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几何不但在中学数学教学中极为重要,而且在整个数学教学中也非常重要。这里我想从我到了天津后看到的到处都有的自行车讲起。大家都会骑自行车。但是我相信,谁也不是先学了骑自行车的理论以后才学会骑车的。小孩学说话也一样,没有一个小孩是通过学语言学来学说话的。骑车和说话都是自然而然就学会了。我的朋友、美国教育家加德纽曾经说过:理解,对数学来说不一定是好事。什么东西都要求理解,要求从理性上去认识它,既不必要,甚至还会适得其反。骑车和说话就是两个例子。因此,理解并非是教学中的头等大事。
Geometry is not only very important in the teaching of middle school mathematics, but also very important in the whole mathematics teaching. Here I would like to talk about bicycles that I have seen everywhere after I arrived in Tianjin. Everyone will ride a bike. But I believe that no one learns to ride a bicycle after learning the theory of cycling first. The same goes for children learning to speak. No child learns to speak by learning linguistics. Cycling and speaking are naturally learned. My friend, American educator Gardny once said: Understanding is not necessarily a good thing for mathematics. Everything requires understanding and requires a rational understanding of it, which is neither necessary nor even counterproductive. Cycling and speaking are two examples. Therefore, understanding is not a top priority in teaching.