Teaching Enlightenment of China's Traditional Mathematics

As can be seen from the international test results in the last section, the mathematics scores of East Asian countries and regions influenced by Confucian culture are generally good. In Chinese mainland, Taiwan Province Province and Hongkong, children aged 13 are among the best in mathematics. Japan, South Korea, Singapore and other countries in the cultural circle of Chinese characters are generally good at mathematics. This phenomenon should be analyzed from the cultural level first. 1. Educational tradition under Confucian culture. The characteristics of education under Confucian culture can be summarized as "studying hard and taking exams". In order to learn, scholars in ancient China advocated "hanging a beam on the head and stabbing a thigh on the cone". The purpose of studying is to pass the imperial examination and gain fame. This tradition has a great influence on mathematics education so far. Specifically, Confucian culture encourages readers to "strive to make contributions in this life", with a clear reading purpose and interest in learning, but no interest in learning. The motivation of reading comes from secular achievements, not the afterlife. Strictly control the family. Parents have high expectations for their children, so they ask their children to study hard, "listen to the teacher", observe discipline and study hard. The old adage of education emphasizes reciting, imitating memory and "Practice makes perfect". "I am familiar with 300 Tang poems, and I can recite them if I can't write." A lot of "math exercises" are the basis of success in the exam. The tradition of "calculation" in ancient mathematics in China. The emperor of China was called the "son of heaven", and mathematics served the astronomical calendar. So calculation is the first important thing, and "reasoning proof" is less involved. The word "mathematics" was widely used after1930s. China's abacus skills and formulas exist in folk culture. In addition, the pronunciation of China numbers is monosyllabic, and the calculation formula is catchy and easy to remember, which is also a big advantage. These characteristics exist in Chinese mainland, Taiwan Province Province, Hongkong, Singapore and other Chinese-inhabited areas, as well as in Japan, South Korea, Vietnam and other countries to varying degrees. 2. The deductive characteristics of Confucian culture itself. First of all, Confucian culture itself is a deductive system. We can make an analogy: Confucian classics are equivalent to mathematical axioms. Zhu and others annotate and extend the classics, construct theorems and demonstrate that the task of scholars is to practice according to Zhu's standard answers. On the surface, it seems that the ideological system of Confucian culture does not pay attention to logical reasoning and deductive argument. But in general, the way of thinking is convergent, closed and deductive. On the contrary, any divergent thinking level involving creation, exploration and discovery is absolutely not allowed as long as it conflicts with the classical exposition. This closed deductive ideology does not encourage innovation, and will naturally stifle all creation, including mathematical creation. In contrast, although Confucianism does not attach importance to mathematics, it does not reject or oppose logical deduction in mathematics. Confucian culture is a kind of interpretive culture. Scholars can only "annotate" the sage's words, and their academic research is to prove that the sage's words are right. This ideology inevitably permeated into the blood of China intellectuals, which suppressed creativity, including the innovative spirit of mathematics. 3. The "textual research culture" of Confucianism in Qing Dynasty provided a stage for the logical reasoning requirements of mathematics. If the Confucian culture is a convergent deductive system on the macro level. Then/kloc-the textual research culture in China in the 0/8th century embodies the Confucian textual research method. In the Daxing Literary Prison in Yongzheng, Qing Dynasty, intellectuals were forced to make a living in the "old paper pile", studying the ancient sound and meaning of every word, the versions, authenticity and authors of various ancient documents, and so on. The textual research school, represented by Dai Zhen (1724- 1777), strongly opposes the vague argumentation method with a serious attitude of verification. Dai Zhen once criticized the previous research method as "imitating what it is by rumors; Choose from all opinions to judge its superiority; Make a false statement to determine its theory; According to isolated evidence, I believe. " In other words, the textual research school further deduces and logicizes the Confucian cultural system at the micro level. Textual research depends on logic. For example, textual research commonly used reduction to absurdity. Assuming that this book was written by someone will go against the fact, so it can't be written by someone. This academic spirit and method of emphasizing evidence and seeking truth from facts is a bridge between textual research school and modern science, especially mathematics. Liang Qichao, a famous scholar, once said: "The 200-year training of textual research school in Qing Dynasty has become a kind of heredity. The mentality of overseas students in China tends to be calm and cautious. This nature is the basic element of establishing science. China has a long history of formal science (mathematics). With his excellent scientific mind, he will definitely become a first-class scientific citizen in the world in the future "("An Introduction to Learning in Qing Dynasty "). This "genetic" gene still exists today. Textual research training = scientific spirit, then mathematical thought = logical method is a matter of course. It is generally believed that the academic characteristics of the Qing Dynasty are textual research. "Ming and Qing Dynasties have taken an academic road from antonym and exegetics to specialized textual research, and then to paying equal attention to righteousness and theory." This kind of textual research has reached the level of exclusion and has formed a culture. We might as well call it "textual research culture". Textual research culture gives full play to the characteristics of "emphasizing evidence and reasoning" in mathematics education. The tradition of "textual research culture" of China intellectuals has filtered the "innovation" level in western mathematics, leaving only "logic", so that the concept of mathematics = logic is generally recognized, while the innovation of mathematics is inevitably neglected. Hu Shi said: "Make bold assumptions and be careful to verify". I'm afraid it's not bold enough to speculate, and more careful verification is needed. Innovative ideas in mathematics are not encouraged. Once there is a small mistake, they will be accused of making a "scientific mistake" and will be unable to lift their heads all their lives. This phenomenon is not uncommon in math class. Fourth, the Confucian "imperial examination system" formed the examination culture. As the baton of education, examination is always the same, but it is more prominent in China. Since Emperor Wen of Sui Dynasty implemented the imperial examination system in 597 AD, it has become the only goal of intellectuals to gain fame through examinations. The examination of eight-part essay in Ming and Qing dynasties makes the educational goal closer to the life pursuit of "being the top scholar and spending the night in the bridal chamber" This concept has become an examination culture, which has been affecting today, and mathematics education is no exception. At a graduation ceremony of new york State University on 1935, Einstein thought that the old school gave students too much "competitiveness" and did not pay attention to cultivating students' "curiosity". Professor Li Zhengdao said in a speech to college students at Fudan University that our tradition has always regarded learning as "learning". Why are you always doing "learning to answer"? These words are aimed at the disadvantages of examination culture. In fact, the exam is a double-edged sword. As a kind of talent selection, fair examination is indispensable, at least today there is no substitute. The unified college entrance examination system in China has played an important role in history and will continue in the future. The disadvantage of the unified examination is that "thousands of troops cross the wooden bridge", and everyone does the same topic, without creativity and personality. The danger of contemporary college entrance examination lies in stereotyped writing. We can't say that we have enough knowledge about the harm of stereotyped writing examination.