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

3rd ed., Add. and revised - M .: 201 6 - 2 56 p.

A methodological guide for the development of mathematical concepts of children 5-6 and 6-7 years old is part of the continuous course of mathematics "School 2000 ..." Includes a brief description of the concept, program and organization of practical activities with children. Additional materials to organize individual work with children are contained in notebooks on a printed basis "One - a step, two - a step ...", parts 1-2, by the same authors. The educational-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 3-4 and 4-5 years old can be carried out according to the set "Play", parts 1-2, authors L. G. Peterson and E. E. Kochemasova, and the continuation for elementary school students is the course of mathematics L. G. Peterson. The manual 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
Program for the development of mathematical representations "One is a step, two is a step ..." (64 lessons) 9
Approximate thematic planning according to the program "One - step, two - step ..." (64 lessons) 12
Approximate thematic planning according to the program "One - step, two - step ..." (86 lessons) 14
Part 1
Lesson 1 16
Lesson 2 19
Lesson 3 22
Lesson 4 25
Lesson 5 29
Lesson 6 32
Lesson 7 34
Lesson 8 38
Lesson 9 40
Lesson 10 45
Session 11 47
Session 12 51
Session 13 55
Session 14 59
Lesson 15 62
Lesson 16 65
Session 17 68
Session 18 71
Session 19 74
Lesson 20 78
Session 21 82
Lesson 22 85
Session 23 89
Lesson 24 94
Lesson 25 98
Session 26 103
Session 27 106
Lesson 28 PO
Session 29 113
Lesson 30 117
Session 31 120
Class 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
Session 12 168
Lesson 13 171
Lesson 14 175
Lesson 15 179
Lesson 16 183
Lesson 17 187
Lesson 18 192
Lesson 19 1%
Lesson 20 200
Lesson 21204
Lesson 22208
Lesson 23 212
Lesson 24 217
Session 25 220
Session 26 225
Lesson 27 229
Session 28 233
Lesson 29 237
Lesson 30 242
Lesson 31 246
Lesson 32 249
List of used literature 254

The teaching aid "One is a step, two is a step ..." is intended for the development of mathematical concepts in older preschool children and preparation for school. It represents component part a continuous mathematics course for preschoolers, primary and secondary schools, which is currently being developed by the Association "School 2000 ..." from the standpoint of the complex development of the child's personality: the development of his cognitive interests, intellectual and creative powers, personality traits *.
The preschool level of the "School 2000 ..." program consists of two parts: "Play" - for children 3-4 and 4-5 years old, and "One - a step, two - a 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 program "Play" and begin their preschool training in mathematics at the age of 5-6 years.

Many modern schools of development focus on the study of mathematics, various productive methods of teaching this exact science are being developed. One of them is Peterson's teaching methodology.

Just about complicated

The author of this world-famous method of teaching mathematics is Lyudmila Gergievna Peterson, Doctor of Pedagogy, Professor, Director of the Center for System-Activity Pedagogy "School 2000 ...", laureate of the Presidential Prize in the field of education.

Peterson's technique is based on the “puff pie” principle. Its essence is that knowledge is taught to children in a simple and accessible form, and the child, as it were, "layers" new information onto existing knowledge. An important feature of the technique is that it is close to the real needs of the child. Perhaps that is why children who study 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 in this technique 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 playful way.

Educational moment

Unlike the traditional teaching methodology at school, where the teacher explains and the student learns, the methodology
Peterson's learning assumes that each child learns 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 personality, while knowledge is assimilated much deeper. Moreover, the depth of study and the level of perception of the information received change each time. Thus, if a child did not learn something in the first year of study using the Peterson method, he has every chance to master this knowledge the next year, although the task will become somewhat more complicated. Material that is too difficult to study, it is possible to postpone for some time, in order to then master it already at a new stage of its development.

Realistic learning

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

Lesson game

Peterson's lessons are like a fun game that
increases interest in the learning process and greatly facilitates it, arouses positive emotions and interest. Children who study according to the Peterson method always have a large numerical stream in front of their eyes. When it is necessary, for example, 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 all the 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, from one glance at which not only children, but also adults will want to play with their children. Moreover, the methodology is structured in such a way that it is not necessary to attend special circles and schools of early development for classes. It is quite possible to teach children according to the Peterson method at home.

The brochure presents the pre-school training program "Steps" in mathematics for children 3-6 years old ("Play" for children 3-4 years old and "One is a step, two is 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 ...". The planning of lessons is given, taking into account the possibility of working on this program with preschoolers of various levels of training.
The main goal of the "Steps" program is to develop in children, in the course of didactic play, thinking, creative forces and activity abilities, general educational skills and personality traits that ensure effective learning at school.
The program is methodically provided with the courses "Play" and "One is a step, two is a step ..." by 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 Program for the preparation of preschoolers in mathematics 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 in mathematics 0 9, which is currently being broken down from the standpoint of integrated development the personality of the child, humanization and humanitarization of mathematical education (supervisor Doctor of Physics and Mathematics, Professor G.V. Dorofeev). The main goal of the mathematics course for schoolchildren is the all-round development of the child: the development of his motivational sphere, intellectual and creative powers, personality traits. Often, preparing children for school comes down to teaching them counting, reading, writing. Meanwhile, the greatest difficulty in primary school not those children who show intellectual passivity, who lack the desire and habit to think, the desire to learn something new are experienced. At the same time, the development of fantasy, imagination, and creative abilities is of particular importance. Thus, the main tasks 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 imaginative thinking (sensation, perception, representation). 3) Formation of methods of mental actions (analysis, synthesis, comparison, generalization, classification, analogy). 4) Development of variability of thinking, creativity, imagination, imagination, constructive skills. 5) Increase the amount of attention and memory. 6) The development of speech, the ability to substantiate their judgments, build the simplest inferences. 7) Developing the ability to purposefully master volitional efforts, establish correct relationships with peers and adults, see yourself through the eyes of others. 8) Formation of general educational skills and abilities (the ability to think over 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 of mathematical reality: with quantity and counting, measuring and comparing quantities, spatial and temporal orientations, that is, with those mathematical concepts that underlie the content of the course in elementary mathematics and determine the depth and quality of assimilation school curriculum. New material is introduced on the basis of the principle of activity, that is, it is not given to children in finished form, 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 the natural connections and relationships of the surrounding world. And the teacher leads children to these discoveries by organizing and directing their learning activities, for example, children are invited to ride 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 shapes, get acquainted with their names, and identify essential features. The form of classes should be mobile, varied and change depending on the tasks.

2 The age characteristics of children determined the saturation of the educational material with play 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 preparation have been moved 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 training of preschoolers, but about changing the mechanism for achieving these goals. One of such mechanisms is the minimax principle, which was formed in didactics on the basis of L.V. Vygotsky, A.N. Leontyeva, 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 required to pass the next stage of training 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 compulsory learning outcomes without overloading, without slowing down the development of more capable children. Thus, the issue of level differentiation of preschool training is being 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 a situation of success for each child, 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 negatively affects their health and mental development. An important feature This program is that it is an organic part of the general course of mathematics, ensuring its continuity at all stages. A direct continuation of the program to primary school is the program for primary school 1 4 L.G. Peterson, and in high school the program for grades 5-9 G.V. Dorofeeva, G.K. Muravina and L.G. Peterson. Thus, this program implements the following didactic principles: 1) the principle of activity ensures the all-round development of children; 2) the minimax principle provides an individual path of development for each child; 3) the principle of comfort ensures the normal psychophysiological state of children; 4) the principle of continuity ensures continuity between all levels of learning. Calendar-thematic planning of lessons in mathematics "One-step, two-step" (1 lesson per week, 28 lessons in total) Plan. Fact. Number Topic of lesson lessons hours 1 1 Numbers Numbers Numbers Number 6. Number Number 6. Number 6

3 6 1 Number 6. Digit Length measurement. 8 1 Measurement of length. 9 1 Measurement of length Number 7. Number Number 7. Number Number 7. Number Number 7. Number It is heavier, lighter. Comparison by mass Measurement of mass Number 8. Number Number 8. Number Number 8. Number Volume. Comparison by volume Measurement of volume Number 9. Number Number 9. Number Number 9. Number Area. Measurement of area Number 0. Number Number 0. Number Number 10. Number Ball.Cube.Parallepiped. Explanatory note The course of speech development and literacy training for preschoolers is the initial link in the continuous course "Teaching literacy" - Russian language-reading-literature for grades 1-11 as part of the educational program "School2100". The general goal of the program is to prepare, in the course of preschool and school developmental education, a functionally literate personality as an indicator of quality learning, to ensure the student's readiness for further development. One way to achieve this goal is to create continuous courses. With regard to teaching the Russian language, continuity is understood as the presence of a sequential chain of educational tasks throughout the entire process of language acquisition, passing into each other and ensuring the constant progress of the student forward at each of the successive time intervals. Continuity at the kindergarten-school border ensures continuity in learning. The preschool course of speech development and preparation for literacy is designed to provide high-quality preparation of children for learning in primary 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 school education: 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) line of motivational readiness. A feature of the program is the use of elements of speech therapy techniques for preschool children, the purpose of which is to prevent errors in reading and writing. The goal of the course is the comprehensive development of the child's personality, his value ideas about the world around him, outlook, intellect, personal qualities.

4 Learning objectives: 1) the formation of motivation for learning and interest in the learning process itself; 2) the development of visual-figurative and the formation of verbal and logical thinking, the ability to draw conclusions, substantiate their judgments; 3) the formation of methods of mental actions: analysis, synthesis, comparison, generalization, exclusion, modeling, design; 4) development of memory, attention, creativity, imagination and variability of thinking; 5) the development of general educational skills: the ability to work in a team, interact, bring the work started to the end; work attentively, with concentration, plan and control your 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 skills of speaking, listening and reading; 8) the development of interest and attention to the word, to one's own speech and the speech of others; 9) enrichment of an active, passive, potential vocabulary: the development of the grammatical structure of speech, the skills of coherent speech 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, phenomena of reality based on the life experience of the child. The solution to these problems is carried out in the process of teaching literacy and teaching writing. Classes are conducted according to the textbook by RN Buneev, EV Buneev, TR Kislov "On the way to the alphabet" and according to the prescriptions of the Buneevs and OV Pronina "Our recipes". Thematic planning of literacy and writing lessons, speech development and preparation 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 recipes" 1 1 Sounds and letters Writing of straight and oblique lines Words. Sounds. Sound a y a Sounds oh, oh, oh Sounds and, s s, and, a, o, e Sound u. vowel sounds and letters. u U 10 1 Sounds m, m. Consonant sounds. Syllables. Hard and m M soft consonants Sounds n, n. Consonants and letters. Syllables. nn 12 1 Sounds p, p. n P 13 1 Sounds t, t. Vowels and letters (a, o, y, u, s, tt

5 e). Consonant sounds and letters (m, n, n, t) 14 1 Sounds k, k kk 15 1 Sounds x, x sounds KX, kx xx 16 1 Sounds f, fj Syllables with the letter f. ff 17 1 Sounds ye, yo, yu, ya. Syllables. f, u, z 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 voiceless consonants Sounds h, sh. Differentiation of sounds. h, n 21 1 Sounds b b. Differentiation of sounds b b, n p, b-n Sounds d and d.; d-t. d-t. d, t 23 1 Sounds s, s ss 24 1 Sounds c. Differentiation sounds ts, c-h Sounds g and d. Differentiation of sounds g-k, g-k Sounds z and z. Differentiation of sounds s-s, s-s. Sibilant consonants. cts gg. sz 27 1 Sounds w w Hissing consonants. w, f 28 1 Sounds r, r... p R

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In kindergarten, one of the areas of work is teaching counting skills. Often, educators use LG Peterson's manual "". Training in this technique can begin from the age of 3 to seven. The content of the educational program becomes more complex with age. This tutorial includes practical tips and demo material.

• studying the properties of objects and numbers;
• patterns;
• numbers;
• quantities;
• spatio-temporal representations.

Children in kindergarten

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

For children 4-5 years old

This part of the manual is not aimed at memorizing and memorizing, 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!You should not give the book 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 pupil's parents.

This tutorial explores the following topics:

• "Reiteration";
• "Earlier, later";
• "Comparison by height";
• "Number and digit 4";
• "Square";
• "Cube";
• "Up, down";
• "Comparison in width";
• "Number and digit 5";
• "Oval";
• "Inside Outside";
• "In front, behind, between";
• "Couple";
• "Rectangle";
• "Number series";
• "Rhythm";
• "Number and digit 6";
• "Order account";
• "Comparison by length";
• "Number and digit 7";
• "Numbers and Digits 1-7";
• "Comparison by thickness";
• "Higher lower";
• "Plan";
• "Number and digit 8";
• "Cylinder";
• "Cone";
• "Prism and Pyramid".

Important!After studying all the topics, the second part of the "Play" contains tasks for repeating all the material.

Each section offers several exercises to practice and consolidate:

• comparison;
• finish drawing shapes;
• connect the dots;
• find an extra item and explain why;
• paint over the desired number or suitable shape;
• passing the maze;
• preparation of 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, teachers develop 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 familiarize themselves with simple arithmetic operations and the expansion of existing knowledge. In this manual for the middle group, the following sections are studied in detail:

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

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

Important!Classes should not be too long. You need to arrange physical minutes and a change of activity.

Preschoolers are encouraged to perform the following types of exercises:

• search for similar signs and differences;
• search for similar shapes and paint over them;
• search for unnecessary items;
• work with tables.

For almost every exercise, the child must give a detailed answer. So it happens. Several lessons are devoted to the study of each topic, because the material becomes more complicated. Therefore, the use of Peterson's textbook on mathematics for children 5-6 years old allows you to implement an integrated approach to learning.

For preschoolers 6-7 years old

IN preparatory group most of the lessons are devoted to practicing arithmetic operations. Among the new topics, the following should be highlighted:

• area measurement;
• length measurement;
• mass measurement;
• clock.

Didactic games

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

The advantage of this technique is that it is not a mathematics textbook for kindergarten, a workbook... And you can study with notebooks "One - a step, two - a step ..." at home. The tasks are appropriate for the child's age and gradually become more difficult. It is advisable to conduct lessons in a playful way so that children do not lose interest in learning a new subject for them.

Peterson Early Childhood 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.
• An activity-based approach - the preschooler learns the world not by receiving 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 like a 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 multiple choice questions.
• A creative approach - here it is important not only to encourage the child's creative activity, but also to 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 independently reason and find the answer. At the beginning of classes, the teacher introduces a new topic, talks about its meaning. Further, he creates a difficult situation, as a result of which there is a "discovery" of new knowledge.

To do this, the teacher invites the pupil 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 lesson 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 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.

He then creates various situations for the new skill to be applied. Or arrange a little self-test. When summing up the results, the teacher says 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 these lessons is to consolidate the knowledge gained. But it doesn't take place in the form of standard memorization. The child independently finds difficulties that prevent him from assimilating a new topic and cope with them. During the summing up, the educator should pay attention to what helped him to come out the winner.

Important!The final lessons are conducted with the participation of two teachers. One of them is organizing educational processand the second one records the results. The purpose of such lessons is to systematize the knowledge gained and check how much the child has learned.

The value of the book in preparing for school

The value of the Peterson 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 teacher to make long-term planning so that teaching mathematics is effective.

A lesson in mathematics at a 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 play 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 promotes the development of creative thinking. Although many people miss this component when studying mathematics. The selected tasks will allow teachers to explain even complex tasks to the child in the most accessible way. As a result of classes in this educational method, children learn to independently cope with tasks. And an adult can only give direction in solving a problem.