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尝试对“平面”做形式化的定义,让学生有机会体会和认识一些数学本源性问题,从小处说是领会平面三大公理意蕴的需要,于大处言是教材培养创新性人才的必然。在人教A版高中教材《数学2》(必修)~([1])中,“平面”概念的引出分为三个环节:观察——观察呈平面状的物体,如课桌面、黑板面、海面等,给学生以感性认知;描述——给“平面”作描述性的定义,“平面”就是从这样的一些物体中抽象出来的,但是,几何里的平面是无限延展的;表示——通常将一个水平放置的平面画成一个平行四边形,用平行四边形表示平面,
Trying to make a formal definition of “Plane ” gives students the opportunity to understand and understand some of the problems inherent in mathematics. From an early age, they need to understand the meaning of the three axioms in plane. inevitable. In the teaching of A version of high school teaching material “mathematics 2” (compulsory) ~ ([1]), the concept of “plane ” is divided into three parts: Observation - Observe the planar objects such as desk, The blackboard, the sea, etc., to students with perceptual knowledge; Description - to “plane ” for a descriptive definition, “plane ” is abstracted from such objects, but the geometry of the plane Is infinitely extended; that - usually a horizontal plane is drawn as a parallelogram, the plane is represented by a parallelogram,