A Research On Hua Hengfang's Notebook On Learning Mathematics-Xue Suan Bi Tan

This paper is based on Hua Hengfang's Notebook on learningmathematics——XUE SUAN BI TAN(学算笔谈). It's an importantwork written by Hua Hengfang in his later years about how to learnmathematics and mathematics education, which consists of twelvevolumes in total. This paper makes a thorough analysis of XUE SUAN BITAN from four aspects, including learning the elementary knowledge ofmathematics, mathematical thought, traditional Chinese mathematics andwestern mathematics. The main conclusions are as follows:Firstly, the elementary knowledge of mathematics of XUE SUANBI TAN arranged followed the principle"from the elementary toprofound".This book is content-rich of introduction to the basics and itsexamples are typical and understandable. Hua Hengfang exhaustivelyanalyzed the key points of learning the elementary knowledge.Secondly, XUE SUAN BI TAN not only introduced"Tian Yuan"and"Si Yuan"but also compared them with"Fang Cheng"and"Ying Nv",which are from < Nine Chapters On Arithmetic >.He did this to givebeginners confidence in learning"Tian Yuan"and"Si Yuan".Thirdly, the western mathematics of XUE SUAN BI TAN based on related works translated by Li Shanlan and Hua Hengfang. It's extractfrom these works. From XUE SUAN BI TAN, we can see that Westernalgebra and calculus are superior to"Tian Yuan"and"Si Yuan"in HuaHengfang's eyes. He argued very clearly that if one wanted to learnmathematics beyond the elementary level, one should begin withgeometry, then go on to study the"Tian Yuan"method, Western algebra,and finally the calculus, in that order.Lastly, Hua Hengfang had a wealth of research, translation andteaching experience. He gave a lot of mathematics learning insights andexpress some views on writing books in XUE SUAN BI TAN.Through the analysis, we can see XUE SUAN BI TAN is aneducation book on mathematics with rich content and suitable forbeginners to learn mathematics in late-Qing dynasty. It has played animportant role in mathematics education and the spread of mathematicalknowledge in late 19th century China.