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How to develop scientific thinking in babies

Once a mathematician (not a teacher, but a real scientist!) Began to conduct a home math circle.
With children 3-5 years old, he did not cram the multiplication table and count from 1 to 9 and vice versa, but was engaged in the development of scientific thinking.
Interesting? What came of this, he said in the book (Zvonkin AK, “Kids and Mathematics. Home Club for Preschoolers”). I read it in one breath and am sharing with you.

For those who are looking for quick practical recommendations – go to the section “For those who want to do math with their children” and further. Who cares what the book is about – see the table of contents as an illustration.
How it was…
“Those same six matches that still remained on the table after the previous task are laid out in a row. I ask each button to attach a button. Standard question:
– What more – matches or buttons?
– Just like that.
“So there are as many buttons as there are matches,” I summarize.
I take all the buttons into a fist and ask to say how many buttons are hidden in my fist. Characteristically, no one makes the slightest attempt to count matches. Yes, and why, in fact? After all, they ask about buttons, which means that you need to count buttons. Dima, as a man with me on the shortest leg, is trying to unclench my fist, others are surprised to ask:
“How can we count them?”
I am laughing:
– Of course, it is impossible to count – the buttons are hidden. But try to guess somehow.
Then a real flurry of riddles falls upon me, most often based on nothing. Everyone screams something different; while only Zhenya shouts the correct answer. I try to listen to him, ask why, but he retreats. Shyness often interferes with his wife. … Andryusha is another problem. He is a very purposeful boy, and in our classes he clearly lacks motivation. The next time I proposed the same task in a different arrangement – there were already no buttons with matches, but soldiers with guns, then they left, and the guns remained, and now the scout needed to find out how many soldiers there were – then he first guessed that guns can be counted. ”

For four years, a “math group” met every week: a caring dad, a mathematician, studied with his four-year-old son and his peers.
“Every week” is perhaps an exaggeration. There were omissions due to departure, illness or employment. Once the children got bored and the classes were interrupted for three weeks.

When the boys went to school, the youngest daughter grew up and dad resumed the club in the “girlish” version. For two years, the girl Zhenya and her friends were engaged in mathematics.

Kolya is better than Vasya, or What kind of math happens?
The traditional understanding of mathematics by adults for children: these are counts and geometric shapes. As a result, “math classes” come down to memorization – “remember, Vasya: this is a circle, this is a square, this is a triangle” – and poor Vasya does not understand why this should be known. With regard to the account, the situation is even simpler. This process was amusingly and accurately described by Zvonkin:
“Let’s take the place of the child and try to learn arithmetic ourselves … but only in Japanese! So, here are the first ten numbers: ´iti, ni, san, si, go, r ´oku, with ´iti, x ’ati, ku, ju. The first task is to memorize this sequence. You will see that it is not so simple. When this finally succeeds, you can begin the second task: try to learn to count in the reverse order, from ju to iti. If this already succeeds, let’s begin to calculate. How much will the dignity add to rock? And take away from city go? And divide the hati into si? Now let’s solve the problem. Mom bought a bunch of apples in the bazaar and gave a single apple to each of the si children; how many apples did she have left? A very difficult, but indispensable condition is not to translate into Russian, even in the mind. … But now you finally learned a cursory score within the judo. How long did it take you? A week? Month?”

You trained mechanical memory, but what is the mathematical meaning here, you still need to understand.

What then is science – mathematics? What is the main thing in it, if not numbers and figures?


this is the law of conservation of quantity
this is the beauty of symmetry
this is probability theory
this is the idea of ​​a sketchy image (from drawings and pictograms to hieroglyphs and to the alphabetical letter)
this is combinatorics
and not only.
Here is a fun task for the development of thinking (transitivity):

“Kolya is better than Vasya, and Vasya is better than Tanya. Who is better than everyone? ”

Ask this puzzle to the children. They will probably give the correct answer, but they will ask with curiosity: what does “better” mean. I’ll tell you a secret: this word is without meaning, it is given to express the degree of a certain abstract quality among the heroes of the task.

The fundamental position of mathematics (however, relating to science as a whole), known to everyone:

this is evidence of their allegations.
Science does not tolerate allegations.

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