Qiu Chengtong has come to China for many times to give speeches on Sino-American education. I have to admit that some of his views are quite intense. For example, many people think that students in China do better in math, physics and chemistry than children of the same age in the United States, while students in China have much more solid basic knowledge but poor innovation ability. Qiu Chengtong unceremoniously poured cold water on this view: "This is a terrible self-anesthesia for many years! I don't think the basic knowledge of China students is very good! "
He said: "The best students in America are really excellent. In this way, whether in the United States or China, the students who can enter Harvard University should be the best students in these two countries. Compared with the best two people, the basic knowledge of American students will never be worse than that of China students, on the contrary, it will be much stronger. "
There is also a saying in education and society that primary and secondary school students in China learn much more math and physics than students in the United States. For example, at a certain age, children in China have learned the mixed operation of addition, subtraction, multiplication and division, while children in the United States stumble in addition and subtraction.
Qiu said: "This is also wrong. In the better primary and secondary schools in the United States, China students should finish all the lessons they have learned and learn flexibly. They are definitely not cramming like China. In some good schools, students in grades 1 1 and 12 learn calculus very well, but I heard that not all high school students in China learn calculus. "
Qiu Chengtong also repeatedly emphasized in some speeches that Chinese, mathematics and writing are the three most important subjects for primary and secondary school students.
He believes that in western education, children's expressive ability is trained from primary school, and their language and writing skills are well trained. Generally speaking, children who have received this kind of training can express their ideas and scientific research results at the conference without difficulty, so they can express their opinions freely in class and get the attention of teachers and classmates. We often talk about why China students go to the United States for graduate studies, and the discussion is not as good as that of foreign students. I think this is a result of their training since childhood.
Besides language, reasoning is a very important part of western education, so mathematics is the most important subject in middle schools and universities. Euclid's geometric theorem may not make a direct contribution to society, but its reasoning method is the most effective logical training. In the past, major universities in the United States attached great importance to two subjects, one was language and the other was mathematics. If you don't get high marks in language and math, they will hardly consider accepting you as his college student. Recently, I also added a writing ability, three courses, language, mathematics and writing, which is the most important training for all famous schools in the United States.
Many American primary and secondary schools have also increased basic legal training. Knowing the law and abiding by the law is the knowledge and morality that modern citizens should possess.
Qiu Chengtong also believes that American children are no less diligent than China students: generally speaking, American primary and secondary schools encourage students to communicate. Before the second year of junior high school, American primary and secondary schools encouraged children to give full play to their strengths and let them go to museums and sports fields as much as possible. Therefore, some educators in China think that American primary and secondary school students are not as good as China. In fact, after grade three and grade one, American children's efforts are not worse than those of China students. They don't need exams to train students, and they also pay great attention to their basic abilities. We see many excellent American children. They didn't begin to exert their enthusiasm and study hard until Grade One or Grade Two. When they get to the university, they won't find their study boring. I have been to several famous schools in America. They work very hard and spend a lot of time in studying important subjects of science. They often study until two or three o'clock before going to bed. However, it is a pity that many children in China have lost their interest and enthusiasm in learning after experiencing the heavy impact of primary and secondary school examinations.
Criticism alone is not enough, but Professor Qiu has given many pertinent suggestions to China students on some occasions. Qiu Chengtong once gave a speech in the famous middle school attached to Beijing Normal University, and shared his growing experience, academic thoughts and views on mathematics with middle school students in detail. In this speech, he expressed several views:
The cultivation of interest determines a lifelong career.
Qiu Chengtong's Speech (Excerpt)
Middle school is a very important stage to cultivate talents, so I am very willing to communicate with middle school students. Because of the selection of mathematics prize for middle school students, I also learned about some domestic middle schools. Generally speaking, it's good, but there are still some areas for improvement. In fact, I have no teacher training, and I have never taught in a middle school. I'm here today mainly to talk about my views on middle school education, especially middle school mathematics education, based on my own personal experience.
Reading widely is very important, and genius may not succeed.
A student's first education is family education, so I will talk about family education in combination with my personal growth experience.
I was admitted to Peizheng Middle School on 1960. Peizheng Middle School is a very famous school, and my primary education was completed in the countryside of Hong Kong, and even the most basic English and arithmetic are not up to standard, so I need to study harder in the first year of middle school to catch up with Peizheng's courses. However, I am used to fooling around in rural schools and have never been interested in learning.
Fortunately, my parents are very strict with me. My late father Qiu Zhenying, 1935, graduated from Xiamen University majoring in political economy, and entered Waseda University in Japan for further study the following year, specializing in political system and political thought history. When my late father was a professor in the college, students often went home to discuss their studies, which made me feel a lot. 10 years old, my father asked my eldest brother and me to practice Liu Gongquan's calligraphy, read Tang poetry and Song poetry, and recite ancient Chinese. I can recite these articles now, and my learning attitude and life attitude are reflected in them.
We love reading martial arts novels. Father felt that the quality of these novels was not high, so he bought a lot of chapters and novels and asked his children to recite poems, such as those in A Dream of Red Mansions. Later, my father let me read the works of Lu Xun, Wang Guowei and Feng Youlan, as well as Goethe's Faust and other western books. These books seem to have nothing to do with my later research on mathematics, but the ideas contained in these books have had a far-reaching impact on my later research.
A successful scholar needs to absorb the accumulated achievements in history and learn from contemporary scholars.
Life is too short, no matter how clever and talented a person is, it is impossible to ignore the achievements of scholars for thousands of years. This is the accumulation of human experience in understanding nature, life and interpersonal relationships, which cannot be achieved overnight, so it is very important for a person to read widely when he is young. Some people think that they are very talented and can make important topics without reading. In my opinion, it makes no sense. For more than forty years, the world-famous mathematicians, physicists and sociologists I have contacted have never seen such a genius.
I referred to the lives of famous scholars in history and found that most famous scholars have good family backgrounds. There are many laws and reasons for people's growth, and the relevant academic views are not consistent. But in any case, a good tutor is very important.
The influence of childhood education on a child is important, and enlightenment education is irreplaceable. It often lays the foundation for a lifelong career.
Although a parent may not have a good education, he can still cultivate his children's study habits and fun when they are very young. Knowledge is not the most important thing for children. The cultivation of interest is the key to his career. My grades in primary school are not ideal, but my father cultivated my interest in learning and became an inexhaustible motive force for my life. I can learn anything I want. In contrast, Chinese-style education often pays attention to instilling knowledge, but ignores the cultivation of children's interests. Some people can't even enjoy learning all their lives.
In any case, after students go home, they must have space and time to review. Parents need comfort and encouragement when encountering setbacks. This is a very important matter.
In addition, parents and teachers need a good communication channel to understand the problems their children encounter. Now some parents are doing things, and they have no time to teach their children and let them indulge. It is irresponsible to ask the school to take care of everything for the children. On the other hand, because there is only one child, parents love their children very much and hope that their children will succeed. Many parents expect too much from their children and often ask them to take some courses beyond their ability. If they make some achievements, they say that their children are geniuses, but they don't know that they are hurting their children. Everyone should try to understand their abilities and study hard.
Plane geometry provides the only logical training during middle school.
The study of plane geometry is the beginning of my personal mathematics career. When I was studying plane geometry in the second grade of junior high school, I first came into contact with simple and elegant geometric theorems, which made me marvel at the beauty of geometry. Plane geometry provides not only beautiful and important geometric theorems, but also the only logical training in middle school, which is the necessary knowledge for every young person. Plane geometry also provides an opportunity to appreciate the beauty of mathematics.
A famous example is the five-point * * circle problem put forward by President Jiang Zemin at Haojiang Middle School in Macau. I found it very interesting when I first listened to it. Many readers are very interested in President Jiang's question and want to deduce this theorem from the basic theorem. Recently, I was surprised to hear that many math educators insisted on not teaching proof because students are not easy to accept this kind of thinking.
It is true that from a student without logical thinking training to receiving such training, there is a price to pay. How to train logical thinking is more important than learning other subjects in middle school.
Whether you are a scientist, a politician or a successful businessman in the future, you need systematic logic training. I hope our middle school will continue this kind of logic training. The development of science in China is related to this.
Personally, I think that even under the current non-ideal exam-oriented education framework, qualified good students should learn and master the basic concepts of calculus and groups in middle schools and apply them to the study and understanding of mathematics and physics in middle schools. Newton and others discovered calculus because of the need of physics. And why is physics difficult to teach and learn in our middle school? I'm afraid the main reason is to avoid using calculus and group theory, so I've racked my brains and tried everything possible. This is tantamount to deviating from the natural and historical laws of the development of physics.
As for trigonometric algebraic equations, probability theory and simple calculus, they are all very important subjects, which are extremely important for students who want to study science and engineering or economics and finance in the future.
Music, art and physical fitness are all important for learning and personality cultivation.
I also want to talk about sports, music, art and the relationship between these courses and mathematics. Plato based his education on sports and music in The Republic. Physical exercise can make us concentrate, while music and art can cultivate our temperament. Both ancient Greeks and Confucian education paid attention to the cultivation of these two aspects, which are very important for learning and personality cultivation.
The learning process is not necessarily gradual, but sudden progress is allowed.
Nowadays, many educators object to students memorizing some formulas, and everything needs to be deduced from basic principles. I think this is a very wrong idea.
Some things are more important than the conclusion, but sometimes it is impossible. Learning is often developed on the basis of predecessors. We can't know everything, we must develop on the basis of what our predecessors have done, and we can understand the macro view of the whole knowledge by thinking about the knowledge of our predecessors repeatedly.
Jump forward and reflect on the achievements of our predecessors. At that time, we all memorized the multiplication table, but in fact, any scientist knows how to deduce the multiplication table. Physicists or engineers undoubtedly use a lot of mathematical formulas derived by mathematicians, but science is still making progress. It can be seen that the learning process is not always gradual, and sometimes sudden progress is allowed. When I say this example, I don't want you to be lazy, but I hope you don't give up and stagnate because you don't understand something.
Many middle schools don't teach calculus. In fact, the foundation of the scientific revolution in the Middle Ages was the establishment of calculus, and our children did not understand calculus, which was equivalent to returning to the dark ages before the Middle Ages. That's a real pity.
I heard that many primary or middle school teachers want students to study in a prescribed way and give full marks after getting the answers prescribed by the teachers. I think this is wrong. There are many solutions to mathematical problems, for example, there are at least dozens of proof methods of Pythagorean theorem, and different proof methods help us understand the content of the theorem. /kloc-gauss, a mathematician in the 0/9th century, used different methods to construct regular heptagons. Different methods come from different ideas, and different ideas lead to different development directions. So every solution to a math problem has profound significance, and you will understand different ideas, so students should be allowed to solve it in different ways.
In fact, many engineers and even physicists sometimes don't strictly understand the methods they use to solve problems, but they know how to use them. For mathematicians who care about how to strictly deduce mathematical methods, it is often to know the results before deducing. Therefore, it is necessary to understand that learning methods sometimes need to think backwards, first know what to do, and then know why to do it. We should handle these relationships flexibly.
American middle schools attach importance to general education.
The basic laws of physics say that an object is always looking for the lowest energy state, in which it is the most stable. Your attitude towards learning, including myself, is basically the same. People always want to find various reasons to have time to do what they like. Just like an electron running in a certain orbit, it can jump after being excited by other energy because it is allowed by its energy. For children's learning, we also need new energy to stimulate them to jump.
This kind of stimulation not only comes from exam results, but also from teachers' classroom teaching, such as some interesting questions or stories of famous mathematicians, which will arouse students' interest. Students all like to listen to stories. There are many interesting stories in history, which are worth learning.
American middle schools pay attention to general education, and subjects other than mathematics, such as literature, physics and philosophy, will stimulate students' thinking ability, which is worth encouraging.
Primary and secondary schools should pay special attention to the cultivation of independent personality.
If students can't get along with others at school and can't enjoy its benefits, it's better to hire a tutor at home. But modern society is a gregarious society. Students must learn to get along with their classmates and respect teachers and classmates who are capable and knowledgeable. Students should know how to respect their classmates' strengths and help students in need. Students should cultivate the ability to communicate and cooperate with others, the ability to think independently, the spirit of teamwork, the sense of responsibility to the people around them and society, etc., and exercise themselves in this environment.
The American teaching system has a lot to learn, although it is not necessarily an ideal system.
For example, high schools and universities in the United States don't give grades, but only give A, B, C and D. This is not a bad thing and can weaken unnecessary competition among students. Haggle over scores and compete for the first place in the class will undermine the cooperation between students and the collective strength will not be respected. In primary and secondary education, we should pay special attention to the cultivation of students' independent personality and character, and students' personality and personal characteristics are fully respected and affirmed.
Many schools abbreviate the requirements for personal character as "pride" (honor) according to the initials, that is, perseverance, respect for others, integrity, diligence and Excellence, which are the basic points of students' self-requirements. The evaluation of this virtue should respect human nature. For students themselves, we should form our own independent values.
For middle school students, it is very important to always keep a pure childlike innocence, keep people's innate curiosity and creativity, and show their personality, which is very important for future study and work. I sincerely hope that all the lovely children present here can grow up happily and healthily.