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Kids and math. Home club for preschoolers

The author of this book, a professional mathematician, talks about his experience in mathematics with preschoolers. The genre of the book is mixed: diary entries are interspersed with discussions of mathematics or psychology, observation of children and their reaction to what is happening are a source for new tasks, and they, in turn, allow us to deepen and develop the ideas outlined by the dotted line.
The book will be interesting to parents of preschool children (as well as their grandparents), kindergarten teachers, primary school teachers and in general to all those interested in the process of developing children’s intelligence.
You can buy a paper-based book on
Do not tell the children the final truths, but awaken their curiosity
First lesson and thoughts around
“How did this happen?
… There are four participants in our circle: my son Dima and his three friends – Zhenya, Petya and Andryusha. Dima is the youngest, he is 3 years and 10 months old; the oldest is Andryusha, he will soon turn five. We sit around the coffee table. Of course, I worry: how am I going to deal with all of them here? To begin with, I tell the children that we will be engaged in mathematics, and to maintain authority, I add that mathematics is the most interesting science in the world. I immediately get the question:

– What is science?

I have to explain:

– Science is when they think a lot.

“And I thought there would be tricks,” Andryusha says somewhat disappointed. He was warned at home that Uncle Sasha would be engaged with them today, and there would be tricks.

“There will be tricks, too,” I say, and curtailing the introduction, I get down to business.

Here is the first task. I put 8 buttons on the table. Without waiting for my instructions, the boys rush together to count them. Apparently, despite their young age, they already have some idea of ​​what mathematics is: mathematics is when they think. When the noise has subsided, I can formulate the actual task: – Now put on the table the same amount of coins. Now there are 8 more coins on the table. We put coins and buttons in two identical rows, opposite each other.

“What more, coins or buttons?” I ask.

Children look at me a little bewildered; they do not immediately manage to formulate an answer:

“No one else.”

“So, equally,” I say. “Now look what I’ll do.” And I am pushing a row of coins so that it becomes longer. “Now what more?”

– Coins, more coins! – the guys shout in unison. I suggest Petya to count the buttons. Although we have already counted them four times, Petya is not at all surprised at my task and counts the number of buttons for the fifth time:

– Eight.

I suggest that Dima count the coins. Dima considers and says:

“Eight too.”

– The same eight? I emphasize in a voice. “So they are equally divided?”

– No, there are more coins! – the boys strongly declare.

In truth, I knew in advance that the answer would be just that. This task is only one of the countless series of tasks that the great Swiss psychologist Jean Piaget gave to test children in his experiments … In his experiments, he established: young children do not understand what seems to us self-evident – if several objects like If you rearrange or move, then their number will not change from this. So, I knew in advance what the children would say. He knew, but for some reason did not prepare any reasonable reaction. What would you do, reader? What would you say to the children?

Unfortunately, the most common trick used by almost all adults in such a situation is to start the children to interpret things with all their might. “Well, how so! – the adult says with simulated surprise. “Where could there be more of them?” After all, we did not add any new coins! After all, we just parted them – and that’s it. After all, before they were equally divided – you yourself said! So, they could not be any more. Of course (highlighted by voice), coins and buttons are left equally! ”

Efforts in vain – such pedagogy does not lead anywhere. More precisely, it leads to a dead end. First, do not hope that your logic will convince the child of anything. He will learn logical structures even later than the law of conservation of the number of objects. Until this happens, logical reasoning will not seem convincing to him. Only the intonation of your voice is convincing. And she will only show the child that he was again not up to the mark and did something wrong. Children do not give up immediately, their common sense is not so easy to break. But if you sat properly, you can achieve that they will no longer rely on their own mind and observation, but will try to guess what the adult wants from them. Adults generally present many inexplicable requirements for children: for some reason, you cannot draw on the wall; for some reason you have to go to bed when the game is in full swing; for some reason you can’t ask: “And when will this uncle leave?”. So now something similar is happening: although I can clearly see that there are more coins than buttons, but for some reason I’m supposed to answer that they are equally divided.

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