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我国著名数学教育家傅种孙先生所写的《平面几何教本》(原名《高中平面几何教科书》)于本世纪三十年代出版后,曾在国内中学教育界影响很大,脍炙人口。只因它是用文言写的,今天不便阅读,五十年代以后渐失流传。现在由先生的几个门生,将这书译成白话文,由北京师范大学出版社重新出版了。我愿意借这机会,谈谈自己多年来学习、使用这本书的一些体会。《教本》的特点之一是在根本处不马虎。大家都知道,几何学是要讲道理的。但是越接近根本处的道理越不好讲,因此,普通几何教科书一般只把不太根本的道理讲得很仔细,而对非常根本的道理,则多半明借直观,暗取常识,敷衍过去。例如,证三线共点的正当做法是:先证其中两线交于一点,然后证第三线也过这个交点。然而普通教科书都默认前一步。而只证后一步;原因是证两线相交要用相当根本的道理
After the publication of Plane Geometry Textbook (formerly known as “High School Plane Geometry Textbook”) written by Mr. Fu Shisun, a famous mathematics educator in China, in the 1930s, he had a great influence on the domestic secondary school education community. Because it was written in classical Chinese, it is not convenient to read today, and it gradually disappeared after the 1950s. Now, several of the gentlemen of the gentleman, the book was translated into vernacular and republished by Beijing Normal University Press. I would like to take this opportunity to talk about some of my experiences in learning and using this book over the years. One of the characteristics of the textbook is that it is not sloppy at all. Everyone knows that geometry is reasonable. However, the closer you approach the fundamentals, the harder it is to say. Therefore, ordinary geometry textbooks generally only take care of the less fundamental truth. However, for very fundamental reasons, most of them are explicit, implicit, and perfunctory. For example, the proper practice for the three lines of the same point is to first prove that two lines intersect at one point, and then that the third line also passes this intersection. However, ordinary textbooks default to the previous step. But only one step later; the reason is that the two lines need to use a very fundamental principle