Generally speaking, the function of mathematics teaching in primary and secondary schools includes two aspects: one is practical function, which is closely related to people's production activities and daily life. The content of mathematics teaching comes from the increasingly rich and perfect production activities and social life of human beings, and through the cultivation of new people from generation to generation, it has played an increasingly obvious and dynamic role in promoting the development and progress of production activities and social life in various times, especially in modern society. The second is spiritual function, which is related to people's thinking and methods. Through children's mathematics teaching, children's wisdom can be fully opened as soon as possible, children's thinking quality and ability can be developed, children's spiritual world can be enriched, an indispensable and extremely important cornerstone can be laid for their future and even the good development of life, and a high-quality life can be created. However, the present situation of mathematics teaching in China is not optimistic, and this dual function of mathematics teaching has not been fully exerted. Specifically, the contents and methods of school mathematics teaching lag behind the development of contemporary science and technology and mathematics; School mathematics teaching is divorced from the requirements of life and social reality. In foreign countries, mathematics teaching in primary and secondary schools has also faced similar phenomena. Since the 1980s, American educational circles have put forward the educational concept of "popular mathematics", emphasizing that in school mathematics teaching, all students should be taught to learn mathematics well, not only to master the basic mathematics knowledge needed by the future society, but also to encourage students to learn more mathematics knowledge actively and effectively. Among many mathematics curriculum schemes, the school mathematics scheme of the University of Chicago is particularly interesting. Its most basic feature is to help students enhance their confidence in learning mathematics, provide rich sources of mathematics, especially emphasize the application of mathematics, and improve the overall level of students' mathematical knowledge and ability. In order to change the present situation and better reflect the requirements and ideas of mathematics teaching reform, our school began to introduce the concept of "popular mathematics" into mathematics teaching in the late 1990s. Our understanding is that the essence of "popular mathematics" refers to re-creating mathematics teaching, making it meet the needs of students and society, liberating from abstract forms, stepping out of ivory towers and moving towards life and the public. The introduction of popular mathematics can help students better understand the close relationship between mathematics and nature and human society, learn to apply mathematical ideas to observe society, solve problems in daily life, and obtain necessary mathematical experience and necessary application skills to adapt to social life. In recent years, we have summarized the experience and lessons of mathematics teaching reform and put forward the following viewpoints: ① Mathematics is valuable to anyone. Almost everyone can learn a lot of math. ③ Encourage students at all levels to actively participate in mathematics teaching. ④ School mathematics is not limited to arithmetic, algebra and geometry, but should be expanded at all stages. ⑤ Classroom should not be divorced from the real world. The main source of the problem lies in the curriculum. ⑦ Teachers should improve their sense of responsibility for mathematics teaching. We believe that mathematics learning should be a learning activity with extensive thinking space and practice space. In the past, mathematics learning often made students feel too far away from their own life practice and boring. In fact, mathematics learning can completely expand students' learning scope to social life and all kinds of activities within their power, integrate education with life, and let students get more direct experiences and feelings. First, around the phenomenon of life, cultivate the habit of students' comprehensive application of mathematics knowledge. In traditional mathematics teaching, students are often presented with generalized conclusions and abstract concepts. Although students can answer very well, they often have no way to start when they encounter similar problems in life.

The mathematical problems in life can not be well solved by a single mathematical knowledge, but need the comprehensive application of various mathematical knowledge and other knowledge. 1. Take common sense of life as the carrier, and comprehensively apply mathematical knowledge. In the usual classroom teaching, we design some math problems in life from time to time, so that students can use what they have learned comprehensively to solve them. For example, in the elementary arithmetic practice class of grade five, students get a description of a drug:

Students are required to arrange medication reasonably according to their weight and illness. This is a common problem in our daily life, and many adults think that such drug instructions are too professional. In fact, they sometimes take the wrong medicine. Because this problem involves a lot of mathematical knowledge points, students need to comprehensively use the following knowledge: abandon irrelevant conditions and take relevant conditions; Contents with weight units; Use of rounding; There are upper limit data, reasonable selection of lower limit data and so on. When solving this kind of problems, students must call all kinds of relevant mathematical knowledge and use it comprehensively to get effective results. Only in this way can the comprehensive and rational use of knowledge be truly achieved. 2. With popular science knowledge as the carrier and comprehensive application of mathematics knowledge and related subject knowledge, today's society is in an information society, and the development of society has led to an increasingly obvious trend of integration among disciplines. Interdisciplinary course aims to integrate students' knowledge and develop their interests and emotions as a whole. Many problems in life need to be solved through the moderate integration of mathematical knowledge and related knowledge. For example, in the teaching of "Year, Month and Day", because "Year, Month and Day" is popular science knowledge that students are interested in, many students already know it. We combine what students have learned in general subjects, and let students know the formation principle and arrangement law of the year, month and day by watching the running diagram of the sun, the earth and the moon and its decomposition diagram displayed by the computer with background music. This arrangement creates a good classroom atmosphere and fully stimulates students' strong thirst for knowledge. In the last part of the course, we designed the practice of swimming in the time tunnel. The teacher led everyone into the tunnel, went back to the past and flew to the future. Every station has comprehensive questions waiting to be answered. These topics combine mathematical knowledge with comprehensive knowledge related to general subjects (for example, 1840 is it a leap year or a normal year? 1949 What are the two days after September 29th? When is the next leap year? In which year are the five leap years? ) string together, students can log in accurately only if they answer correctly, which greatly stimulates students' sense of participation and plays a role in consolidating new knowledge, promoting mastery and systematizing what they have learned. At the same time, with the help of historical events reflected in the listed years, ideological education can be carried out appropriately. The teachers specially arranged several landings in1840-the Opium War years; 1949 People's Republic of China (PRC) establishment day; 1997 Hong Kong Reunification Day, etc. Second, use life scenes to improve the ability of primary school students to solve practical problems. The extension of mathematics learning is equivalent to life, and the process of learning mathematics is also the process of studying the life around. Good mathematics teaching should start from learners' life experience and existing knowledge background, and provide students with opportunities to fully carry out mathematical practice activities and exchanges, so that they can truly understand mathematical ideas, master mathematical knowledge, use mathematical methods and gain rich experience in mathematical activities.

For example, in the teaching of the fifth grade math class "Mathematics in Life-Length and Surface Area and Volume of Cube", a large three-dimensional picture of the school office appeared on the computer screen. As shown in the figure:

The teacher assumed a problem scenario: our children drink school milk every day, and the factory delivers it in batches. The school wants to take the school milk out of this big office every other room to make a temporary small warehouse, and the other room will continue to be the teacher's office. How to separate? Can you help me come up with the best plan? After discussion and research, the students put forward various schemes. After discussion, it is agreed that the best scheme is that there is a beam in the middle of the room, and from the perspective of saving materials and aesthetics, the method of borrowing beams should be adopted. The one with the window is the teacher's office, because the teacher needs enough light for his work, and the other room needs to open another door as a small warehouse to facilitate access. Then the teacher gave three tasks: task one: calculate the volume of the small warehouse. Task 2: Paint the top and walls of the office. What is a painting area? (Door and window area is 5.2 square meters) Task 3: Office building, per square meter 180 yuan. What is the estimated cost? This kind of teaching combines these three tasks in real life with mathematical knowledge reasonably. For the warehouse, our main concern is how many items (volume) can be put down; The actual painted area is often not the six faces of a long cube surface area, and there will be a phenomenon of missing faces (drawing five faces and removing the area of doors and windows); Only one side of the floor is needed, and the floor budget is made with the estimated knowledge. In the process of implementation, we find that after introducing the concept of "popularizing mathematics" into teaching, students are full of interest in mathematics and are no longer afraid of mathematics classes. Math class is close to their lives and makes them feel kind. Now they dare to use what they have learned in mathematics and put forward their own views on the problems in life. Mathematics has really entered the reality of children's lives and truly embodied its value. Through study, students deeply realize that life is rich. Third, in view of practical problems, let primary school students learn to learn cooperative learning and autonomous learning. Students often encounter some common but unsolved problems in their lives, or they are the focus of students' general concern in social life. Through the exploration of these problems, students can have a broader space for mathematics learning. According to students' age characteristics and life experience, we have created a kind of mathematics learning project with themes and projects as the breakthrough point, which closely links mathematics with life, mathematicizes life problems, and embodies the concept of "popularizing mathematics" in students' mathematics learning. For example, the fifth-grade students in our school are dissatisfied with the surrounding environment of the school. Under the guidance of the teacher, the students are free to form a special research group. In the group, the students work together, and some are responsible for counting the traffic of various vehicles at the school gate within the specified time; Some are responsible for consulting all kinds of exhaust pollution information and so on. Then they use the mathematical knowledge they have learned, such as averages, statistical tables and charts. , conducted a special study and wrote a small paper on the investigation of the surrounding environment of the campus.