杨辉数学及其教育思想研究

杨辉是我国古代数学的巅峰时代宋元数学的代表人物之一。他的数学著作共五种，二十一卷。分别是：《详解九章算法》十二卷，《日用算法》二卷，《乘除通变本末》三卷，《田亩比类乘除捷法》二卷，《续古摘奇算法》二卷。后三种，人们通常称为《杨辉算法》七卷。其中《日用算法》的原书已经失传，其他书籍在流传过程中，也有不少散佚了，但杨辉依然是迄南宋末为止著作保留最多的数学家。
杨辉不仅是一位数学家，而且是一位教育家。他的多数著作都是为数学普及和数学教育服务的。为了使人们学习数学时，更方便容易，杨辉还自编了“习算纲目”作为教学大纲，这在中国古代的数学教学上还从未有过。杨辉在数学教材的编写上非常下工夫，除了有教学大纲之外，很多内容也是用人民群众容易记诵的“歌诀”形式表达出来。这样，杨辉便把枯燥的数学知识用通俗易懂的方式传播了开来，给我们后人提供了宝贵的学习财富。
关键词：杨辉数学；教育思想；数学教育

Abstract
Yang Hui is one of the mathematics representative at Song and Yuan times in China. There are five kinds and twenty-one volumes of Yang’ 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.
Yang is not only a mathematician, but also a mathematics educator. Most of his works served for the popularization and education of mathematics. 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, 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 provided a valuable learning for our posterity.
Key words：Yang hui of mathematics; Education idea; Mathematics education

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