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Zhang Jingzhong (1936-), male, professor, academician of the Chinese Academy of Sciences, honorary dean of the Institute of Computing Science and Technology of Guangzhou University, director of the Guangdong Mathematical Education Software Engineering Technology Research Center, chairman of the International Association of Educational Mathematics (IAEM), chairman of the Academic Committee of the National Digital Learning Engineering Technology Research Center, chairman of the Sichuan Computer Society, editor-in-chief of Computer Application, chairman of the Fourth China Association of Popular Science Writers, and chairman of the first Chinese Society of Educational Mathematics. He has won the second prize of the National Invention Award, the second prize of the National Natural Science Award, the second prize of the National Science and Technology Progress Award (three times), the first prize of the Natural Science Of the Chinese Academy of Sciences, the gold medal of the Hong Kong International Invention Exhibition, the first prize of the National Excellent Science Popularization Works, the National Book Award, the Five One Project Award, etc. He has won the National May Day Labor Medal, the National Outstanding Teacher award, and the Guangdong Nanyue Teaching and Education Outstanding Teacher Special Award.
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In 1995, Zhang Jingzhong was elected as an academician of the Chinese Academy of Sciences. He has made outstanding contributions to the field of readable machine proof of geometric theorems, educational mathematics, distance geometry and dynamical systems, subject education in the field of information technology, and mathematical science. Zhang Jingzhong is well-known in the field of "educational mathematics", he put forward the basic views and theories of "educational mathematics", committed to reforming mathematics education by making mathematics easier, establishing a geometric problem solving method and corresponding axiomatic system with rules to follow, and proposing the basic theories and methods of calculus without limit concepts.
On December 19-21, 2019, the first seminar on the application of deep integration of online drawing boards and disciplines was held in Chengdu. At the seminar, Zhang Jingzhong, an academician of the Chinese Academy of Sciences from Guangzhou, said that mathematical experiments, especially Internet mathematical experiments, have a considerable theoretical, technical and content foundation, and the future of the modernization of mathematics education supported by the professional dynamic mathematics teaching tool "network drawing board" can be expected. The arrival of 2020 has opened the third decade of the 21st century, and vigorously promoting the deep integration of information technology and subject teaching has become an important task to promote the reform and development of basic education.
<h1 toutiao-origin="h5" > Zhang Jingzhong. </h1>
Zhang Jingzhong was always close to middle school students. On the campus of The Experimental Middle School in Haizhuwai Chinese, Guangzhou, students occasionally meet him. He wears a jacket and a pair of sneakers, which is not low-key, but it always arouses the eyes of children who are curious. Nandu reporter learned that the school is the first middle school in the country to open a "academician education mathematics innovation experimental class".
"Mathematics itself is really too hard." Zhang Jingzhong said that the key is not the problem of teaching methods, but to start with the transformation of mathematics itself. He once quipped that mathematics is a subject for "stupid people", do not complicate simple problems, is the key to open the door of mathematics. Under his popular science, more and more middle school students have achieved excellent results in the middle and high school entrance examinations.
Focus on "Making Math Easier"
In September 2019, Zhang Jingzhong, a famous Chinese mathematician, mathematics educator and academician of the Chinese Academy of Sciences, was awarded a bronze tire gold-plated medal "Celebrating the 70th Anniversary of the Founding of the People's Republic of China". This commemorative medal is awarded to those who have received national commendations and awards and above and are still alive after the founding of the People's Republic of China.
In the computer experiment building of Guangzhou University, Nandu reporters searched for Zhang Jingzhong. Before the search, a book written by Zhang Jingzhong, "The Mathematician's Vision", deeply attracted the Nandu reporter. This book, through a series of "simple problems" familiar to middle school students, shows how mathematicians start from these ordinary and well-known facts, step by step, analyze and dig out profound laws with wide application. Academician Zhang Jingzhong, the author behind it, has been studying the practical proposition of "making mathematics easier" for decades.
"'The desert is lonely and the sun is set', in the eyes of ordinary people, this is a good frontier scene." In the eyes of mathematicians, it is possible that the former sentence means a vertical line drawn above the horizontal line, and the latter sentence means that a straight line and a circle are tangent. This vision is relatively sketchy and not meticulous. Zhang Jingzhong said, "For example, a line segment, one more point on both sides, one less point, the length has not changed, and we ordinary people seem to be the same at all." But if two dots are added, the finite coverage theorem holds, otherwise it does not hold. In this way, the mathematician's vision is very accurate and meticulous. ”
Zhang Jingzhong has always paid special attention to calculus education from junior high school to high school. He clearly saw that the junior high school stage was a "watershed" in students' mathematical literacy. "Those who learn mathematics well get better and better, and those who learn poorly feel more and more difficult." Zhang Jingzhong explains, "The geometry I started learning in junior high school involves logical reasoning, and trigonometry and algebra involve the abstraction of mathematics. This is an improvement over the way of thinking in elementary school, and at the key point of this improvement, if the child is not guided well, the child will feel that he is not the material for learning mathematics, lose confidence, and the grade will go down. ”
In the 1970s, when Zhang Jingzhong was teaching in Xinjiang, he found that when students had difficulties in understanding mathematics, on the one hand, they could solve it through teaching methods, and on the other hand, they could also solve it by changing the "concept" of mathematics, which was very effective. Taking calculus, which is difficult for students to understand, in Zhang Jingzhong's "Educational Mathematics Series", there is a book "Calculus that goes straight to the point". Starting from the simple statement that "instantaneous velocity is sometimes greater than the average velocity, sometimes smaller than the average velocity", the basic theory of calculus is established without the concept of limits and the theory of real numbers, "differentiation is not differentiated, integral is not product".
Advocate of "Mathematics for Education", Seeds results in Guangzhou
Zhang Jingzhong is the initiator of the idea of "educational mathematics". Zhang Jingzhong said that transforming mathematics to make it more suitable for teaching and learning is the task of "educating mathematics.". At the HaizhuWai Chinese Experimental Middle School in Guangzhou, students can see "academician teacher Zhang Jingzhong several times a year, and the school is the first middle school in the country to open the "Academician Education Mathematics Innovation Experimental Class".
Zhang Dongfang, the head teacher of the experimental class, told Nandu reporters that in 2012, Guangzhou launched the "Thousand Teachers and Thousands of Seedlings Project", and the class she led had the honor of becoming an academician education mathematics innovation experimental class. Zhang Dongfang, who has always been a hardcore book fan of Zhang Jingzhong, heard the news of "academician entering the school", she was very excited, and she immediately returned to the school to take over the class before the maternity leave was over.
Zhang Dongfang said that in traditional mathematical tutorials, the knowledge points are relatively scattered. Academician Zhang believes that the triangle can be used as a breakthrough, he believes that the triangle is a bridge between geometry and algebra, is a channel for communicating elementary mathematics and advanced mathematics, "as long as you know the inner angle of the triangle and the basic fact that it is 180 degrees, you can expand the learning to the entire system, every point can be colluded, it can allow students to have associative, sustainable memory." This holistic learning has a profound impact on students' future learning. ”
Zhang Dongfang believes that the core literacy of mathematics lies in allowing students to experience the abstract thinking and logical reasoning of mathematics, and Academician Zhang has given a fundamental model for exploring mathematics. She introduced that the first batch of students in the experimental class scored 133.95 points (out of 150) in mathematics, which is exciting. She sighed that some students dream of being scientists, some dream of being astronauts, "Mathematics is the basic discipline and tool discipline of the entire science, and learning mathematics well can make children have more opportunities to master cutting-edge science." ”
Zhang Dongfang recalled that Academician Zhang would come to the school about five times a semester, "thinking that he was like an ordinary teacher, and he never wanted flowers to give lectures." In addition to meeting and asking for advice, Zhang Dongfang will also email Zhang Jingzhong to discuss teaching," he always replied to on the same day. "I think he's a person with an educational heart and a big love, he goes everywhere to popularize science, hoping that Chinese children will learn mathematics more easily." I can feel the craftsman spirit of the older generation of educators. ”
The successful experience of Haizhu Wai Chinese Experimental Middle School was replicated. It is understood that schools in Beijing, Shanghai, Chongqing, Shandong and other places have gradually joined the experimental ranks of educational mathematics. In an interview with Nandu reporters, Zhang Dongfang conducted a year-long volunteer teaching in Guizhou, and in the middle of the year, she invited Academician Zhang to come and give lectures to the children. "The 80-year-old man spent a whole day on the road, and he donated all the books he bought for the lecture fee to the children in the mountainous area, and gave special lectures to the teachers in the mountainous area."
In addition, Zhang Jingzhong and the research team also used The leading dynamic geometry technology, intelligent reasoning technology, symbolic arithmetic and network interaction technology in China to develop the first leading science teaching tool "Network Drawing Board" in the Internet environment in China, which helps the development of teaching resources in primary and secondary schools and promotes the development of basic subject education informatization.
"Mathematics is not only science and technology, but also culture"
A native of Runan County, Henan Province, Zhang Jingzhong became a first-year student in the Department of Mathematical Mechanics at Peking University in September 1954. He once mentioned in a speech that the person who influenced him the most as a child was his grandmother. "It was the anti-Japanese era when the soldiers were in a panic, and she often led my brother and me into the depths of the sorghum in the sound of the cannon, took out a worn-out copy of the "Ancient Literature and Guanzhi" from her arms, and taught us to read..."
In the 1950s, Peking University attached great importance to the basic curriculum, and the Department of Mathematics and Mechanics shone brightly. Mathematician Cheng Minde talks about calculus, mathematician Jiang Zehan talks about analytic geometry, fluid mechanicsian Zhou Peiyuan talks about general physics, and mechanician Professor Wang Ren talks about theoretical mechanics. The course is not heavy, and students have plenty of time to read, think and discuss. Ample time gives Zhang Jingzhong the opportunity to read more books and read more literature and lay a good foundation.
In 1974, Zhang Jingzhong was a contemporary class teacher at the 21st Regiment Children's Middle School of the 2nd Agricultural Division of the Xinjiang Production and Construction Corps, teaching plane geometry, and in teaching, he felt that the traditional geometric problem solving methods relied too much on techniques and were difficult for students to master, and began to explore new and effective methods. Soon, he found that solving geometry problems with area relations was very effective and easy to master. He conducted an in-depth study of this technique, initially developing it from a special technique to a general approach.
In 1979, Zhang Jingzhong became a lecturer at the University of Science and Technology of China, responsible for the calculus teaching of the Department of Mathematics and the Junior Class. In order to overcome the difficulties of introductory differentiation, he proposed a limit definition method for non-ε languages, as well as a continuous induction method. Based on these efforts and the area method proposed in 1974, the basis of the idea of educational mathematics was formed: the existing parts of the mathematical method that were incompatible with the laws of education should be reformed. This forms the main content of the book From Mathematics Education to Educational Mathematics (published in 1989).
Zhang Jingzhong said that mathematics is not only science and technology, but also culture. The continuation and development of culture requires the understanding and participation of the masses. He said that mathematics education and mathematical science are no less important than mathematical research. Therefore, Zhang Jingzhong spent a lot of time and energy engaged in science popularization. He was elected an academician of the Chinese Academy of Sciences in 1995 for his outstanding contributions to the reading machine proof of geometric theorems, educational mathematics, distance geometry and dynamical systems, subject education in the field of information technology, and mathematical science popularization.
Today, Zhang Jingzhong is the honorary dean of the Institute of Computing Science and Technology of Guangzhou University and the director of the Guangdong Mathematical Education Software Engineering Technology Research Center. He told Nandu reporters that as a university teacher, you should put more energy into teaching. "I remembered the experience of studying at Peking University, Cheng Minde and Professor Jiang Zehan were already very famous mathematicians, there was no PPT at that time, the teacher wrote the board book word by word on the blackboard, and gave lectures meticulously." Zhang Jingzhong said, "I think teaching and educating people is a very happy thing, looking at the young man's vitality, seeing that the students have things that they do not understand, you can enlighten him with a few words, and at this time I feel very happy." ”
"Mathematics education is important, and around the world this question has not been well answered for decades. We seem to have found it, and it was the greatest satisfaction of my life. Zhang Jingzhong said.
Focus on the automatic solution of mathematical problems
Huang Yong, a 61-year-old retired teacher at Guangzhou University, was a doctoral student brought out by Zhang Jingzhong in his early years. He recalled to the Nandu reporter that before studying for a doctorate, he taught at the Sichuan College of Arts and Sciences in Dazhou, Sichuan, while Zhang Jingzhong was working at the Chengdu Branch of the Chinese Academy of Sciences as the director and researcher of the Mathematical Science Research Laboratory. "Teacher Zhang is very humble." Huang Yong said, "I was 38 years old when I was studying for my doctorate, and I took a train from Dazhou to Chengdu to visit Teacher Zhang's house, and he came out to pick me up, which made me remember deeply. ”
"At that time, Mr. Zhang was already a very famous figure and professor." Huang Yong said, "In the years of studying for a doctorate, I spent a lot of effort on the teacher, thanking him for letting me enter a very new and very interesting field. Huang Yong introduced that in the 1990s, he followed Zhang Jingzhong to Guangzhou Normal University (now Guangzhou University) to form a team and devote himself to the study of geometric theorems in the field of artificial intelligence, which has a very great impact on my life, and machine proof as a method has a lot of enlightening effects in artificial intelligence." ”
At the end of the 1978 National Science Congress, Zhang Jingzhong and Yang Lu, a university classmate, close friend and long-term research partner, were transferred to the Department of Mathematics of the University of Science and Technology of China to teach. Since then, many teachers in the Department of Mathematics of the University of Science and Technology of China have deeply felt that it is necessary to go abroad for study, further study or cooperative research to grasp the frontier of scientific research and improve the level of research, so many teachers and students have gone abroad.
In the 6 years of teaching at the University of Science and Technology of China, Zhang Jingzhong and Yang Lu and others stayed in China to cooperate in a "spurt" and published dozens of papers, many of which were very outstanding and highly praised by their counterparts at home and abroad. Later, Zhang Jingzhong found that there were still important problems to be solved in the field of machine proof cultivated by the famous mathematician Mr. Wu Wenjun, so he decided to deepen his cultivation in this field.
The young scholar Zou Yu was Zhang Jingzhong's first doctoral student at Guangzhou University and is currently working on the team. Zou Yu said that the human-like proof of letting the machine automatically generate geometric theorems is a cutting-edge problem, especially how to automatically construct an effective auxiliary line solution, which is very challenging and difficult.
"Academician Zhang asked us not to pursue the quantity of papers, but to pursue quality." He said, "Academician Zhang is amiable and approachable, gives us a lot of freedom, choose a content that you want to do, as long as there are any problems, you can send him an email, as long as he comes to the school, he will find students to communicate and understand the status of our scientific research." ”
Zhang Jingzhong told Nandu reporters that the practical significance of this study lies in how to use computers to solve some problems that humans need clever skills to solve.
"'Alpha Dog' has won the world championship in Go, but computers can't do math problems for children. The computer simulates the solution of college entrance examination questions, and its goal is to study the principles and methods of artificial intelligence to solve problems. "This scientific problem has been raised since the 1950s when artificial intelligence was introduced, and it has not been solved ideally." ”
Zhang Jingzhong believes that the use of computers to replace people for scientific research is obstructive and long, but the future must be of great help to mankind. "Closer to it, humanoid automatic solutions can replace teachers to tutor students, and farther away, they can replace scientists for scientific research and innovation, which is of great significance."
Zhang Jingzhong, 83 years old, still maintains nearly 10 hours of working hours a day. Every time he went to an academic conference in a foreign country, in addition to listening to lectures and eating, he always rushed into his room and rarely went out.
Zhang Jingzhong said that it is expected that through the efforts of generations of scholars, the mathematical literacy of Chinese can be improved, scientific development can be promoted, and the country can better eliminate poverty. "I hope that in my lifetime, I will see the curriculum standards for teaching mathematics further, set an example for mathematics education around the world, and bring a new atmosphere."
Dialogue Zhang Jingzhong
O Future human-like solutions can help scientists think
Nandu: What research have you been focusing on in recent years?
Zhang Jingzhong: Automatic human solutions to mathematical problems, research and practice of educational mathematics, and subject education information technology. Nowadays, the effectiveness of educational mathematics is emerging, and the effect of basic mathematics education is being greatly improved.
Nandu: How to evaluate the effectiveness of research and practice in the field of educational mathematics?
Zhang Jingzhong: The main assessment is to enter the classroom to see if it is easier for students to learn, whether they have learned, more happy and more excited. It is manifested in their emotions, in their studies, and in the final test scores. It is also necessary to track whether the students are better at understanding than other students after graduation to high school and college.
Nandu: The humanoid automatic solution sounds interesting.
Zhang Jingzhong: Human-like problem solving is similar to human methods to solve mathematical problems, or various problems. Some mathematical problems can be solved by computers, but the answers given are very complicated, so that the teacher cannot change the paper. Human-like answers give answers, just as students do, like the kind that is usually required by education, which can be easily understood and tested by people. The research began in the 1950s and is still struggling to come. If there is a breakthrough in this regard, computers and artificial intelligence will be of great help to humans, and even help scientists to think.
o Educational mathematics was successfully experimented in Guangzhou
Nandu: Why did the educational mathematics experiment choose to be carried out in Guangzhou and be successful?
Zhang Jingzhong: After coming to Guangzhou for so many years, I feel that this is a city with open minds, and the educational mathematics experiment that I did not dare to try for 32 years was successful in Guangzhou, which is the biggest promotion of research. In terms of exploration of educational software, the establishment of the research institute also set up a project, the school gave more than one million yuan of funds, of course, we all know that more than one million yuan for the development of software is a drop in the bucket, and then an entrepreneur in Macao supported our fund of more than ten million yuan, in order to develop this called "network drawing board" software development.
Nandu: As a scientist and academician who grew up with the Republic, what are your hopes for the motherland's education?
Zhang Jingzhong: I think that through my work, I can fully improve the mathematical literacy of the next generation of students in the field of mathematics education, which will have a positive effect on the realization of the Chinese dream. The education community should enhance mathematics education and encourage innovation, and the quality of life of Chinese will improve accordingly.
Written by: Nandu reporter Su Helen
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