What? Is there a number kingdom? Who are there and what do they do?
why do monsters eat 24 and 44, and why don't they eat 5? Was the monster subdued later? Who subdued it and how? ......
This is a fairy tale that the reporter read when he was a child, and its name is "Eating Animals". When I think about it, I am afraid that the terrible "food-counting beast" will eat all the figures from my heart, hoping that I can find out its fatal weakness and save the citizens of several kingdoms.
Until recently, I didn't know that the author's name was Li Yupei. At that time, he was just an ordinary lecturer at Capital Normal University. Since the first popular mathematics book "Wonderful Curve" in 1977, he has published more than 1 popular mathematics books with more than 1 million words. However, over 6 years old, he still regards writing interesting math stories for children as his main job after retirement.
When the reporter called his home to ask for an interview, Miss Li replied shyly:
"Me? ..... Not qualified? 1
Two days later, in an ordinary room outside Beijing's North Fourth Ring Road, I met Miss Li, who was over sixty. He explained his job like this: leading children, especially preschool and primary school children, into the interesting world of mathematics.
"Mathematics itself is not boring. Why are so many children afraid?"
"My purpose in writing math fairy tales is simple, that is, to make children love math and make them feel that math is interesting and fun." Teacher Li came straight to the point: "Mathematics itself is not boring. Why are so many children afraid?"
isn't math boring?
I told him a child's words: I think mathematicians are just a group of people sitting in front of a desk all day, doing calculations on paper. How can you say it is not boring? "Do you know that the United States has a particularly famous mathematics popular science book called Aha! A brainwave? " Teacher Li asked.
I shook my head.
"There is a hero named Professor Quibell, who always has some interesting questions. For example, he said that all his animals except two are dogs, all except two are cats, and all except two are parrots. How many animals does he always keep? "
I'm just about to calculate.
Miss Li pointed to a title in a book and showed it to me: "□□□ +□□ = 1996. What are these two numbers?"
！ ! My head suddenly turned a little bit.
These two questions, which don't even seem to involve multiplication and division, are a little complicated and seem to have a little subtle relationship. Why, why are they so ... "strange"! Is there only one answer? !
"have fun?" Teacher Li used this word!
"There are many interesting things like this in mathematics. For example, the number 9, whenever it is a multiple of 9, the numbers on its various digits must add up to a multiple of 9. " I quickly gave a few examples in my mind: 18, 27, 36, 54 ... Hey, it seems that it's really the case that the dislocation in order is seeking order in complexity. The golden section in mathematics has created countless beautiful buildings and arts, such as Venus and Mona Lisa. Infinitely acyclic decimals have created fantastic pyramids ... This is the fun and wonder of mathematics. You feel that you can't control it, but it is always around you, and you will find yourself unconsciously applying it. Einstein gave such a definition to algebra:' Algebra is as interesting as hunting. The beast hiding in the Woods, you call him X, and then you approach it step by step until you catch it/"But what do our children face every day? What comes up is an example, or a formula. When the teacher tells you how to do it, he gives a few more words, so that the children can follow the gourd painting and then leave a few homework questions. This is the math class. What can you find interesting from it? Every day is such a content and program, how can you like it? How can you learn well if you don't like it? "
Our conversation has become a speech by Miss Li alone:
"Some people say, OK, then I'll tell something lively and interesting. He asked a bear to say a mathematical formula, or asked a bird to calculate a problem in front of the blackboard. This result is the same as that of a teacher standing in front of the blackboard and giving a lecture. Or is it a unilateral indoctrination of knowledge that has no application and no plot at all? How can it attract people? How can that kind of study not be rote learning?
"For example,' the sum of any two sides of a triangle must be greater than the third side'. I think it is best to use one of the most common examples in life, which is why everyone wants to get close to the road. You can draw several ways for them to choose, and then ask them why they all choose the most direct way. They'll say that's the shortest way. Why is it recent? How to prove it? "It is easy for them to understand, think and even draw inferences quickly when they are connected with the most common and applied things in their lives.
"Of course, there are some laws in mathematics that are difficult for children to grasp. At this time, we have to find some ways to help them remember their wishes."
When they first started to learn division and fractions, many children could not remember to install . "You can't be a divisor or denominator. Li Yupei wrote a fairy tale called Sleepwalking in Kingdom :
All the beds in Kingdom are bunk beds, but no one in the bunk bed wishes the protagonist Xiao Yi to be curious. Why doesn't anyone live there? The citizen of Kingdom explained that because can't lie under the score. Xiaoyi doesn't understand. Let's help him imagine that if the number on the fractional line is 2 and there is a number of 2/, such as A, then 2 = × A, but is multiplied by any number to get , so there can be no number of A. If the fractional line is , then the equation becomes = × A. Similarly, A is an uncertain number, so can't stay below the fractional line.
"Maybe they still don't understand the latter reason, but at least children can quickly remember that can't live in the' lower berth'-it can't be a denominator and divisor."
In the kingdom of , there are no men and women, because is neither positive nor negative;
Outsiders can only shake hands with people in Kingdom , but they can't hug, because shaking hands is equivalent to addition, but hugging is multiplication. When you hug with Kingdom , you become , and you can't go back.
the residents of the kingdom of are very light, no, it should be said that they have no weight, but as long as they stand behind other numbers, they can be 1 times heavier, and if they stand behind the decimal point, they can be 1 times lighter ...
"If these characteristics of are expressed in a way and language that children like, they will find it interesting and fun, and they may even think about something by themselves. Teacher Li said that one of his students accepted this view in his teaching, and before each math class, he put on an animated film "Donald Duck Roaming in the Kingdom of Mathematics" and began to lecture. Although an animated cartoon only lasts for more than 1 minutes, it attracts children at once, which is better than a lecture.
"He has no curiosity, interest or even fantasy about the unknown world. People trained in this way can only be artisans, but not architects. 1
Among Li Yupei's popular science works, one kind is his original-mathematical fairy tales.
"It can be said that there are many other kinds of scientific fairy tales, but few mathematical fairy tales." He is very sure of his work. "I think this is exactly what I am good at and like."
"Mathematics itself is an abstract and accurate science, but fairy tales are daydreams. Isn't this contradictory?" "No contradiction! 1 Li Yupei immediately produced the evidence-
The German mathematician Wilslas said: A mathematician who has no taste of a poet is by no means a perfect mathematician.
Lenin also said: Fantasy is an extremely valuable quality. Some people think that only poets need fantasy, which is unreasonable and stupid prejudice! Fantasy is also needed in mathematics. Even without it, it is impossible to find that most of the fairy tales of Calculus are fantasy, exaggeration and personification, but it does not mean that all its contents are irrelevant fantasies. " Li Yupei, for example, said, "The famous English fairy tale Alice in Adventure is full of absurd experiences, but because its author is a mathematician at Oxford University in England, it contains many mathematical interests, and it has been quoted by many professional papers on mathematics."
"Children want to fly into the sky, dive into the ant nest, and understand what insects say. They often regard the bench as a horse, the clouds in the sky as a flock, the rag doll as a real doll, and tell them the truth. Everything is alive in their minds. Why can't they use this feature to turn rigid and boring numbers into life?"
Someone once said: To say that math is boring is equivalent to standing outside the garden and saying that the flowers are not beautiful.
Li Yupei thinks that children should be led to the big garden of the kingdom of mathematics by taking advantage of their nature of liking fantasy and having fun. The War between Rational Numbers and Irrational Numbers is a famous work by Li Yupei 22 years ago-
The protagonist Xiao Yi wakes up and finds a war on the hillside outside the window. Take a closer look, while waving the big flag of "rational number", while waving the big flag of "irrational number".
why are rational numbers and irrational numbers fighting? Oh, it's about the name.
Listen to what π, commander of irrational numbers, said: "We irrational numbers and rational numbers are also numbers. Why are they' rational' and we' unreasonable'? What kind of rudeness are we? "
right! How can irrationality exist! Xiaoyi is also thinking about it.
"Because people first discovered rational numbers and didn't understand them when they saw our irrational numbers, they chose such an ugly name as irrational numbers. But now that people have fully understood us, it is time for us to take off the "unreasonable" hat. The idea of Commander 1
π is to rename rational numbers as "ratio numbers" and irrational numbers as "non-ratio numbers": "The most fundamental difference between rational numbers and irrational numbers is that all rational numbers can be converted into the ratio of two integers, but irrational numbers can't be converted anyway.
The more she thought about it, the more reasonable she felt. She decided to write a letter to the international mathematical organization after returning home to help irrational numbers achieve their wishes.
This article is still selected by many popular science books.
Teacher Li explained: "Writing mathematical fairy tales cannot be divorced from mathematics itself, which is the most difficult. Rational number and irrational number are a difficult point in primary school mathematics. Because the name is strange. I thought, can you write a fairy tale to make it clear? So there were two factions fighting over the name.
"There must be a commander in a war. Who will be the commander? Among rational numbers, the most important number is the natural number 1, and the number that children learn first is also 1. With 1, all natural numbers such as 2, 3, 4, etc. can be generated, and then scores can be generated. The commander of rational number is of course 1; So who will be the commander of irrational numbers? Only children know a little about π. 1
Citizens in the digital kingdom have their own distinctive characteristics because of their different "images": the number is cheerful, cheerful all day, and can eat and sleep; Count 1 sentimental, unhappy all day, eating less and unable to sleep; Count 7, a little old man, hunched, unable to walk, can only hop on one leg; Number 8 is a tumbler, with a bald head, but infinite wisdom ...
"The most terrible thing about modern education is that it takes up all the children's time. Every day, they have to do homework late at night, and they have to make up lessons on Saturday and Sunday. Otherwise, they have to learn piano and painting. Where can children have their own time? After a long period of time, learning and living will make you unhappy at all.
"We often think that a teacher with good teaching results is to make the students understand everything in the textbook, and there is no problem at all. But in fact, this is probably the worst teacher. Because the children have no thoughts and ideas except what the teacher taught them. What about the end? He has no curiosity, interest or even fantasy about the unknown world. People trained in this way can only be artisans, but not architects. 1
Li Yupei believes that the best primary and secondary education should be popularized.
"why? Because the purpose of popular science is to tell him all the stories, allusions and interesting stories related to the knowledge to be learned, to arouse their interest, and then he may imagine, think and learn actively. "
How many inventions and great ideas come from fantasy!
Let's count them together: TV sets, washing machines, fax machines, airplanes, telephones, steam locomotives ... and even the discovery of electricity. So, why shouldn't there be illusions in the field of mathematics? "
The famous American popular science scientist Ma Nail Gardner wrote in Aha! In the preface of A brainwave, the origin of the title is explained as follows: "At first, the proof of a certain theorem was a paper of more than 5 pages, full of special reasoning, but a few years later, another unknown mathematician suddenly had a brainwave and made a concise and beautiful solution with only a few lines. Now psychologists call it the' aha' reaction. This is really once understood, you can't' aha', and the title comes from this. "
"What does this brainwave' aha' reaction depend on?" Teacher Li asked me.
"Is it a fantasy?" "It's a bold fantasy, plus hard thinking."
"I hope that what children get from me is more thinking methods and concepts."
"What if children only read your story and ignore the math in it?"
"that doesn't matter. Read math if you can understand it, and read stories if you can't understand it. My books are not textbooks, and they don't take exams. They can read whatever they like. " Teacher Li said confidently. "My book is not designed for students who like mathematics and study well. I hope all the children can love it and understand it. " "Then you can't achieve your goal of inspiring their interest in mathematics?" I asked anxiously. "Then what do you think is the purpose of learning mathematics?" Teacher Li asked me.
I stared at him and waited for him to say.
"Learning mathematics, on the one hand, is mathematical knowledge, on the other hand, is more important. In life, it is enough to have some basic mathematical knowledge, such as knowing how to calculate, knowing how much to pay for things, and how much money people should give you. But mathematical thought is a very important tool in one's life. That's why it's necessary from primary school.