Research On Math Educational Thought Of Yang Hui

Yang Hui, courtesy name Qianguang, was a mathematician from Qiantang (now Hangzhou) during the late Southern Song Dynasty. He is one of the representatives in the Song and Yuan Dynasty Mathematics, which are the peak times of ancient Chinese mathematics. There is no biography about him in "Sung History", and no detailed records in other history books, either. Even so, his contribution to ancient Chinese mathematics and great achievements in mathematics can not be ignored.There are five kinds and twenty-one volumes of Yang’s mathematical works. They are: the twelve volumes of "Xiang Jie Jiu Zhang Suan Fa", the two volumes of "Ri Yong Suan Fa", the three volumes of "Cheng Chu Tong Bian Ben Mo", the two volumes of "Tian Mu Bi Lei Cheng Chu Jie Fa" and the two volumes of "Xu Gu Zhai Qi Suan Fa". The last three works are commonly called the seven volumes of "Yang Hui Suan Fa". Although the original book of "Ri Yong Suan Fa" has been lost and the other books are partly scattered during the process of spreading, Yang is the mathematician who has the most works retained from the late Southern Song Dynasty.As a prominent mathematician, his achievements played a role as link in ancient Chinese mathematics. The "Kai Fang Zuo Fa Ben Yuan" map of Jia Xian in Northern Song Dynasty was reserved in his book "Xiang Jie Jiu Zhang Suan Fa", and part of the achievements in Liu Yi’s book "Yi Gu Gen Yuan" were recorded in "Yang Hui Suan Fa". From his work, we realize that the mathematicians, such as Jia Xian and Liu Yi, have made great contribution to ancient Chinese mathematics. Moreover, on the basis of systematic collation of previous mathematicians’work, Yang developed the "Cheng Chu Jie Fa", which had a profound influence on mathematics in the Ming and Qing Dynasty. His works have been spread to overseas during the Ming Dynasty, especially in Korea and Japan, which have a great and extensive impact on their mathematics development.Yang is not only a mathematician, but also a mathematics educator. Most of his works served for the popularization and education of mathematics. For his fully planed and purposed in the complication of the three volumes of "Cheng Chu Tong Bian Ben Mo", the whole set of books had a very complete system. In order to make the mathematics easier to learn, Yang composed the "Xi Zuo Gang Mu" as a teaching syllabus, which was never seen in ancient Chinese mathematics before. Yang put a great effort on compiling mathematics teaching materials, in addition to the syllabus, much of the teaching content was expressed in the form of "verses", which is easier to be remembered by people. So the profound mathematics was widely spread in the form of easy-going ways by Yang, which made his mathematics works circulated and preserved in folk and provided a valuable learning for our posterity.