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正方体是学生比较熟悉的几何体,它包含了立体几何中研究的点、线、面元素及各元素间的关系。它为我们学习线线、线面、面面的位置关系提供了具体而丰富的实例,能为辨析概念,突破难点提供直观的模型,使一些问题巧解。正方体制作也比较简便,可以达到学生人手一个,便于在学习中使用。但必须说明平面是无限延展的,直线是无限延伸的,不能局限于正方体模型中的正方形和线段。也就是说,对各元素间的关系可由正方体模型引入,但又不能受模型的限制。 一、借助正方体进行概念教学 (一)平面的基本性质 如图1,正方体AC1中,任
The cube is a geometry that students are familiar with. It contains the points, lines, surface elements, and the relationships between elements in the three-dimensional geometry. It provides concrete and rich examples for us to learn the positional relationship between line, line, and face. It can provide an intuitive model for identifying concepts, breaking through difficulties, and solving some problems. The production of cubes is also relatively simple and can reach one student’s hand and is easy to use in learning. However, it must be stated that the plane is infinitely extended, and the straight line is infinitely extended. It cannot be confined to squares and line segments in the cube model. In other words, the relationship between elements can be introduced by the cube model, but it cannot be limited by the model. First, the use of cubes to carry out the concept of teaching (A) the basic nature of the plane Figure 1, the cube AC1, any