面对一个数学问题,不同的人有不同的反应,那要看每个人平日的思维习惯、他所受过的教育和训练、还有每个人不同的教学经历。以下我们试用一道数学题目观察不同的反应,用意绝不是要判断哪一种思维方式最优越,而在于说明从多个角度了解问题的益处。其实,哪一种思维方式较佳,往往与面对的题目有关,不可一概而论。而且即使某一种思维方式导致一个简捷的 Faced with a mathematical problem, different people have different reactions. It depends on each person’s habits of thinking on weekdays, his education and training, and the different teaching experiences of each person. In the following, we try to observe different reactions with a mathematics topic. The intention is not to judge which way of thinking is superior, but to explain the benefits of understanding the problem from multiple perspectives. In fact, what kind of thinking method is better is often related to the subject in question and cannot be generalized. And even if one way of thinking leads to a simple