Zhang Siming, Vice President of the High School Attached to Peking University： In the next few years, there will be a big breakthrough in mathematics education.

Zhang Siming, vice president of the middle school affiliated to Peking University, believes that in the next few years, there will be a big breakthrough in the teaching form of mathematics. Teachers are no longer photocopiers of knowledge, and students are no longer warehouses of knowledge.

Zhang Siming, vice president of the middle school affiliated to Peking University, is a special math teacher. Although he runs in two campuses, he was born in 1957 and still insists on attending six classes a week. "Math teacher is the only title I hope to keep."

Following Zhang Siming, boring and profound mathematics has become "fun" and "colorful", which not only permeates many details of life, but also helps solve many practical difficulties.

For example, Zhang Siming’s topics for students are: calculating the relationship between the spacing of stamp perforations and the position of round holes at corners; Find the relationship between the water level in the bottle and the heat preservation effect of the thermos bottle; Study which kind of consumer groups are more suitable for different mobile phone charging packages; When the passenger flow is large, how to operate the elevators in the hotel reasonably? ……

Obviously, to solve such homework problems, students need to observe, experiment and measure on the spot, choose effective solutions, tools and strategies, analyze and count information, and be good at reflection and criticism. It is a comprehensive research-based learning.

In an interview with The Paper (www.thepaper.cn) on April 1, Zhang Siming said: "Education must be combined with the life practice that students can practice, not empty talk but transposition and experience. Education is effective when students have real feelings. "

He said that China’s mathematics education has always attached importance to basic knowledge and teachers’ leading role, but students’ independent learning, exploration, creative ability and personality development are not enough, which is the key quality of competitive talents in the 21st century.

"Knowledge that can be applied is powerful knowledge." Zhang Siming believes that mathematics teaching in the 21st century will shift from "imparting knowledge" to a practical mode characterized by encouraging learning and taking students as the center, and students’ independent learning, independent creation and personality development will receive more attention.

Therefore, from many years of teaching practice, he explored the teaching mode of "guiding learning, exploring and solving independently", which brought mathematics back to life, guided students to learn mathematics by doing, experienced the internal connection of mathematical knowledge, and obtained the methods and experience of studying problems, turning learning into a process of students’ active construction of knowledge.

In the process of solving problems, Zhang Siming saw the personality differences of students when solving problems, and found the different ways of thinking of students. "This is the personality specialty that we should cultivate, and many children like to do it very much, which also shows their brilliance in creation." Zhang Si said.

Winter vacation in 2016,Zhang Siming’s assignment for Grade Three students is to find out mathematics in beauty and China. "To my surprise, they told me a lot I didn’t know. Some told me that the LOGO of Apple’s mobile phone is made of nine golden sections. Some found all the medal curves; Others wrote out the color function of the whole set of playing cards. A junior high school student can take the initiative to learn with this idea, and his understanding of mathematics is extraordinary."Zhang Si said.

[Dialogue]

The role of mathematics in educating people has not been fully demonstrated.

The Paper:Some people think that the mathematics education in China is the best in the basic education stage. What do you think of this statement?

Zhang Siming:Standards and measurement methods are different and cannot be generalized. Some aspects are definitely the best, such as calculation ability and reasoning ability. The basic skills are particularly good, and the implementation of teaching is a tradition of Chinese education, which has reasonable places. But some aspects are not necessarily, such as problem-solving ability, openness, multi-angle thinking and critical thinking. However, with the frequent integration of international education, both China and the West are developing in a more effective way. Under such exchanges, more and more things will be learned from each other.

The Paper:What do you think are the major defects in China’s current mathematics education system?

Zhang Siming:In terms of teaching,Mathematics includes not only computational reasoning, but also the scientific spirit of seeking truth from facts, stressing efficiency, pursuing Excellence and pluralistic dialectics.In my opinion, the role of educating people has not been fully demonstrated.

Besides,In teaching, we still pay more attention to the middle stage, and fail to show the "source" and "flow" of mathematics, that is, the source and value more clearly and completely.There are also some other problems, such as the workload, studying only for exams, and the Olympic Mathematics becoming a stepping stone for students’ exams and further studies prematurely.

The original intention of Olympiad is to understand mathematics and how mathematicians think.

The Paper:With regard to the Olympic Mathematics, you began to coach students to participate in competitions in 1987. What do you think of the current "national Olympic Mathematics fever"?

Zhang Siming:The purpose of the early olympiad was to cultivate children’s interest in mathematics, not to solve difficult problems and enter higher schools, but to understand mathematics and how mathematicians think through olympiad. I think this is very good. In the early years, Mr. Hua Luogeng and many mathematicians in Beijing used the weekend time to open math interest classes and talk about such interesting things as mathematics in the honeycomb. The students who attend the class are all interested in mathematics and completely voluntary. Not utilitarian, this is the orientation of basic education.

The Paper:Some schools are keen to use the Olympic Mathematics as a means to test children’s ability, logic and talent. Is it reasonable?

Zhang Siming:Because the comprehensive examination is not allowed, students are not allowed to express their strengths. The most convenient way may be to make an Olympic math test paper, which parents and schools have been used to for so many years. But I think, when further education is no longer a problem, we will pay more attention to quality. Colleges and universities will also understand more and more that all people do not rely solely on competition as a selection method, but also need to have more personalized performance. But it will be a process.

Our research group is also pushing many new questions to change the system of setting questions in the college entrance examination. In the selection, in addition to the competition, there will be open questions, inquiry questions and situational questions in the future. For example, some multiple-choice questions that can be blindly correct are not the ones that can really select talents.

The job of more teachers in the future is to tap and integrate resources.

The Paper:How do you understand innovative teaching in mathematics?

Zhang Siming:Innovative teaching includes both teaching methods and teaching concepts. I think, first of all, we must understand teaching. Teachers are no longer photocopiers of knowledge, and students are no longer warehouses of knowledge. The introduction of technology will have a great impact on learning methods. Now everyone is still discussing the efficiency of classroom teaching. With the progress of science and technology, more targeted personalized teaching will develop rapidly. Even mathematics, which is highly abstract and difficult for self-study, will change in the context of the era of big data, such as Khan Academy in the United States. At present, the national curriculum standards will also advocate the use of advanced technology to help learning. Within a few years, there will be a big breakthrough in the teaching form of mathematics.

The Paper:Then how should our teachers deal with the coming great changes?

Zhang Siming:Teachers should have an open mind, at the same time, they should also change their learning methods and have more understanding of technology. Not all things can be taught by you, and not all the students you teach will. Some teachers may feel lost, but I think some teachers will still be in the classroom in the future, and more teachers’ job is to tap and integrate resources, observe and intervene in the learning process, and provide different guidance according to students’ feedback.

The biggest problem of the head teacher system is that there are too many "nanny functions"

The Paper:For more than five years, the senior high school affiliated to Peking University has implemented full-shift, and what is the consideration for canceling the head teacher system?

Zhang SimingThe biggest problem of the head teacher system is that there are too many "nanny functions" in the growth of students, which limits the space for students’ independent development. But junior high school still needs a class teacher, which helps children form a collective concept.

All the students in Grade One and Grade Two of the High School Attached to Peking University leave classes to form seven academies, which are managed vertically and developed according to different characteristics. Full-time tutors are responsible for students’ academic planning, parents’ contact and psychological counseling. Full-time tutors must communicate with all the students in charge every three weeks. It is valuable to explore this form in a school. China is so big that it is impossible to train all the people in one way.