History of Mathematics Education

mathematics eduction in China has a long history, as early as in the Western Zhou Dynasty, mathematics has been as one of the "six arts", become a specialized study, the early Tang Dynasty, the State Children's Supervisor set up more arithmetic hall, with arithmetic doctor and assistant professor, using Li Chunfeng and other compilations of annotations of the "arithmetic scripture ten books" as the The ten books of arithmetic were used as teaching materials. In the Ming Dynasty, these teaching materials were used for the examination of arithmetic (see History of Chinese Mathematics).

Modern primary mathematics education can be said to have begun in the late Qing Dynasty (1903) after the promulgation of the decennial school system, the abolition of the imperial examinations, and the establishment of primary and secondary schools. At that time, elementary schools were set up with arithmetic classes, and secondary schools were set up with math classes (including arithmetic, algebra, geometry, trigonometry, and bookkeeping). In the early years of the Republic of China (1912-1913), when the nonce and dickey school system was announced, the secondary school system was changed from five years to four years, and bookkeeping was no longer taught in the math courses. The longest implementation of the 1922 announcement of the nonce school system, primary and secondary schools were changed to six years, each divided into two grades of junior and senior high school, junior high school four years, senior high school two years, junior high school and high school are three years. Junior high school math taught arithmetic, algebra, plane geometry, high school math taught plane trigonometry, high school geometry, high school algebra, plane analytic geometry (high school was divided into arts and sciences, part of the science subjects plus the teaching of three-dimensional analytic geometry and the preliminary calculus), this system was basically used until 1949. After the founding of the People's Republic of China, primary and secondary education was reformed, and the school system was changed to six years of elementary school, three years of junior and senior high school, and arithmetic was gradually canceled in junior high school.In the 1950s, senior high school mathematics was once suspended to teach planar analytic geometry, and then resumed and increased the teaching of preliminary calculus, as well as the theory of probability and the preliminary knowledge of electronic computers. Modern higher mathematical education in China also began in the late Qing Dynasty, when the Beijing Tongwenkuan, founded by the foreign affairs faction in 1862, which was originally a foreign language school, was transformed into a specialized secondary school with the addition of the Astronomy and Arithmetic Hall in 1866 and the enrollment of students in 1867. In 1868, Li Shanlan was hired as the chief instructor, and set up the courses of algebra, geometry (originally), plane and spherical trigonometry, and calculus, which, it can be argued, was a means of teaching Western students more systematic mathematics. In 1898, during the Hundred Days' Reform, the Peking University Hall was established, the first national university in modern China, and in 1902, the Tongwenkan was incorporated into the Peking University Hall.

After the Xinhai Revolution, in 1912, Jingshi University Hall was renamed Peking University, and the first mathematics department (equivalent to the Department) was created, and in 1919, it was renamed the Department of Mathematics, which was the first mathematics department in China. Along with the earlier establishment of the Department of Mathematics of Nankai University (1920), Xiamen University (1926), Sun Yat-sen University (1926), Sichuan University (around 1926), Tsinghua University (1927), Zhejiang University (1928) and so on. In addition, between 1912 and 1915, the Beijing Higher Normal School (1912, formerly known as the Normal Hall of the Peking University Hall established in 1902), Wuchang Higher Normal School (1913), Nanjing Higher Normal School (1915), each set up a mathematical and physical (chemistry) section, they were changed to Beijing Normal University (1922), Wuhan University (1928), Southeast University (1923; 1928 and changed to the Central University), and have established the Department of Mathematics, during or after the establishment of other comprehensive universities, teacher training colleges and universities and schools of higher learning with a science department have successively established the Department of Mathematics.

In the early days of the establishment of the departments, the implementation of mathematics education varied greatly, and it was only later that the Ministry of Education laid down the principle of compulsory courses. The main lecturers were mostly returned foreign students, and most of the textbooks used, except for a few self-edited ones, were in foreign languages or their translations. In terms of curricula, the level of mathematics education in institutions of higher learning is not low, but the quality of teaching varies considerably from one school to another. Mathematics students, each school is usually only a few in each year class.

In 1931, Tsinghua University began to train graduate students in mathematics, followed by Zhejiang University, Central University, Peking University, and during the War of Resistance against Japan by Peking University, Tsinghua University, Nankai University composed of (Kunming) Southwest United University, the mathematical research work is also more concentrated in these schools. Among them, Tsinghua University, Zhejiang University and Wuhan University also published journals with mathematical papers.

In addition to cultivating mathematical talents at home, foreign students were also sent through some channels, for example, there were quotas for mathematics in the foreign students sent by public examination using the Chinese-American Gengzhi, Chinese-British Gengzhi and Chinese-French Gengzhi.

In the 1930's, a few foreign mathematicians, such as W.F. Osgood, N. Wiener, and J. (-S.) Adama, were also invited to China to give lectures. From the Xinhai Revolution to the founding of the People's Republic of China is the foundation period of China's modern mathematical education, many of the older generation of mathematicians, such as Jiang Lifu, Xiong Qinglai, Chen Jianguong, etc. to overcome the difficulties, hard work, and cultivated a number of mathematical talents; the number of although not large, but for the modern mathematical roots in the soil of China, made a valuable contribution.

After the founding of the People's Republic of China, under the centralized leadership of the People's Government, the educational system of the Soviet Union was adopted, and mathematics education underwent great changes. After the restructuring of faculties and departments in 1952, teacher training colleges and comprehensive universities have set up mathematics departments, the country has a uniformly formulated teaching plan and syllabus, the extensive introduction of Soviet teaching materials, the setting up of compulsory courses and their contents in each school standardized to ensure a certain level. The basic mathematics courses were generally equipped with exercises, which helped students in a more concrete way. Mathematics specialties in teacher training colleges are similar to those in comprehensive universities in terms of basic courses, with the addition of pedagogy, psychology, mathematical teaching methodology and educational internships. At one time, mathematics majors at comprehensive universities were divided into a number of specialized groups in the final year to one and a half years, such as algebra, number theory, geometry, topology, function theory, general function analysis, differential equations, probability theory and mathematical statistics, etc., and students were able to come into contact with some of the cutting-edge work in modern mathematics. The specialized group was later withdrawn and the curriculum became more diverse.

From the late 1820s, the Department of Mathematics at Zhejiang University began to use discussion classes to develop students' ability to work independently and engage in scientific research; others, such as the Southwest United University, have also used them. In the 1950s, in conjunction with the teaching of specialized groups, this practice was further promoted, and the mathematics departments of major universities gradually carried out scientific research and enrolled graduate students. Because of the increasing number of domestic mathematical talents, the teaching staff gradually changed the situation of relying mainly on returned foreign students, and foreign textbooks were gradually replaced by textbooks organized by the Ministry of Education as well as individually written textbooks, which were generally more relevant to the reality of the country. 1957 onwards, a number of schools carried out research in applied mathematics, added specialties or groups in computational mathematics, and offered courses such as operations research, probabilistic statistics, and other courses. Courses such as probability statistics were more commonly offered, and the relevant personnel were trained. Students in science and engineering departments generally study a certain amount of higher mathematics.

The above shows that, after the establishment of the People's Republic of China **** and the State, mathematics education in quantity and quality have undergone significant changes, and gradually develop and improve. However, there are some problems, such as: compulsory courses are too heavy, many courses require too much specialization and too high, the teaching system is too much demand for uniformity, failing to teach according to the student's ability, resulting in an excessive burden of learning, the foundation is not firm, and to the theory and practice of the sometimes incomplete understanding of the work of the wavering, so that the development of mathematical education has been affected. Nevertheless, the achievements of mathematics education in this period are still very great. The training of general mathematical talents has been able to establish a foothold in the country.

From 1966, the "Cultural Revolution", mathematics education suffered a serious setback. 1977, economic, political, scientific and educational reforms have been put forward in all aspects of the guidelines and measures; the development of the spirit of seeking truth from facts, the strengthening of the autonomy of the school, the flexibility of the teaching system, the increase in the number of electives, so that the schools have the conditions to develop their own individuality. The spirit of pragmatism, the strengthening of school autonomy, the flexibility of the teaching system, and the increase in elective courses have given each school the conditions to develop its own strengths and to form its own characteristics. Since the policy of "vigorously developing applied research and emphasizing basic research" has been clearly stated, pure and applied mathematics are each given their own place, and the long-standing differences in understanding of the relationship between theory and practice have finally been clarified. In addition to the specialties of basic mathematics, computational mathematics and applied mathematics, comprehensive universities and teacher training colleges have set up specialties in mathematical logic, control theory, system science, information science, probability theory and mathematical statistics, operations research and economic mathematics, and many engineering colleges and universities have also set up specialties in applied mathematics. Students in higher educational institutions of science, engineering, agriculture, medicine and even economics and management are taking more courses in higher mathematics than in the past. In the last decade, with the rapid development of science and technology, and the gradual spread of computers, calculators, and the global Internet, school mathematics has assumed ever-increasing responsibilities. The use of computers has gone beyond problem solving to give insight into the study of science, leading to higher demands on math education. The role of computers in today's world is comparable to that of physics in the first half of the twentieth century. Through computer simulations, unknown mathematical phenomena can be revealed. It has given such a big boost to mathematics as the telescope did to astronomy and the microscope did to biology. On the other hand, the ingenious use of computers has enabled researchers to make full use of their learning and intelligence, and one can be convinced that calculators and computers should be used in mathematics education at all times.

Professor Hiroshi Fujita, president of the Japanese Association for Mathematical Education, believes that there are three major peaks in the history of mathematics: 1. the birth of Euclidean geometry in the third century B.C.E.; 2. the discovery and development of calculus in the 17th-18th centuries; and 3. the origins of modern axiomatic mathematics. The unifying advances in contemporary mathematics, including advances in computer science, can be called the fourth peak in the history of mathematics. These developments in mathematics and science and technology should be reflected in mathematics education. The Middle School Mathematics Teaching Group of ICME 9 believes that for children and young people aged 11-16, mathematics curricula, related materials, and teaching activities should skillfully assist students in making the transition from child to adult behavior. The middle school mathematics curriculum should consider the interface with both the elementary school curriculum and the high school curriculum.

In mathematics, symbols are essential language. It is a tool for human thinking and communication, and it can express mathematical ideas and laws clearly and concisely. Mathematical symbols are involved in several branches of mathematics, and in science and technology, the use of mathematical symbols can effectively seek patterns and make generalizations. With the help of mathematical symbols, problems can be standardized. Therefore, the mathematics curriculum should help students to establish a correct concept of the subject and build a correct sense of symbols. Middle school students are exposed to a large number of mathematical symbols in the study of mathematics, therefore, in the teaching of concepts, attention should be paid to the natural introduction of symbols. In algebra, it is necessary to talk about arithmetic and algorithms, and in geometry, it is necessary to clarify the nature of the characteristics of the figure, and to correctly reveal the relationships and laws reflected in the symbols. The high school mathematics curriculum is facing a major reform. The Principles and Standards for School Mathematics Programs, developed and published by the National Council of Teachers of Mathematics (NCTM) in 2000, have attracted worldwide attention. High school students are expected to learn a wide range of functions, including trigonometric functions, exponential functions, and more. Students should consolidate and extend what they have learned in the early grades in areas such as geometry, measurement, data analysis, and probability. They should continue to develop their proficiency in mathematics, especially in problem solving, mathematical formulation, and reasoning and argumentation.The ICME 9 High School Mathematics Teaching Team agreed that the teaching of mathematical thinking should be an important part of the high school mathematics curriculum. Mathematical modeling ideas were generally valued by the participating experts.

There are many differences between countries, and there are different emphases in the specific organization of the senior secondary mathematics curriculum. For example, the United Kingdom's advanced level (A-level) mathematics, mainly for the higher mathematical requirements of the polytechnic candidates, such mathematics class students need to learn pure mathematics, statistics, theoretical mechanics and other content. In South Korea, there is a science high school for gifted and talented students, and a theoretical science high school for cryptography and higher strings. India has a tradition of good numeracy skills, even illiterate vegetable vendors have excellent arithmetic skills. In keeping with this tradition of good computational skills, they still do not allow the use of calculators in the teaching of mathematics today. The College Mathematics Education Group and the University Mathematics Education Group of ICME 9 study a wide range of issues in higher mathematics education, respectively. Due to the large number of majors in university faculties and the varying mathematical requirements of each major, the conference focused on the teaching of advanced mathematics in basic university public **** courses. The participants believed that with the deepening of the teaching reform in primary and secondary schools, and with the changes in the university education system, the reform of university mathematics teaching is imperative: (1) university mathematics should provide a good foundation for students to study their majors; (2) university mathematics should cultivate students' good quality of thinking and their learning ability; (3) university mathematics should provide students with mathematical tools for their future professional work; and (4) the current university mathematics teaching cannot catch up with the development of primary and secondary schools, therefore, the teaching methods of university mathematics must be reformed.

Japanese experts believe that Japanese university mathematics has entered a critical juncture. There are three reasons for this: first, the level of mathematical knowledge and ability of first-year university students is seriously declining; second, the university education system is changing, and mathematics teaching has not yet been adapted to this change; and third, university mathematics education is inappropriately coordinated with the students' future professional studies, or even disconnected from each other. For this reason, Japan's Ministry of Education, Culture, Sports, Science and Technology (MEXT) organized experts to conduct an in-depth investigation and put forward a reform plan.