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 a brief description of the concept, program and organization of practical classes with children. Additional materials for organizing individual work with children are contained in printed notebooks “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 “Player”, part 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 for 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 - a step, two - a step ..." is intended for the development of mathematical representations of children of senior preschool age and preparation for school. It is an integral part of a continuous course of mathematics for preschoolers, primary and secondary schools, which is currently being developed at the School 2000... .
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 - 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 “Player” program and begin their preschool training in mathematics at the age of 5-6.

In 2016, mathematics textbooks for grades 1-4 by Peterson L.G. not included in the official list of books recommended by the Ministry of Education of the Russian Federation.

To understand whether this program is suitable for your child, you can, if you understand its features. Whether these features are positive or negative, each parent will decide for himself.

Fast pace

The pace at which children progress through the program is very fast. Often, literally one lesson is given to one topic, and then the child moves on to a new type of task. There are no step-by-step exercises and examples of problem solving in the textbook.

For example, in the textbook Moro M.I. in the first half of the third grade, students go through numbers up to 1000. During the same time, children who study according to Peterson's book take dozens, millions and billions.

Weak theoretical part and lack of clear structure

There is no theoretical part as such in the textbook. On individual pages there are small tips in the form of tables or figures. It doesn't bother the kids. After all, you don't have to learn the rules. You open the book - and you can immediately start solving examples.

The lack of a theoretical part is a problem for parents. If the child missed a lesson or listened inattentively to the teacher, you need to somehow fill in the gaps in knowledge at home. Since there are no rules in the textbook, it is difficult for parents to figure out exactly what to explain to the child.

I found a way out of the situation: I prepared my own small manual, where I wrote down for each lesson from the textbook what topics we are going through, as well as solution algorithms and rules on these topics.

Teaches non-standard solutions

Peterson invites children to independently come up with algorithms, formulas, and ways to solve problems. For example, break the figures according to some criterion, find a pattern and continue it, figure out how to solve the problem. In this textbook, it is encouraged if the child comes to a solution without the help of a teacher.

The problem is that teachers rarely follow the recommendations of the authors and do not wait until the student comes up with the algorithms himself. This is due to lack of time. When you do not have time to go through the main program with the children (addition and subtraction in a column, for example), there is no way to give schoolchildren time for long reflections. You have to show the worked out scheme of the solution.

The textbook is poorly developed section "Geometry"

In other elementary school textbooks, several chapters are devoted only to geometry. In Peterson's textbook, geometry is given, as it were, in passing, at the end of each chapter in the form of questions. As a result, children are not always able to understand these topics, to distinguish the perimeter from the area. The section "Geometry" remains at the mercy of the teacher.

Lots of abstract concepts

Already from the first or second grades, the concept of “variable” is found in textbooks. At the end of each lesson, the children are offered the exercise "Blitz-survey". These are very short puzzles for composing an expression in which letters are used instead of numbers. Instead of the usual "5 apples" it says "b apples".

Children in elementary school still do not quite understand what to do with numbers, and when letters are added to them, like abstract "b apples", it becomes quite difficult for schoolchildren.

Even parents do not always understand such tasks, let alone children.

But for those who figured out this topic in elementary school, it will be much easier to learn algebra.

Many game tasks for the development of logical thinking

Solve a rebus, go through a maze, paint over a figure or part of it, connect the dots - all these buildings develop logical thinking and are constantly found in the textbook. Children love them very much, they decide with pleasure, even at breaks.

In fact, the Peterson program is suitable for children with different abilities. Now I have a very "average" class, which, despite the fast pace and other difficulties of the program, copes well with the score and tasks. It's all about the approach of the teacher. Whether or not a student learns a program depends on the teacher by 80%.

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 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 of mastering this knowledge next year, although the task will become 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 distinctive feature of the Peterson methodology is 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, causes 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 early development schools for classes. It is quite possible to teach children according to the Peterson method at home.

Toy (L.G. Peterson, E.E. Kochemasova)

The introduction of the state educational standard opens up the possibility of competently and creatively using various educational programs. In our kindergarten, the program "Player" L.G. Peterson E.E. is being implemented. Kochemasova.
Many years of experience shows that for the effective education of children, it is important to form their cognitive interest, desire and habit of thinking, the desire to learn something new. It is important to teach them to communicate with peers and adults, to engage in joint play and socially useful activities, etc. So the main tasks of mathematical development of preschoolers in the program "Player" are:
1) the formation of learning motivation, focused on the satisfaction of cognitive interests, the joy of creativity;
2) increase in the amount of attention and memory;
3) formation of methods of mental actions (analysis, synthesis, comparison, generalization, classification, analogy);
4) development of variative thinking, fantasy, creative abilities;
5) the development of speech, the ability to argue one's statements, to build the simplest conclusions;
6) development of the ability to purposefully control volitional efforts, establish the right relationships with peers and adults, see oneself through the eyes of others;
7) the formation of general educational skills and abilities (the ability to think over and plan one's actions, make a decision in accordance with given rules, check the result of one's actions, etc.).
The solution of these tasks fully corresponds to the achievement of the targets at the stage of completion of preschool education, outlined in the Federal State Educational Standard of DO, namely:

• the child masters the main cultural methods of activity, shows initiative and independence in various types of activity - play, communication, cognitive research activities, design, etc .;
• the child actively interacts with peers and adults, participates in joint games;
• is able to negotiate, take into account the interests and feelings of others, empathize with the failures and rejoice in the successes of others, adequately shows his feelings, including a sense of faith in himself, tries to resolve conflicts;
• the child has a developed imagination, which is realized in various activities, and above all in the game;
• the child owns different forms and types of play, distinguishes between conditional and real situations, knows how to obey different rules and social norms.

In the process of familiarizing children with different areas of mathematical reality: with quantity and counting, measuring and comparing quantities, spatial and temporal orientations. A new building is not given to children ready-made, it is comprehended by them through independent analysis, comparison, and identification of essential features. Thus, mathematics enters the life of children as a "discovery" of regular connections and relations of the world around. Therefore, classes are essentially a system of didactic games, during which children explore problem situations, identify essential features and relationships, compete, and make “discoveries”. During these games, personality-oriented interaction of an adult with a child and children among themselves, their communication in pairs, in groups, is carried out. Children do not notice that training is in progress - they move around the room, work with toys, pictures, balls, LEGO cubes ... The whole system of organizing classes is perceived by the child as a natural continuation of his play activity.
The saturation of the educational material with game tasks determined the name of the manual - "Player".
The level of specially organized situations that children live through is gradually changing: they move from actions with specific objects to actions with graphic models of the objects under study, gain experience in sign fixation and expression in speech of observed properties and patterns, and the degree of independence of children increases. Therefore, the parts of the course are also called differently: for younger preschoolers (parts 1 and 2) they are called "Player", and for older preschoolers (parts 3 and 4) - "Player - a step to school".

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 a link in the continuous course of mathematics for preschoolers, elementary 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.

Explanatory note.
The program for the mathematical development of preschoolers "Steps" is the initial link in the continuous course of mathematics for preschoolers, primary and secondary school students of the educational program "School 2000 ...". The main goal of the "School 2000..." program is the comprehensive development of the child, the formation of his abilities for self-change and self-development, a picture of the world and moral qualities that create conditions for successful entry into the culture and creative life of society, self-determination and self-realization of the individual. This goal is realized in accordance with the stages of cognition and age characteristics of the development of children in the system of continuous education.

Goals and objectives of preschool education of children.
At the stage of preschool preparation, the educational process is organized on the basis of the main characteristics of the first pre-conceptual stage of cognition (the stage of objective actions) and the age periodization of the psychological development of children by D.B. Elkonin. In the preschool period, the child's primary awareness of the external influences of the surrounding world occurs, therefore, its development is associated with the formation of cognitive processes and abilities for basic mental operations based on objective actions during game types of communication. It means. that in addition to the development of attention, memory, and speech traditional for preschool training, mental operations should be formed in children:
analysis of the properties of the objects or phenomena under study;
comparison of the properties of objects;
generalization, that is, the identification of common properties of objects in a group;
distribution of objects into groups according to the selected property;
classification according to the selected property;
synthesis based on the selected structure;
specification;
analogy.

Content
Foreword
I. Explanatory note
1. Goals and objectives of preschool preparation of children in the program "Steps"
2.Organization of the cognitive process
3.Organization of the educational process
4. Managing the preservation and support of children's health
II.Programs
1. The program of the course "Toy" for children 3-4 years old and 4-5 years old
2. The program of the course "One - a step, two - a step ..." for children 5-6 years old and 6-7 years old
III. Methodological support
IV. Approximate planning of educational material
1. Thematic planning for the course "Toy" for children 3-4 years old and 4-5 years old
2. Thematic planning for the course "One - a step, two - a step ..." for children 5-6 years old and 6-7 years old (64 lessons)
3. Thematic planning for the course "One - a step, two - a step ..." for children 5-6 years old and 6-7 years old (86 lessons).

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• Playing step to school, Practical course of mathematics for preschoolers, Guidelines, Part 3, Peterson L.G., Kochemasova E.E., 2011