International Mathematical Olympiad (IMO) is an international competition with mathematics as its content and middle school students as its object. It has a history of more than 30 years. As an international competition, the International Mathematical Olympiad was put forward by international mathematical education experts, which exceeded the level of compulsory education in various countries and was much more difficult than the college entrance examination. According to experts, only 5% of children with extraordinary intelligence are suitable for learning the Olympic Mathematics, and it is rare to reach the top of the international mathematical Olympics all the way. Now, IMO has become the most influential academic competition in the world, and it is also recognized as the highest level mathematics competition for middle school students. The math contest in China started at 1956. At the initiative of famous mathematicians such as China and the Soviet Union, initiated by chinese mathematical society, the four cities of Beijing, Tianjin, Shanghai and Han took the lead in holding high school mathematics competitions.
1934 and 1935, the Soviet union began to hold middle school mathematics competitions in Leningrad and Moscow, and named them Mathematical Olympics. From 65438 to 0959, Romanian Mathematical Physics Society invited middle school students from Eastern European countries to participate in the first International Mathematical Olympiad held in Bucharest, and it has been held once a year since then, and it has been held for 50 times so far.
In recent years, China's achievements in the Mathematical Olympiad, like those of China's athletes in the Olympic Games, have advanced by leaps and bounds. From the 40th to 43rd sessions, the total score of China team was the first for four consecutive years.
The Olympic Games is relatively in-depth, and the vigorous development of the Mathematical Olympic Games has greatly stimulated children's interest in learning mathematics and has become a useful activity to guide them to be positive, explore actively and grow healthily. It involves many practical problems, such as counting, graph theory, logic and pigeon hole principle. To solve this kind of problem, it is generally necessary to analyze and summarize the mathematical significance of the actual problem, abstract the actual problem into a mathematical problem, and then use the corresponding mathematical knowledge and methods to solve it. In this process of constructing mathematical model, students' ability to look at and deal with practical problems from a mathematical point of view can be effectively cultivated, students' awareness and ability to solve practical problems with mathematical language and models can be improved, and students' ability to reveal mathematical concepts hidden in practical problems and their relationships can be improved. In this creative thinking process, students can see the practical function of mathematics, feel the charm of mathematics and enhance their sensitivity to the beauty of mathematics. Today, with the emphasis on quality education, this educational function of Olympic mathematics has more important practical significance.
Name of Award: International Olympic Mathematics Competition
Other names: International Mathematical Olympiad
Established: 1959
Organizer: It will be hosted by participating countries in turn.
Award introduction:
The International Olympic Mathematics Competition is an international mathematics competition for middle school students, which has great influence in the world. The purpose of international Olympic competition is to discover and encourage young people with mathematical talent in the world, create conditions for scientific education exchanges among countries, and enhance the friendly relationship between teachers and students in various countries. This contest (1959) was initiated by Eastern European countries and funded by UNESCO. The first competition was hosted by Romania and held in Bucharest from July 22 to 30. 1959. Bulgaria, Czechoslovakia, Hungary, Poland, Romania and the Soviet Union participated in the competition. After that, the International Olympic Mathematics Competition was held in July every year (1980 only once), and the participating countries gradually expanded from Eastern Europe to Western Europe, Asia and America, and finally expanded from 1967 to the whole world. At present, there are more than 80 teams participating in this competition. The United States entered the competition in 1974 and China entered the competition in 1985. After more than 40 years of development, the operation of the International Mathematical Olympiad has gradually become institutionalized and standardized, and a set of established routines has been followed by previous hosts.
The International Olympic Mathematics Competition is hosted by the participating countries in turn, and the funds are provided by the host countries, but the travel expenses are borne by the participating countries themselves. Participants must be middle school students under the age of 20, with 6 people in each team and 2 mathematicians as the team leader. The test questions were provided by the participating countries, then selected by the host country and submitted to the examiners' committee for voting, resulting in six test questions. The host country does not provide test questions. After the test questions are determined, they will be written in English, French, German, Russian and other working languages, and the team leader will translate them into the national language. The examiners' committee is composed of leaders of various countries and the chairman designated by the host country. This chairman is usually the authority on mathematics in this country. There are seven duties of the examiners' committee: 1), selecting examination questions; 2), determine the scoring standard; 3) Accurately express the test questions in the working language, and translate and approve the test questions translated into the languages of the participating countries; 4) During the competition, determine how to answer students' questions in writing; 5) Resolve the different opinions on grading between individual team leaders and coordinators; 6) Determine the number and scores of medals.
The exam is divided into two days, 4.5 hours a day, and three questions are tested. Six players from the same team were assigned to six different examination rooms to answer questions independently. The answer sheet will be judged by the national team leader and then negotiated with the coordinator designated by the organizer. If there is any objection, it will be submitted to the examiner's Committee for arbitration. 7 points for each question, out of 42 points.
There are first prize (gold medal), second prize (silver medal) and third prize (bronze medal) in the competition, and the ratio is roughly1:2: 3; The total number of winners cannot exceed half of the students participating in the competition. The award criteria of each session are related to the results of the current exam.
To do the problem, we should do it selectively and pertinently:
"The sea of questions is boundless and the types of questions are limited." You must have solid basic skills in learning mathematics. Basic skills are solid, and it is natural to learn "Olympic Mathematics". After children really master the learning method of "Olympic Mathematics", it is particularly important to insist on doing a certain number of exercises every day. The premise of doing the problem is to have a thorough understanding of what you have learned. Doing the problem is not only difficult, but also simple, moderate and difficult. The ratio is best controlled at 3: 5: 2. Thereby avoiding the phenomenon that children can still do difficult problems and the accuracy of basic questions is always low. After the beginning of the fifth grade, we should insist on doing about ten questions every day. In order to improve the speed of children's problem solving, according to the difficulty of the problem, each time is limited to 40-60 minutes, and then parents strictly time and judge the score according to the standard answer. Write down the questions that you can't do or do wrong. Capable parents can explain to their children themselves. If you don't understand the problem for the time being, you'd better consult the relevant experienced teacher until you understand it! ! ! It is our ultimate and most important goal to solve the problems found in the problem-solving in time! If you haven't done anything wrong before, you must let your child do it at least once from time to time! The choice of topics can be decided by children and parents through discussion according to the courses they are studying and the suggestions of their tutors. After learning a few knowledge points, you must do some comprehensive papers or comprehensive questions, mainly for the "weak" links of children's learning, and ask the tutor to do more questions for children. Another purpose of doing problems is to cultivate children's ability to draw inferences from others and achieve mastery through a comprehensive study. Note: you must have a thorough and profound grasp of what you have learned before you start doing the questions, otherwise no matter how many questions you do, you will only get twice the result with half the effort and you will not get the desired effect.
Introduction of China Mathematical Olympics (CMO)
The national middle school students' mathematics winter camp is a higher-level mathematics competition based on the national high school mathematics league. Starting from 1985, sponsored by Peking University, Nankai University, Fudan University and China University of Science and Technology, chinese mathematical society decided to hold the national mathematics winter camp for middle school students every year 1 month from 1986.
The winter camp lasts five days. The first day is the opening ceremony, the second and third days are the exams, the fourth day is the academic report or sightseeing, and the fifth day is the closing ceremony to announce the exam results and awards. The CMO exam is completely simulated by IMO, with 3 questions a day and 4.5 hours in a limited time. Each question is 21(3 times of IMO questions), and the full score of 6 questions is 126. All provinces, municipalities and autonomous regions sent players to participate in the competition, as well as teams from Hong Kong, Macao and Taiwan and Russia. The topic is more difficult than the International Mathematical Olympics, and it is highly technical. There are first prizes to third prizes in the competition. Top students will enter the China National Training Team to prepare for the International Mathematical Olympiad in July of the same year.
Since 1990, the team competition of Chen Shengshen Cup has been held in the winter camp. Starting from 199 1, the national middle school students' mathematics winter camp was officially named China Mathematical Olympics (CMO). It has become the highest level, the largest scale and the most influential mathematics competition for middle school students in China.
Overview of Olympic Mathematics Competition
mathematical contest
Mathematics competition is one of the effective means to discover talents. Most of the winners of some major mathematics competitions have made great achievements in their later careers. Therefore, all developed countries in the world attach great importance to mathematics competitions. In the past ten years, mathematics competitions in middle schools in China have developed vigorously, with increasing influence. In particular, middle school students in China have been among the best in the most influential and highest-level international mathematical olympiad for many times, and their achievements have attracted worldwide attention, fully demonstrating the intelligence and mathematical ability of the Chinese nation.
It is necessary and beneficial to know the history of international and domestic competitions and the significance of several competitions.
History of international competitions
In the world, competitions based on numbers have a long history: there were competitions to solve geometric problems in ancient Greece; During the Warring States Period in China, horse racing between Qi Weiwang and Tian Ji was actually a game of game theory. In the 16 and 17 centuries, many mathematicians liked to ask questions to challenge other mathematicians, and sometimes they held some open competitions. In several open competitions of equations, there is one of the most famous Fermat's Last Theorem: when the integer n≥3, the equation has no positive integer solution; ……
Modern mathematics competition is still a problem-solving competition, but it is mainly held among students (especially senior high school students). The purpose is to discover and cultivate talents.
Mathematics competition in the modern sense began in Hungary. 1894, in order to commemorate the appointment of Evos, President of the Society of Mathematics and Physics, as Minister of Education, the Society of Mathematics and Physics passed a resolution: a math contest named after Evos will be held every year 10, with three questions each time and a time limit of four hours. Any reference books are allowed. These problems are good at mysterious and strange forms, and generally have concise solutions and creative characteristics. Under the leadership of Evos, this mathematics competition has played a great role in the development of mathematics in Hungary. Many accomplished mathematicians and scientists are winners of previous Evos competitions, such as Fryer of 1897 and Von Kamen of 1898.
Influenced by Hungary, Eastern European countries vigorously held math competitions:1Romania in 902, the former Soviet Union in 1934, Bulgaria in 1949, Poland in 1950, and Czechoslovakia in195 years ago.
It was the former Soviet Union that named the middle school students' mathematics competition "Mathematical Olympics". The name is adopted because there are many similarities between mathematics competition and sports competition, both of which advocate the Olympic spirit. The result of the competition is surprising, and it is often found that a powerful country in mathematics competition is also a powerful country in sports competition, which gives some enlightenment.
1934 in Leningrad, 1935 in Moscow, the relevant state universities organized regional mathematics competitions, which were called "Middle School Mathematics Olympics". At that time, famous mathematicians in Moscow took part in this work. The mathematical Olympics in the former Soviet Union were divided into five levels: school Olympics, county Olympics, regional Olympics, * * * * United Nations Olympics and national Olympics, and then six representatives were selected to participate in the international mathematical Olympics.
The most enthusiastic about organizing the international mathematics competition is Romanian professor Roman. After his planning, the first International Mathematical Olympiad (IMO) was held in July 1959 in Blaso, the ancient Romanian capital, which opened the curtain of the international mathematical competition. At that time, there were 52 students from seven countries in Eastern Europe, including Romania, Bulgaria, Hungary, Poland, the former Czechoslovakia, the former German Democratic Republic and the former Soviet Union. Each country has 8 players, while the former Soviet Union sent only 4 players. It will be held once a year in the future (except 1980, which was suspended due to the financial difficulties of the host Mongolia). By the time 1990 3 1 was held in China, it had grown to 308 contestants from 54 countries and regions. By 1995, when the 36th tournament is held in Canada, the number of doubles will increase to 73 countries and regions, with more than 400 participants.
The operation mode of the International Maritime Organization has been institutionalized, and its competition rules stipulate that:
(1) The host country of IMO in the year is held by the participating countries (or regions) in turn, and the required funds are borne by the host country. The whole activity was hosted by the host country, presided by the examiners committee composed of national leaders, and the test questions and answers were provided by the participating countries. Each country has 3-5 questions (or none), and the host country does not provide test questions, but forms a topic selection Committee to evaluate and preliminarily screen the test questions provided by each country. Mainly consider whether the test questions are repeated before, and classify the test questions according to algebra, number theory, geometry, combinatorial mathematics, combinatorial geometry and so on. , determine the difficulty of the test questions (A, B, C), and select about 30 questions. If there are new answers to these questions, it is also required to provide answers other than the original answers and translate them into English for the examiner to choose.
(2) Each team shall organize a team with no more than 8 members, including no more than 6 members (students from middle schools or schools at the same level), 1 team leader and deputy team leader. The exam will be held in two days, with 3 questions each, 4.5 hours each and 7 points each, so the highest score of each player is 42 points.
(3) The official languages of IMO are English, French, German and Russian, and participating countries need about 26 languages. At that time, the team leaders will translate the test papers into the national language and get the approval of the coordination Committee. The marking is first judged by leaders and deputy leaders of various countries, and then negotiated with the Coordination Committee (each coordinator is responsible for marking a test question). If there are differences, the examiners' committee will arbitrate, and the negotiation will be conducted in a trusting and friendly atmosphere.
(4) The number of winners of IMO accounts for about half of the participants, and the winners of the first, second and third prizes are awarded in order of their scores, with an average ratio of 1:2:3. In addition, the examiner's committee can award special prizes to students who have made a very beautiful (meaning simple, ingenious and original) or mathematically meaningful answer to a question.
In order to avoid the interruption of 1980 again, IMO set up a special committee (some translated as venue committee) to determine the host of each session.
According to IMO regulations, the host of each session must send an invitation to all the participating countries in the previous session, and the new participating countries must show their willingness to participate in the competition to the host, and then the host will send an invitation.
Among the countries outside Eastern Europe, Finland was the first to join (1965 7th), and France, Britain, Italy, Sweden and the Netherlands joined in succession in 1960s. 1974, the United States and Vietnam joined. Since then, the number of participating countries has increased year by year, covering Europe, the United States, Asia, Africa and Oceania, and IMO has become a truly global mathematics competition.
1988 In the 29th session, IMO set up an honorary prize for the first time at the suggestion of Hong Kong, and awarded it to those players who got full marks in at least one question although they didn't win gold, silver or bronze medals. This measure greatly mobilized the enthusiasm of all participating countries and their players.
The spirit of IMO is the Olympic spirit: "The important thing is not to win, but to participate." Accordingly, since the 24th 1983, although each team (6 people) has calculated their total scores and knows how many people rank according to the order of total scores, the organizing committee does not award prizes to the team winners, because IMO is only an individual competition, not a team competition.
198 1 22nd, the United States is the host of IMO. Greitzer, chairman of the American Mathematical Olympiad Committee, sent a letter inviting China to participate, and chinese mathematical society wrote back and agreed to participate. Later, he failed to make the trip and only sent visiting scholars from the United States as observers.
1984, at the first meeting of chinese mathematical society's popularization work held in Ningbo, it was decided to send two contestants to participate in the 26th IMO in 1985, so as to learn about the situation and accumulate experience. Due to the hasty selection time, only 1 outstanding students from Beijing and Shanghai were arranged to participate. Results 1 person won the third prize, and their average score with Israel was 17, while their total score was 32. Starting from 1986, China sent six players to participate in the competition.
The brilliant achievements of China athletes have greatly stimulated the enthusiasm of millions of middle school students to learn scientific and cultural knowledge, and also greatly enhanced the national pride of the people of China.
Domestic competition situation
It's not too late to hold a math contest in China. After liberation, under the initiative of Professor Hua and other mathematicians of the older generation, middle school mathematics competitions were held from 65438 to 0956, and resumed in Beijing, Shanghai, Fujian, Tianjin, Nanjing, Wuhan, Chengdu and other provinces and cities, and high school mathematics leagues were also held jointly by Beijing, Tianjin, Shanghai, Guangdong, Sichuan, Liaoning and Anhui. From 65438 to 0979, 29 provinces, municipalities and autonomous regions in Chinese mainland held middle school mathematics competitions. Since then, the enthusiasm for developing mathematics competitions all over the country has never been higher. 1980, at the first national conference on the popularization of mathematics held in Dalian, it was decided to take the mathematics competition as a regular work of the Chinese Mathematical Society and the mathematical societies of all provinces, municipalities and autonomous regions, and hold the "National Senior High School Mathematics Joint Competition" 10 on the first Sunday in mid-June every year. At the same time, the mathematical circles in China are actively preparing to send athletes to participate in the International Mathematical Olympics. 1985, the national junior high school mathematics league was held; 1986 held the "Huajin Cup" Youth Mathematics Invitational Tournament; 199 1 year, the national primary school mathematics league was held.
At present, China's senior high school mathematics competition is divided into three levels: the national league tournament in the middle of June every year, which is 65438+ 10; The following year 1 month CMO (winter camp); The training and selection of the national training team began in March of the following year.
The American Middle School Mathematics Competition has a great influence on the middle schools in China. The competition is also divided into three rounds: AHSME, with 30 multiple-choice questions, which should be completed within 90 minutes; There are 15 empty questions in the American Mathematics Invitational Tournament (AIMS), and the answers are all positive integers not exceeding 999, which should be completed within 3 hours; The American Mathematical Olympiad (USAMO), the highest mathematics competition in the United States, has five questions each time and takes 3.5 hours to complete.
Our country has taken a series of effective measures to make our country's mathematics competition activities extensive, orderly, in-depth and lasting, and do a good job in the training and selection of all kinds of mathematics competitions at all levels. First, create a good scene for the math competition; Primary and secondary schools organize teaching interest group activities every year, and set the time, place, tutor and auxiliary content; There are plans to provide intensive counseling and training for some math "seedlings" in order to establish a math Olympic amateur school. Secondly, strengthen the counseling power of mathematics competition; Mathematical Olympic coaches at all levels should constantly improve their teaching and teaching quality. Third, optimize the mathematics competition counseling system; Compile and publish basic mathematics competition training materials or counseling books, collect and sort out domestic and foreign mathematics competition materials, study and refine the thinking methods and skills of solving problems in mathematics competitions, and improve and perfect the selection mechanism and counseling methods of mathematics competitions.
The "National Mathematical Olympiad for Primary Schools" (founded in 199 1) is a popular activity, which is divided into a preliminary contest (every March) and a summer camp (every summer).
The "National Junior Middle School Mathematics League" (founded in 1984) is held by the mathematics competition organizations of all provinces, municipalities and autonomous regions in the form of "taking turns to host", which is held in April every year, with a trial and a second trial.
The National High School Mathematics League (founded in 198 1) is held in the same way as the junior high school league. It is divided into initial test and second test. About 90 students who have achieved excellent results in this competition are eligible to participate in the "China Mathematical Olympics (CMO) and the National Winter Camp for Middle School Students" hosted by chinese mathematical society (every year 1 month).
Under the guidance of the policy of "improving on the basis of popularization", the national mathematics competition is in the ascendant. Especially in recent years, Chinese athletes have made gratifying achievements in the international mathematics Olympics, which has aroused the enthusiasm of teachers, students and mathematicians in primary and secondary schools, and the mathematics competition has entered a new stage. In order to make the national mathematics competition sustainable, healthy and in-depth, the outline of mathematics competition is formulated at the request of teachers, students and mathematicians at all levels in middle schools.
This syllabus is based on the spirit and foundation of the "Full-time Middle School Mathematics Syllabus" formulated by the State Education Commission. The syllabus is pointed out in the column of teaching purpose; To realize the four modernizations, we must cultivate students' interest in mathematics and stimulate them to learn mathematics well. The specific measures are: "Students who have spare capacity for study should fully develop their mathematical talents through extracurricular activities or offering elective courses", "We should pay attention to the cultivation of their abilities …" and focus on cultivating students' computing ability, logical thinking ability and spatial imagination ability, so that students can gradually learn important thinking methods such as analysis, synthesis, induction, deduction, generalization, abstraction and analogy. At the same time, we should pay attention to cultivating students' independent thinking and self-study ability. "
The contents listed in the syllabus are the requirements of teaching and the minimum requirements of the competition. In the competition, there are higher requirements for the understanding and flexible application of the same knowledge content, especially the proficiency of methods and skills. And "classroom teaching. Priority of extracurricular activities is a principle that must be followed. Therefore, the content of extracurricular lectures listed in this syllabus must fully consider the actual situation of students, so that students can master it step by step and at different levels, implement the principle of "less but better", strengthen the foundation and constantly improve.
-Try it.
The outline of the preliminary test competition of the national senior high school mathematics league matches the teaching requirements and contents stipulated in the full-time middle school mathematics syllabus, that is, the knowledge scope and methods stipulated in the college entrance examination are slightly improved, and the preliminary test of probability and calculus is not taken.
Second division
1. Plane geometry
Basic requirements: master all the contents determined by the junior high school competition outline.
Supplementary requirements: area and area method.
Several important theorems: Menelius Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem.
Several important extreme values: fermat point, the point with the smallest sum of the distances to the three vertices of a triangle. The plane of the distance to the three vertices of a triangle
Square and the smallest point-center of gravity. The point in a triangle with the largest product of the distances from three sides-the center of gravity.
Geometric inequality.
Simple isoperimetric problem. Understand the following theorem:
In the set of N-polygons with a certain circumference, the area of the regular N-polygon is the largest.
In a set of simple closed curves of a cylinder with a certain circumference, the area of a circle is the largest.
In a group of N-sided polygons with a certain area, the perimeter of the regular N-sided polygon is the smallest.
In a set of simple closed curves with a certain area, the circumference of a circle is the smallest.
Motion in geometry: reflection, translation and rotation.
Complex number method, vector method.
Planar convex set, convex hull and their applications.
2. Algebra
Other requirements based on the first test outline:
Image of periodic function and periodic and absolute value function.
Triple angle formula, some simple identities of triangle, triangle inequality.
The second mathematical induction.
Recursion, first and second order recursion, characteristic equation method.
Function iteration, find n iterations *, simple function equation *.
N-element mean inequality, Cauchy inequality, rank inequality and their applications.
Exponential form of complex number, Euler formula, Demefer theorem, unit root, application of unit root.
Cyclic arrangement, repeated arrangement, combination. Simple combinatorial identities.
The number of roots of an unary n-degree equation (polynomial), the relationship between roots and coefficients, and the pairing theorem of imaginary roots of real coefficient equations.
Simple elementary number theory questions should include infinite descent method, congruence and Euclid besides the contents contained in the junior middle school syllabus.
Division, nonnegative minimum complete residue class, Gaussian function [x], Fermat's last theorem, Euler function *, Sun Tzu's theorem *, lattice point and its properties.
3. Solid geometry
Polyhedral angle, properties of polyhedral angle. Basic properties of trihedral angle and straight trihedral angle.
Regular polyhedron, euler theorem.
Proof method of volume.
Sections, sections, and surface flat patterns will be made.
4. Plane analytic geometry
Normal formula of straight line, polar coordinate equation of straight line, straight line bundle and its application.
The region represented by binary linear inequality.
The area formula of triangle.
Tangents and normals of conic curves.
Power and root cause axis.
5. it
Dove cage principle
Exclusion principle.
Extreme principle.
Division of sets.
Cover.
Note: The basic principle of the second test proposition of the national senior high school mathematics league is to be close to the international mathematics Olympics. The overall spirit is slightly higher than the requirements of the high school mathematics syllabus, and the knowledge is slightly expanded, and some contents that are not in the classroom are appropriately added as extracurricular activities or teaching contents of the Olympic school.
Teachers and coaches are required to master the contents listed above step by step, and carry out appropriate teaching according to the specific conditions of students.
The content marked with * will not be tested in the second test for the time being, but may be tested in the winter camp.
Developed by chinese mathematical society Popularization Committee
(August 2006)
Since 198 1 the National Senior High School Mathematics League was held by the chinese mathematical society Popularization Committee, under the guidance of the principle of "continuous improvement on the basis of popularization", the national mathematics competition is in the ascendant, attracting millions of students to participate in it every year. From 65438 to 0985, China stepped into the International Mathematical Olympiad, which strengthened the international exchange of extracurricular mathematics education. In the past 20 years, China has become one of the powerful countries of the International Maritime Organization. Mathematics competition plays a positive role in developing students' intelligence, broadening their horizons, promoting teaching reform, improving teaching level and discovering and cultivating mathematics talents. This activity has also stimulated teenagers' interest in learning mathematics, attracted them to actively explore, and constantly cultivated and improved their creative thinking ability. The educational function of mathematics competition shows that this activity has become an important part of middle school mathematics education.
In order to make the national mathematics competition sustainable, healthy and in-depth, chinese mathematical society Popularization Committee has formulated 1994 "Outline of High School Mathematics Competition", which has played a good guiding role in the development of high school mathematics competition, and the activities of high school mathematics competition in China are becoming more and more standardized and regular.
In recent years, the implementation of the new syllabus has changed the system, content and requirements of middle school mathematics curriculum in China to some extent. At the same time, with the development of mathematics competitions at home and abroad, there are some new requirements for the knowledge, ideas and methods involved in the competition, and the original high school mathematics competition outline can no longer meet the development and requirements of the new situation. After extensive consultation and many discussions, the outline of senior high school mathematics competition was revised.
This syllabus is based on the spirit and foundation of Mathematics Syllabus for Full-time Senior Middle Schools. "Mathematics Teaching Syllabus for Full-time Senior Middle Schools" points out: "To promote the development of every student, we should not only lay a good foundation for all students, but also pay attention to developing students' personalities and specialties; ..... In class and extracurricular teaching, it is advisable to proceed from students' reality, take into account students with learning difficulties and spare capacity, meet their learning needs through various ways and methods, and develop their mathematical talents. "
Students' mathematics learning activities should be a lively and personalized process, which should not be limited to acceptance, memorization, imitation and practice, but also advocate reading self-study, independent exploration, hands-on practice and cooperative communication, all of which are helpful to give full play to students' initiative in learning. Teachers should give specific guidance according to students' different foundations, levels, interests and development directions. Teachers should guide students to actively engage in mathematics activities, so that students can form their own understanding of mathematics knowledge and effective learning strategies. Teachers should stimulate students' enthusiasm for learning, provide them with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematical activities. For students who have spare time to study and have a strong interest in mathematics, teachers should set up some elective contents for them, provide them with enough materials to guide them to read and develop their mathematical talents.