In the 1978 National Mathematics Competition, there was a question in the examination paper, which overwhelmed many candidates.
Mr. Hua Luogeng, the author of the question, also thought it was too difficult, and it took him more than 20 lines to solve it. At that time, there was a mathematician who wondered, is there an easier way to solve this problem?
In the end, he solved it with his elementary school math knowledge, using only two lines. What he did not expect was that his "little trick" actually won the first prize of the Natural Sciences of the Chinese Academy of Sciences and the second prize of the National Natural Sciences, and was even written into textbooks for promotion.
This mathematician is Zhang Jingzhong, an academician of the Chinese Academy of Sciences and a famous mathematics educator.
Academician Zhang Jingzhong
Based on this topic, Zhang Jingzhong created the solution idea of "elimination method", which has now become a compulsory course in the Olympic numbers.
Not only is it brilliant in China, but international math teachers also recognize the simple and practical "elimination method". Like Chinese children, foreign students are also afflicted by mathematics. In the 1950s and 1960s, the United States used a lot of manpower and material resources to do a good job in mathematics education, but with little success.
The United States has money and people, but it doesn't know how to do it.
Once Zhang Jingzhong's "elimination method" was proposed, it was internationally regarded as a breakthrough in the computer proof of geometric theorems, and even considered to be "the most significant breakthrough in the field of geometry in the past two hundred years".
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Zhang Jingzhong's ability to become an excellent mathematician is inseparable from his diligence and great mathematical talent.
In 1954, Zhang Jingzhong from Runan County, Henan Province, was admitted to the Department of Mathematical Mechanics of Peking University, and this year's Department of Mathematics of Peking University later produced 6 academicians.
Zhang Jingzhong is not tall, thin and small, usually showing people with a bald head, and everywhere he goes, he is a Henan cavity. Don't look at his appearance, but his results are very good. In his sophomore year, Zhang Jingzhong published a mathematical paper in the "Mathematical Bulletin", which was calculated in the department.
What is even more unexpected is that Zhang Jingzhong still has a talent in literature and art, and as early as the age of fifteen or sixteen, he joined the literary and art propaganda team in his hometown of Runan, and went from village to village to perform programs. He loved to write poetry and published it, so he became a celebrity in the mathematics department.
The good university life met with twists and turns, because of "inappropriate speech", Zhang Jingzhong was sent to the distant Xinjiang labor reform. However, the young Zhang Jingzhong is still full of optimism about life.
In 1974, Zhang Jingzhong was a front-line math teacher in Xinjiang, teaching junior high school, and he found that most students had difficulty learning mathematics.
When I was in elementary school, it was not obvious, everyone was similar, and after learning geometry and algebra in junior high school, the mathematical scores between students began to diverge, and the gap widened.
Why is that?
After observation and reflection, Zhang Jingzhong believes that the mathematical knowledge in the textbook is not created for students, so it is difficult to learn. In order to make students understand and learn, teachers have adopted the method of instilling basic theorems into students as knowledge, but the effect is average, and mathematics has become "old and difficult" since then.
Therefore, in order to change the status quo of mathematics teaching, it is necessary to recreate this mathematical knowledge to adapt to the child's acceptance level.
There is a view that after thousands of years of tempering, these contents have matured and nothing can be changed.
Zhang Jingzhong did not agree, and he summed up a new set of logic in practice.
Start with calculations and then shift to reasoning, easy before difficult. For example, to prove a full equal triangle, it takes three conditions and is not easy to master.
Zhang Jingzhong first proposed a condition to reduce the difficulty, and then the next step of reasoning, and proposed the common side theorem, the common angle theorem, and the common height theorem.
"One condition is obviously more learnable than three, and reasoning is logical and very effective. This was very convenient to solve the problem, and later became a compulsory topic for the Olympiad. ”
He advanced the sine that needed to be studied in the third grade to the first semester of the first grade, and used the rectangular area formula that the elementary school was already familiar with to guide the students to understand the sine step by step. In the exam, all of the more than 50 students in the class answered correctly.
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In 1979, Zhang Jingzhong was appointed as a lecturer in the Department of Mathematics of the University of Science and Technology of China, teaching "calculus", further sorting out and summarizing the methods tried in Xinjiang, and publishing relevant articles.
This article on students' "way of thinking" breaks the solidified model of teaching mathematical concepts, and in a plain and easy-to-understand way, allows children to truly understand certain mathematical concepts, rather than rote memorization.
In 1989, Zhang Jingzhong published "From Mathematics Education to Educational Mathematics", summing up his 15 years of teaching practice experience and formally putting forward a new perspective on "educational mathematics".
What is Educational Mathematics?
His understanding is to work on simplifying mathematics, transforming it, making it easier.
"Mathematics can be compared to eating walnuts, and walnuts have to be smashed open to eat them. Some walnut shells are so closely linked to the walnut kernels that it is difficult to eat if smashed. Mathematics education to study, is how to smash walnuts to eat walnut kernels; and education mathematics, is to study the varieties of improved walnuts, so that walnuts are more delicious, more nutritious, easier to smash open and eat clean! ”
In mathematical learning, there are two obstacles.
One is boring and the other is difficult.
Nowadays, students are facing the pressure of exams, it is difficult to feel the fun of mathematics, and their brains are filled with "formulas, concepts, and problem-solving routines". But learning mathematics is not a process of rote memorization, but a process of understanding, challenge, and interest.
Zhang Jingzhong believes that learning mathematics is a lot of fun, for example, it can give people a great shock.
He often gave the example of Einstein studying middle school geometry. The teacher told Einstein that "the three high lines of the triangle must intersect at one point", and Einstein was greatly shocked, and he thought that there must be more such mysteries in the world that have not yet been discovered, and such a passion for exploration inspired Einstein to pursue scientific truths throughout his life.
So, how to pass on the mathematical pleasures that Einstein enjoyed to the majority of students?
One might say, how does the average student compare to Einstein's IQ? The talent difference is too far, so there is a reason why we can't learn math well!
This involves a question, mathematical learning, do you need talent?
Zhang Jingzhong believes that mathematics is different from music, chinese and other disciplines, if there is no talent, it is difficult to become a singer; even if you go to the best college of literature, you may not be able to become a famous poet.
The mathematician Gauss said that any normal person who insists on continuous thinking will reach the same conclusion.
An obvious example is that Hua Luogeng Middle School only scored more than 60 points in mathematics, and then suddenly discovered his mathematical talent, dropped out of school, helped in the family shop, studied mathematics books every day, and was called "Luo Duzi". Hua Luogeng's deep thinking made him eventually become a generation of mathematical masters.
Hua Luogeng
Zhang Jingzhong is also like this from the perspective of teaching practice for many years, there are no students who can't learn mathematics well, only teachers who can't teach.
The mathematics textbooks currently used are stacked with conceptual terms and "teach mathematics with a straight face", so they are mysterious and frightening. Zhang Jingzhong believes that mathematics textbooks should be moderately colloquial in language, and mathematics should be innovated, and attention should be paid to changes in concepts and methods to make it more suitable for children and make mathematics easier.
How can it be made easy? He summarized several principles.
First, it is easy to be familiar with it.
Second, it's easy to be simple.
Third, it's easy to figure it out.
Fourth, intuitive is easy.
The theory is easy to understand, whether it can be successful or not depends mainly on how to do it. The education reform involved the whole body, and few schools dared to take the risk of letting Zhang Jingzhong experiment.
A particularly good school was meant to participate, but parents and students were worried that they could not afford to lose. In the end, more than 100 students from several classes of a school in Guangdong Province were selected to do experiments in educational mathematics, and in this regard, Guangdong still dared to be the first.
This experimental class is a "poor class" with an average score of more than 60 points in mathematics admission. At that time, the school signed an agreement with the parents that if the students in the experimental class could not enter the high school, the high school would take them in.
It is this "affordable" poor class, after the mathematics teaching experiment in Zhang Jingzhong, it is like "enchanted", not only the children's grades are improving by leaps and bounds, but also the interest in learning mathematics is also much stronger.
In the middle school entrance examination, these children graduated with an average score of more than 130 points and a minimum of more than 120 points in mathematics. "This is a matter of 2015, and now, that group of children have been admitted to universities, and it is a very good domestic excellent university, with an excellent rate of 100%."
Zhang Jingzhong's educational mathematics concept achieved initial success, and later Zhang Jingzhong conducted experiments in Guizhou, Chengdu and other places, and achieved remarkable results.
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There are two types of mathematicians in the world.
There are many mathematicians in the first category, who continue to climb the peak of mathematics and challenge the limits of human beings; the second type of mathematicians are very few, and they constantly use simple methods to narrow the distance between mathematics and ordinary people, so that people can appreciate the use of mathematics, the beauty of mathematics, and the spirit of mathematics.
Zhang Jingzhong is the second type of mathematician, a mathematical master who is full of enthusiasm for mathematical education and has spent his life popularizing mathematical knowledge.
However, some people believe that scientists should concentrate their energy on scientific research to produce results, and that engaging in science popularization is "not doing the right thing", and it is impossible to continue scientific research.
Zhang Jingzhong is very disagreeable with such a statement, he believes that scientific research and science are all surnamed Ke, and it is indispensable to complement each other. Scientists do scientific research is the main work, but science popularization is more responsibility.
And to be able to do this, it is inseparable from his decades of silent efforts. In the two roads of scientific research and science popularization, he has achieved a good combination.
Because he has been a beneficiary of popular science since he was a child, he has read popular science books such as "100,000 Whys" and "What Time" and "How Cars Run"; Gu Junzheng's "Scientific Interest" in China, Liu Xuanyu's "Mr. Ma on Teaching" and "Mathematics Garden", Wang Junqian's "Mathematical Train" and other popular science books have brought far-reaching influences to his life.
These books are not only interesting to read, but also can bring a long aftertaste and repeated thinking, and there are so many unexpected mysteries in things that originally look ordinary. Reading these books prompted Zhang Jingzhong to learn more scientific knowledge and also stimulated the desire to create.
He found that writing popular science works is very thoughtful, and it is not easier than scientific research.
"For example, "The Mathematician's Vision", sixty thousand words were written for five years. To make middle school students understand, college students and graduate students also feel that there is something new, it is necessary to work hard. ”
Nowadays, Zhang Jingzhong has many identities, including academicians of the Chinese Academy of Sciences, doctoral supervisors in computer science and mathematics, famous computer scientists, mathematicians, and mathematics educators.
He valued mathematics educators most.
The key is that he understands students, understands mathematics, and tells the method and is grounded, so he is welcomed by many schools and students across the country.
Wang Xiaochuan
Wang Xiaochuan, CEO of Sogou, is a recognized academic bully who has won the gold medal of the 8th International Olympiad in Informatics (IOI) and the first prize of the China Youth Invention Competition established by Yang Zhenning.
Behind these, it is inseparable from the basic discipline of mathematics.
After decades of cultivation in the lecture hall, Zhang Jingzhong taught Tao Li all over the world, but few people knew that Zhang Jingzhong was Wang Xiaochuan's mentor.
In the junior high school stage, Wang Xiaochuan once received Zhang Jingzhong's guidance on his learning mathematics, which benefited him a lot.
"Teacher Zhang Jingzhong's profound mathematical skills, understanding of mathematics, and my points have profoundly affected me, and I especially hope that Teacher Zhang's mathematical ideas will affect more people, more teachers and teenagers."
Wang Xiaochuan made such an appeal in public.
Over the past few decades, Zhang Jingzhong has been enthusiastic about popular science education, published more than 20 popular science works, in 1990 was rated as a popular science writer with outstanding contributions since the founding of the People's Republic of China, and in 1994 by the China Children's Publishing House as one of the top ten golden writers.
In 1995, the "Zhang Jingzhong Educational Mathematics" series of books ("Exploration of Educational Mathematics", "New Road of Plane Geometry", "Research on The Solution of New Road of Plane Geometry", "Basic Research of New Road of Plane Geometry") was awarded the first prize of the Ninth China Book Award and the first prize of the "National Education Book Award".
In order to make more children no longer "afraid" of mathematics and fall in love with mathematics, Academician Zhang Jingzhong combed through decades of teaching practice experience, summarized and improved many methods of "making mathematics easier", and collected them into a popular science book such as "Mathematics Hidden in Life: Zhang Jingzhong Teaches You to Learn Mathematics".
Academician Zhang Jingzhong started from the familiar life scenes, told an interesting mathematical story, and vividly introduced how to find and draw extraordinary conclusions from these simple problems.
Grandpa Academician wants to tell children that mathematics is no longer an abstract and boring formula on paper, but a fun game that is closely related to daily life.
Therefore, the book "Mathematics Hidden in Life: Zhang Jingzhong Teaches You to Learn Mathematics" is not about solving a certain type of mathematical problem, it tells us the idea and method of thinking about mathematical problems.
Because there is only one necessary condition for learning mathematics well, that is, to be interested in mathematics, and once you are interested, you may become a mathematician.
"Now we are talking about artificial intelligence, involving mathematics, statistics, logic and other disciplines, in the final analysis, it is still mathematics."
——Zhang Jingzhong
In this book, Academician Zhang Jingzhong not only carried out the popularization of mathematics in terms of content, but also tried to express poetry and beauty in language, and the language of prose culture will make it easy for students to enter the forest of mathematics.
It can be said that reading this book will not only be able to learn mathematics well, but also increase the level of composition by a large margin.
Academician Zhang Jingzhong told us with decades of experience in educational mathematics: "Cultivating children's interest is the most effective way to learn mathematics well." ”
Parents may wish to start with this book, explore the magic of "making mathematics easy", let children fall in love with mathematics, learn mathematics well, and perhaps this magical treasure book that instinctively stimulates children's interest.
"Mathematics Hidden in Life: Zhang Jingzhong Teaches You to Learn Mathematics"
Suitable for children aged 8-14 years old to read and use,
Academician Grandpa presented gifts to children,
Let students fall in love with mathematics in games,
Learn to see things through the eyes of a mathematician.
In fact, "Mathematics Hidden in Life: Zhang Jingzhong Teaches You to Learn Mathematics" is one of the "Chinese Masters Science Series" (all 14 volumes). The primary and secondary school stage is the key stage for children to establish their own knowledge system. If there is a famous person's click, it will undoubtedly be more effective with half the effort.
Classic Reading Books for Primary and Secondary Schools: Chinese Masters Science Popularization Series (all 14 volumes)
It just so happens that the authors of the "Chinese Masters Science Series" have concentrated the top masters and academicians in many fields, and the great scientists have popularized the science books for teenagers and cultivated the children's scientific spirit.
When children encounter problems in their lives that cannot be solved, they can follow many masters to find answers.
For example, how does nature use its unique language to convey the news of seasonal changes to humans?
Primary and secondary school science classic reading series: "The Language of Nature" by Zhu Kezhen
The answer is hidden in Zhu Kezhen's "The Language of Nature", Zhu Kezhen's grandfather is an academician of the Chinese Academy of Sciences, the founder of modern Chinese geography and meteorology
If you have questions about engineering and construction, such as whether there is a bridge that cannot be built? You can listen to Grandpa Mao Yisheng talk about the principle of building bridges in "Bridge History", Mao Yisheng Grandpa is a world-famous bridge expert Oh ~
Maybe you still have questions about the earth, especially the age of the earth, this question can definitely find a satisfactory answer from Li Siguang's "Crossing the Horizon". Grandpa Li Siguang, you must have heard of it, he is a famous geologist in China
Primary and secondary school science classic reading book series: "Crossing the Horizon" by Li Siguang
No matter what questions you have, the big names in science will answer them for you. This set of books is a gift from the master of popular science to children, helping children to embark on the road of scientific growth faster and better.
Attached: Bibliography of the Chinese Masters Science Series (all 14 volumes).
"Mathematics Hidden in Life" by Zhang Jingzhong (Famous Mathematics Educator)
"Mathematical Garden Travels" by Ma Xiwen; Wang Meng et al. comments
"Magical Mathematics" by Tan Xiangbai
A Brief and Interesting History of Chemistry by Ye Yonglie
"The Adventures of the Bacteriological World" by Gao Shiqi (Chinese Science Popularization Bull)
"Crossing the Horizon" by Li Siguang
"Where Did Grandpa's Grandpa Come From" by Jia Lanpo (one of the discoverers of the Peking man's skull)
"The Footprints of Time" by Tao Shilong
The Language of Nature by Zhu Kezhen
The Forest That Woke Up (United States) by John Burroughs translated by Wang Junjian Yang Yong
"The History of Bridges" by Mao Yisheng
"100,000 Whys" by Mi Ilin; translated by Wang Wen
"The Secret of the Ocean" by Lei Zongyou
"The Thief Who Stole The Brain" by Pan Jiazheng (Chief Engineer of the Three Gorges)
This set of books has a total of fourteen books, the original price of 319 yuan, the current price of 158 yuan free shipping, on average, 1 book is only 10 yuan. It includes mathematics, meteorology, architecture, chemistry, geography, biology and many other disciplines.
All books are written by the master himself, using in-depth and simple language and rigorous scientific logic to help children establish their own knowledge system, so today we specially recommend this set of "primary and secondary school science classic reading books" written by China's top scientists to help children embark on the road of scientific growth.
Reading in large characters and displaying illustrations show more scientific rigor
Eye-catching yellow paper, cherish the eyes of children
It can be said that it is very sweet!
Please click on the link below to purchase:
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Brain Hole Historical View Recommendation: Chinese Master Science Series [all 14 volumes] ¥158 Purchase