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在教学中,启发学生利用新知识去发现旧知识间的一些规律,能够引起他们浓厚的兴趣。如学生在高中三年级或大学一年级学了微积分后,诱导他们观察圆面积公式S=ЛR~2与圆周长公式C=2ЛR;球体积公式V=4/3ЛR~3与球面积公式S=4ЛR;……等之间的关系,他们很快会发现公式间存在着微分关系和积分关系(见下表),此时,他们容易处于一种兴奋状态。再进一步提出:如何从理论上证明所观察出的这种关系?这必然会激起他们进一步探索的欲望,也有利于培养学生发现性思维能力。
In teaching, inspiring students to use new knowledge to discover some of the laws between old knowledge can arouse their interest. If the students have studied calculus in the third year of high school or the first year of university, they are induced to observe the formula for the circle area S=ЛR~2 and the circle length formula C=2ЛR; the volume formula for the ball V=4/3ЛR~3 and the sphere area formula S. The relationship between =4ЛR;......etc. They will soon find that there is a differential relationship and an integral relationship between formulas (see the table below). At this time, they are easily in an excited state. It is further proposed: how to theoretically prove the observed relationship? This will inevitably stimulate their desire for further exploration, but also help cultivate students’ ability to discover sexual thinking.