One step, two steps. Practical course of mathematics for preschoolers. Guidelines. Peterson L.G., Kholina N.P.

3rd ed., add. and reworked. - M.: 201 6 - 2 56 p.

A methodological guide for the development of mathematical representations of children 5-6 and 6-7 years old is part of the continuous mathematics course "School 2000 ...". Includes short description concepts, programs and organization of practical classes with children. Additional materials for organization individual work with children are contained in notebooks on a printed basis “One is a step, two is a step ...”, parts 1-2, by the same authors. The educational and methodical set "One - a step, two - a step ..." is focused on the development of thinking, creative abilities of children, their interest in mathematics. Preparatory work with children aged 3-4 and 4-5 years old can be carried out according to the set "Player", parts 1-2, authors L. G. Peterson and E. E. Kochemasova, and the continuation for elementary school students is the mathematics course L. G. Peterson. The allowance can be used in classes with preschoolers in kindergartens, institutions "Primary School - Kindergarten" and other preschool educational institutions, as well as for individual work of parents with children.

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Content
Introduction 3
The program for the development of mathematical representations "One - a step, two - a step ..." (64 lessons) 9
Approximate thematic planning according to the program "One - a step, two - a step ..." (64 lessons) 12
Approximate thematic planning for the program "One - a step, two - a step ..." (86 lessons) 14
Part 1
Session 1 16
Session 2 19
Session 3 22
Session 4 25
Session 5 29
Session 6 32
Session 7 34
Session 8 38
Session 9 40
Session 10 45
Session 11 47
Lesson 12 51
Lesson 13 55
Lesson 14 59
Lesson 15 62
Lesson 16 65
Lesson 17 68
Lesson 18 71
Lesson 19 74
Lesson 20 78
Lesson 21 82
Lesson 22 85
Lesson 23 89
Lesson 24 94
Lesson 25 98
Lesson 26 103
Lesson 27 106
Lesson 28 PO
Lesson 29 113
Lesson 30 117
Lesson 31 120
Session 32-34 124
Part 2
Lesson 1 125
Lesson 2 128
Lesson 3 133
Lesson 4 137
Lesson 5 140
Lesson 6 143
Lesson 7 147
Lesson 8 150
Lesson 9 154
Lesson 10 160
Lesson 11 164
Lesson 12 168
Lesson 13 171
Lesson 14 175
Lesson 15 179
Lesson 16 183
Lesson 17 187
Lesson 18 192
Lesson 19 1%
Occupation 20 200
Lesson 21 204
Lesson 22 208
Lesson 23 212
Lesson 24 217
Lesson 25 220
Occupation 26 225
Lesson 27 229
Occupation 28 233
Occupation 29 237
Occupation 30 242
Occupation 31 246
Occupation 32 249
List of references 254

The educational and methodical manual "One is a step, two is a step ..." is intended for the development of mathematical representations of older children preschool age and preparation for school. It represents constituent part a continuous course of mathematics for preschoolers, elementary and basic schools, which is currently being developed in the Association "School 2000 ..." from the standpoint of the integrated development of the child's personality: the development of his cognitive interests, intellectual and creative powers, personality traits *.
The pre-school level of the program "School 2000..." consists of two parts: "Player" - for children 3-4 and 4-5 years old, and "One - step, two - step ..." - for children 5-6 and 6-7 years old. However, it is possible to work according to the program “One - a step, two - a step ...” with those children who have not completed the “Player” program and begin their preschool training in mathematics at the age of 5-6.

Many modern schools of development emphasize the study of mathematics, various productive methods of teaching this exact science are being developed. One of them is the Peterson teaching method.

Just about complex

The author of this world-famous methodology for teaching mathematics is Ludmila Gergievna Peterson, Doctor of Pedagogical Sciences, Professor, Director of the Center for Systemic-Activity Pedagogy "School 2000...", Laureate of the Prize of the President of the Russian Federation in the field of education.

The Peterson technique is built on the principle of a “layer cake”. Its essence is that knowledge is taught to children in a simple and accessible form, and the child, as it were, "layers" new information on existing knowledge. An important feature of the methodology is that it is close to the real needs of the child. Perhaps that is why children studying according to the Peterson method know much more than their peers and are ahead of them in development by about 1 - 2 years. Moreover, training by this method can begin as early as the age of three. Even topics that are difficult to master are given to children in a simple, accessible form, which most often takes place in an interesting way. game form.

educational moment

Unlike the traditional school teaching methodology, where the teacher explains and the student learns, the methodology
learning Peterson suggests that each child acquires new knowledge independently. To do this, he is given certain tasks, which he still does not know how to solve. In order to cope with the task, the child must offer some kind of solution, version, hypothesis, explain and test it. Truth is born as a result of joint discussion, creative work that educates a person, while knowledge is assimilated much deeper. Moreover, the depth of study and the level of perception of the information received are changing each time. Thus, if a child has not learned something in the first year of study according to the Peterson method, he has every chance to master this knowledge in next year, but the task becomes somewhat more complicated. It is possible to put aside material that is too difficult to study for some time, in order to then master it already at a new stage of its development.

Realistic learning

Another one distinguishing feature Peterson's methodology lies in the fact that it is as close as possible to the real world, which is especially important at an early stage in the development of children of primary preschool age. The fact is that complex abstract concepts and formulas for kids are too difficult to master, especially in terms of their practical application in life.

lesson game

Lessons according to the Peterson method resemble an exciting game that
increases interest in the learning process and greatly facilitates it, cause positive emotions and interest. Children who study according to the Peterson method always have a large numerical trickle before their eyes. When it is necessary, suppose, to add two numbers - 3 and 1, he puts his finger on the number 1 and takes three steps forward. If you need to subtract 2 from 5, he puts his finger on the number five and takes two steps back. That's the whole game logic!

visibility

During the written lessons in the lessons according to the Peterson method, colorful bright notebooks and educational and visual aids and toys are used, at a glance which not only children, but also adults will want to play with their children. Moreover, the methodology is designed in such a way that it is not necessary to attend special circles and schools for classes. early development. It is quite possible to teach children according to the Peterson method at home.

The brochure presents the preschool program "Steps" in mathematics for children 3-6 years old ("Toy" for children 3-4 years old and "One - a step, two - a step ..." for children 5-6 years old), which is the initial link of a continuous course of mathematics for preschoolers, primary and secondary schools of the educational system "School 2000 ...". Class planning is given, taking into account the possibility of working under this program with preschoolers of various levels of training.
The main goal of the "Steps" program is the development in children during the didactic game of thinking, creative forces and activity abilities, general educational skills and personality traits that ensure effective learning at school.
The program is methodically supported by the courses "Player" and "One - a step, two - a step ..." by the authors L. G. Peterson, E. E. Kochemasova and N. P. Kholina, which have been tested in wide pedagogical practice with positive results since 1992 of the year.

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1 Mathematics training program for preschoolers L.G. Peterson, N.P. Kholina “One step, two steps Explanatory note The course of mathematics for preschoolers is the initial link of a single continuous course of mathematics 0 9, which is currently broken down from the standpoint of the integrated development of the child's personality, the humanization and humanitarization of mathematical education (supervisor Doctor of Physical and Mathematical Sciences, Professor G.V. Dorofeev). The main goal of the mathematics course for schoolchildren is the comprehensive development of the child: the development of his motivational sphere, intellectual and creative forces, personality traits. Often, preparing children for school comes down to teaching them to count, read, and write. Meanwhile, the greatest difficulty in primary school not those children who show intellectual passivity, who lack the desire and habit of thinking, the desire to learn something new, experience it. At the same time, the development of fantasy, imagination, and creative abilities is of particular importance. Thus, the main objectives of this course of mathematics for preschoolers are: 1) Formation of motivation for learning, focused on the satisfaction of cognitive interests, the joy of creativity. 2) Development of figurative thinking (sensations, perceptions, ideas). 3) Formation of methods of mental actions (analysis, synthesis, comparison, generalization, classification, analogy). 4) Development of variability of thinking, creative abilities, fantasy, imagination, constructive skills. 5) Increase the amount of attention and memory. 6) The development of speech, the ability to justify one's judgments, to build the simplest conclusions. 7) Developing the ability to purposefully control volitional efforts, establish the right relationships with peers and adults, and see oneself through the eyes of others. 8) Formation of general educational skills and abilities (the ability to think and plan actions, implement a decision, guess about the results and check them, strictly obey the given rules and algorithms, etc.). 9) fostering interest in the subject and the learning process in general. These tasks are solved in the process of familiarizing children with different areas mathematical reality: with quantity and counting, measurement and comparison of quantities, spatial and temporal orientations - that is, with those mathematical concepts that underlie the content of the elementary mathematics course and determine the depth and quality of assimilation of the school curriculum. new material is administered on the basis of the principle of activity, that is, it is not given to children in ready-made, but is comprehended by them through independent analysis, comparison, and identification of essential features. Mathematics should enter the life of children not as a theory, but as a "discovery" of regular connections and relationships in the world around them. And the teacher leads the children to these discoveries by organizing and directing them. learning activities for example, children are invited to roll two objects through the gate. As a result of their own objective actions, they establish that the ball is rolling because it is “round”, without corners, and the corners prevent the cube from rolling. Thus, children learn to recognize geometric figures, get acquainted with their names, identify essential features. The form of classes should be mobile, varied and change depending on the tasks.

2 Age characteristics of children determined saturation educational material game tasks. However, the use of a large number of games does not mean a decrease in the level of mathematical content. On the contrary, many topics traditional for preschool education have been transferred to an earlier period, and the range of issues under consideration has been significantly expanded in the direction of the formation of fundamental mathematical ideas in children. It should be emphasized that we are not talking about changing the requirements of the standard program for the mathematical preparation of preschoolers, but about changing the mechanism for achieving these goals. One of such mechanisms is the minimax principle, which was formed in didactics based on the ideas of L.V. Vygotsky, A.N. Leontieva, L.V. Zankova and others. It means such an organization of work with children, when knowledge is given to the maximum possible (in the zone of their proximal development), and the requirements for the elimination of knowledge are presented at the minimum necessary for passing the next stage of education and determined by the state standard. In other words, the success of learning is achieved not by facilitating tasks to the level of the weakest children, but by developing in each child the desire and ability to overcome difficulties. The use of the minimax principle allows all children to achieve the level of required learning outcomes without overloading, without slowing down the development of more capable children. Thus, the issue of level differentiation of preschool education is solved: each child moves forward at his own pace. In preschool age, emotions play perhaps the most important role in personality development. Therefore, an individual approach is of paramount importance, creating for each child a situation of success, an atmosphere of goodwill, where all children, regardless of their abilities, “feel at home”. The principle of comfort is a necessary component of working with children, since failure to comply with this requirement adversely affects their health and mental development. An important feature of this program is that it is an organic part of the general course of mathematics, ensuring its continuity at all stages. The direct continuation of the program in elementary school is the program for elementary school 1 4 L.G. Peterson, and in the secondary school program for 5 9 grades G.V. Dorofeeva, G.K. Muravina and L.G. Peterson. Thus, the following didactic principles are implemented in this program: 1) the principle of activity ensures the comprehensive development of children; 2) the minimax principle provides an individual development path for each child; 3) the principle of comfort ensures the normal psycho-physiological state of children; 4) the principle of continuity ensures successive links between all levels of education. Calendar-thematic planning of classes in mathematics "One-step, two-step" (1 lesson per week, 28 lessons in total) Plan. Fact. Quantity Theme of the lesson hours 1 1 Numbers Numbers Numbers Number 6. Number Number 6. Number 6

3 6 1 Number 6. Digit Measurement of length. 8 1 Length measurement. 9 1 Length measurement Number 7. Number Number 7. Number Number 7. Number Number 7. Number Heavier, lighter. Weight comparison Weight measurement Number 8. Number Number 8. Number Number 8. Number Volume. Comparison by volume Measurement of volume Number 9. Digit Number 9. Digit Number 9. Digit Area. Area measurement Number 0. Number Number 0. Number Number 10. Number Ball.Cube.Parallepiped. Explanatory note The course of speech development and literacy for preschoolers is the initial link of the continuous course "Teaching literacy" - Russian language - reading - literature for grades 1-11 as part of the educational program "School2100". The overall goal of the program is to prepare a functionally literate personality in the course of preschool and school developmental education as an indicator of quality education, to ensure that the student is ready for further development. One way to achieve this goal is to create continuous courses. In relation to teaching the Russian language, continuity is understood as the presence of a sequential chain of learning tasks throughout the entire process of mastering the language, turning into each other and ensuring the student's constant advancement in each of the successive time periods. Continuity is on the border of "childish garden-school» provides continuity in training. The pre-school course for the development of speech and preparation for literacy is designed to provide high-quality preparation of children for education in elementary school according to the Educational Program "School 2100". The development of a preschooler is carried out along four main lines that determine his readiness for schooling: 1) the line of formation of voluntary behavior; 2) the line of mastering the means and standards of cognitive activity; 3) the line of transition from egocentrism to the ability to see the world from the point of view of other people; 4) the line of motivational readiness. A feature of the program is the use of elements of speech therapy methodology for preschool children, the purpose of which is to prevent errors in reading and writing. The purpose of the course is the comprehensive development of the child's personality, his value ideas about the world around him, his outlook, intellect, and personal qualities.

4 Learning objectives: 1) formation of learning motivation and interest in the learning process itself; 2) the development of visual-figurative and the formation of verbal-logical thinking, the ability to draw conclusions, justify one's judgments; 3) formation of methods of mental actions: analysis, synthesis, comparison, generalization, exclusion, modeling, design; 4) development of memory, attention, creativity, imagination, variability of thinking; 5) development of general educational skills: the ability to work in a team, interact, bring the work started to the end; work carefully, with concentration, plan and control their actions; 6) development of communication skills with adults, with peers, the ability to see the world through the eyes of another person; 7) development of speaking, listening and reading skills; 8) development of interest and attention to the word, to one's own speech and the speech of others; 9) enrichment of the active, passive, potential vocabulary: development of the grammatical structure of speech, coherent speech skills based on the speech experience of a child of a native speaker; development of the ability to operate with language units: sound, syllable, word, phrase, sentence; 10) expansion of ideas about the world around, the phenomena of reality based on the life experience of the child. The solution of these problems is carried out in the process of teaching literacy and teaching writing. Classes are conducted according to the textbook by R.N. Buneev, E.V. Buneev, T.R. Pronina "Our prescriptions". Thematic planning of classes in teaching literacy and teaching writing, developing speech and preparing for teaching writing (1 lesson per week, 28 lessons in total). Plan. The fact of the lesson Calendar-thematic planning in preparation for teaching literacy and writing Number of hours "On the way to the ABC" "Our copy-books" 1 1 Sounds and letters Writing straight and oblique lines Words. Sounds. Sound a s a Sounds o, e o, e Sounds i, s s, and, a, o, e Sound y. vowel sounds and letters. y y 10 1 Sounds m, m. Consonant sounds. Syllables. Hard and m M soft consonants Sounds n, n. Consonant sounds and letters. Syllables. nn 12 1 Sounds p, p. p P 13 1 Sounds t, t. Vowel sounds and letters (a, o, u, i, s, tt

5 e). consonant sounds and letters (m, n, p, t) 14 1 Sounds to, to kk 15 1 Sounds x, x. sounds KX, kx xx 16 1 Sounds f, f y Syllables with the letter f. ff 17 1 Sounds ye, yo, yu, ya. Syllables. e, u, i 18 1 Sounds l, l. differentiation of sounds l, y ll 19 1 Sounds v, v, f, f. differentiation of sounds v, v, f f v, f. Voiced and deaf consonants Sounds h, sch. Differentiation of sounds. h, u 21 1 Sounds b b. Differentiation of sounds b b, p p, b-p Sounds d and d.; dr. dr. e, t 23 1 Sounds s, ss 24 1 Sound c. Differentiation of sounds c-s, ts-ch Sounds g and g. Differentiation of sounds g-k, g-k Sounds z and z. Differentiation of sounds s-z, s-z. whistling consonant sounds. tss gg. zz 27 1 Sounds w w Hissing consonant sounds. w, w 28 1 Sounds of r, r. p p

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In kindergarten, one of the areas of work is teaching counting skills. Often, educators use the manual L. G. Peterson "". Training according to this technique can be started from 3 years to seven. The content of the educational program becomes more complex with age. This manual includes practical advice and demonstration material.

• study of the properties of objects and numbers;
• patterns;
• numbers;
• quantities;
• space-time representations.

Children in kindergarten

At a younger age, they study only numbers with them, and at an older age they study simple arithmetic operations with them. All classes should be carried out taking into account the leading activity of the child in the preschool period - the game. But lessons should be held regularly so that the knowledge gained is systematized.

For children 4-5 years old

This part of the manual is not aimed at memorization and memorization, but at educating children in the ability to independently draw conclusions, reason and prove their point of view. There is no need to impose mathematics on him, teachers should try to motivate him.

Important! The book should not be given completely at once: you need to cut off the sheets as you complete the tasks and put them in a separate folder. And at the end of the school year, it can be given to the parents of the pupil.

This tutorial covers the following topics:

• "Repetition";
• "Earlier, later";
• "Comparison in height";
• "Number and number 4";
• "Square";
• "Cube";
• "Up, down";
• "Width comparison";
• "Number and number 5";
• "Oval";
• "Inside Outside";
• "In front, behind, between";
• "Pair";
• "Rectangle";
• "Number series";
• "Rhythm";
• "Number and number 6";
• "Ordinal account";
• "Comparison by length";
• "Number and number 7";
• "Numbers and Numbers 1-7";
• "Comparison by thickness";
• "Higher lower";
• "Plan";
• "Number and figure 8";
• "Cylinder";
• "Cone";
• "Prism and Pyramid".

Important! After studying all the topics in the second part of the "Toy", tasks for repeating all the material are collected.

In each section, several exercises are proposed for practicing and consolidating:

• comparison;
• draw figures;
• connect the dots;
• find an extra item and explain why;
• paint over the desired number or a suitable figure;
• passage of the labyrinth;
• making proposals.

Exercise has a positive effect on the development of fine motor skills and speech development. All topics are illustrated, because when working with preschoolers, you need to use visual material. It is important that the teacher does not give the children ready-made answers, but helps them find the answer to the questions on their own. At the age of 4-5 years, teachers form an interest in the study of mathematics.

boy doing math

For the middle group 5-6 years old

In Peterson's book "Mathematics for Preschoolers" for the middle group, children begin to be introduced to simple arithmetic operations and the expansion of existing knowledge. In this guide for the middle group, the following sections are studied in detail:

• properties of objects;
• comparison;
• addition;
• work on spatial representations ON, OVER, UNDER;
• work on the concepts of "right", "left";
• subtraction;
• work on the concepts of "between", "in the middle", "inside", "outside";
• one-many;
• study of numbers and numbers.

In the middle group, more time is allocated for the study of each topic, because these are the first steps for children to school.

Important! Classes should not be too long. It is necessary to arrange physical minutes and a change of activity.

Preschoolers are offered to perform the following types of exercises:

• search for similar features and differences;
• search for similar shapes and color them;
• search for extra items;
• work with tables.

For almost every exercise, the child must give a detailed answer. Thus, it happens. Each topic is given several lessons, because the material becomes more complicated. Therefore, the use of Peterson's book in mathematics for children 5-6 years old makes it possible to realize A complex approach to learning.

For preschoolers 6-7 years old

AT preparatory group Most of the classes are devoted to the development of arithmetic operations. New topics include the following:

• area measurement;
• length measurement;
• mass measurement;
• watch.

Didactic games

Peterson's book "Preparing for School Years 6-7" offers handouts so that preschoolers can apply knowledge in practice and better master the knowledge gained.

The advantage of this technique is that this is not a textbook on mathematics for kindergarten, but workbook. And you can study in notebooks “One is a step, two is a step ...” at home. The tasks are age-appropriate and progressively more difficult. It is desirable to conduct lessons in a playful way so that children do not lose interest in learning a new subject for them.

Peterson preschool education: how to conduct classes

The learning process for this manual should be based on the following methodological principles:

• Creating a favorable psychological environment is one of the main principles in teaching. A comfortable environment has a beneficial effect on the general condition of the child.
• The activity approach - a preschooler learns the world not by getting ready-made answers, but as a result of an independent search. The adult is more of an observer.
• Individual approach - the teacher creates situations in which each child in the group feels part of the team.
• Integrity - the learning process is not limited to kindergarten. One of the tasks of the teacher is to convey to parents the importance of continuing the educational process during other activities.
• Variation - the use of tasks with several answers.
• Creativity - not only encouragement is important here creative activity child, but also joint work with adults.
• Continuity.

There are 3 types of situations in the lesson:

• "discoveries" of new knowledge;
• workout;
• final.

A feature of the first type of classes is the implementation of educational goals with the study of new mathematical topics. Children are left with the opportunity to think and find the answer on their own. At the beginning of the lesson, the teacher introduces a new topic, talks about its meaning. Next, he creates difficult situation resulting in the discovery of new knowledge.

To do this, the teacher offers the student to perform an action using new knowledge. Thanks to this, the adult leads the preschooler to the realization that he is not yet ready to perform new skills. Solution of practical exercises on a new topic and its consolidation. In this lesson, the main goal of the teacher in this type of class is to involve the child in the educational process.

Didactic material

The teacher, asking leading questions, encourages the child to choose a way to solve a difficult situation. As a result of the successful application of new knowledge in practice, it is imperative to praise the child. At the end, the teacher pronounces the solution algorithm, without going beyond the game method.

Then he creates different situations for the application of the new skill. Or organize a little self-examination. When summarizing the results, the educator pronounces the conditions due to which it was possible to achieve the result.

A training session can be carried out in a playful way. The purpose of such lessons is to consolidate the acquired knowledge. But it does not take place in the form of standard memorization. The child independently finds difficulties that prevent him from learning a new topic and coping with them. During the debriefing, the educator should pay attention to what helped him to emerge as a winner.

Important! Final classes are conducted with the participation of two teachers. One of them organizes the educational process, and the second writes down the results. The purpose of such lessons is to systematize the acquired knowledge and check how much the child has mastered it.

The value of the book in preparing for school

The value of Peterson's classes can hardly be overestimated if they were carried out taking into account all the recommendations. Its advantage is that it is suitable for individual work with children. It is easier for the educator to make long-term planning so that teaching mathematics is effective.

Mathematics lesson at preschool educational institution

When using this technique, preschoolers do not lose interest in learning. This is due to the fact that in the classroom they use game methods, introduce fairy-tale characters. Many studies have proven the effectiveness of teaching in this way. Children are taught to think independently, to look for solutions.

Also, the use of Peterson's book contributes to the development of creative thinking. Although many in the study of mathematics miss this component. The selected tasks will allow teachers to explain even complex tasks to the child as clearly as possible. As a result of classes according to this educational method, children learn to cope with tasks on their own. And an adult can only suggest a direction in solving a problem.