Math counting activities

Methods of mathematical development (exam)

1. Basic mathematical concepts: set, number, digit, natural series of numbers, number system, counting, computing, measuring activity, magnitude, shape, geometric figure, time, space.
The FEMP methodology in the system of pedagogical sciences is designed to assist in preparing preschool children for the perception and assimilation of mathematics - one of the most important subjects in school and the comprehensive development of the child.
The FEMP technique has a specific, purely mathematical terminology .
This is:

- many;

- number;

- counting and computing activities;

- value;

- geometric figures;

- time;

- space.

Sets consist of elements. The elements of the set are the objects that make up the set. These can be real objects (things, toys, drawings), as well as sounds, movements, numbers, etc. .

The elements of a set can be not only individual objects, but also their combinations . For example, when counting in pairs, triplets, tens. In these cases, the elements of the set are not one object, but two, three, ten - a set.
Thus, sets are considered as a set, a set , a collection of any objects and objects, united by a common, for all, characteristic property .
Any property can be considered as belonging to some objects.

For example, some flowers, berries, cars and other objects have the property to be red . The property of being round is possessed by the moon, the ball, the wheels of bicycles and cars, parts of various machines and machine tools, etc.

Thus, each property is associated with a set (objects) that have this property. It is also said that the set is characterized by the given property - or the set is given by specifying the characteristic property.
Under the characteristic property of a set is meant such a property, which all objects belonging to a given set (elements of this set) have, and not a single object that does not belong to it, i.e. this item is not its element.
If some set A is specified by specifying the characteristic property P , then this is written as follows:
A = { x | Р ( x )}
and reads like this: “ A is the set of all x such that x has the property P ”, or, in short, “A is the set of all x with the property P ”. When they say: "the set of all objects that have the property P", they mean those and only those objects that have this property.

Thus, if the set A is given by the characteristic property P , then this means that it consists of all objects that have this property, and only of them. If some a has the property P , then it belongs to the set A , and vice versa, if the object a belongs to the set A , then it has the property P .

Mathematics deals more with infinite sets (numbers, points, figures and other objects), but basic mathematical ideas and logical structures can be modeled on finite sets.

Naturally, in pre-mathematical preparation usually deals with finite sets .
COUNT - first and main mathematical activity , based on element-by-element comparison of finite sets.

NUMBER is the general unchanging category of the set , which is an indicator of the cardinality of the set. This is just a sound designation.
Theoretical foundations for the formation of elementary mathematical concepts in preschoolers include a detailed study of only the system of natural numbers . Therefore, when we say "numbers", we mean natural numbers.
DIGITS - a system of characters (“letters”) for writing numbers (“words”) (numerical characters). The word “digit” without specification usually means one of the following ten characters: 0 1 2 3 4 5 6 7 8 9 (so-called “Arabic numerals”). Combinations of these numbers generate two (or more) digit numbers.
The number has 2 values ​​: number and ordinal.
With a quantitative value of , we are interested in the number of elements in the set. We use the question HOW MUCH? and we start counting with the cardinal number ONE.
When the ordinal value is , we are interested in the place of the number among others or the ordinal number of the element in the set. The question is WHICH COUNTS? and set the direction of the account. Ordinal numbers are used, counting begins with the word FIRST.
When we talk about quantity, it does not matter the direction of the count, the object from which the count began. The final number does not change. With an ordinal count, the final number may change.
COUNTING ACTIVITY is considered as an activity with specific elements of the set, in which a relationship is established between objects and numerals. The study of numerals and sets of objects leads to the assimilation of counting activities.
CALCULATION ACTIVITY - is an activity with abstract numbers, carried out through addition and subtraction. The simple naming of numerals will not be called counting activity. The system of computational actions is formed on the basis of quantitative knowledge.
VALUE is the quality and property of an object, with the help of which we compare objects with each other and establish a quantitative characteristic of the compared objects.

Concept the value in mathematics is considered as the main one.

The perception of magnitude depends on the distance from which the object is perceived, and also on the magnitude of the object with which it is compared . The farther an object is from the one who perceives it, the smaller it seems, and vice versa, the closer it is, the larger it seems.

The characteristic of the size of the object also depends on its location in the space . The same object can be characterized either as high (low), or as long (short). This depends on whether it is in a horizontal or vertical position. So, for example, in the figure, objects are located in a vertical position and are characterized as high and low, , and in another figure (in a horizontal position), these same objects are characterized as long and short.

The value of an item is always relative , it depends on which item it is compared to . Comparing an object with a smaller one, we characterize it as a larger one, and comparing the same object with a larger one, we call it a smaller one.

So, the value of a particular object is characterized by the following features : comparability, variability and relativity.

1) comparability implemented by:

- overlay,

- application,

- by measuring with a standard measure,

- comparison by eye.

2) relativity - depends on the object with which we are comparing, on the distance at which we are comparing, on the location in space.

3) variability . Size is closely related to size. And size is a property of magnitude variability. Each item has its own generic purpose. It can change its dimensions without changing its essence.
GEOMETRIC FIGURE is an abstract concept with the help of which we personify all the objects around us in form.

A geometric figure is the presence of points on a plane, limited by space.

SHAPE is the outline, the outer appearance of an object.

Form (lat. forma - shape, appearance) – the mutual arrangement of the boundaries (contours) of the subject, object, as well as the relative position of the points of the line.
TIME is a philosophical concept that is characterized by the change of events and phenomena and the duration of their existence.
Time has properties :

- fluidity (time does not stop)

- irreversibility and uniqueness

- duration .

Orientation in space involves orientation towards oneself, away from oneself, from other objects, orientation on the plane and orientation on the ground.

2. Subject and tasks of the course "Methods of mathematical development and teaching of mathematics". Connection of the methodology of mathematical development with other sciences.
The methodology for the formation of elementary mathematical representations in the system of pedagogical sciences is designed to assist in preparing preschool children for the perception and assimilation of mathematics - one of the most important subjects in school, to contribute to the education of a comprehensively developed personality.
Having stood out from preschool pedagogy, the methodology for the formation of elementary mathematical representations has become an independent scientific and educational area.
The subject of her research is the study of the basic patterns of the process of formation of elementary mathematical representations in preschoolers in the context of public education.
The range of tasks solved by the method is quite extensive:

- scientific substantiation of program requirements for the level of development of quantitative, spatial, temporal and other mathematical representations of children in each age group;

- determination of the content of factual material for preparing a child in kindergarten for learning mathematics at school;

- improvement of the material on the formation of mathematical representations in the kindergarten program;

- development and implementation into practice of effective didactic tools, methods and various forms of organizing the process of developing elementary mathematical concepts;

- implementation of continuity in the formation of basic mathematical concepts in kindergarten and the corresponding concepts in school;

- development of the content of training highly qualified personnel capable of carrying out pedagogical and methodological work on the formation and development of mathematical concepts in children in all parts of the preschool education system;

- development on a scientific basis of methodological recommendations for parents on the development of mathematical concepts in children in a family setting.

She has the closest connection with preschool pedagogy . The methodology for the formation of elementary mathematical representations is based on the tasks of teaching and mental education of the younger generation developed by preschool pedagogy and didactics: principles, conditions, ways, content, means, methods, forms of organization, etc. This connection is mutual in nature: research and development of problems the formation of elementary mathematical concepts in children, in turn, improve the pedagogical theory, enriching it with new factual material.
Multilateral contacts exist between private methods that study the specific patterns of the process of raising and teaching young children: the method of forming elementary mathematical representations, speech development, theory and methodology of physical education, etc.
Preparing children for learning mathematics at school cannot be carried out successfully without connection with the methodology of primary teaching of mathematics and those aspects of mathematics itself , which are the theoretical basis for teaching preschoolers and primary school students .

Reliance on these sciences allows, firstly, to determine the volume and content of knowledge that should be mastered by children in kindergarten, and serve as the foundation of mathematical education; secondly, to use teaching methods and means that fully meet the age characteristics of preschoolers, the requirements of the principle of continuity.

Education should be built taking into account the patterns of development of cognitive activity, the personality of the child , which is the subject of study of psychological sciences . Perception, representation, thinking, speech not only function, but also intensively develop in the learning process.

Psychological features and patterns of perception by a child of a variety of objects, numbers, space, time serve as the basis for developing a methodology for the formation of elementary mathematical representations. Psychology determines the age capabilities of children in acquiring knowledge and skills that are not something frozen and vary depending on the type of education.

3. Stages of development of the methodology of mathematical development: empirical, classical, modern.
Issues of mathematical development of preschool children are rooted in classical and folk pedagogy. Various counting rhymes, proverbs, sayings, riddles, nursery rhymes were good material in teaching children to count, they made it possible for the child to form concepts about numbers, shape, size, space.

In the course of mastering them, children not only mastered the recalculation of objects, but also the ability to perceive and realize the changes taking place in the reality around them: natural, color, spatial and temporal; quantitative, changes in shape, size, location, proportions. This ensured the natural development in children of certain ideas, ingenuity and ingenuity.

Thus, the Czech humanist thinker and teacher Ya.A. Comenius (1592-1670) in the book "Mother School" (1632) recommends even before school to teach the child to count within twenty, the ability to distinguish between larger-smaller, even-odd numbers, compare objects by size, recognize and name some geometric shapes, use in practical activity units of measurement: inch, span, step, pound, etc.

J. G. Pestalozzi (1746-1827), a Swiss democratic teacher, pointed out the shortcomings of the teaching methods existing at that time, which were based on cramming, and recommended teaching children to count specific objects, understand operations on numbers, and the ability to determine time. The teaching methods proposed by him presuppose the transition from simple elements to more complex ones, the widespread use of visualization, which facilitates the assimilation of numbers by children. The ideas of J. G. Pestalozzi later (mid-19th century) served as the basis for reform in the field of teaching mathematics at school.
Advanced ideas in teaching children arithmetic before school were expressed by the Russian democrat teacher, the founder of scientific pedagogy in Russia K. D. Ushinsky (1824-1871). He considered it important to teach the child to count individual objects and their groups, to perform addition and subtraction, to form the concept of ten as a unit of account. However, all this was just wishes, without any scientific justification.
The writer and teacher Leo Tolstoy published in 1872 the "ABC", one of the parts of which was called "Account". Criticizing the existing teaching methods, L.N. Tolstoy suggested teaching children to count "forward" and "backward" within a hundred and numbering, based on children's practical experience gained in the game.

Methods for developing ideas about number and form in children were reflected and further developed in the systems of sensory education of the German teacher F. Fröbel (1782-1852), the Italian teacher Maria Montessori (1870-1952), etc.

M. Montessori's pedagogical activity proceeded most effectively in the first half of the 20th century. The use of materials for the development of mathematical representation in children in the education and upbringing of a child was based on a certain style of interaction between an adult and a child; the need to monitor the behavior of children in a specially created environment; organizing joint free work with the child, etc. The M. Montessori system provides for the development of the child's sensorimotor sphere and, in the future, intellect. The "golden" mathematical material, which is especially distinguished by its significance, is first mastered by the child as a set of beads in different quantities, then in symbols (numbers), after that - as a means of mastering the ability to compare numbers. Thus, the decimal number system is presented to the child visibly and tangibly, which leads to the successful mastery of arithmetic.

The issues of the methodology of mathematical development are of particular importance in the pedagogical literature of elementary school at the turn The authors of the methodological recommendations at that time were advanced teachers and methodologists. The experience of practical workers was not always scientifically substantiated, but it was tested in practice. Over time, he improved, stronger and more fully revealed progressive pedagogical thought.
At the end of the 19th - at the beginning of the 20th century methodologists had a need to develop a scientific foundation for the arithmetic technique . A significant contribution to the development of the methodology was made by advanced Russian teachers and methodologists P.S. Guriev, A.I. Goldenberg, D.F. Egorov, V.A. Evtushevsky, D.D. Galanin and others.

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448 -> Lecture The system of work on the development of speech in kindergarten Tasks for the development of speech of preschool children
448 -> Teacher: Bakhorina O.

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