如何培养自己大胆设想,敢于探究,勇于创新,是数学学习与研究的一个重要课题.本文以一道课本习题的教学为例,探讨如何引导学生开展研究性学习.高中数学课本的各种版本的双曲线部分都有这样一道习题:证明:双曲线的一个焦点到一条渐近线的距离等于双曲线的虚半轴长.该问题是根据双曲线的焦点和点到直线的距离公式设置的,看似简单,大多数师生都是一解而过,其实,回味无穷,十分有趣,笔者认为是一道不可多得的 How to cultivate their own bold ideas, dare to explore, to be creative, is an important issue in mathematics learning and research.This article takes a textbook exercises as an example to explore how to guide students to carry out research learning.All kinds of high school mathematics textbooks of double It is proved that the distance from one focal point of a hyperbola to an asymptotic line is equal to the imaginary semi-axial length of the hyperbola, which is set according to the formula of the hyperbolic focal point and the distance from point to line Like a simple, most teachers and students are a solution, in fact, memorable, very interesting, I think is a rare