Learning mathematics can be compared to eating walnuts. Walnuts must be broken before they can be eaten. Some walnut shells are closely connected with walnut kernels. Chengdu people vividly call it "rice planting walnut". If they are not properly crushed, if they are broken, they will taste bad. Mathematics education should study how to smash walnuts and how to eat walnuts; And educational mathematics is to study and improve the varieties of walnuts, so that walnuts are better to eat, more nutritious and easier to eat!
Keywords: popular science and scientific research
When I was a child, reading popular science books was my interest, but now writing popular science books is my responsibility.
Yangcheng Evening News: Academician Zhang, how did you start writing popular science?
Zhang Jingzhong: I am mainly engaged in scientific research. Society has provided us with the conditions and environment for scientific research, and we certainly have the responsibility to explain to you the situation of the research object and the significance of the research work. The state requires that a popular science book must be written when climbing a project. I think this regulation is very good, which shows that popular science work is not only the responsibility of popular science writers, but also the responsibility of scientists.
Of course, I have my own reasons for doing popular science work. When I was a child, I liked reading popular science works. Fables's books let me see a novel world, and Ilya's works let me know that many ordinary things contain extraordinary stories and truths. Popular science books inspire me to think, to explore, and to have a desire for research and innovation. I often think that if I can publish a book one day, I will also write a good popular science book. In this way, I put the responsibility of writing popular science books on myself.
The interesting mathematics series edited by Professor Zhang is as follows:
1, math serial; 2. "Beauty in Mathematics"; 3. Rubik's cube, etc. 4. Romance in mathematics; 5. Ten interesting random questions.
It is not easy to read a popular science book and write a dozen lines. For two and a half days.
Yangcheng Evening News: Scientific research consumes a lot of your energy. Can you still find time?
Zhang Jingzhong: It's really not easy to write popular science works. How to choose a topic and how to make an analogy, we must think twice before making changes. Some things were written by great scientists. Do you dare, teach fish to swim? Can you give readers new inspiration? Both are challenges. For example, Zu Chongzhi, an ancient mathematician in China, pointed out that the score of 355/ 1 13 is a good approximation of pi, which is called density. What is the confidentiality rate? This is a good popular science topic. Math master Hua pointed out that among all fractions with denominator less than 366, there is no fraction closer to π than density. To illustrate the reason, he used Diophantine theory in number theory. Later, in a popular science book, another famous mathematician further demonstrated by the method of continued fraction that among all fractions with denominator less than 6000, there is no fraction closer to π than density.
Can you explain the benefits of secrecy more fully in a simpler way? After repeated thinking, I found that I can simply demonstrate a better conclusion with junior high school students' mathematical knowledge: among all the scores with denominator less than 16500, there is no score closer to π than the secret rate! It is also pointed out that there is a fraction whose denominator is 16604, which is indeed closer to π than density. This truth was only written in a dozen lines in the book, but it took more than two days to remember it.
Yangcheng Evening News: Popular science writers need not only scientific research, but also humanistic literacy ... What do you think of the relationship between scientific spirit and humanistic literacy?
Zhang Jingzhong: Generally speaking, science pursues truth, humanity pursues goodness and art pursues beauty. Truth, goodness and beauty should be the pursuit of everyone, and the three complement each other. In fact, many scientists write popular science articles, but it takes too much time and energy to write well, and social evaluation is often not as good as scientific research papers. For example, the title evaluation does not recognize popular science articles. Under this guidance, most people who can do research are naturally unwilling to work hard on popular science.
Writing a good popular science article may require humanistic accomplishment and a little artistic accomplishment, but more importantly, it is an understanding of the nature of scientific achievements and an innovative spirit.
I have written a paper and repeated to my predecessors what Hua implicitly instructed me to study in the future.
Yangcheng Evening News: I heard that you started writing papers when you were studying at Peking University, and you also dealt with the great mathematician Hua?
Zhang Jingzhong: When studying analytic geometry, I saw a theorem in a textbook, saying that if the function f(x) satisfies the function equation f(x+y)=f(x)+f(y) is continuous, it must be a "homogeneous linear function", that is, f(x)=a? I think, what will happen if f(x) is discontinuous? Applying the "arbitrary axiom of choice" in the set theory that I saw after class, I solved this problem. So I wrote an article and sent it to advances in mathematics, which was published quickly and smoothly.
Soon, the editorial department wrote that there was a letter from a reader asking where the problem solved by this article came from. What did the predecessors do? I wrote back that the question was raised by myself and I didn't know the works of my predecessors. The editorial department also wrote that when doing research and writing papers, it is necessary to understand the background of the research problem and the relevant achievements of predecessors, which is responsible to readers and should be understood when doing research. So I went to the reference room to look up documents. Year after year, three weeks ago, I found a German document at 1920, which has solved this problem. I wrote the results to the editorial department, and the editorial department posted a notice in the journal saying that the author had written a letter stating that the results were repeated with someone's previous works and apologized to the readers as the end of the matter.
Senior Shao Pincong, who later worked in the Institute of Mathematics, revealed to me that the letter from readers mentioned by the editorial department was actually the opinion of Mr. Hua, the editor-in-chief of the magazine. Because he went abroad, he didn't read my article until it was published. When he found that his work was repeated by his predecessor, he instructed the staff to write to me, urging me to learn the basic rules of doing research work. This experience has benefited me for life. Teacher Hua's enthusiasm for after-school study makes me unforgettable!
Keywords: Olympics
It is biased to attack the Olympic Games blindly.
The examination system is even more to blame.
Yangcheng Evening News: In recent years, "Olympic Mathematics" has become a common practice in various places. Although there is no lack of opposition, the limelight is still strong. what do you think?
Zhang Jingzhong: At one time, there were many voices attacking the math contest in the media. I have noticed that some education experts even think that math competitions are more harmful than pornography and gambling. My first thought is that there are many things worth opposing in China, which are far from math competitions in terms of priorities. Read these opponents' views carefully again: what they oppose is actually some math competition training that misleads children for profit.
Mathematics competition is not suitable for all students, it is an activity organized for a few mathematics lovers among teenagers. These math enthusiasts are estimated to be no more than 5% of the 200 million primary and secondary school students.
The negative impact of overheated training activities in mathematics competition is related to many factors such as the entrance examination system and the over-concentration of educational resources, and this account can not be regarded as the head of mathematics competition. For teenagers' extracurricular interest activities, the positive countermeasures should not be to limit the blockage, but to open up sources and divert resources. Carry out a variety of extracurricular activities, such as piano competitions and animation competitions. So that more teenagers can get their place. If they are all successful and recognized as mathematical competitions, the problem of overheating of mathematical competition training activities will naturally be solved or alleviated.
Olympic mathematics learning should not be restricted.
The reflection is the bonus for winning the prize.
Yangcheng Evening News: When many parents choose interest classes for their children, they often choose items that can be scored in the college entrance examination and senior high school entrance examination.
Zhang Jingzhong: This still shows that there are fewer successful games and fewer recognized games. In fact, all disciplines can hold Olympic Games, such as physics Olympic Games, chemistry Olympic Games and computer Olympic Games. At present, it is not developed enough and its recognition is not high. I think the information technology competition should be recognized next, because there are many children who are suitable for learning information technology and software, which will far exceed 5%, and there is a great demand for such talents in society.
Many children got together and signed up for the Olympic math training class. I understand that most of them don't really understand. However, there are advantages. When he returns to class after studying, the original things will feel relaxed. Although he can't do the topic of the Olympics, at least he knows there is such a topic, so he can ask questions like this to broaden his horizons.
I don't think the olympiad should be restricted. What needs to be reflected is the practice of adding points to the college entrance examination and senior high school entrance examination after winning the Olympic Games. Without extra points, there will be no people who study for grades, and parents will not be so blind in registering. Those who are really interested and have special skills are willing to learn without extra points.
Keywords: educational mathematics
The difficulty in mathematics is that the shell is too hard.
We should study how to open it more easily.
Yangcheng Evening News: Some people in the education circle think that mathematics in primary and secondary schools is difficult, which makes children have a headache. Do you agree?
Zhang Jingzhong: I think junior high school is easy, but senior high school is difficult. It's easier to learn in class, but the exam is difficult. Students can't get good grades only by what they read in textbooks, so they have to make up a lot of extra-curricular things.
Mathematics itself is more difficult, such as 2/3+3/2. According to general thinking, it should be numerator plus numerator, denominator plus mother. But this is not right, we should divide it first. My experience is that mathematics itself is very difficult, so we must find ways to make it simple and change the organization of mathematical knowledge.
The organization of knowledge is closely related to the difficulty of learning. For example, in English, the names of 12 months are January and February .................................................................................................................................................. If we improve it: it is called Monthone in January, Monthtwo in February, and so on. We can understand it right away and learn it much easier by remembering it. So is the language of life, and so is the language of science-mathematics?
Foreign education also faces the problem of difficult mathematics. Since the 1950s and 1960s, the United States has invested a lot of manpower and material resources to do a good job in mathematics education, but with little effect. A famous American mathematician said that we have money and people, but we have no direction. I think so too. The key to their failure is that they have not found the right direction. They only study how to teach mathematics, without considering transforming mathematics itself to make it easier. The concept of "educational mathematics" that I put forward in 1989 is to make mathematics simple.
Yangcheng Evening News: How to understand "Educational Mathematics"?
Zhang Jingzhong: Simply put, it is to transform mathematics to make it more suitable for teaching and learning. Learning math can be compared to eating walnuts. Walnuts must be broken before they can be eaten. Some walnut shells are closely connected with walnut kernels. Chengdu people vividly call it "rice planting walnut". If they are not properly crushed, if they are broken, they will taste bad. Mathematics education should study how to smash walnuts and how to eat walnuts. And educational mathematics is to study and improve the varieties of walnuts, so that walnuts are better to eat, more nutritious and easier to eat!
Committed to making mathematics simple.
I hope thousands of students will benefit from it.
Yangcheng Evening News: You have put a lot of energy into math education and popular science. In recent years, you have devoted yourself to the research and development of the teaching tool "Super Sketchpad". Do you regard it as your career?
Zhang Jingzhong: Mathematics education, popular science and teaching tool "Super Sketchpad" are all theoretical studies. For example, no one has developed such a system to answer junior high school students' math questions with computers. The key is to use what students have learned and solve problems automatically in a way that students understand, which is very difficult.
It is generally believed that trigonometry is difficult to learn in middle school. Originally, junior high school students had to learn to solve arbitrary triangles, but now this content is put into high school, but everyone thinks it is too difficult. If this part is easy, primary school students will understand it easily! This is a scientific research topic. I have studied this problem for many years, and now it has been solved. The preliminary teaching experiment shows that the new method makes it easier for students to understand triangles.
It is necessary to study how to make mathematics easier. This is true of elementary mathematics, and so is advanced mathematics. Newton, Lagrange, Fermi and Courand all made great efforts to make calculus easy to understand. Hua personally compiled advanced mathematics textbooks and tried to write new ideas. Academician Lin Qun has been doing this for more than ten years, and he will talk about this problem after studying in middle school. It must be very difficult to improve a subject that has developed for hundreds of years on the basis. Once progress is made, it will benefit thousands of students in Qian Qian, and its significance is immeasurable. Learning can be fun, but it's not easy.
Yangcheng Evening News: Do you want to create "painless mathematics"?
Zhang Jingzhong: Yes, it can reduce the pain of study. But I don't believe that learning is easy. Real learning requires hard work, and you can only learn superficial things if you want to relax. But if the learning method is right, it will be more efficient and interesting.
There are two kinds of writing popular science works, one is to put interest outside science to adjust the mood of learners; The other is to find out the interest in science. It is the interest in knowledge itself that makes learning interesting. The latter is the direction of my efforts.
Yangcheng Evening News: I heard that you especially like being a teacher. Are you willing to talk whether you are invited by middle school or university?
Zhang Jingzhong: This is also learning and research. Teaching and learning learn from each other. A great mathematician like Chen Shengshen must teach students calculus. When I was studying in Peking University, the first-year courses were taught by Academician Jiang Zehan and Academician Cheng Minde. At that time, there was no need for professors to give much SCI (Science Citation Index) and how much project funds to fight for. Professors mainly taught and educated people. Unfortunately, it is difficult to do this now.