Zu Chongzhi (AD 429-500) was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. He read many books on astronomy and mathematics since childhood, studied hard and practiced hard, and finally made him an outstanding mathematician and astronomer in ancient China.

Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi. Before the Qin and Han Dynasties, people used "the diameter of three weeks a week" as pi, which was called "Gubi". Later, it was found that the error of Gubi was too large, and the pi should be "the diameter of a circle is greater than the diameter of three weeks". However, there are different opinions on how much is left. Until the Three Kingdoms period, Liu Hui put forward a scientific method to calculate pi-"secant" which approximated the circumference of a circle with the circumference inscribed by a regular polygon. Liu Hui calculated the circle inscribed with a 96-sided polygon and got π=3. 14, and pointed out that the more sides inscribed with a regular polygon, the more accurate the π value obtained. On the basis of predecessors' achievements, Zu Chongzhi devoted himself to research and repeated calculations. It is found that π is between 3. 14 15926 and 3. 14 15927, and the approximate value in the form of π fraction is obtained as the reduction rate and density rate, where the six decimal places are 3. 14 1929. There's no way to check now. If he tries to find it according to Liu Hui's secant method, he must work out 16384 polygons inscribed in the circle. How much time and labor it takes! It is obvious that his perseverance and wisdom in academic research are admirable. It has been more than 1000 years since foreign mathematicians obtained the same result in the secrecy rate calculated by Zu Chongzhi. In order to commemorate Zu Chongzhi's outstanding contribution, some mathematicians abroad suggested that π = be called "ancestral rate".

Zu Chongzhi exhibited famous works at that time and insisted on seeking truth from facts. He compared and analyzed a large number of materials calculated by himself, found serious mistakes in the past calendars, and dared to improve them. At the age of 33, he successfully compiled the Daming Calendar, which opened a new era in calendar history.

Zu Chongzhi and his son Zuxuan (also a famous mathematician in China) solved the calculation of the volume of a sphere with ingenious methods. They adopted a principle at that time: "If the power supply potential is the same, the products should not be different." That is to say, two solids located between two parallel planes are cut by any plane parallel to these two planes. If the areas of two sections are always equal, then the volumes of two solids are equal. This principle is based on the following points. However, it was discovered by Karl Marx more than 1000 years ago. In order to commemorate the great contribution of grandfather and son in discovering this principle, everyone also called this principle "the ancestor principle".

I really feel that He Laoshi has solid basic skills, rich experience, advanced educational ideas and high theoretical level after reading Ten Things Excellent Senior High School Mathematics Teachers Know by Teacher He Qi. Being able to stand in the front-line teacher's point of view, I have a very clear view on how a front-line teacher can become an excellent teacher. After reading it, I feel that I still have many shortcomings. In particular, he talked about several things in senior high school mathematics teaching, which left a deep impression on me. Now I want to share with you.

In this book, Teacher He Qi first mentioned that a high school math teacher must have a healthy body, a positive attitude and a perfect personality if he wants to be an excellent teacher. Teachers' broad mind can infect students, purify their minds and benefit them for life. Secondly, as a teacher, we must have a love, which is the core of teachers' morality. Teachers' care for students will affect their life. We strictly demand that students learn to be adults before they talk about success. At present, all kinds of temptations in society are flooding our living environment, so we should educate students to distinguish right from wrong, distinguish true from false, and guide their growth in the right direction and path. The second phase of curriculum reform made it clear that teachers should respect students' personality differences, respect each student and establish a harmonious relationship between teachers and students. For high school students, especially freshmen, teachers should help them improve their learning methods and master the skills of learning mathematics, so effective learning is particularly important.

We often hear students or parents mention a question: when I was in junior high school, I learned math very well, and I got no less than 90 points in every exam. Why is it so difficult to learn high school mathematics? Even hovering around the passing line is normal, but an excellent senior high school teacher should understand the actual level of students' mathematical ability and guide students to change their mathematics learning methods to adapt to high school's large-capacity and fast-paced learning. In response to such problems, Mr. He Qi proposed that we should always be guided by methods, so we must:

(1) Understand the difference between high school mathematics and junior high school mathematics. From the content and requirements of teaching materials to the analysis of the ability demand of learning knowledge. Compared with junior high school mathematics, senior high school mathematics has rich knowledge, high thinking requirements, difficult topics, strong abstraction and generality, and strong flexibility and comprehensiveness. There are many concept symbols, strict definitions, high argumentation requirements and abstract thinking, and the accumulation and application of mathematical thinking methods in teaching materials are emphasized. Students are required to have not only the ability of calculation, but also the ability of logical reasoning, and use certain mathematical thinking methods to solve problems. For example, the first chapter of senior one mathematics textbook is set and proposition, followed by inequality and function, especially the nature part of function. The content of this series is difficult one after another. Even after graduating from high school, some students are still afraid of the content of functions. However, discussing the classification of quadratic coefficients in inequality is easy for many students to ignore and lacks the consciousness of classification discussion. In contrast, junior high school mathematics is mainly based on constant mathematics teaching, with flat and intuitive content, and some knowledge is often repeated training and mechanical imitation. Because the new curriculum standard emphasizes the spiral rise of learning, the arrangement of knowledge chapters in the textbook is not coherent enough, the structure is loose, the slope of the textbook is slow and intuitive, and each concept is equipped with enough examples and exercises. At the same time, junior high school has low requirements for abstract thinking, and the threshold for entering higher schools in junior high school is lowered, which greatly reduces students' mathematical foundation and ability, such as poor computing ability, inability to simplify algebra, inability to solve equations, inability to accurately draw quadratic function images, and so on. These undoubtedly increase the difficulty of high school teaching. To this end, he proposed that an excellent senior high school mathematics teacher must fully understand the changes in junior high school mathematics content and requirements, strive to find the connection point between junior high school and senior high school knowledge, adjust previous teaching experience, organize classroom teaching according to students' recent development fields, and improve classroom efficiency.

For example, the solution of absolute value inequality in senior high school: the definition of absolute value, classification discussion, and the division of absolute value zero into inequality groups. It is an excellent opportunity for students to experience the classified discussion method initially.

(2) Find the breakthrough point of mathematics teaching in junior and senior high schools.

The connection point of junior high school knowledge mainly includes two aspects: first, the content deleted in the second phase of junior high school curriculum reform, and some knowledge that is not connected with senior high school textbooks but needs to be used by senior high school. Second, although junior high school involves it, it is relatively simple, while senior high school needs to master formulas, theorems and common thinking methods skillfully. It is necessary to spend more time sorting out and supplementing, which is the foundation for students who have mastered it and for students who have never studied it. Conditional can offer junior high school content convergence course.

(3) Do a good job in the first class of senior high school mathematics. If the first math class in senior high school is handled well, it can stimulate students' interest in learning and desire for knowledge, thus mobilizing students' initiative in learning and making a good start for the next study. The first class is the teacher's chance to show himself. A good first class helps teachers to establish a good image in students' minds and has a great influence on the teaching effect of the whole stage. Every student wants his new teacher to be a scholar worthy of worship, but at the same time, he uses his own standards to measure his words and deeds, which puts higher demands on teachers. Once recognized by students, they can "learn from others and believe in their way", thus achieving better teaching results. From the content point of view, the first lesson can be a lesson in the textbook, or it can be a knowledge framework and structure of high school mathematics, and some learning methods are introduced preliminarily.

(4) Guide students to learn high school mathematics.

After a period of high school mathematics study, we can understand the students' learning situation of high school mathematics through questionnaire survey, find problems and give guidance in time. Including: the guidance of class notes; Guidance for learning new content; Guidance for analyzing problems; Homework and after-class review consolidate guidance. Guiding students to keep sorting out class notes is a systematic planning of knowledge, combing the internal relations of knowledge, systematizing fingers and cultivating students' ability of induction and generalization.

To do well in the above aspects, an excellent teacher should obviously have systematic and solid professional knowledge and basic methods. , and understand the development trend of this discipline. Moreover, only by constantly improving themselves can teachers broaden their knowledge, apply them freely in teaching and make the classroom lively and interesting. In addition, to be an excellent math teacher, you should also have the following abilities: First, excellent senior high school math teachers should have their own profound understanding and thinking about mathematics. Mathematics is not just a boring formula and theorem, but a way of thinking for us to understand the world and analyze problems. Guide students to find and solve math problems in life, experience the fun of learning math, and enhance their learning confidence. Second: Excellent senior high school math teachers have strong math basic skills and teaching skills without exception. Their mastery and extensive knowledge of mathematics and the variety of replacement of machine guns make them "difficult" teachers in students' minds. They are not only good at learning and summarizing, but also good at understanding the recent situation of mathematics, capturing new information, grasping important and difficult points and finding the key to the problem. Choose the appropriate way to design the situation of mathematical problems to implement teaching and stimulate students' interest in learning. Third, excellent senior high school math teachers will creatively deal with textbooks, that is, "using textbooks" instead of "teaching textbooks". They will deeply understand the writing intention, connect with the students' reality, constantly supplement the corresponding content, be brave in innovation, or carry out special research or small topic research, so as to better "use living teaching materials" and creatively carry out teaching work.

In addition, he also mentioned that an excellent senior high school math teacher can also evaluate students' mathematical cognitive structure. It is not enough to know only the contents of junior high school, but also to evaluate students' ability to learn mathematics, which is not all directly proportional to their math scores. Evaluating students' cognitive structure can provide information for teaching and decide what kind of teaching methods to adopt. It can also provide diagnosis for mathematics learning and find out the reasons that affect the learning quality. Teachers should fully investigate and understand students' knowledge and skills, proficiency and understanding of mathematical thinking methods, so as to design teaching activities suitable for students, fully mobilize students' original cognitive structure to "assimilate" and "adapt" new knowledge, and improve classroom efficiency.

In short, in order to become an excellent senior high school math teacher, we must have rich basic knowledge of mathematics, combine the current spirit of reform, seriously understand the spirit of the second classroom, creatively use teaching materials, teach students in accordance with their aptitude as much as possible, fully understand each student's growth environment and experience, discover students' personality characteristics, give full play to students' subjectivity, let them experience the thinking process of solving mathematical problems, grasp the essence of mathematics, and learn to learn mathematics. Teacher He Qi pointed out the direction for the development of senior high school math teachers and made me understand my own shortcomings. In today's increasingly fierce competition, we will work harder.