初中学生因受年龄的限制,接受能力较差,因而教材内容都是基础的。但是,教师在教学中若能恰当地给学生讲解一些高等数学的思想,那就不但能为他们的进一步学习打下铺垫,而且也会提高他们学习数学的兴趣。比如讲初中几何第二册“圆”的部分时,就可讲些极限的观点。这样对他们进入高中及大学后学习数学分析是有好处的。下面就简单谈一谈“逐步淘汰原则”在教学中的渗透,供参考。例正方形的边长为a,以各边为直径在形内画半圆,如图1,求所围成部分的面 Because of the age restrictions, junior high school students have poor ability to accept, so the contents of the textbooks are all basic. However, if teachers can properly explain some advanced mathematics to students in teaching, it will not only lay a foundation for their further study, but also improve their interest in learning mathematics. For example, when we talk about the “circle” of the second volume of junior high school geometry, we can talk about some extreme viewpoints. This is good for them to learn mathematical analysis after entering high school and university. The following is a brief discussion on the penetration of the principle of “phasing out” in teaching for reference. The length of the side of the square is a, and the semicircle is drawn inside the shape with the diameter of each side. As shown in Figure 1, find the part of the surface