Modern technologies for mathematical development of preschool children

Modern technologies for mathematical development of preschool childrenpresentation

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In recent years, the term “technology” has been increasingly used in the theory and practice of preschool education. In relation to the methods of mathematical development of preschoolers, they talk about technologies of teaching, mathematical development, technologies for the development of quantitative concepts in preschoolers, technologies for logical-mathematical development and training of preschoolers.

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A characteristic feature of the technology is its clear structuring and algorithmization, which is understood as the identification of sequential procedures and operations, united by the internal logic of the functioning and development of a given process.

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Modern technologies for the mathematical development of preschoolers are aimed at: activating the child’s cognitive activity, the child’s mastery of the connections and dependencies of objects and phenomena in the surrounding world.

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PROBLEM - GAME TECHNOLOGY. One of the most effective technologies, close to the child in its essence. It is based on the child’s active, conscious search for a way to achieve a result based on his acceptance of the goal of the activity and independent reflection on upcoming practical actions leading to the result. The goal is to develop children’s cognitive and creative abilities in logical and mathematical activities.

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PROBLEM-BASED GAME TECHNOLOGY allows the child to: master the means (sensory standards, speech, diagrams and models) and methods of cognition (comparison, examination, classification, seriation), accumulate logical and mathematical experience.

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PROBLEM - GAME TECHNOLOGY At work. Mikhailova Z. A. is presented in the system of the following means: logical and mathematical games; logical and mathematical story games (activities); problematic situations and questions; creative tasks, questions and situations; experimentation and research activities.

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2. Plot-based logical-mathematical game. Nosova E.A. A set of such games and exercises has been developed (“Help the ants”, “Find the treasure”, “Have settled in the houses”, “Who is visiting Winnie the Pooh and Piglet”), which are presented in the book “Logic and Mathematics in Kindergarten”. The author divided all the games into groups: games to identify and abstract the properties of objects; games for children to master comparison, classification and generalization; games for mastering logical actions and mental operations.

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This technology can be represented by successive steps: from mastering the game in joint activities of an adult and a child to participation in games at the amateur level; transition to participation in games at a higher level; newly emerging games of an adult with children or children successfully playing them (distinguished by a changed plot, a transformed course of the game)

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3. Creative tasks, questions and situations. help the child: establish various connections, identify cause by effect, and most importantly, the child begins to experience pleasure from mental work, from the thinking process, from awareness of his own capabilities.

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4. A problem situation is considered as: a means of mastering search actions, the ability to formulate one’s own thoughts about search methods and the expected result. (entertaining tasks, joke tasks that make children think and establish connections between objects by shape, ratio of parts, their location in space, quantitative value).

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5. Experimentation and research activities. The main way to develop a child’s investigative behavior is through his own research practice. Carried out in children's experimentation, during which children master: actions of measuring, combining, transforming various materials and substances; conservation principle; get acquainted with instruments (thermometer, scales, mirror, magnet, etc.); learn to use educational books as a source of information. (when comparing the weight of dry and wet sand, children notice that wet sand is heavier. After additional questions from the teacher, the children formulate the conclusion: “There is water in wet sand, so it is heavier”).

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Experimentation and research activities. results of research activities: new information about the object under study, its properties, qualities, structure, connections with other objects (about geometric shapes, quantities, different methods of measurement, number dependencies); new information about another (additional) object under study (about simple instruments for measuring lengths; about the reflection of objects in water, a mirror; the action of a magnet); knowledge about research methods and its results (about simple experiments, experiments, making assumptions, the need for variation when choosing methods for organizing research, evaluating the result and forecasting further research).

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TRIZ TECHNOLOGY It is based not just on teaching children mathematics, but on discovering ways to obtain the correct result. Problem situations are part of TRIZ technology. The authors propose to identify problematic situations from cartoons, feature films, educational Internet, fairy tales, short stories, and plot games that are well known to the child (the contradiction in K. Chukovsky’s work “Fedorino’s Grief”: leave the dishes for Fedora so that she can cook and eat food or deprive her of the dishes for bad treatment?). According to TRIZ theory, you need to “turn harm into benefit.”

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TRIZ TECHNOLOGY For the mathematical development of children, it is recommended to use the following types of TRIZ exercises: “Search for common features” - find as many common features as possible in two different objects; “The third odd one” - take three objects that are different along the semantic axis, find in two of them similar features that are not in the third; “Search for opposite objects” - name the object and as many objects opposite it as possible.

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TRIZ TECHNOLOGY Along with TRIZ exercises, technology offers special games compiled by the teacher based on plots known to children, such as: “Good-bad” (a triangle is chosen as the object, it is necessary to name all the good things that are connected in people’s lives with the triangle: it looks like a roof at home, stable, looks like a scarf; and everything is bad: sharp, doesn’t roll, falls over). “Choose three” (it is proposed to name three words related to mathematics and tell what they are for and how they can interact; - “circle”, “four”, “small” - in the game you can use four circles as plates for dolls) . “Yes and no” (the teacher thinks of a word, and the children solve it by asking questions so that the teacher can only answer “yes” or “no.”).

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HEURISTIC TECHNOLOGY The essence of heuristic technology (G.A. Repin) is to immerse the child in the situation of a discoverer. The child is invited to discover knowledge unknown to him. The purpose of the technology is to help the child open channels of communication with the world of mathematics and understand its features.

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HEURISTIC TECHNOLOGY The authors of heuristic technology recommend using cognitive and creative (creative) methods. Cognitive methods include: the method of assimilation, the method of heuristic questions, the method of errors, etc. - Methods of assimilation - “feeling”, “instilling” of the child into the state of the object being studied, “humanizing” the object through sensory-figurative and mental representations and knowing it from the inside. (imagine that you are the number 5 (conventional measure, triangle, cylinder). What are you? Why do you exist? Who are your friends? What are you made of? What do you like to do?) - Heuristic questions - allow the child to obtain information about the object being studied (Who? What? Why? Where? With what? How? When?), which provide an opportunity for an unusual vision of the object. — The error method is the use of errors to deepen the educational process. The method helps to overcome the teacher’s negative attitude towards children’s mistakes and the children’s fear of making a mistake. (For example, when a child incorrectly claims that 4 is less than 3, ask the question: can it really be that 4 is less than 3. Yes, it can if we are talking about 4 days and 3 weeks.)

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HEURISTIC TECHNOLOGY Creative methods include methods of inventing, hyperbolizing, brainstorming, and the synectics method. — The method of inventing is to create a previously unknown product as a result of using mental modeling techniques: replacing one quality with another, finding the properties of an object in another environment. For example, draw a city with inhabitants - fabulous numbers. — The hyperbolization method involves increasing or decreasing the object being studied and its individual parts or qualities in order to identify its essence. For example, think of a polygon with the most angles. — Agglutination is a combination of qualities, parts of objects that are incompatible in real life. For example, the top of an abyss, an empty set.

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HEURISTIC TECHNOLOGY The brainstorming method is very popular at the present stage. The situation of introducing brainstorming can arise spontaneously when solving any cognitive problem, during a game-activity. The teacher can invite the children to put forward any solutions to the problem, successful or unsuccessful. Ideas can be written down. (For example, how to rescue a bead from “ice captivity” (a bead in an ice cube)? Ideas: cut through the ice! Hold it in your hands and the ice cube will melt.) The teacher accepts any ideas without emotional and rational evaluation. Children come to conclusions themselves based on analysis, after all the ideas have been expressed.

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INFORMATION TECHNOLOGY Today, information technologies affect all spheres of life, serve the general and personal interests of a person, and are aimed at revealing his potential. The computer provides new gaming and learning opportunities for preschool children.

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INFORMATION TECHNOLOGIES Currently, at the Research Institute of Preschool Education, in the Russian Federation, the theoretical foundations for the use of scientific information technologies in the educational system of preschool educational institutions are being developed. Several series of programs for preschoolers have already been created, which, depending on the pedagogical focus, are divided into groups: - Educational (of a subject nature) - mathematics, native language, music..., the content and course of the games presented in them are clearly outlined. — Developmental — they encourage children to engage in creative independent play and communication with peers (children themselves look for ways to solve game problems, are free to choose plots and means for conveying them. — Diagnostic — they allow you to identify the level of certain skills, abilities, interests of the child. In a certain In a sense, any computer program can be considered developmental if it helps improve perception, memory, imagination, and thinking.

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TECHNOLOGY OF THE ACTIVITY METHOD “SITUATION” (Lyudmila Georgievna Peterson) The activity approach is such an organization of the educational process in which the child masters culture not by simply transmitting information, but in the PROCESS OF HIS OWN ACTIVITY.

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Technology “SITUATION” Includes 6 successive stages: Introduction to the situation; Updating knowledge and skills; Difficulty in the situation; “Discovery” of new knowledge; Inclusion of new knowledge (method of action) into the system of knowledge and skills; Understanding.

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1. Introduction to the situation Problems solved in the joint activities of adults and children: Creating conditions for children to develop an internal need to be included in activities, formulating by children the so-called “children’s” goal.

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2. Updating knowledge and skills Problems solved in joint activities of adults and children: Organization of cognitive activity in which mental operations are purposefully updated, as well as the knowledge and experience of children necessary for them to “discover” new knowledge.

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3. Difficulty in a situation Tasks solved in the joint activity of an adult and children: Facing a difficulty, analyzing the situation that has arisen: fixing the difficulty, identifying its cause (lack of knowledge, familiar methods of action). “COULD YOU? WHY CAN’T YOU?”

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4. “Discovery” of new knowledge Problems solved in joint activities of adults and children: Choosing a way to overcome difficulties, putting forward and justifying hypotheses. Determining the order of actions. Implementation of the plan is the search and “discovery of new knowledge (methods of action) through the use of various forms of organization of children’s activities, ensuring, on the one hand, overcoming difficulties (achieving a “children’s” goal, and on the other hand, solving program tasks of teaching education, development (“adult” "goal). Fixation of new knowledge (mode of action) in speech and, possibly, symbolically. “What should you do if you don’t know something, but really want to know?”, “How can we find out?)

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5. Inclusion of new knowledge (method of action) into the system of knowledge and skills Problems solved in joint activities of adults and children: Using new knowledge (method of action) together with previously mastered methods, with speaking out loud the algorithm, method. Self-test using a sample and (or) mutual test (if planned). Using new knowledge (methods of action) in joint activities: work in pairs, micro-groups (if planned). What will you do now? ? How will you complete the task? Where do you start? How will you know that you have completed the task correctly?

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6. Comprehension of the tasks solved in the joint activities of adults and children: Children’s recording of the achievement of a “children’s” goal. Talking through the teacher (in the junior and middle groups) or children (in the senior or preparatory group for school) of the conditions that made it possible to achieve this goal. Emphasis on successful experience in overcoming difficulties through identifying and eliminating their causes. “Where were you?”, “What were you doing?”, “Who did you help?” — the teacher helps children comprehend their activities and record the achievement of the “children’s” goal. And then, with the help of questions: “How did you succeed?”, “What did you do to achieve the goal?”, “What knowledge (skills, personal qualities) were useful to you?” - leads children to the fact that they achieved a “children’s” goal due to the fact that they learned something, learned something, showed themselves in a certain way, that is, brings together the “children’s” and “adult” goals (“Succeeded ..., because they found out (learned)...").

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THANK YOU FOR YOUR ATTENTION

Gaming technologies as a means of developing the mathematical abilities of preschool children.

Gaming technologies as a means of developing mathematical abilities of preschool children

Gaming technologies as a means of developing the mathematical abilities of preschool children.

“The ability to think mathematically is one of the noblest abilities of man” (Bernard Shaw)

Disturbing trends have emerged over the past decade. In the educational work of kindergartens, school forms and teaching methods began to be used, which do not correspond to the age characteristics of children, their perception, thinking, and memory. The formalism in teaching that arises on this basis, the overestimation of demands on children, the inhibition of the pace of development of some and the inattention to the difficulties of others are rightly criticized. Children are involved in types of cognitive activities for which they are not functionally ready. Feeling the great potential of a preschooler, adults often begin to force children to study mathematics. It would seem that the child only needs to remember ready-made knowledge and use it at the right time and in the right place. However, this does not happen, and such knowledge is perceived by children formally. At the same time, according to N.N. Poddyakov, the law of development of thinking is violated and the essence of what is being studied is distorted.

Preschool children have an inexhaustible interest in the new and unknown. Children are not afraid of the difficult and incomprehensible; they try to learn everything and achieve everything. Sometimes they lack the attention of adults, their support, timely help or advice in difficult, from a child’s point of view, situations. Therefore, the child loses interest in the subject. This is due to the fact that each preschooler has his own intellectual and psychophysical potential for acquiring knowledge. And to make it interesting for everyone, it is necessary to use a differentiated approach to children [4, p.10]

The acquisition of mathematical concepts by preschoolers is essential for mental development. Whoever studies mathematics from childhood develops attention, trains his brain, his will, cultivates perseverance and perseverance in achieving the goal (A. Markushevich)

To develop children’s mathematical abilities it is necessary:

identify the level of mathematical development of preschool children;
use a variety of games to develop mathematical abilities;
create conditions for combining the efforts of families and kindergarten teachers, promoting the successful development of mathematical abilities.

The subject of mathematics is so serious that no opportunity should be missed to make it more entertaining (B. Pascal)

What is the development of mathematical concepts in the historical aspect?

Completely new, at first glance, ideas, concepts, original ideas have their own history. This story is reflected in various literary sources.

Historical and mathematical information is of significant interest in this regard. They allow us to trace the dependence of the development of mathematics on the needs of human society, its relationship with related sciences and technology. In works on the history of mathematics, psychology, pedagogy, methods of teaching mathematics, a historical-genetic approach to the development of certain ideas and concepts in preschool children has been developed (L.S. Vygotsky, G.S. Kostyuk, A.M. Leushina, Zh. Piaget, A.A. Stolyar, etc.).

Behind the particular problem of teaching children the basics of mathematics is the global philosophical problem of a community of people who have common “origins” in everything, including the development of mathematical knowledge. In this sense, mathematics can be figuratively called the “international” language of communication, since even at the elementary level of communication, the most accessible signs and symbols for communication are “finger counting,” showing numbers, time on a clock, orientation to various geometric shapes, etc. These standards turn out to be understandable at the non-verbal level of communication.

The modern method of forming elementary mathematical concepts in preschool children uses the genetic principle. It is based on the study of the development of mathematics, starting from ancient times (T.I. Erofeeva, A.M. Leushina, Z.A. Mikhailova, V.P. Novikova, L.N. Pavlova...).

After all, the ability to think mathematically is one of the noblest human abilities (B. Shaw)

One of the main goals of preschool education is the intellectual development of the child. It not only comes down to teaching a preschooler to count, measure and solve arithmetic problems, but to develop the ability to see, discover properties, relationships, dependencies in the world around him, and the ability to “construct” them with objects, signs and words. Many scientists emphasize the role of preschool age in human intellectual development (about 60% of the ability to process information is formed by the age of 5-11). Mathematics develops flexibility of thinking and teaches logic. All these qualities will be useful for children when studying at school. Mathematics is the science of the young. It cannot be otherwise. Mathematics is mental gymnastics, which requires all the flexibility and endurance of a person (N. Viper).

A special role in the development of elementary mathematical concepts belongs to gaming technologies. Thanks to games, it is possible to concentrate the attention and attract the interest of even the most active preschool children. At the beginning, they are captivated only by game actions, and then by what this or that game teaches. Gradually, children develop an interest in mathematics. As M.V.Lomonosov wrote: “Then you need to learn mathematics so that it puts your mind in order.” A system of exciting mathematical games and exercises will help us teachers prepare children for school and allow them to master the preschool education program:

formation of a stock of knowledge, skills and abilities that will become the basis for further training;
mastering mental operations (analysis and synthesis, comparison, generalization, classification);
development of variable and imaginative thinking, creative abilities of children;
developing the ability to understand a learning task and complete it independently;
developing the ability to plan educational activities and carry out self-control and self-assessment;
developing the ability to self-regulate behavior and demonstrate volitional efforts to complete assigned tasks;
development of fine motor skills and hand-eye coordination.

The FEMP program is aimed at developing logical and mathematical concepts and skills in a playful way. Children are introduced to new materials on the basis of an active approach, comprehended through independent analysis, comparison, and identification of essential features. In this regard, I assign a special role to non-standard didactic means. For preschool children, play is of exceptional importance: play for them is study, play for them is work, play for them is a serious form of education [6, p. 78].

V.A. Sukhomlinsky wrote: “In play, the world is revealed to children, the creative abilities of the individual are revealed. Without play there is not and cannot be full-fledged mental development. Play is the spark that ignites the flame of inquisitiveness and curiosity.”

A game is valuable only if it contributes to a better understanding of the mathematical essence of the issue, clarification and formation of a preschooler’s mathematical knowledge. [8, p.13]

All didactic games for the formation of elementary mathematical concepts are divided into several groups:

number and number games;
time travel games;
games for spatial orientation;
games with geometric shapes;
games for logical thinking.

Modern logic and mathematical games are varied. In them, the child masters standards, models, speech, masters methods of cognition, and develops thinking.

These include:

GCD for FEMP (“Extraordinary Adventures in the City of Mathematical Riddles”, “Visiting the Dwarf Watchmaker”, “Petrushka’s Toys”, “Space Travel”);
mathematical tournaments (“Clever Men and Clever Girls”, “What, Where, When?”);
quizzes, competitions (“Journey to Wonderland”, “Visiting the Mathematics Fairy”, “Tasks for Dunno”).
Riddles of mathematical content: “Who has one leg, and even that one without a shoe?”; “One hundred and one brothers, all in one row, belted with one sash”; “An annual bush drops a leaf every day, A year will pass - the whole leaf will fall off” [2, p.15].
Printed board games: “Color and Shape”, “Mathematical Lotto”, “Our Game Library”, “Magic Mosaic”, “Puzzles”.
Schematic and modeling games: “Logic tables”, “Pick up the parts”, “Find mistakes”, “Chameleon cube”, “Counting sticks”.
Games - puzzles on plane modeling: “Tangram”, “Pythagoras”, “Vietnamese game”, “Mongolian game”, “Magic circle”, “Columbus egg”, “Pentamino”.
Three-dimensional modeling games: “Nikitin Cubes”, Cuisenaire sticks, Dienesh blocks, “Tetris”, “Ball”, “Geometric Constructor”.
Games - fun, labyrinths, mathematical crosswords, charades, puzzles: “Tea set”, “Cubes for everyone”, “Make an elephant”, “Mill” [3, p.12].
The problems are jokes (the essence of the problem is masked by external conditions): “Can it rain for two days in a row?” (No). “Which figure has neither beginning nor end?” (at the ring). “Three brothers have one sister. How many children are in the family? (4) “How can you pick a branch without scaring away the birds on it?” (impossible, it will fly away)
Educational games in mathematics: “Which button did the Absent-Minded Man lose?”, “Who lives where?”, “How many pairs of shoes?” (children’s task is to name the missing numbers).
Games of checkers, chess. Checkers is an indispensable “simulator” for those who want to become smarter and learn to think logically. You can use the following games: “Wolf and Sheep”, “Fox and Geese”, “Quartet”, “Leopard and Hares”.
Games with a motivational situation: “Travelling around the room”, “Be attentive”, “Place it in boxes” [5, p. 65].

For the effective organization of mathematical activities, for the development of children’s mathematical abilities, a subject-development environment must be organized in the group, mathematics and experimentation corners must be created in accordance with the age of the children. In the mathematics corner you can place:

visually - demonstration mathematical material;
educational books for children;
board and printed games;
didactic, educational games;
checkers, chess;
Cuisenaire sticks, Dienesh blocks;
cubes with numbers, signs;
counting sticks;
a variety of entertaining math material.

The material is in the zone of independent cognitive and gaming activity and is periodically updated. Timely change of aids maintains children's attention to the corner and attracts them to perform a variety of tasks, promoting the assimilation of the material. Children have free access to it [7, p. 120]

The introduction of developing “Game technology” is carried out in accordance with the principle “from simple to complex” and a personality-oriented learning model. “Game technology” must meet psychologically sound requirements for the use of game situations in the teaching process of a kindergarten. The game or elements of the game give the educational task a specific, relevant meaning, mobilize the mental, emotional and volitional forces of children, and orient them towards solving the assigned tasks. Game is one of the wonderful phenomena of life. An activity that seems useless and at the same time necessary. Unwittingly charming and attracting people as a vital phenomenon, the game turned out to be a very serious and difficult problem for scientific thought. Play, along with work and study, is one of the main types of human activity, an amazing phenomenon of our existence. Teaching mathematics in the form of a game can and should be interesting, varied, entertaining, but not entertaining [1, p. 82] The mathematical development of a child is a labor-intensive and lengthy process, and the result depends on the systematic and planned nature of activities with the child. Educational games will help children in the future successfully master the basics of mathematics and computer science in a fun way, prevent intellectual passivity, and develop perseverance and determination. A game is valuable only if it contributes to a better understanding of the mathematical essence of the issue, clarification and formation of the preschooler’s mathematical knowledge and abilities.

LIST OF SOURCES USED

Wenger L.A., Dyachenko O.M. "Games and exercises to develop mental abilities in preschool children." "Enlightenment" 1989 – 127 pages.
Volina V.V. “Riddles, puzzles, games” “Bustard” 2003 – 32 pages
Volina V.V. “Funny numbers” “Bustard” 2002 32pp.
Erofeeva T.I. "Introduction to mathematics: a methodological guide for teachers." – M.: Education, 2006. – 112 p.
Zaitsev V.V. "Mathematics for preschool children." Humanitarian. Ed. — 64 pages
Kolesnikova E.V. “Development of mathematical thinking in children 5-7 years old” - M: “Gnome-Press”, “New School” 1998. 128 pp.
G.P. Popova, V.I. Usacheva; “Entertaining mathematics” Volgograd: Teacher. 2006 – 141 pages
Shevelev K.V. “Preschool mathematics in games” “Mosaic – Synthesis. 2014-65 pp.