At this point, the known "arithmetic" with exact historical records appeared in the Sui Dynasty. At the beginning of the founding of People's Republic of China (PRC) (58 1), the Guo Zi Dian (renamed imperial academy in 607) was established as a specialized educational administrative department, the highest academic research institution and the Central National University. This is the first time in the history of China that an independent education administrative department has appeared. Guo Zi Temple (prison area) has Guo Zi, imperial academy, four schools, calligraphy and arithmetic. The first three are general education, mainly studying Confucian classics, while the latter two are special education. Arithmetic is a unique school that specializes in mathematics in ancient China. Compared with modern times, it can be regarded as a mathematics college. There were 2 doctors (lecturers), 2 teaching assistants (tutors) and 80 arithmetic students in Sui Dynasty.
The 18th Bachelor Plan fully inherited and developed the system of Sui Dynasty in the Tang Dynasty, and the imperial academy system was further developed, mainly by expanding the scale of the school and perfecting the relevant system of the school. There were seven schools of thought in imperial academy in the early Tang Dynasty, including Guo Zi School, imperial academy School, Sixiao School, Wenguangtang (all schools of general classics), Legalism School (legal school), Calligraphy School (calligraphy school) and Mathematics School (mathematics school). In the Tang Dynasty, it was stipulated that there were 2 doctors and 30 students, and 30 students were taught in two "majors", each with 15 students, with a schooling period of 6 to 7 years. In the Six Classics of Tang Dynasty, it is recorded that "Dr. Arithmetic teaches civil and military officials below eight grades, and the life of Shu Ren's son", which shows that imperial academy counts students as children from lower-level officials and generally richer families. Students who enter the Mathematics Museum will study different subjects. This course is divided into two parts. Part of it is Sunzi's Calculations and Cao Wu's Calculations, which will be completed in 1 year. Chapter 9 Arithmetic and island calculation will take 3 years to complete, while Zhangqiu's calculation and Xiahou Yang's calculation will take 1 year to complete, zhou yun's. The other part is "Zhu Shu" for 4 years, "Ji Gu" for 3 years, and also graduated in 7 years. Two majors study numerology and third-class numbers at the same time. In addition to two common kinds of knowledge, 10 was later called the ten classic books of calculation, which were ancient and modern mathematical works edited and annotated by the imperial court at that time, and then behavioral mathematics textbooks were promulgated by the imperial edict. This is unique in the history of education.
There are two unique points, one is the examination system, and the other is the way out for graduation. There is no exam for admission, and the competent department will send you according to your family background. But after you enter the school, there are many and strict exams, and you have to take them every once in a while. If there are ten-day tests, monthly tests, seasonal tests, annual tests, etc. Mathematics has a day off every ten days. The exam on the previous day was called the ten-day exam, which was presided over by the lecturer "Doctor". Later, because the ten-day exam was once every ten days, it was too frequent and the burden on teachers and students was too heavy, so it was cancelled. The final exam is once a month, called the monthly exam; Take the exam once every quarter, which is called quarterly exam. The annual exam at the end of each year is a relatively important exam, and the result of the annual exam determines whether the students will stay or not. If you are "inferior" in the exam for three consecutive years, you will be expelled from the school. Of course, for students, the most important thing is the graduation exam, which is presided over by the leaders of imperial academy. There are two main test methods: "posting and reading" and "asking for meaning". The so-called "post-reading" is to fill in the blanks according to the original text of the textbook, open a page of the textbook at will, block both sides, leave a line empty first, and then "paste" 3 to 6 words in it for students to write. The two textbooks "Mathematics Notes" and "Number of the Third Kind" are all tested in this way. Generally, 10 space is given, and 9 spaces are matched to pass. The so-called "asking questions" refers to simple questions and answers to textbook questions, requiring "knowing mathematical skills and understanding mathematical principles in detail". It can be said that it requires not only mastering arithmetic rules and abilities, but also familiarity with basic principles, thus including knowledge and abilities. The two majors of post reading in the exam are the same, and questions are asked for each major according to different textbooks, with a total of 10 questions. The first major "Nine Chapters Arithmetic" has three questions, and the other seven textbooks each have 1 question. In the second major, there are 7 questions about composition and 3 questions about calculating ancient classics, and 6 questions in 10 pass (below 5 points are "inferior", above 6 points are "medium" and above 8 points are "excellent"). Mathematics students who have passed the graduation exam (called "Chinese style") can directly take the ritual exam (re-examination), one of the imperial examinations, without taking the provincial exam, the initial exam. In the Tang dynasty, after passing the imperial examination and passing the Chinese style, you were qualified to be an official. After passing the examination by the official department, you could be awarded the official position of "from Jiupin".
For the first time in Chinese history, the Tang Dynasty promoted the establishment of local official schools according to administrative regions. There is a statistic in the ancient book "Tongdian" that the number of students in state and county schools reached 67 100 during the Tianbao period, which fully proved that feudal education reached a new peak. At the same time, private schools have been established. In private schools, you can not only learn to read and write, but also learn a little arithmetic, which makes arithmetic education flourish among the people.
An interesting story about the popularization of mathematics education in the Tang Dynasty happened around 855 AD. According to the historical records of Tang Que, there are two small officials in Qingzhou who need to be promoted. However, the positions, working years and comments in the files of these two people are almost identical, and the responses collected around them are similar. Who should be promoted? The officials in charge of this work were very nervous. They went to ask their boss, Qingzhou Shangshu Yang. Yang said that one of the biggest advantages of a small official is that he can calculate skillfully. When I work out a math problem, the first person who gets the correct answer will be promoted. His topic was: someone was walking on the sunset path in the Woods and overheard some thieves discussing how to distribute stolen cloth on the trees. They said that if everyone was divided into six horses, there would be five left. If everyone is divided into seven parts and there are eight ponies, how many thieves are there in the forest and how many pieces of cloth are there? After Yang had a problem, he ordered two small collectors to calculate on the stone steps in front of the hall. In a short time. One of them got the right answer first, and he was promoted. No official opposes and praises this method of employing people. In the history books, Shi Yang is an unselfish official with strict orders. He has a high level of cultural knowledge, and senior officials are "taken from public opinion". Under the historical conditions at that time, it was really commendable that the following officials could be hired only after the business assessment was carried out.
The development of arithmetic in Tang Dynasty was original. However, its development path is quite bumpy. In the third year of Xianqing (658) and the second year of Longshuo (662), the abandoned mathematics museum was rebuilt, and the number of students was reduced to 10. There are 300 students in Guo Zi Academy, 500 students in Imperial College and 500 students in four courses. It can be seen how serious the habit of emphasizing Confucian classics, history and science was at that time. People who devote themselves to mathematics are also paid extremely low. Dr. Arithmetic is from Grade 9, but Dr. Guo Zi is from Grade 5. In the late Tang dynasty, the examination of Ming suan also stopped. Therefore, this is a major setback in the development of arithmetic. The pioneer of official arithmetic in Tang Dynasty laid a good foundation for the great development of arithmetic in Song Dynasty.