Mathematics
PREFACE
Changes in the content of schooling have significantly increased the requirements for the level of mathematical understanding of kindergarten graduates.
The need to establish continuity in the work of kindergarten and school is reflected in the title of the book - “Mathematics in Kindergarten”.
The concepts of natural numbers, geometric figures, quantities, etc., which children have to learn in school, are abstract, but they reflect the connections and relationships inherent in objects in the outside world.
The primary source of knowledge is sensory perception derived from experience and observation. In the process of sensory cognition, ideas are formed - images of objects - their properties and relationships.
Understanding the logical definitions of concepts is directly dependent on how children go through the first sensory stage of cognition.
The richer their ideas about the quantitative and spatial properties and relationships of real objects, the easier it will be for them in the future to move from these ideas to mathematical concepts through generalization and abstraction.
Successful mastery of mathematical concepts is directly dependent on the development of perception, i.e., sensory development of children. The very ability to generalize and abstraction develops on the basis of the practice of identifying the properties of real objects, comparing and grouping them according to the selected properties. Therefore, special work on the formation of mathematical concepts is carried out throughout preschool childhood in close connection with all educational work in kindergarten.
Children receive elementary ideas about set and number, about the relationships of quantities, about the simplest geometric figures, about the main spatial directions and relationships between objects, about the duration of certain time periods (days, weeks, months). They master ways of identifying quantitative and spatial relationships: practical comparison of numbers of sets (overlapping, applying, pairing, using labels, etc.), comparing the sizes of objects, counting and measuring quantities.
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Learning to measure quantities allows you to deepen the concept of number. When learning to count, preschoolers often develop an incompletely correct approach to estimating quantities. The unit is perceived by them as a separate object, separateness, outside of its quantitative content.
In the process of measurement, the unit of measurement (measurement) seems to split the measured quantity (length, volume) into parts, each of which is equal to it. The number obtained as a result of measurement clearly acts as an indicator of the relationship between the whole and its part. Measurement emphasizes the relativity of a number, its dependence on the size of the chosen measure: the larger the measure, the smaller the number obtained as a result of the measurement. Teaching children not only to count, but also to measure, develops in them a correct approach to estimating quantities and allows them to further reveal the meaning of generally accepted measures of measurement, which they will become familiar with at school.
Preschoolers learn a small number of mathematical terms: the names of geometric shapes (circle, square, etc.), elements of shapes (angle, side), and computational operations (add, subtract, turn out, equal). The teacher begins to use words such as quantity, number, figure when working with children of the middle group, but does not strive to ensure that the children use them. They learn the meaning of these words gradually, as they accumulate relevant experience. It is unacceptable to replace “difficult” words with “easier” but inaccurate ones. This leads to the formation of misconceptions. The teacher does not use words such as set, aggregate, element, geometric, model, diagonal when working with children. Children learn to reflect mathematical connections, relationships, and actions in clear, concise formulations. They develop an interest in mathematical knowledge and the ability to demonstrate strong-willed efforts to solve problems of a mathematical nature. Much attention is paid to the development of initial skills of inductive and deductive thinking, mental operations: analysis, synthesis, comparison, the ability to abstract and generalize, ingenuity and ingenuity, spatial concepts and imagination.
Children are given mathematical knowledge in a certain system and sequence, while the dose of new things should be small and manageable for assimilation. Therefore, each task is divided into smaller parts, which are studied sequentially.
New material from any of the sections of the program (“Quantity and Counting”, “Value”, “Form”, etc.) is sequentially studied in 2-5 lessons, first in the first part, and later in the second. In the future, they return to repetition after 2-3 weeks. The period of returning to the past is increasingly increasing. However, each studied program task should be in the field of view of the teacher until the end of the school year.
The teacher must know how the program for each age group is structured. This will make it possible not only to determine the level of mathematical development of children in their group, but also to present the role and place of each lesson in the system of all work on the development of elementary mathematical concepts in preschoolers.
The main form of work on the formation of mathematical concepts is classes. During the classes they solve most of the software problems. Children form ideas in a certain sequence and develop the necessary skills and abilities.
Great importance is attached to the organization of observations of the quantitative side of the environment, the use by children of knowledge and skills of mathematical content in various types of children's activities.
Didactic games and gaming exercises are widely used in classes and in everyday life. By organizing games outside of class, they consolidate, deepen and expand children’s mathematical understanding. In some cases, games carry the main educational load, for example, in developing spatial orientation.
Children who have missed more than one lesson are dealt with individually to prevent them from falling behind the rest of the children.
Particular attention is paid to individual lessons with those children who, due to their developmental characteristics, cannot learn new knowledge in class on an equal basis with everyone else. They are worked with somewhat ahead of schedule in order to prepare them for work in the classroom.
The active activity of children in the classroom is ensured, first of all, by the correct combination of work on new and repeated material, alternating types of work and forms of its organization, i.e., the structure of the lesson.
The structure of the lesson is determined by the volume, content, combination of program tasks, the level of acquisition of relevant knowledge and skills, and the age characteristics of the children.
Studying new material includes three types of work: firstly, the teacher shows and explains new tasks, demonstrates a sample, identifying the properties and connections of mathematical objects. Children observe the actions of the teacher, listen to his instructions, explanations, and answer questions;
secondly, some children perform individual tasks under the direct supervision of the teacher, others observe the actions of a friend, listen to him, make corrections, supplement, answer questions;
thirdly, children independently work with handouts, mastering new skills.
In the first lesson, all three types of work can be used, then learning a new one takes up most of the time. On
In another lesson, learning something new takes half the time limit, the second is devoted to repeating what has been learned. Children’s independent work with handouts is planned for the next lesson and half of the time is allocated to this.
In the junior and middle groups, they are limited to working on topics I-2, so classes consist of 2-3 parts. In senior and preparatory groups, classes consist of 3-4 parts, since work is carried out on 2-3 topics.
The content of the classes determines the organization of their implementation. It is important that when explaining new material, all children see the actions of the teacher or child. Later, to consolidate knowledge and skills, tasks are given to all children at the same time. They work at the table either facing the teacher, or sideways, but in no case with their backs, since when checking the completion of a task, the teacher constantly draws the children’s attention to the model, to various kinds of visual aids.
No more than 4 children are seated at six-seat tables; if necessary, an additional 1-2 tables are placed. If it is necessary to check how children have acquired knowledge and skills, work with preschoolers is organized at the teacher’s desk. When exercises related to movement (outdoor games, etc.) are given during a lesson or at the end of it, the place for them is prepared in advance.
The methodology for working with children of each age group is presented in separate chapters. The description of methods and techniques for working in sections of the program is preceded by general recommendations for teaching children of this age in mathematics classes.
Lesson notes are included with each chapter. They should only be considered as possible options. In no case should this exclude the creativity of educators, since it is obvious that there are no universal techniques that would be suitable for working with children of any group. Stencils should not be allowed in the work or formal use of the material.
To help the teacher act depending on specific conditions, various techniques are given that allow one to successfully solve the same program tasks. When preparing for a lesson, the teacher carefully considers its content, taking into account the knowledge and skills of his pupils, decides how to more effectively use certain methods and techniques, and visual material. It provides children with the opportunity to take initiative in acquiring and applying knowledge, stimulates their ingenuity and intelligence, and encourages them to use mental actions.
The search and application of teaching methods that ensure not only the formation of mathematical concepts in children, but also the development of mental functions (perception, memory, thinking, imagination) is the key to successfully preparing children for learning mathematics at school.
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September.
No. 1. Topic: Introducing the concepts of “one” and “many”. Etc. tasks. To form ideas about the concepts of “many” and “one”. Work on the ability to coordinate the numeral “one” with nouns in gender and case. Develop the ability to compare objects by color, identify patterns in color changes. (Peterson “Player”, p. 16)
No. 2. Topic: Comparison of collections of objects by quantity. As many. Etc. tasks. Form ideas about the equality of groups of objects based on pairing (by overlapping, drawing lines, etc.). To consolidate ideas about the concepts of “one” and “many”. To train children in the ability to identify patterns in the arrangement of objects. (Peterson “Player”, p. 17)
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No. 3. Topic: Same amount, more, less. Etc. tasks. Compare groups of objects by quantity using pairs (same, more, less). Form ideas about the conservation of quantity. (Peterson “Playing Game”, p. 19)
No. 4. Topic: Same amount, more, less. Etc. tasks. Reinforce the concepts of “one” - “many”, the ability to compare groups of objects by quantity based on pairing. Form ideas about the conservation of quantity. Development of logical thinking. (Peterson “Player”, p. 20)
OCTOBER
No. 1. Topic: Same amount, more, less. Etc. tasks. To consolidate ideas about the conservation of quantity, about comparing groups of objects based on pairing, about the concepts of “one” and “many”. Learn to see the components of a group of objects, each of which has a specific color. Help children find patterns. (Peterson “Player”, p. 22)
No. 2. Topic: Properties of objects. Count to two. Etc. tasks. Develop the ability to count to two based on comparison of two groups of objects containing 1 and 2 elements. Establish two ways to equalize groups of items by quantity. Learn to identify common properties of groups of objects. (Peterson “Playing Game”, p. 23)
No. 3. Topic: Counting to two. Numbers 1 and 2. Ex. tasks. Introduce the numbers 1 and 2 as symbols denoting one and two objects, respectively. Develop the ability to correlate numbers 1 and 2 with quantity; spatial representations: closer, further. (Peterson “Playing Game”, p. 24)
No. 4. Theme: longer, shorter. Etc. tasks. Form spatial representations: longer, shorter. Strengthen counting to two, the ability to correlate numbers 1 and 2 with quantity. Start working on the formation of spatial representations: right, left. (Peterson “Playing Game”, p. 28)
NOVEMBER
No. 1. Topic: Circle. Etc. tasks. Form an idea of a circle on an objective basis, the ability to recognize a circle in objects in the environment. Strengthen counting to two, the ability to correlate numbers 1 and 2 with quantity. Develop the ability to identify a pattern in the arrangement of figures and continue it. (Peterson “Player”, p. 29)
No. 2. Topic: Ball. Etc. tasks. To form, on an objective basis, ideas about the ball, the ability to recognize the ball in objects in the environment. Strengthen counting to two, the ability to correlate numbers 1 and 2 with quantity. Work on the formation of spatial representations: right, left. (Peterson “Playing Game”, p. 31).
No. 3. Topic: Wider, narrower. Etc. tasks. Form spatial concepts: wider, narrower. Strengthen counting to two, the ability to correlate numbers with quantities. Develop the ability to find signs of similarity and difference between objects, identify a pattern in the arrangement of figures and continue it. (Peterson “Player”, p. 32)
No. 4. Topic: Counting to three. Number 3. Ex. tasks. Introduce the formation of the number 3 based on a comparison of two groups of objects containing 2 and 3 elements; count to three. To consolidate the ability to compare groups of objects based on pairing, to equalize their quantities in two ways. Form ideas about the triangle on a subject basis; the ability to identify signs of similarities and differences between figures, and to find an extra figure. (Peterson “Player”, p. 35)
DECEMBER
No. 1. Topic: Number 3. Ex. tasks. Introduce the number 3 as a symbol denoting three objects. Develop the ability to correlate numbers 1-3 with quantity. Expand your understanding of geometric shapes. Develop the ability to identify a pattern in the arrangement of figures and continue it. (Peterson “playing game”, p. 37).
No. 2. Topic: On, over, under. Etc. tasks. Form spatial relationships: on, above, under. Strengthen counting to 3, the ability to correlate numbers 1-3 with quantity, compare by quantity based on pairing, equalize groups of objects by quantity in two ways. Develop the ability to count the required number of objects from a group. Strengthen the ability to compare objects by length. (Peterson “Playing Game”, p. 39).
No. 3. Topic: Above, below. Etc. tasks. Form spatial representations: above, below. Fix the score within 3, the ability to correlate numbers 1-3 with the quantity. Strengthen spatial concepts: closer, further. Develop the ability to group objects according to common characteristics. (Peterson “Player”, p. 41)
No. 4. Topic: Earlier, later. Etc. tasks. Form temporary ideas: earlier, later. Strengthen the ability to count objects, designate the quantity with the corresponding number. Develop the ability to identify signs of similarities and differences between objects or figures. (Peterson “Playing Game”, p. 43)
JANUARY
No. 1. Topic: Counting to 4. Number 4. Number 4. Ex. tasks. Introduce the formation of the number 4 based on a comparison of 2 groups of objects; count to 4. Introduce the number 4 as a symbol denoting 4 objects, learn to correlate numbers 1-4 with quantity. Strengthen the ability to compare groups of objects by quantity based on pairing, equalize the number of objects in two ways. To develop the ability to identify objects from a group based on their characteristic properties. (Peterson “Playing Game”, p. 44)
No. 2. Topic: Square. Etc. tasks. Introduce the square on a subject basis, consolidate knowledge about geometric shapes. Maintain counting within 4, ability to correlate numbers with quantity; to develop the ability to find signs of similarity and difference and, on their basis, combine objects with similar characteristics and isolate from a group objects that differ in some way. (Peterson “Player”, p. 47)
No. 3. Topic: Cube. Etc. tasks. Form an idea of a cube on an objective basis, the ability to recognize a cube in objects in the environment. Form spatial representations: left, right, middle. Fix the count within 4, the ability to correlate numbers with quantities. Strengthen temporary ideas: later, earlier. (Peterson “Player”, p. 49)
No. 4. Subject: Above. At the bottom. Etc. tasks. Create space representations: above, below; the ability to find signs of similarities and differences between objects and combine them into groups based on these signs. Reinforce ideas about geometric shapes on a subject basis, count within 4, compare groups based on making pairs. (Peterson “Player”, p. 51)
FEBRUARY
No. 1. Subject: Left, right, middle. Etc. tasks. Form spatial representations: left, right, middle. Fix counting within 4, the ability to correlate numbers 1-4 with quantity, spatial and temporal relationships; the ability to find signs of similarities and differences and express them in speech. (Peterson “Player”, p. 52)
No. 2. Topic: Counting to 5. Number 5. Number 5. Ex. tasks. Introduce the formation of the number 5 based on a comparison of two sets containing 4 and 5 elements; count to 5. Introduce the number 5 as a symbol representing 5 objects. Strengthen the ability to compare groups of objects based on pairing, equalize their quantities in two ways. (Peterson “Player”, p. 54)
No. 3. Topic: Inside, outside. Etc. tasks. Form spatial representations: inside, outside. Fix the score within 5, the ability to correlate numbers 1-5 with the quantity. Develop the ability to organize shapes by size. (Peterson “Playing Game”, p. 57)
No. 4. Topic: In front, behind, between. Etc. tasks. Form spatial representations: in front, behind, between. Strengthen counting within 5, the ability to correlate numbers 1-5 with quantity, ideas about geometric shapes and space-time relationships. Develop the ability to identify the properties of shapes (color, size, shape) and compare shapes based on these properties. (Peterson “Player”, p. 58)
MARCH
No. 1. Topic: Couple. Etc. tasks. Form ideas about paired objects. Strengthen the ability to compare objects by length, width, height. Fix the score within 5, the ability to correlate numbers with quantities. To develop the ability to identify, based on comparison, signs of similarity and difference between objects, and to express them in speech. (Peterson “Player”, p.60)
No. 2. Topic: Oval. Etc. tasks. To form an idea of an oval on an objective basis, the ability to find oval-shaped objects in the environment. Fix the score within 5, the ability to correlate numbers with quantities. Strengthen ideas about triangle, square, circle. (Peterson “Playing Game”, p. 62)
No. 3. Topic: Rectangle. Etc. tasks. Form an object-based idea of a rectangle, the ability to find rectangular-shaped objects in the environment. Fix the score within 5, the ability to correlate numbers with quantities. To develop the ability to identify the properties of objects, to find signs of similarity and difference, and on their basis to select from the totality objects that differ in some way. Strengthen the skills of comparing objects by length and width, ideas about geometric shapes. (Peterson “Player”, p. 64)
APRIL
No. 1. Topic: Number series. Etc. tasks. Based on objective actions, form ideas about order and number series. To develop the ability to navigate in space “from oneself”, to identify and continue a given pattern. Strengthen the ability to correlate numbers 1-5 with quantity. (Peterson “Player”, p. 67)
No. 2. Topic: Ordinal counting. Etc. tasks. Form ideas about ordinal counting. Strengthen ideas about preserving quantity, the ability to correlate numbers 1-5 with quantity. To develop the ability to compare figures, identify signs of similarity and difference, and express them in speech. (Peterson “Playing Game”, p. 69)
No. 3. Topic: Travel game. Etc. tasks. Strengthen children's understanding of numbers and numbers 1-5, the ability to recognize geometric shapes, space-time relationships. (Peterson “Player”, p. 70)
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Mood now - mathematics, preschooler
Series of messages “Children 2-3 years old.
Lesson notes": Part 1 - Comprehensive lesson on speech development and modeling in the first junior group on the topic: "Kolobok" Part 2 - Long-term planning of art classes in the junior group Part 3 - Summary of a drawing lesson in the 1st junior group "Beautiful flowers for bees" Part 4 - Summary of a drawing lesson in the 1st junior group "Snail" Part 5 - Long-term planning in mathematics in the 2nd junior group. gr. Part 6 - Planning according to the Rainbow program for children of the 2nd junior group Part 7 - Modeling classes in the first junior group ... Part 12 - Exercises, educational games for a child of the third year of life Part 13 - How your child develops. Home tests Part 14 - Sleepy positions. Night indicator
