. Thinking has a number of forms - from judgments and conclusions to creative and dialectical thinking and individual characteristics as a manifestation of the mind using existing knowledge, vocabulary and an individual subjective thesaurus (i.e.:
1) a dictionary of the language with complete semantic information;
2) a complete systematized set of data about any field of knowledge, allowing a person to freely navigate in it - from the Greek. thesauros - stock).
The structure of the thought process.
According to S. L. Rubinshtein, every thought process is an act aimed at solving a specific problem, the formulation of which includes a goal and conditions. Thinking begins with a problem situation, a need to understand. At the same time, the solution of the problem is a natural completion of the thought process, and its termination when the goal is not achieved will be perceived by the subject as a breakdown or failure. The emotional well-being of the subject, tense at the beginning and satisfied at the end, is connected with the dynamics of the thought process.
The initial phase of the thought process is the awareness of the problem situation. The very formulation of the problem is an act of thinking, often it requires a lot of mental work. The first sign of a thinking person is the ability to see the problem where it is. The emergence of questions (which is typical for children) is a sign of the developing work of thought. The person sees more problems the wider the circle of his knowledge. Thus, thinking presupposes the existence of some basic knowledge.
From understanding the problem, thought moves to its solution. The problem is solved in different ways. There are special tasks (tasks of visual-effective and sensorimotor intelligence) for the solution of which it is enough to correlate the initial data in a new way and rethink the situation.
In most cases, a certain base of theoretical generalized knowledge is needed to solve problems. The solution of the problem involves the involvement of existing knowledge as means and methods of solution.
The application of the rule involves two mental operations:
Determine which rule needs to be involved for the solution;
Application general rules to the particular conditions of the problem
Automated action patterns can be thought of as thinking skills. It is important to note that the role of thinking skills is great precisely in those areas where there is a very generalized system of knowledge, for example, in solving mathematical problems. When solving a complex problem, a solution path is usually outlined, which is recognized as a hypothesis. Awareness of the hypothesis generates the need for verification. Criticality is a sign of a mature mind. An uncritical mind easily takes any coincidence as an explanation, the first solution that comes up as the final one.
When the test ends, the thought process moves on to the final phase - judging by this issue.
Thus, the thought process is a process that is preceded by awareness of the initial situation (conditions of the task), which is conscious and purposeful, operates with concepts and images, and which ends with some result (rethinking the situation, finding a solution, forming a judgment, etc.). )
There are four stages of problem solving:
Training;
Solution maturation;
Inspiration;
Checking the found solution;
The structure of the thought process of solving the problem.
1. Motivation (desire to solve a problem).
2. Analysis of the problem (highlighting "what is given", "what needs to be found", what redundant data, etc.)
3. Search for a solution:
Finding a solution based on one well-known algorithm (reproductive thinking).
Finding a solution based on choosing the best option from a variety of known algorithms.
Solution based on a combination of individual links from various algorithms.
Search for a fundamentally new solution (creative thinking):
a) based on in-depth logical reasoning (analysis, comparison, synthesis, classification, inference, etc.);
b) based on the use of analogies;
c) based on the use of heuristic techniques;
d) based on the use of an empirical trial and error method.
4. Logical substantiation of the found idea of the solution, logical proof of the correctness of the solution.
5. Implementation of the solution.
6. Verification of the found solution.
7. Correction (if necessary, return to stage 2).
So, as we formulate our thought, we form it. The system of operations that determines the structure of mental activity and determines its course is itself formed, transformed and consolidated in the process of this activity.
Operations of mental activity.
The presence of a problematic situation, from which the thought process begins, always aimed at solving some problem, indicates that the initial situation is given in the representation of the subject inadequately, in a random aspect, in insignificant connections.
In order to solve the problem as a result of the thought process, it is necessary to come to a more adequate knowledge.
To such an increasingly adequate cognition of its subject and the solution of the problem facing it, thinking proceeds through diverse operations that make up various interrelated and mutually transitioning aspects of the thought process.
These are comparison, analysis and synthesis, abstraction and generalization. All these operations are different aspects of the main operation of thinking - "mediation", that is, the disclosure of more and more essential objective connections and relationships.
Comparison, comparing things, phenomena, their properties, reveals identity and differences. Revealing the identity of some and the differences of other things, comparison leads to their classification. Comparison is often the primary form of knowledge: things are first known by comparison. It is also an elementary form of knowledge. Identity and difference, the basic categories of rational cognition, appear first as external relations. Deeper knowledge requires the disclosure of internal connections, patterns and essential properties. This is carried out by other aspects of the thought process or types of mental operations - primarily by analysis and synthesis.
Analysis is the mental division of an object, phenomenon, situation and the identification of its constituent elements, parts, moments, sides; by analysis we isolate phenomena from those random, unimportant connections in which they are often given to us in perception.
Synthesis restores the whole dissected by analysis, revealing more or less significant connections and relationships of elements identified by analysis.
Analysis dismembers the problem; synthesis combines data in a new way to resolve it. Analyzing and synthesizing, thought proceeds from a more or less vague idea of the subject to a concept in which the main elements are revealed by analysis and the essential connections of the whole are revealed by synthesis.
Analysis and synthesis, like all mental operations, first arise on the plane of action. Theoretical mental analysis was preceded by a practical analysis of things in action, which dismembered them for practical purposes. In the same way, a theoretical synthesis was formed in a practical synthesis, in production activities of people. Formed first in practice, analysis and synthesis then become operations or aspects of the theoretical thought process.
Analysis and synthesis in thinking are interconnected. Attempts at one-sided application of analysis outside of synthesis lead to a mechanical reduction of the whole to the sum of its parts. In the same way, synthesis without analysis is also impossible, since synthesis must restore the whole in thought in the essential interconnections of its elements, which are distinguished by analysis.
Analysis and synthesis do not exhaust all aspects of thinking. Its essential aspects are abstraction and generalization.
Abstraction is the selection, isolation and extraction of one side, property, moment of a phenomenon or object, essential in some respect, and its abstraction from the rest.
So, considering an object, you can highlight its color without noticing the shape, or vice versa, highlight only the shape. Starting with the selection of individual sensible properties, abstraction then proceeds to the selection of non-sensory properties expressed in abstract concepts.
Generalization (or generalization) is the rejection of single features while maintaining common ones with the disclosure of significant relationships. Generalization can be made by comparison, in which common qualities are distinguished. This is how generalization takes place in the elementary forms of thought. In higher forms, generalization is accomplished through the disclosure of relationships, connections and patterns.
Abstraction and generalization are two interrelated sides of a single thought process, through which thought goes to knowledge.
Cognition takes place in concepts, judgments and inferences.
A concept is a form of thinking that reflects the essential properties of communication and the relationship of objects and phenomena, expressed by a word or a group of words.
Concepts can be general and singular, concrete and abstract.
Judgment is a form of thinking that reflects the relationship between objects or phenomena, it is the affirmation or denial of something. Judgments can be false and true.
Inference is a form of thinking in which a certain conclusion is drawn on the basis of several judgments. There are inductive, deductive, and analogical inferences. Induction is a logical conclusion in the process of thinking from the particular to the general, the establishment of general laws and rules based on the study of individual facts and phenomena. Analogy is a logical conclusion in the process of thinking from particular to particular (based on some elements of similarity). Deduction is a logical conclusion in the process of thinking from the general to the particular, the knowledge of individual facts and phenomena based on the knowledge of general laws and rules.
Individual differences in mental activity.
Individual differences in the mental activity of people can manifest themselves in the following qualities of thinking: the breadth, depth and independence of thinking, the flexibility of thought, the speed and criticality of the mind.
The breadth of thinking is the ability to cover the whole issue without losing at the same time the parts necessary for the cause.
The depth of thinking is expressed in the ability to penetrate into the essence difficult questions. The quality opposite to the depth of thinking is the superficiality of judgments, when a person pays attention to the little things and does not see the main thing.
Independence of thinking is characterized by the ability of a person to put forward new tasks and find ways to solve them without resorting to the help of other people.
The flexibility of thought is expressed in its freedom from the shackling influence of methods and methods of solving problems fixed in the past, in the ability to quickly change actions when the situation changes.
Quickness of mind is the ability of a person to quickly understand a new situation, think it over and make the right decision.
The criticality of the mind is the ability of a person to objectively evaluate his own and other people's thoughts, carefully and comprehensively check all the propositions and conclusions put forward. The individual features of thinking include the preference for a person to use a visual-effective, visual-figurative or abstract-logical type of thinking.
There are individual styles of thinking.
The synthetic style of thinking manifests itself in creating something new, original, combining dissimilar, often opposite ideas, views, thought experiments. The motto of the synthesizer is "What if ...".
The idealistic style of thinking manifests itself in a tendency to intuitive, global assessments without implementation. detailed analysis problems. The characteristic of idealists heightened interest to goals, needs, human values, moral problems, they take into account subjective and social factors in their decisions, strive to smooth out contradictions and emphasize similarities in various positions. "Where are we going and why?" is a classic idealist question.
The pragmatic way of thinking is based on direct personal experience, on the use of those materials and information that are readily available, striving to get a specific result (albeit limited), a practical gain as soon as possible. The motto of the pragmatists: "Something will work", "Anything that works"
The analytical style of thinking is focused on a systematic and comprehensive consideration of an issue or problem in those aspects that are set by objective criteria, it is inclined to a logical, methodical, thorough (with an emphasis on details) manner of solving problems.
The realistic style of thinking is focused only on the recognition of facts, and “real” is only that which can be directly felt, personally seen or heard, touched, etc. Realistic thinking is characterized by concreteness and an attitude towards correcting, correcting situations in order to achieve a certain result.
Thus, it can be noted that the individual style of thinking affects the way the problem is solved, the line of behavior, and the personal characteristics of a person.
Types of thinking.
Depending on what place the word, image and action occupies in the thought process, how they relate to each other, three types of thinking are distinguished: concrete-active or practical, concrete-figurative and abstract. These types of thinking are also distinguished on the basis of the characteristics of the tasks - practical and theoretical.
Visual-effective thinking is a type of thinking based on the direct perception of objects, real transformation in the process of actions with objects. The type of this thinking is aimed at solving problems in the conditions of production, constructive, organizational and other practical activities of people. practical thinking is primarily technical, constructive thinking. The characteristic features of the visual actionable thinking are pronounced observation, attention to details, particulars and the ability to use them in a particular situation, operating with spatial images and schemes, the ability to quickly move from thinking to action and vice versa.
Visual-figurative thinking is a type of thinking characterized by reliance on representations and images; the functions of figurative thinking are associated with the representation of situations and changes in them that a person wants to receive as a result of his activity that transforms the situation. Highly important feature figurative thinking - the establishment of unusual, incredible combinations of objects and their properties. In contrast to visual-effective thinking, in visual-figurative thinking, the situation is transformed only in terms of the image.
Verbal-logical thinking is mainly aimed at finding general patterns in nature and human society, reflects general connections and relationships, operates mainly with concepts, broad categories, and images, representations in it play a supporting role.
All three types of thinking are closely related to each other. Many people equally developed visual-effective, visual-figurative, verbal-logical thinking, but depending on the nature of the tasks that a person solves, one, then another, then a third type of thinking comes to the fore.
Chapter II. Methodological and mathematical foundations of the formation
visual-effective and visual-figurative
thinking of younger students.
clause 2.2. The role of geometric material in the formation of visual-effective and visual-figurative thinking of younger students.
The mathematics program in the elementary grades is an organic part of the mathematics course in the secondary school. Currently, there are several programs for teaching mathematics in primary grades. the most common is the three-year elementary school mathematics program. This program assumes that the study of relevant issues will be carried out during the 3 years of primary education, in connection with the introduction of new units of measurement and the study of numbering. In the third grade, the results of this work are summed up.
The program includes the possibility of implementing interdisciplinary connections between mathematics, labor activity, speech development, fine arts. The program provides for the expansion of mathematical concepts on concrete, life material, which makes it possible to show children that all those concepts and rules that they get acquainted with in the lessons serve the practice, were born from its needs. This lays the foundation for the formation of a correct understanding of the relationship between science and practice. The mathematics program will equip children with the skills necessary to solve new educational and practical problems on their own, educate them in independence and initiative, habits and love for work, art, a sense of responsiveness, perseverance in overcoming difficulties.
Mathematics contributes to the development in children of thinking, memory, attention, creative imagination, observation, strict sequence, reasoning and its evidence; gives real prerequisites for further development visual-effective and visual-figurative thinking of students.
This development is facilitated by the study of geometric material associated with algebraic and arithmetic material. The study of geometric material contributes to the development of cognitive abilities of younger students.
According to the traditional system (1-3), the following geometric material is studied:
¨ In the first grade, geometric material is not studied, but geometric shapes are used as didactic material.
¨ In the second grade, they study: a segment, right and indirect angles, a rectangle, a square, the sum of the lengths of the sides of a rectangle.
¨ In the third grade: the concept of a polygon and the designation of points, segments, polyhedra with letters, the area of a square and a rectangle.
In parallel with the traditional program, there is also an integrated course "Mathematics and Design", the authors of which are S. I. Volkova and O. L. Pchelkina. The integrated course "Mathematics and Design" is a combination in one subject of two subjects that are diverse in the way they are mastered: mathematics, the study of which is theoretical in nature and not always equally complete in the process of studying, it is possible to realize its applied and practical aspect, and labor training, the formation of skills and skills, which is of a practical nature, not always equally deeply supported by theoretical understanding.
The main provisions of this course are:
A significant strengthening of the geometric line of the elementary course of mathematics, which ensures the development of spatial representations and imaginations, including linear, planar and spatial figures;
Intensification of the development of children;
The main goal of the course "Mathematics and Design" is to ensure the numerical literacy of students, give them initial geometric representations, develop visual-effective and visual-figurative thinking and spatial imagination of children. To form elements of design thinking and constructive skills in them. This course provides an opportunity to supplement the subject "Mathematics" with the design and practical activities of students, in which the mental activity of children is reinforced and developed.
The course "Mathematics and Design" on the one hand contributes to the actualization and consolidation of mathematical knowledge and skills through the targeted material of logical thinking and visual perception of students, and on the other hand, creates conditions for the formation of elements of design thinking and design skills. In the proposed course, in addition to traditional information, information is given about lines: a curve, a broken line, a closed one, a circle and a circle, the center and radius of a circle. The idea of angles is expanding, they are getting acquainted with three-dimensional geometric shapes: a parallelepiped, a cylinder, a cube, a cone, a pyramid and their modeling. Provided different kinds constructive activity of children: construction from sticks of equal and unequal lengths. Planar construction from cut out ready-made figures: triangle, square, circle, plane, rectangle. Volumetric design with technical drawings, sketches and drawings, designing according to the image, according to the presentation, according to the description, etc.
The program is accompanied by an album with a printed base, which contains tasks for the development of visual-effective and visual-figurative thinking.
Along with the course "Mathematics and Design" there is a course "Mathematics with the strengthening of the line on the development of the cognitive abilities of students", authors S. I. Volkova and N. N. Stolyarova.
The proposed mathematics course is characterized by the same basic concepts and their sequence as the current mathematics course in elementary school. One of the main goals of the development of the new course was the creation of effective conditions for the development of cognitive abilities and activities of children, their intellect and creativity, expanding their mathematical horizons.
The main component of the program is the purposeful development of the cognitive processes of younger students and the mathematical development based on it, which includes the ability to observe and compare, notice the common in the different, find patterns and draw conclusions, build the simplest hypotheses, test them, illustrate with examples, and classify objects. , concepts on a given basis, develop the ability to make simple generalizations, the ability to use mathematical knowledge in practical work.
The fourth block of the program in mathematics contains tasks and assignments for:
Development of cognitive processes of students: attention, imagination, perception, observation, memory, thinking;
Formation of specific mathematical methods of action: generalizations, classifications, simple modeling;
Formation of skills to practically apply the acquired mathematical knowledge.
The systematic implementation of purposefully selected content-logical tasks, the solution of non-standard tasks will develop and improve the cognitive activity of children.
Among the programs discussed above, there are developmental education programs. The developmental education program of L.V. Zanyukov was developed for a three-year elementary school and is an alternative education system that has been and is still in practice. Geometric material permeates all three elementary school courses, i.e. it is studied in all three grades compared to the traditional system.
In the first grade, a special place is given to acquaintance with geometric figures, their comparison, classification, identification of the properties inherent in a particular figure.
"It is this approach to the study of geometric material that makes it effective for the development of children," says L. V. Zanyukov. Its program is aimed at developing the cognitive abilities of children, so the math textbook contains many tasks for the development of memory, attention, perception, development, and thinking.
Developing education according to the system of D. B. Elkonin - V. V. Davydov provides for cognitive functions (thinking, memory perception, etc.) in the development of the child. The program aims to form mathematical concepts in younger students based on meaningful generalization, which means that the child is moving in educational material from the general to the particular, from the abstract to the concrete. The main content of the presented training program is the concept of a rational number, which begins with the analysis of genetically initial relations for all types of numbers. Such a relation that generates a rational number is the ratio of magnitudes. With the study of the quantities and properties of their relations, the course of mathematics begins in the first grade.
Geometric material is associated with the study of quantities and actions with them. Crossing out, cutting out, modeling, children get acquainted with geometric shapes and their properties. In the third class, methods for directly measuring the area of figures and calculating the area of a rectangle on given sides are specially considered. Among the available programs there is a program of developmental education by N. B. Istomina. When creating her system, the author tried to take a comprehensive account of the conditions that affect the development of children, Istomina emphasizes that development can be carried out in activities. The first idea of Istomina's program is the idea of an active approach to learning - the maximum activity of the student himself. Both reproductive and productive activities affect the development of memory, attention, perception, but thought processes develop more successfully with productive, creative activity. "Development will go on if the activity is systematic," Istomina believes.
And outwardly - open behavior, and internally - with their mental processes and feelings. Conclusions on the first section For the development of all cognitive processes of a younger student, the following conditions must be observed: 1. Learning activities must be purposeful, arouse and maintain a constant interest among students; 2. Expand and develop the cognitive interests of ...
The whole test as a whole, which indicates that their levels of development of mental operations of comparison and generalization are higher than those of poorly performing schoolchildren. If we analyze individual data by subtests, then difficulties in answering individual questions indicate a poor knowledge of these logical operations. These difficulties are most often found in low-achieving schoolchildren. This is...
Junior student. Object of study: the development of figurative thinking among students in grade 2 high school No. 1025. Method: testing. Chapter 1. Theoretical foundations of the study of figurative thinking 1.1. The concept of thinking Our knowledge of the surrounding reality begins with sensations and perception and proceeds to thinking. The function of thinking is to expand the boundaries of knowledge by going beyond ...