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在中学里添设解析几何课是有很多好处的。这样做一方面可以消除中学数学课程(特别是算术和三角)的松懈现象,另一方面又可以减轻高等学校中的数学课程的负担,很多专业的教学进度因而将能大大加快。当然,要在中学设置解析几何,首先必须根据中学数学教育的特点和可能条件,来选择这一课程的内容。与高等学校的数学课程相比,中学数学的内容是比较具体的,因此,数学概念的引入和数学理论的展开必须更紧密地联系实际,教学过程也自然要进行得缓慢一些。其次,既然中学数学已经包括了初等代数、初等几何和平面三角等内容,增添新的课程内容当然必须在同学已有的这些知识的基础上来考虑,而且通过新添课程的学习,最好能在运用和发展了旧有知识的同时,还能使全部数学知识更为巩固和系统化。我觉得只要适当地选择解析几何课的内容,它是完全可以满足以上的条件和具有以上的优点的。目前高等学校数学課程中解析几何的内容虽然随专业的不同而有差別,但是我们还是可以就其主要的共通内容来考虑哪些适宜于放到中学里去。解析几何按其所討論的几何图形所在的范围,可以分成平面解
There are many advantages to adding analytical geometry lessons in secondary schools. In doing so, on the one hand, the laxity of mathematics courses in middle school (especially arithmetic and trigonometry) can be eliminated. On the other hand, the burden on mathematics courses in institutions of higher learning can be reduced. The progress of many professional courses can thus be greatly accelerated. Of course, to set analytical geometry in middle school, you must first select the content of this course according to the characteristics and possible conditions of middle school mathematics education. Compared with the mathematics curriculum in colleges and universities, the content of middle school mathematics is more specific. Therefore, the introduction of mathematical concepts and the development of mathematical theory must be more closely linked to reality, and the teaching process must naturally proceed slowly. Second, since middle school mathematics already includes elementary algebra, elementary geometry, and plane triangles, the addition of new course content must of course be based on the students’ existing knowledge, and it is best to learn through new courses. The use and development of old knowledge can also consolidate and systematize all mathematical knowledge. I think that as long as the contents of analytic geometry classes are properly selected, it can fully satisfy the above conditions and have the above advantages. Although the content of analytical geometry in the mathematics curriculum of higher education institutions is different from that of the majors, we can still consider what is suitable for the middle school in terms of its main common content. Analytic geometry can be divided into planar solutions according to the range of geometry in which it is discussed.