物理学告诉我们,常规条件下冰与水的密度比一般是9∶10,所以我们日常所看到的浮在水面上冰山,有9/10在水下,只有1/10的显露在水上面.高中数学教材中的概念就像冰山显露在水上面的部分,它仅仅向我们呈现了数学“冰冷的美丽”的一面,而隐藏在水下的数学概念发现过程的“火热的思考”常常被我们所忽视.荷兰数学家H·Freudenthal有一句名言:“没有一种数学思想,以它被发现时的 Physics tells us that the density ratio of ice to water under normal conditions is generally 9:10, so we see the daily iceberg floating on the water, 9/10 underwater, only 1/10 of the exposed water The concept in high school math textbooks is like the part of the iceberg that emerges above the water, which merely presents us with a ”cold and beautiful“ side of mathematics, hidden in the fiery pondering of the underwater mathematical process of discovery ”Often overlooked by us, the Dutch mathematician H. Freudenthal has a famous saying:" There is no mathematical thought at all when it was discovered