Modern technologies for mathematical development of preschool childrenpresentation
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Modern technologies for mathematical development of preschool children
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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
Theory and technology of development of mathematical concepts in children
Methodological recommendations for the formation of ideas about quantities in preschool educational institutions Features of the development of ideas about quantities Methodological recommendations for the formation of ideas about quantities in children in preschool educational institutions It is difficult to perceive the essence of quantities First, we consider objects that are sharply contrasting in size (3-4 times) and identical in all other characteristics (color , form, …). We study one quantity using a wide variety of visual material. Next are exercises on classifying objects by size. It is easier to perceive the size of an object. First, we compare objects located directly in front of someone who is close, than at a distance by the child or in his hands, then at a distance, then from memory and imagination. Comparisons of contrasting values are easier to perceive. The younger the children, the more contrasting in size we present objects for comparison: first - unequal, then - equal in size. Young children are interested in. With younger preschoolers we look at large objects, then large objects, and for older preschoolers, we gradually reduce the size of the handout material. Children tend to consolidate signs of size. We show identical objects of different sizes: “There are bears behind a specific object: “small ball”, large, medium, small...”. We reveal the relative nature of the “big bear” Magnitude: “The bear is larger than a hare, but smaller than an elephant.” Children do not correlate the sizes of objects with body sizes, they ignore this sign “Piaget’s Phenomenon”; other signs (color, shape) interfere with the perception of size. We discuss the problem, showing ways of comparing size by application (application) and superposition (trying on). We do a lot of work comparing objects by size, quantity, shape. We practically introduce the methods of size comparison (application and overlay). We give special exercises to develop the eye. It is easier to compare the sizes of flat objects. Only when planar comparison is mastered do we move on to three-dimensional rather than three-dimensional objects. It is difficult to distinguish different ones in one object. First, we consider objects with a clearly expressed one parameter, and the size parameters then explain that an object can be characterized by several parameters: “ribbons are the same in length, but different in width.” We compare objects first according to one parameter, then - according to two, then - according to three: “The house is big, because it is long, wide, tall.” Proportions in the drawings are not observed. We train in depicting objects of different sizes and discuss the correspondence of their sizes.
