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解析几何是用代数的方法研究几何问题的一门科学,它是由初等数学过渡到高等数学的桥梁,是形数结合的有力工具。鉴于几何题材的论证方法,在逻辑结构方面特别突出,于是训练学生养成严谨的逻辑习惯和发展积极的逻辑思维,便成为本课程的教学使命之一。基于这个观点,教材的叙述,对思路的来龙去脉,应不厌求详,要使学生不但知其然,而且知其所以然。现就六年制重点中学高中数学课本《解析几何》中,几个问题特提出来商榷。
Analytic geometry is a science that uses algebraic methods to study geometric problems. It is a bridge between elementary mathematics and higher mathematics. It is a powerful tool for combining shapes and numbers. In view of the argumentation method of geometric subject matter, it is particularly prominent in the logical structure. Therefore, training students to develop rigorous logic habits and develop positive logical thinking has become one of the teaching missions of this course. Based on this point of view, the narrative of the teaching materials, the ins and outs of the train of thought, should not be tired of details, to make students not only know the truth, but also know why. In the analysis of analytic geometry in the high school mathematics textbook for the six-year key middle school, several questions have been specifically asked for discussion.