Content Introduction Chapter 1 Theoretical foundations for the formation of universal educational activities among primary school students

1.2. Techniques for the Formation of Cognitive Universal Learning Actions in Mathematics Lessons
Meta -subject results are methods of activity that are applicable both within the framework of the educational process and in real life situations.
A distinctive feature of the school course of mathematics is much greater than in many other subjects, its meta -subject focus, more cognitive.
The subject "Mathematics" has great potential for the formation of all types of UUD. The realization of these opportunities at the stage of primary general education depends on the methods of organizing the educational activities of younger students. In this regard, in the initial course of mathematics, a number of methodological innovations have been implemented related to the logic of constructing the content of the course, with the formation of computational skills, with teaching younger students to solve problems, with the development of a system of tasks that create didactic conditions for the formation of subject and meta -subject skills in their close relationship. Teaching mathematics is especially important in the formation of cognitive and regulatory UUD students. The subject contributes to the development of mental activity, as it forms the main intellectual abilities:
Analytical (the ability to comprehensively analyze information, classify, draw an analogy and comparison).
Logical (the ability to reason, think, draw the right conclusions).
Deductive (the ability to isolate particulars from general information, generalize, find patterns).
Critical (the ability to critically evaluate the available information, weed out false ideas and conclusions).
​ Abstract thinking (the ability to translate information about real objects into symbols, manipulate these symbols, find some solution and apply this solution again to objects in practice).
Figurative thinking (the ability to mentally compare objects of different meanings, formulate comparisons, simplify the understanding of complex ideas, presenting them at a more understandable level).
Concentration - (the ability to hold attention for a long time).
You can add to the listed abilities such properties of intelligence as mathematical thinking, technical thinking, algorithmic thinking, combinatorial thinking. Today it is impossible to be a pedagogically competent specialist without studying the arsenal of modern educational technologies. Depending on the type of lesson, various technologies are used to form UUD. For example, information and communication technologies and problem-based learning are used in the lessons of learning new material; game technologies - in repetition lessons; project method - in the lessons of systematization of the studied material, etc.
The main stages of the formation of UUD in mathematics lessons:
Stage 1: Primary experience and motivation . At this stage, techniques are used that allow the student to understand the significance of the topic being studied, the goals and objectives of the upcoming work.
Stage 2: Acquisition of knowledge . Priority are techniques aimed at the formation of independently successfully assimilate new knowledge, stimulating the cognitive activity of students.
Stage 3: Training in the application of knowledge, self-control and correction . Methods of group or individual work of students are applied to carry out educational activities in accordance with the plan; techniques aimed at developing the skills of finding and correcting errors; implementation of self- and mutual control.
Stage 4: Control . The final stage, which uses techniques that organize control of the level of formation of UUD and its practical use.
The formation of cognitive UUD in mathematics lessons ensures that students gain experience in working with information, namely:
Be able to search for the necessary information using various resources, including the Internet.
Be able to structure information, find the most effective solutions.
Solve problems with too much or too little information.
​ Process mathematical information for its further use, record and fix it using ICT and other means, use measuring tools, etc.
Techniques for the formation of cognitive UUD in mathematics lessons:
1.Problem learning.
Problem-based learning is understood as a system of evidence-based methods and tools used in the process of developmental learning. Which involves the creation of problem situations under the guidance of a teacher and the active independent activity of students to resolve them with the aim, first of all, of the intellectual and creative development of students, as well as their mastery of knowledge, skills, abilities and methods of cognition.
Problem-based learning provides opportunities for creative participation of students in the process of mastering new knowledge, the formation of cognitive interests and creative thinking, a high degree of organic assimilation of knowledge and motivation of students.
In fact, the basis for this is the simulation of a real creative process by creating a problem situation and managing the search for a solution to the problem. At the same time, the awareness, acceptance and resolution of these problem situations occurs with the optimal independence of students, but under the general guiding guidance of the teacher in the course of joint interaction. The creation of problem situations that determine the initial moment of thinking is a necessary condition for the organization of the learning process, which contributes to the development of productive thinking of students, their creative abilities. The very fact of encountering the difficulty with the impossibility of the proposed task with the help of existing knowledge and methods gives rise to the need for new knowledge.
Creating problem situations, the teacher must also find methods for mastering the motives of learning, the cognitive interest of students in the problem. When cognitive interest is aroused, it can be preliminary or simultaneous with the creation of a situation, or these two methods themselves can also serve as methods for creating problem situations. Creating a problem situation in the lesson contributes to the development of students' memory. The activity of thinking and the interest of students in the issue under study arises in a problem situation, even if the teacher poses and solves the problem. But the highest level of activity is achieved when the student himself forms the problem in the situation that has arisen, puts forward an assumption, substantiates the hypothesis, proves it and checks the correctness of the solution to the problem. No problems and methods of teaching can serve as an effective means of activating the learning process without understanding the nature of control in the "student-teacher" system. In order for the student to consciously and deeply assimilate the material, and at the same time he formed the necessary methods of cognitive activity, there must be a certain sequence of mental actions of the student. And for this, the activity of the student must be organized by the teacher at all stages of learning. Cognitive interest in educational material, caused by a problematic situation, is not the same for all students. To enhance this interest, the teacher seeks to create an increased emotional mood in the lesson, using special methodological methods of emotional impact on students before, or in the process of creating a problem situation. The use of elements of novelty, emotional presentation of educational material by the teacher are important ways of forming intrinsic motivation. In the process of problem-based learning, students develop such cognitive UUD as:

• 
  independent selection and formulation of a cognitive goal;
  
• 
  application of information retrieval methods, including using computer tools;
  
• 
  the ability to structure knowledge;
  
• 
  the ability to consciously and voluntarily build a speech statement in oral and written form;
  
• 
  statement and formulation of the problem, independent creation of activity algorithms in solving problems of a creative and exploratory nature.
  
• 
  analysis of objects in order to highlight features (essential, non-essential) synthesis as a compilation of a whole from parts, including self-completing, filling in the missing components;
  
• 
  choice of grounds and criteria for comparison and classification of objects;
  
• 
  summing up under concepts, deducing consequences;
  
• 
  establishing causal relationships,
  

construction of a logical chain of reasoning, hypotheses and their justification. Thus, cognitive universal learning activities contribute to the individual's awareness of significant connections, relationships, patterns, and at a higher level of his development, the child independently seeks information of interest to him on the problem, and then strives to learn complex theoretical issues in solving problems of a particular science. At the same time, the level of development of cognitive universal educational actions can be understood as arbitrary control of educational activities, the development of perception, thinking, speech, memory, and imagination.
2.Project training.
In modern pedagogy, the project method is considered as one of the personality-oriented learning technologies that integrates a problem-based approach, group methods, reflective, presentational , research, search and other methods. It is not used instead of systematic subject-based education, but along with it as a component of the education system. Project-based learning is the organization of the educational process aimed at solving learning problems by students on the basis of independent collection of information according to these characteristics and interpretation, mandatory justification and adjustment of subsequent productive learning activities, its self-assessment and presentation of the result. At the same time, learning takes on a great personal meaning, which significantly increases the motivation for learning itself. To date, in our country there is not much information about the use of the project method in teaching mathematics. Obviously, the complexity of mathematics itself often serves as an excuse for the traditional position of the teacher, because it is easier to explain in detail and “solve” a certain number of standard examples than to create conditions for students to study new things on their own.
For a primary school teacher, the most attractive thing about this method is that in the process of working on an educational project, students:
- it becomes possible to carry out approximate, “estimated” actions that are not immediately evaluated by a strict controller - a teacher;
- the foundations of systemic thinking are born;
- the skills of putting forward hypotheses, forming problems, searching for arguments are formed;
- develop creativity, imagination, fantasy;
- Purposefulness and organization, prudence and enterprise, the ability to navigate in a situation of uncertainty are brought up.
In addition, in the process of project implementation, there is a natural learning of joint intellectual actions. After all, this method is nothing but an attempt to model life. Educational project from the point of view of the student is an opportunity to maximize their creative potential. This activity will allow you to express yourself individually or in a group, try your hand, apply your knowledge, benefit, show the publicly achieved result. This is an activity aimed at solving an interesting problem, often formulated by the students themselves in the form of a task, when the result of this activity - the found way to solve the problem - is practical, has an important applied value and, which is very important, is interesting and significant for the discoverers themselves. The educational project from the point of view of the teacher is an integrative didactic means of development, training and education, which allows students to develop and develop specific design and research skills and abilities in students, namely to teach:

• 
  problematization (consideration of the problem field and highlighting sub -problems , formulating the leading problem and setting tasks arising from this problem);
  
• 
  goal-setting and planning of meaningful activities of the student;
  
• 
  introspection and reflection (the effectiveness and success of solving the problem of the project);
  
• 
  presentation of the results of its activities and the progress of work;
  
• 
  presentations in various forms, using a specially prepared design product (layout, poster, computer presentation, drawings, models, theatrical, video, audio and stage performances, etc.);
  
• 
  search and selection of relevant information and assimilation of the necessary knowledge;
  
• 
  practical application of school knowledge in various, including atypical, situations;
  
• 
  selection, development and use of a suitable manufacturing technology for a design product;
  
• 
  conducting research (analysis, synthesis, hypotheses, detailing and generalization).
  

The method of projects is one of the specific opportunities to use life for educational and educational purposes. That is why we can say that the project method expands the horizons in pedagogical theory and practice. He opens the way showing how to move from verbal education to education in life itself and life itself.
3. Didactic games.
What can make a younger student think, start thinking about this or that mathematical task, question, task? Interest can serve as the main source of motivation for junior schoolchildren to mental work. Therefore, the teacher must look for and find means and ways to arouse children's interest in mathematics. The interest aroused in children in individual tasks, as entertaining exercises and didactic games, arouses interest in mathematics itself. The value of the game in the classroom can not be overestimated. Here the horizons of the child, ingenuity develops. The game makes it possible to switch from one type of activity to another and thereby relieve fatigue, fatigue. Games with their content, form of organization, rules and effectiveness contribute to the formation of skills to analyze, compare, contrast. This affects the development of attention, observation, memory, spatial representations, and imagination. Great importance is attached to the game by researchers in the formation of cognitive interest as the basis for the development of cognitive activity in general, and logical UUD in particular. Researcher I.M. Dmitrieva in her dissertation indicates that at the beginning of schooling, the cognitive activity of children is closely related to the game. During this period, two motives dominate in the child, one of which is associated with the desire to learn, and the other is associated with the desire to play. Establishing a balance between these motives and harmonizing them is the most important task of training and education.
The development of cognitive actions is based on cognitive interest, which in turn stimulates cognitive activity and leads to cognitive activity in the process of which all cognitive actions are formed. There are various types of games that can be used in working with children of primary school age, but at the same time, special attention in matters of intellectual, cognitive development of children, the development of cognitive UUD belongs to didactic games.
The essence of the didactic game used in mathematics lessons is that students solve mental problems proposed to them in an entertaining way, find solutions themselves, while overcoming certain difficulties. The student perceives the mental task as a practical, playful one; it increases his mental activity. The sensory development of students in a didactic game is inextricably linked with the development of their logical thinking and the ability to express their thoughts in words. When solving a mathematical problem, students develop skills such as:

• 
  Information search;
  
• 
  Structuring knowledge;
  
• 
  Reflection of methods and conditions of action, their control and evaluation, criticality;
  
• 
  Choosing the most effective ways to solve problems depending on the conditions;
  
• 
  Formulation of the problem;
  
• 
  Independent creation of ways to solve problems of a creative and exploratory nature
  
• 
  Establishment of causal relationships;
  
• 
  Building a logical circuit.
  

Thus, the ability to formulate judgments, conclusions, the ability to apply one's knowledge in different conditions develops, namely, cognitive UUDs are formed. This becomes possible only if children have concrete knowledge about the objects and phenomena that make up the content of the game.
4. Support schemes for solving various types of problems.
Such schemes are good to use when compiling a short note. Depending on the condition of the task, it is modified by the student himself. The use of these schemes brings results. Records. Depending on the condition of the task, it is modified by the student himself. The use of these schemes brings results. Materialization of the logical scheme for analyzing the text of the problem, starting with a symbolic representation of the question and all the data (known and unknown) necessary to answer it. In such a model, the sequence of actions to solve the problem is fixed. In the first version of the task text modeling, a variety of sign-symbolic means (segments, Ionic signs, etc.) can be used. In this case, each of the task data is represented as separate specific symbols. In the second version of modeling, graphs (the simplest mathematical models) are the most convenient. The sequence of operations of the solution in the form of a graph follows from more general schemes, which reflect the main relationships between the data of the problem. Since models of this type represent the final result of orientation in the text of the problem, their construction requires the ability to carry out a complete analysis of the text, to select all components (objects, their sizes, relationships between them, etc.). When creating different types of models, it is very important to determine what information should be included in the model, what means (symbols, signs) will be used for each selected component of the text, which of them should have the same symbolism, and which ones should be different. In the process of building a model and working with it, the text is analyzed and translated into mathematical language: known and unknown objects, quantities, relationships between them, basic and intermediate questions are identified. The use of support schemes in a mathematics lesson for solving various types of problems allows students to develop the following skills:

• 
  the ability to display educational material in reference diagrams and tables;
  
• 
  the ability to read meaningfully and highlight essential features;
  
• 
  the ability to generalize and structure knowledge;
  
• 
  the ability to choose the most effective ways to solve problems depending on the conditions;
  
• 
  the ability to synthesize, as a compilation of a whole from parts, including with the completion of missing components.
  

Thus, from all that has been said, we can conclude that at each lesson of mathematics, work can be carried out to develop cognitive ULD, which is a necessary condition for the implementation of second-generation standards. They are one of the criteria for assessing the achievement of the main goal of modern education: to teach how to learn and thereby become subjects of the educational process. The system of work on the formation of cognitive UUD using active methods allows you to activate the creative activity of students, develop an active life position, form a creative personality. The use of ICT in the classroom gives good results:
- develops creative, research abilities of students, increases their activity;
- contributes to a more meaningful study of the material, the acquisition of self-organization skills;
- increases interest in the subject.
Research activity contributes to the formation in children of the above universal learning activities. And the use of information and communication technologies also attracts students to research in such lessons and makes the level of teaching consistent with modern educational requirements.