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In Russia, we are used to multiplying numbers in the traditional way that we were taught in school, writing down the multiplier numbers in a column (). However, in Asian countries such as Japan and China, it is considered differently. For a contemplative oriental mentality, an indispensable visualization is important. Even the Arabic numerals generally recognized in the world are written by the Chinese and Japanese in hieroglyphs. It is with the peculiarity of the Asian graphic system that the Japanese and Chinese method of multiplying numbers is associated.

This video shows you how to multiply in Japanese and Chinese:

It will seem to many that this method of Japanese or Chinese multiplication is too complicated and confusing, but this is only at first glance. It is visualization, that is, the image of all points of intersection of straight lines (multipliers) on one plane, that gives us visual support, while the traditional method of multiplication involves a large number of arithmetic operations only in the mind. Chinese or Japanese multiplication helps not only to quickly and efficiently multiply two-digit and three-digit numbers by each other without a calculator, but also develops erudition. Agree, not everyone can boast that in practice they know the ancient Chinese method of multiplication (*), which is relevant and works great in the modern world.

*) Japanese or Chinese multiplication table? Archaeologists in Japan have found a wooden tablet with a fragment of the multiplication table, which was supposedly made in the 8th century. Scientists believe that such tables were used by Japanese imperial officials, who needed to master various sciences, including arithmetic.
The discovered tablet is the oldest of all previously found in Japan. Interestingly, the hieroglyphs used to write the numbers are very similar in style to those that were used as an official letter during the Chinese Tang dynasty of the 7th-10th centuries. Based on this, the scientists assumed that the table was copied from the Chinese arithmetic textbook of that time, that is, the entire Japanese multiplication table was borrowed from China.

It was to their neighbors in China that high-ranking Japanese went every year to learn from them different sciences, such as arithmetic. The ancient Chinese multiplication table was not an easy one, as it involved multiplying two-digit numbers by each other. It is unlikely that all Japanese officials could learn such a table by heart, therefore they carried with them to work something like a cheat sheet, a fragment of one of which is a tablet found by archaeologists in Japan.

So, the Japanese multiplication table was borrowed from the Chinese, who, according to some hypotheses, were among the creators of the first arithmetic system, as evidenced by archaeological finds containing fragments of the multiplication table, the age of which scientists have estimated at 2700-3000 years.

What is mental arithmetic and why every person needs it.

Mental arithmetic is a program for the integrated development of the intellect and thinking of children, based on the formation of the skill of quick verbal counting

In the classroom, children learn quick counting using a special counting board (abacus, soroban). Teachers explain how to correctly sort the knuckles on the knitting needles so that kids can almost instantly get an answer to complex example... Gradually, the attachment to the accounts weakens and the children imagine the actions that they performed with the accounts in their minds.

The program is designed for 2-2.5 years. First, the guys master addition and subtraction, then multiplication and division. A skill is acquired and developed through repeated repetition of the same actions. The methodology is suitable for almost all children, the teaching principle is from simple to complex.

Classes are held once or twice a week and last one to two hours.

The ancient abacus abacus, on which children count, have been known for more than 2.5 thousand years.

In Japan, abacus counting is included in the official school curriculum.

For more than 50 years, mental arithmetic has been part of the public education system in Japan. Interestingly, after graduation, people continue to improve their oral counting skills. In the Land of the Rising Sun, mental arithmetic is considered a kind of sport. They even hold competitions on it. In Russia, international tournaments in Mental Arithmetic are now also held annually.

Mental arithmetic develops mechanical and photographic memory

When children count, they use both hemispheres of the brain at once. Mental arithmetic develops photographic and mechanical memory, imagination, observation, improves concentration.

The general level of intelligence rises. This means that it is easier for children to assimilate large amounts of information in a short time. Success in foreign languages... It is no longer necessary to spend the whole day memorizing poetry and prose.

Slower schoolchildren have a faster reaction rate. They begin not only to count at lightning speed, but to think faster and make decisions not related to arithmetic.

There are also unexpected results. One day a boy who played tennis came to the center. The mother said that her son had problems with coordination of movements. Unexpectedly, it was possible to solve them precisely at the expense of intensives in mental arithmetic.

Mental arithmetic is more difficult for adults, the optimal age for starting classes is 5-14 years

It is possible to develop the brain with the help of mental arithmetic at any age, but the best results can be achieved before the age of 12-14. Children's brain is very flexible and mobile. At a young age, neural connections are most actively formed in it, so our program is easier for children under 14 years old.

The older a person is, the more difficult it is for him to abstract from his experience and knowledge and simply trust the abacus. I mastered this technique at the age of 45 and constantly doubted whether I was getting it right, whether there was no mistake. This greatly interferes with learning.

But what harder to man master this account, the more benefit from it. A person, as it were, overcomes himself, each time he gets better and better. Classes are not in vain, the brain of an adult is also actively developing.

Just do not expect the same results from an adult as from a child. We can learn the technique, but we won't be able to count as quickly as a second grader does. Experience shows that the optimal age from which it is better to start classes is 6 and 7 years.

The best results are achieved by the one who exercises regularly at home.

A prerequisite for training is daily abacus training. Just 10-15 minutes. Children need to work out the formula that the teacher gave them in the lesson, and bring their actions to automatism. Only in this case will the child learn to count quickly. The organizational role of parents is important here, who need to monitor regular exercise.

Children do not get tired in the classroom due to the constant change of activities

The main activity in mental arithmetic is counting on the abacus. Children count in different ways: by ear, in workbooks, at the blackboard on a demonstration abacus, using the Cheerful Soroban electronic simulator, on a mental map (this is a graphic image of an abacus, with the help of which children imagine how the bones are moved on the abacus).

Image copyright Getty Images Image caption I wouldn't get a headache ...

"Mathematics is so difficult ..." You have probably heard this phrase more than once, and perhaps even pronounced it aloud yourself.

For many, mathematical calculations are not easy, but here are three easy ways to help you complete at least one arithmetic operation- multiplication. No calculator.

It is likely that at school you got acquainted with the most traditional way of multiplication: first you learned the multiplication table by memory, and only then you began to multiply each of the digits in a column, which are used to write multi-digit numbers.

If you need to multiply multi-digit numbers, then finding the answer will take a large sheet of paper.

But if this long set of lines with numbers going one under the other makes your head spin, then there are other, more visual methods that can help you in this matter.

But there are some artistic skills that come in handy.

Let's draw!

At least three methods of multiplication involve drawing intersecting lines.

1. Mayan way, or Japanese method

There are several versions regarding the origin of this method.

Some say that it was invented by the Mayan Indians who inhabited areas of Central America before the arrival of the conquistadors in the 16th century. It is also known as the Japanese multiplication method, as teachers in Japan use this visual method when teaching. junior schoolchildren multiplication.

The bottom line is that parallel and perpendicular lines represent the digits of those numbers that need to be multiplied.

Let's multiply 23 by 41.

To do this, we need to draw two parallel lines representing 2, and, backing slightly, three more lines representing 3.

Then, perpendicular to these lines, we will draw four parallel lines representing 4 and, slightly indented, another line for 1.

Well, is it really difficult?

2. Indian way, or Italian multiplication by "lattice" - "gelosia"

The origin of this multiplication method is also not clear, but it is well known throughout Asia.

"The" Gelosia "algorithm was transmitted from India to China, then to Arabia, and from there to Italy in the XIV-XV centuries, where it was called" Gelosia ", because it looked like Venetian latticed shutters," writes Mario Roberto Canales Villanueva in his book on different ways of multiplying.

Let's take the example of multiplying 23 by 41 again.

Now we need to draw a table of four cells - one cell per digit. Let's sign the corresponding number on top of each cell - 2,3,4,1.

Then you need to divide each cell in two diagonally to get triangles.

Now we first multiply the first digits of each number, that is, 2 by 4, and write 0 in the first triangle, and 8 in the second.

Then we multiply 3x4 and write 1 in the first triangle and 2 in the second.

Let's do the same with the other two numbers.

When all the cells of our table are filled in, we add the numbers in the sequence shown in the video and write down the resulting result.

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The first digit will be 0, the second is 9, the third is 4, and the fourth is 3. Thus, the result is 943.

Do you think this method is easier or not?

Let's try another multiplication method using a picture.

3. "Array", or table method

As in the previous case, this will require drawing a table.

Let's take the same example: 23 x 41.

Here we need to divide our numbers into tens and ones, so we will write 23 as 20 in one column, and 3 in the other.

Vertically, we write 40 at the top, and 1 at the bottom.

Then we will multiply the numbers horizontally and vertically.

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But instead of multiplying 20 by 40, we discard the zeros and simply multiply 2 x 4 to get 8.

Do the same by multiplying 3 by 40. We hold 0 in parentheses and multiply 3 by 4 to get 12.

Let's do the same with the bottom row.

Now let's add zeros: in the upper left cell we got 8, but we dropped two zeros - now we add them and we get 800.

In the upper right cell, when we multiplied 3 by 4 (0), we got 12; now we add zero to get 120.

Let's do the same for all other held zeros.

Finally, we add up all four numbers obtained by multiplying in the table.

Result? 943. Well, how did it help?

Variety is important

What can be said for sure is that all these different methods gave us the same result!

We still had to multiply a few things in the process, but each step was easier than when multiplying in the traditional way, and much more intuitive.

So why is it that few places in the world in mainstream schools teach these calculation methods?

One of the reasons may be the emphasis on teaching "mental calculations" - to develop mental abilities.

However, David Weese, a Canadian mathematics teacher working in public schools in New York, explains it differently.

"I recently read that the reason the traditional multiplication method is used is to save paper and ink. This method was not thought to be the easiest to use, but the most economical in terms of resources, as ink and paper were in short supply." Wiz explains.

Despite this, he believes that alternative multiplication methods are very useful.

“I don’t think it’s useful to immediately teach schoolchildren to multiply, forcing them to learn the multiplication table, but without explaining to them where it came from. Because if they forget one number, how can they advance in solving the problem? the Japanese method is necessary because with it you can understand general structure multiplication, which is a good start, "says Wiz.

There are a number of other methods of multiplication, for example, Russian or Egyptian, they do not require additional drawing skills.

According to the experts with whom we spoke, all these methods help to better understand the process of multiplication.

“It’s clear that everything is good. Mathematics in today's world is open both inside and outside the classroom,” sums up Andrea Vasquez, a math teacher from Argentina.