Formation of representations of the relationship between «one to many» — the traditional theme of mathematical education of preschool children. For a long time this subject during the second youngest group of 10-13 sessions withdrawn. Today’s program gives it even less training. Obviously, because they consider irrelevant topic. It is no secret: in most cases, children 3-4 years own account within five (instead of the expected response «Many birds» can clearly hear: «Four birds»). However, not rushed me? Maybe methodical value of the theme is still unconditional? But not in the traditional interpretation (when the objective is to develop quantitative concepts), and its significance — form and develop basic mental operations (mental activities).

What we see the flaw? In most cases, the group «one-many» forms educator, children demonstrating results. The last remains only to fix the result (ie to perform the reproductive activities). In addition, a similar methodical approach brings children to act in accordance with the instructions: «Put here a fungus, and here — a lot of» (the reproductive effects), «Find one item», «Find things a lot.» And the teacher (especially in the first session on the subject) as recommended picks homogeneous didactic material (the same birds, Christmas trees, mushrooms, mugs, etc.). In our view, the task totally motivated and children is unclear. And time is not clear, therefore, violated the most important principle of developing training — awareness, the essence of which is: the situation should so build and select such tasks to the children understand and make sense of that study, and why, why learn this stuff (of course, not in the version » Teach, to you it will come in handy later in life «). In other words, the subject of this principle to the fore learning motivation, the process of understanding and acceptance of the learning task, providing child self-esteem and self-control, which ultimately boils down to a single goal — to do the job of the teacher («Take a bird»).

We can argue, if the goal is aimed at the formation of ideas about the number of «one-many» approach is natural. Yes, but experience shows that even a year-old child without special training designate one understands the meaning of an apple, a candy cane. We believe: that is why the methodical approach from the perspective of both the teaching of mathematics, and from the perspective of the development of thinking does not give result. Consequently, the task in such a counterproductive, do not fulfill the basic developmental function (do not develop thinking, attention, perception). Targets only train executive functions. And we have another task — to develop attention, perception, thinking. Therefore, to maintain the didactic and methodological value of the subject in the course of employment should be introduced elements which, at first, put children in the perceived situation; secondly, it will create a situation where the subject must choose from the groups based on consciously identified features. In our view, such a didactic approach is fundamentally change the course of lessons. And from the standpoint of not only the goal — to develop mathematical children, but also the one which is now a priority. It is a personality-oriented developing training. Not to be unfounded, with specific examples show how, in our opinion, it is possible to build in the second class the younger group, the relevant recommendations of any program of mathematical education of preschool children.

Occupation first

Subject. Signs of items: same — different. Isolation of a single object from the group.

Goal. Learn to allocate the object from the group of characteristic features and form a group of separate items; establish a relationship between the number «one» and «many»; develop attention, perception, communication activities.

Material. Set of multicolored (two to four colors), but the same size beads, wood or plastic; set of colored bricks of the same color; small box inside painted in the colors of the balls; one box with two (four) branches, colored beads.

Note. How many colors to use, solves the teacher. If the level of development of children is that appropriate to limit two-color balls, use a box with two compartments.

Organization. Activity takes place in a relaxed atmosphere playroom — the teacher with the children is on the floor. Or transplants of children drawn together around two tables, taking place in the end, so that everyone can clearly see what he is manipulating.

Outline Activity 1

Goal. Activate account; stimulate interest and cognitive activity; learn to identify similarities in subjects like equal and different, to allocate a countable number of «one» and a set of «a lot.»

Mentor (shows shaking the closed lid of the box with two or four compartments, which are spread respectively color balls the same size). Do you think that’s in the box? (Main task: to bring children to understand: give an exact answer can only look inside the box.) This box live colored balls.

See how many of them! What balls live here — the same or different? (Answers.) Yes, the balls are identical in size but different in color. (The conversation should stimulate the statements of all children.) A thought … (calling the names of several children, ask leading questions undesirable; conversation should take place approximately as follows.)

They are all the same? (No. These red, the blue, the green, the yellow.) For these and those (pointing to the red and yellow balls) — the same or different? (Diff.) What are they different? (Children must reiterate: red and yellow.) You want to say: different color? (Yes.) And what are they the same? (This question is difficult to answer, although the children intuitively understand what the similarities. They are usually taken in both hands on the ball and try to attach them to each other.) I’ll help you: beads the same size. (Then the teacher suggests referring to each child, to take out of the box, two identical balls, the other two identical balls, two balls of different color; once again the two different color of the ball, etc .; asked to comment on what they are — the same or different and if different, what’s the difference between them. Then add up all the balls in the box, in their «house». Attention is drawn pas children that the color of each ball must match the color separation of the box.)

All the balls were in their houses? (Answers.) But one ball lost. (Mentor discreetly lays one ball is not in an office.) Why do we think that he got lost? (The ball is out of his house. Red Ball lives in the red house.) And now let’s play. You close your eyes and when you open on my signal, have to say, that has changed. (Mentor shifts balls: blue to green, etc. Children are «stray» ball and put it in place. It is useful to them blurts out what they see: a blue ball and a lot of yellow balls. Educator comments after children .) One blue ball lost. Blue ball go in the blue box! .. Now here all the blue balls.

Task 2

Goal. Learn to identify similarities in subjects like equal and different, to distribute items on the basis of color, highlight a countable number of «one» and a set of «a lot.»

Mentor (handing out small colored boxes of the same color as the balls).

Closely balls to live in one box, and they decided to live apart. Who lives this ball? (Shows the green ball.) (Answers.) Why are you (the name) you think so? That’s right, you have a green box. Green ball will live in it. What is like a ball and a box? (Color.)

In the same way the teacher gives children the remaining balls. If someone does not ask for the ball, adult asks him: «And to your box this ball suitable? Inappropriate? What color do you give the ball? Why yellow? That’s right, the yellow box. «

Mentor. Who’s in the box, only one ball? Please look: Katya and Tanya only one ball in the box. Here’s to you, Tanya, another ball; here’s to you, Kate, another ball … Who can say how many now Katie balls — one or more than one? Who has a lot of balls? (Answers.) And I have many balls? (No one.)

Further, using the spare balls caregiver gives the child who has a few balls of one color, another, but a different color and asked: «What kind of balls now Koli much?

And about which we can say that this ball one? (The yellow one, and a lot of blue.) Do not mind if someone says: «Yellow — one, and blue — five.» One can only note: «Here’s how you can still speak, but is not so able. However, it soon will learn. «

Activity 3

Goal. Develop motor skills and coordination; learn to identify the similarity in identical and different subjects.

Mentor (shows colored blocks and offers to each child to take a brick by brick, similar to the ball in color). Why are you (to the child) take the brick?

What he looks like your balls? (Color.) Show me the brick, which is not similar to the color of your balls, not the color. That’s right: this and this. Who has a brick? (Showing one of his remaining bricks.) Who does not like that? (Answers.) Why do you (to the child) think that you are not the same brick? (I have a blue and this red.)

The provider gives every child the second one brick, but after they determine the same. If someone asks brick, offers to tutor him one of the three building blocks, so that eventually became two of the same.

Mentor. Now, let’s play! I will show a brick and say, «The same!». Do any of you would be exactly the same, I must say: «I have!» — And the show. Who is not so, says nothing.

The first variant. Mentor shows a brick and asks, «Show a brick, but not like my color.» Of course, the need to respond those who do not like that. Not an easy task. But its significance is that not only develops hand-eye coordination, but also flexibility, awareness, coordination of perception. After all, the child should perceive the information to evaluate it, to relate to the installation and only then react accordingly.

The game is played slowly. The teacher is required to assess the actions of children: «What I asked to see a brick? (Not so.) And how do you show? (Am.) And why it is not so? (It has another color.). «

Option Two. The provider is not showing a sample, asks children to show his brick is not blue and not red. Or: «Show me not green and not blue. Tell me, what color. » (Green, yellow, red.)

Note: this kind of job well to develop the right-left asymmetry of the brain and the ability to control their activities.

By breaking down the children into pairs, the teacher shows how two building blocks can create a «gate». Children roll their balls into the gates push from a short distance. First, the balls rolls one child and one of their catches. The children then switch roles. A job can be complicated, offering to roll balls into the goal, according to their color.

Task 6

Goal. To develop attention, perception, self-control.

At the suggestion of the tutor the children balls stacked in a large box, and bricks — in a little. The results are discussed. The task is completed, if the color matches the color of brick boxes.

Second Session

Subject. Signs of items: same — different. Isolation of a single object from the group.

Goal. Learn to allocate the object from the group of characteristic signs and, accordingly, constitute a group; intensify in the speech word one, two, much the same, different; develop attention, perception, communication activities.

Material. Set of multicolored (two to four clearly distinct color) balls, wooden or plastic, in two sizes (the ones that served as the material for the first class, and less); set of colored bricks of the same color; mesh with ribbons for balls; small boxes, painted inside, respectively, color balls and separated by a partition (a strip of cardboard the same color); one box with two (four) branches, colored beads, respectively colors; two shelves with flanges for installation in a row of balls.

Organization. Classes are held in a free atmosphere. Together with the children the teacher is around two tables (if the group is small), or four, drawn rectangle. Mentor sits in the end. Children need to see all things that lie in front of him on the table. Shelves are installed on a stand behind the teacher.

Outline Activity 1

Goal. Learn to distribute objects on various grounds.

Mentor (shaking, shows the familiar box). You remember that inside the box there is something? (Balls). What balls? The same or different? (Colored, different in color). And the size? (The same.) To check. (Opens the box, which contains colored balls in two sizes.) You guessed it? (None.) And why make a mistake? (During the conversation, the teacher leads the children to understand: as long as the box is closed, say exactly what is in it is difficult.) Why did you decide that the balls the same? (This was the last time.) I told you that everything will be exactly the same? (No.)

What is the essence of the conversation? An adult not only stimulates the cognitive interest of children, but also teaches them to approach the situation analytically, rather than relying on a template; teaches investigate the situation (ie, to understand cause-and-effect relationship of the phenomenon.)

Mentor. So what has changed? (Balls not only different colors, but also large and small.) Yes different sizes! Look! Now you have to take on the ball. Be careful (shows big red bead): The ball should be of the same color but a different size.

The results are discussed. The errors are corrected; further the game goes on, but in a slightly different way. It should show a ball of the same size, but of a different color; the same color and size; different color but the same size. The game is played as long as the children do not disassemble all the balls (each at least three balls).

Mentor. Who has all the balls of the same color? the same size? two colors? three colors? (Answers). Now I have a red box with two compartments. What is necessary to lay down beads in red box, and how they should be put down? (The question is discussed. Children have come to the conclusion: in the red box, add up the red balls in one compartment — big, in the other — a little.) Fold balls.

On the table are put three boxes of other colors, divided similarly. Children should be expanded to the rest of them beads. The difference between this job: a selected number of balls that in one of the boxes in the same department was only one ball. If someone is difficult, the teacher is helping him.

Mentor. What color is the ball was left alone? (Small green.) Poor ball! To him it was not boring, sat down beside him another ball. (Shows a few spare balls, involving actions less active children.) What should be hooked ball to a little green? True, another ball — a small, green. Who can say how much is now little green balls? That’s right, two! And if one little green ball to put, how many? That’s right, three!

Note. The purpose of these fragments classes: in an unobtrusive way to familiarize with the sounds of an ordinal numeral. This technique — «organization of peripheral perception» — leads to involuntary memorization of vocabulary and the correct formation of the ability to apply it in a given situation.

Task 2

Goal. Learn to identify the similarity in identical and different things, distributing objects on the basis of color; allocate a countable number of «one» and a set of «a lot.»

See. Activity 1, Task 2 Work carried out with colored bricks.

Activity 3

Goal. Develop coordination and hand muscles.

To warm up (see para. 1 activity, reference 4). These exercises can be added as follows:

1. On account of «time» is widely dilute the fingers of both hands, at the expense of «two» fingers impact (compression palm).

2. The same movement, but at the expense of «time» to separate the fingers on one hand and on the other to compress (at the expense of «two»).

Task 4

Goal. Develop motor activity, hand-eye coordination and precision movements.

With the help of the tutor the children put more balls into the net, tightening the braid and tie a knot on the neck. The useful task: developing flexible fingers. Then the children put (again by showing an adult) near (close) on the edge of two brick and the «jump» through them the ball.

If the group to cope with the task, it can be more difficult: 1) bricks are placed, and then the ball can «jump» through two brick (it is desirable that children have mastered the movement of the ball, immersed in the net);

2) The bricks are placed flat (now the ball has to «jump» brick by brick);

3) twist the ball, holding the ribbon on the table (on the floor), first clockwise, then counterclockwise.

Task 5

Goal. Develop the ability to distribute objects on various grounds; teach be a simple logical sequencing.

Mentor (introduces children to the game situation). Balls-jumpers decided to rest and other spheres, by contrast, went to visit. In order not to get lost on the way, they are lined up like this — one after another. (Display: put on the shelf red ball behind him — blue, red again. And all the same size.) Who can say what the ball will be next? Why blue? (They are by turns.) Put more balls on the shelf. In what order? That’s right, red, blue …

What have we got? Now two neighbors each ball of the same color (indicating the location of the balls on the shelf ~ right and left). What color are the neighbors at this ball? And this? (Answers.) At any balls, only one neighbor? (The first and last).

But I am yellow and green balloons on a secret told that, too, want to go for a visit. Here’s shelf: arrange, please, yellow and green balls. How do you get them apart? That’s right, first yellow ball, then green, then yellow, green … Is it possible to be different? (Yes, green, yellow, green, yellow …)

Note. If there are a couple of shelves, you can offer to make a sequence of small balls: pick similar in size but different in color (red and yellow, blue and green, red and green), and then compare the selection and note the similarities and differences.

Third Session

Subject. Signs of items: similar — dissimilar. Isolation of a single object from a group based on certain criteria.

Goal. Learn to compare objects on different grounds and to provide a single object from a group of specified grounds, identify and compile indications of similarities and differences of objects and groups of objects; develop attention, perception, thinking, speech.

A. BELOSHISTAYA, Doctor of Education, Professor, Murmansk State Pedagogical University

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