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In the mind, they count differently, different people use different techniques; accordingly, different things develop.
You can count in your mind according to a given algorithm once and for all, and then the ability to clearly execute commands develops.
And you can always come up with a convenient way to calculate, because all the numbers are different. Coming up with different ways, we scroll in our head – what properties of the number to use. At the same time, the very things that are called scary words like commutativity and associativity are made intuitively understandable…
This, in particular, is an excellent preparation for algebra.
Well, at least the skill of counting in the mind is definitely developing. Plus the amount and speed of short-term memory, which, in theory, contributes to the development of analytical abilities. In addition, sometimes it is stupidly easier and faster to calculate in your mind than to climb for a calculator 🙂
I remember when I was a kid having fun: you take a bus ticket. There are six digits – the ticket number. You need to mentally place mathematical signs between them, so that in the end you get 10. Today, you can practice with phone numbers in this way.
Of course it develops! Develops the ability to count) In the age of smartphones, this is a very outlandish skill. In any case, engaging in mental activity will stimulate blood circulation in the brain (and prevent Alzheimer's), and this will be better than admiring pictures on the sides…Sometimes it can help in life, not to be cheated in the store, or, for example, win a bet on chocolate…
If you are a construction worker or engineer, for example, this can help you in your professional field. And if no kidding is a necessary and useful skill, but it is important not to overestimate the benefits of juggling numbers – it is better if it is not a trained mechanistic algorithm, but an understanding of the algebra of numbers…
The best thing I've ever read on this subject is ” Of course you're joking, Mr. Feynman!”:
Just then a Japanese man entered the restaurant. I'd seen him before, wandering around the city trying to sell an abacus. He started talking to the waiters and challenged them, claiming that he could add up numbers faster than any of them.
The waiters didn't want to lose face, so they said, “Yes, yes, of course. Why don't you go to that customer and have a competition with him?”
This man came up to me. I tried to resist: “I don't speak much Portuguese!”
The waiters laughed. “With numbers, it doesn't matter,” they said.
They brought me a pencil and paper.
The man asked the waiter to name a few numbers to add up. He beat me to pieces, because while I was writing the numbers, he was already adding them up.
Then I suggested that the waiter write two identical lists of numbers and give them to us at the same time. The difference was small. He's bought me some decent time again.
However, the Japanese got into a rage: he wanted to show how smart he was. «Multiplikato![multiplication], ” he said.
Someone wrote a task. He won against me again, although not so much, because I'm pretty good at multiplying.
And then this person made a mistake: he suggested division. What he didn't understand was that the more difficult the task, the more likely I was to win.
We were given a long division problem. Draw.
This made the Japanese man very uneasy, because he was obviously very good at performing arithmetic operations with the help of an abacus, and here he was almost defeated by a restaurant customer.
“Raios cubicos!” he says vindictively. Cubic roots! He wants to take cubic roots using arithmetic! It is difficult to find a more complex fundamental problem in arithmetic. It must have been his forte in the counting exercises.
He writes a number on paper — any large number — I still remember it: 1729.03. He starts working on this number and mutters something and grumbles, “Boo-boo-boo-hmmm-hmmm-boo” – he works like a demon! It just dives into that cube root!
Meanwhile, I just sit in my seat.
One of the waiters says, ” What are you doing?”
I point to the head. “I think so,” I say. Then I write on paper 12. After some time — 12,002.
The man with the bills wipes the sweat from his forehead and says, ” Twelve!”
“Oh, no! I object. – More numbers! I know that when you use arithmetic to take the cube root, each subsequent digit requires more work than the previous one. This is not an easy job.
He goes back to work and mutters, ” Ugh-ugh-hm-ugh-hm-hm…” I add two more digits. Finally, he looks up and says, ” 12.0!”
The waiters just glow with happiness. They say to the Japanese, ” Look! He does it in his head, and you need an abacus! And he has more numbers!”
He was absolutely exhausted and left, defeated and humiliated. The waiters congratulated each other.
How did the user win against the accounts? The number was 1729.03. I happened to know that there were 1,728 cubic inches in a cubic foot, so it was clear that the answer was little more than 12. A surplus of 1.03 is just one part out of almost 2,000, and I learned in calculus that for small fractions, the excess of the cubic root is one-third of the excess of the number. So all I had to do was find the fraction 1/1728, then multiply the result by 4 (divide by 3 and multiply by 12). That's how I managed to get a whole bunch of numbers.
A few weeks later, this man walked into the bar of the hotel I was staying at. He recognized me and came up to me. “Tell me,” he said, ” how did you manage to solve the cube root problem so quickly?”
I started explaining that I had used an approximate method, and it was enough for me to determine the percentage of error. “Let's say you gave me the number 28. The cubic root of 27 is 3…”
He takes the score: goo — goo — goo-goo-yes, “he agrees.
And then I realize: he doesn't know numbers. When you have an abacus, you don't need to memorize a lot of arithmetic combinations; you just need to learn how to click your knuckles up and down. You don't need to remember that 9 + 7 = 16; you just know that when you add 9, you need to move the decimal up and the single down. Therefore, we perform basic arithmetic operations more slowly, but we know the numbers.
Moreover, the very idea of an approximate calculation method was beyond his comprehension, despite the fact that it is often impossible to find a method for calculating the cube root accurately. So I never managed to teach him how to take the cube root or explain how lucky I was that he chose the number 1729.03.
Metal score develops your imagination and more! The benefits for children are described in detail on our website https://le-junior.com/programs/mental-math/.
The fundamental goal of mental arithmetic training is to develop photographic memory, concentration, logic, imagination, observation, and creative thinking.
Any account makes our brain active and more flexible, develops the skill of processing a large amount of information in terms of quantity and variety, which is extremely necessary in this age of information technology.