论文部分内容阅读
下面我们提出“直线与平面”一章中下列各节的练习: 1.“直线与平面公理”;2.“空间直线的相互位置关系; 3.“相互平行的直线与平面”;4.“二异面直线所成的角”; 5.“平面的垂线和斜线”。在提出练习以前,我们首先作某些教学法的说明: 1.在前几课中的口头练习必须以每个学生都有的直观教具演示。在以后,从平行于直线的平面的定理开始,口算的习题应以图画阐明,此项图画可以是事先画好的,也可以在读出习题的条件时画在黑板上。这时,仅在理解条件或在解题过程中发生困难时,才采用直观教具。在这个階段应教会学生看图。所以,对具有想象内容的口答习题,应当向学生提出同一几何图形的相互位置关系的各种不同的图形。(参阅下列习题中所引用的图形。)
Below we present the exercises in the following sections of the chapters “Linear and Plane”: 1. “Linear and Planar Axioms”; 2. “The mutual positional relationship of spatial lines; 3. “Lines and planes parallel to each other”; 4. “ The angle formed by the straight lines of two different planes; 5. “The vertical lines and oblique lines of the plane.” Before putting forward the exercises, we first make some explanations of teaching methods: 1. The oral exercises in the previous courses must be The demonstration of visual aids that all the students have will be followed, starting from the theorem of the plane parallel to the straight line, the oral calculation exercise should be illustrated by a picture, this picture can be drawn in advance, or can be drawn when reading the conditions of the exercise. On the blackboard, visual aids are used only when the conditions are understood or when difficulties arise in the process of solving problems. At this stage students should be taught to look at diagrams. Therefore, for students who have imaginative content, they should submit the same questions to the students. The various figures of the mutual positional relationship of geometric figures (see the figures quoted in the exercises below).