Thinking is understood as the cognitive activity of the individual, which is characterized by a generalized and mediated reflection of the surrounding reality in its essential connections and relationships. When children come to school, they still have primitive thinking. Their judgments combine the most diverse incredible ideas about the surrounding world. For example, a 6-year-old child believes that “The sun does not fall because it is hot.” Therefore, the most important task of school education is the development of children’s thinking.
As L. S. Vygotsky pointed out, a child enters school age with a relatively weakly developed function of intelligence, compared to perception and memory, which are much better developed. First-graders easily and quickly memorize bright, emotionally impressive material. At the same time, they are inclined to literal memorization. And only gradually do the techniques of arbitrary, meaningful memorization begin to form. The thinking of younger schoolchildren is emotional and figurative. Children still think in forms, sounds, sensations. This also applies to children with clearly expressed mathematical abilities, only it can manifest itself in a peculiar way.
The peculiarity of this type of thinking should be taken into account in the content of the educational work. An example of this is the following methodological technique that teachers use when teaching comparison of numbers. Children are introduced to the mathematical symbols > and < at the same time, so they often confuse their meanings. If you offer children a task to compare the numbers 3 and 5 and put a greater than or less than sign between them, you can get an incorrect answer in the form of the entry 3 > 5. In this case, you should first figure out the reason for the error. You need to ask the student to read the entry he made. If he reads “three is less than five”, then the reason for the error is that the student has not learned the mathematical symbols “more” and “less”. In this case, further teaching is built using the technique of comparing a mathematical symbol with some specific image that is understandable to the child, for example, with a chick’s beak, which is open to a larger number and closed to a smaller one, i.e. 3 < 5 and 5 > 3. This technique makes it easier for the child to learn mathematical symbols and move towards abstract thinking.
Based on these features, an important task of primary school is the gradual development of emotional-figurative thinking in the direction of abstract-logical, which continues in middle and ends in senior classes. At the first stage, it is necessary to transfer the child’s mental activity to a qualitatively new level – to develop thinking to the level of understanding cause-and-effect relationships. In primary school, intelligence develops very intensively, so the teacher’s activity in organizing such training that would contribute to the development of the child’s thinking to the greatest extent is of great importance. Such a transition contributes to the restructuring of other mental processes – perception, memory.
The transfer of thinking processes to a qualitatively new level should constitute the main content of the work of teachers on the mental development of primary school students.
In primary school, a child gradually moves from mental actions with specific objects to actions “in the mind”. This transition occurs in several stages. At first, he follows the actions, demonstration and explanation of the teacher, and then begins to act on his own with objects in mathematics lessons – with sticks, cubes, cards, etc. At this stage, he acts under the guidance of the teacher. The next stage is when he expresses this action verbally, without performing the action itself. At this point, the child must learn to imagine objects and actions with them. Based on these ideas, the child moves on to the next stage – to action “in the mind”. When teaching mathematics, all these stages must be completed sequentially and without omissions.
In the mathematics program, the authors try to maintain this sequence by establishing a certain relationship between theory and practice; for example, the formation of concepts about numbers and arithmetic operations occurs during the completion of practical exercises.
As is known, the development of a child’s thinking is inextricably linked with the development of speech. Thinking is externally manifested in speech, thought exists in a word and is expressed in a word. When entering school, a child already has a practical command of speech and the structural features of the language, his vocabulary reaches 4,000 words. Upon entering school, the stage of self-mastery of the language is completed. Further mastery of the language and the development of thinking on its basis occurs already in the conditions of specially organized education at school. Education at school not only develops the child’s speech and enriches his vocabulary, in particular, with mathematical terms and concepts. The main thing is that the child masters written speech and acquires an important skill not only orally, but also in writing to express his thoughts. Gradually, speech and verbal means become the main ones in understanding the world around him.
When considering the relationship between the development of thinking and the acquisition of speech, we should recall the words of L. S. Vygotsky, when he asked: “Why should a child study his native language at school if he knows how to decline and conjugate long before school?” Answering this question, L. S. Vygotsky notes that, indeed, even before school, a child practically knows the grammar of his native language, but he does not know that he knows it. This knowledge of the language is unconscious. Only in the process of studying at school does a child learn to be aware of what he is doing and begins to voluntarily operate his skills. These skills are transferred from the realm of the unconscious to the realm of conscious, intentional, voluntary possession. Such a transition in the mental sphere is ensured by the study of language and speech exercises at school. The formation of skills that ensure the speech activity of schoolchildren should proceed in the following directions:
— skills necessary for speaking and writing;
— skills necessary for listening and reading.
The skills necessary for speaking and writing include:
— the ability to understand to whom and for what purpose the statement is addressed;
— the ability to construct the statement correctly and meaningfully;
— the ability to control the content of one’s own statement.
The skills necessary for listening and reading include:
— the ability to understand the purpose of listening or reading;
— the ability to determine the nature of the message by external signs (by the speaker’s facial expressions and gestures, by the headings and illustrations in the text);
— the ability to understand the meaning of words, phrases, mathematical symbols, and expressed thoughts.
The list of these necessary speech skills is far from complete, but it shows the important areas of work that a teacher needs to do to develop the thinking of younger (and older too) schoolchildren during the development of their speech activity. The teacher should always remember that it is at a young age that children are most receptive to learning and further mastering speech. Therefore, it is important to lay the foundation for the skills of mastering mathematical terms at this age.
For the development of abstract thinking, the study of grammar is of great importance. When teaching grammar, a child is required to perform various mental operations, for example, to highlight the features of words, find common ground in them, establish grammatical features, while abstraction is required – distraction from the specific meaning of the word.
In summing up the consideration of the issue of the relationship between the development of thinking and speech in schoolchildren, it should be remembered that in pre-revolutionary Russian gymnasiums they studied two “dead” languages - Greek and Latin. Why did they do this? (By the way, in those gymnasiums that are reopening in our time, these languages are not always studied). This was done because the study of classical languages, due to their structure and abstraction from the semantic basis, effectively contributed to the development of children’s thinking. In this sense, “dead languages” echo mathematical symbols and the rules for writing and reading mathematical expressions.
When working on the difficult task of developing the thinking of primary school students, the teacher should keep in mind the theory of the stage-by-stage formation of mental actions, which was created by P. Ya. Galperin and N. F. Talyzina.
At the first stage, students are given a preliminary introduction to the purpose of the upcoming actions, and the necessary motivation for the action is created. It is important to create internal motivation, which is determined by interest in the process of activity itself during training, while external motivation determines the performance of actions under the influence of external conditions.
At the second stage, a diagram of the orientation basis of the action is drawn up – OBA, which gives a general idea of the method of its implementation, i.e. how this action should be performed. At this stage, the sequence and nature of the implementation of operations included in the educational activity are determined.
At the third stage, the action is performed in a material or materialized form. A material action is understood as an external, practical action with material (real) objects. A materialized action is understood as a student’s action with the help of models, diagrams, symbols, tables, posters, drawings, supports, etc. These are actions with objects presented in a sign-symbolic form. At this stage, it is important for students to begin using speech to comment on the educational actions they perform. Usually, in the learning process, they begin with performing actions in a materialized form, i.e., first, theoretical knowledge is formed, and then they move on to performing actions in a material form.
At the fourth stage of external speech, it is necessary to pronounce the action as external speech – in the form of loud speech or in writing. This is an important condition for the successful execution of the action. At this stage, the action is mastered in an expanded form without skipping any operations. It is necessary to ensure that all the constituent elements of educational actions are mastered by students in speech form. Usually, at first, students use words from everyday speech, and then gradually begin to move on to using the language of a given science, in our case, they operate with mathematical terms.
At the fifth stage of internal speech, the action is no longer accompanied by external speech, but is spoken to oneself and begins to move into the stage of automatic execution.
At the sixth stage, the action is already performed mentally without the use of any external supports. Learning actions are performed automatically.
Of course, the development of thinking is not quite gradual and straightforward, it encounters considerable difficulties, therefore it requires systematic work from the teacher to manage the thinking activity of schoolchildren. Here it is appropriate to recall the methodology of primary education, created by the talented teacher S.N. Lysenkova, which includes commented management of learning. Its essence is that children learn to think out loud and explain their learning activities. At first, the teacher does and shows this, and then some students begin to comment on their actions, and gradually – all the rest. For younger students, this is a kind of game and they play it with interest. In this way, the educational activity of the entire class is managed.
Let’s give an example of organizing commented management in a first-grade math lesson.
– Lead, Pavlik! (Example on the board)
– I write 5, I write “plus”, I write 2, I count: I put the pointer on the number 5, I add 2 (one, two), I get 7, I write 7.
– Lead, Yulia!
– I write 10, I write “minus”, I write 8, I write “it works out”. 10 is 8 and 2, we subtract 8, 2 remains, I write 2.
– Now write after me. I write 6, I write “minus”, I write 3, I write “it works out”, we count (pause), we write the result (pause), we raise our hand.
In this way, they teach thinking out loud, always only out loud, so that each action is accompanied by a word, then this word can be directed, and through the word, the student’s thought can be directed. Whether students write on the board or in a notebook, they always pronounce what they write in parallel. This effectively develops children’s speech, making it expressive.
This commented management allows the teacher to continuously monitor the process of perception and assimilation of educational material, prevent mistakes, and make adjustments if necessary. In this way, it acts as one of the means of feedback. As students move forward and develop, commenting begins to be accompanied by reasoning – this is evidentiary commenting reasoning, it is used when solving problems, performing exercises and complex tasks. This technique achieves the development of skills for logical reasoning, performing actions and proofs, and thinking independently.
Commented control develops in children a complex learning skill of three actions – “I think, I speak, I write down”.
Modern research has shown that the thinking abilities of primary school students are much broader than previously thought. For example, they can learn fairly abstract, theoretical material in the conditions of specially organized training. There are large reserves for mental development, which are practically not used in mass education. This is clearly demonstrated by the results of teaching primary school students according to the developmental education system of D. B. Elkonin – V. V. Davydov, as well as L. V. Zankov.
Research by American scientists to assess the impact of a person’s age on the ability to think outside the box has shown surprising results. It turned out that six-year-olds give the greatest number of unconventional solutions – 37%, seven-year-olds give 17% of unconventional solutions. In other age groups, this percentage drops sharply to only 2%. Children aged 6-7 have the highest ability to think outside the box, and by the age of 10-12, these abilities disappear in 98% of people. Why does this happen? Why is the education system unable to realize even a minimal degree of this creative potential? Therefore, an urgent task of didactics is to study the processes of developing creative abilities, as well as theoretical and empirical thinking of primary school children.