以连带勒让德方程本征值问题的求解为例展示“简单问题的解往往是复杂问题求解的基础，复杂的问题往往可以转化为简单的问题来解决”这一朴素的科学思想.在较为简单的勒让德方程本征值问题的基础上构造出连带勒让德方程本征值问题的本征解—连带勒让德多项式，回避了可能超纲的知识点.呼吁在未来的教材编写中尽量展示尝试求解问题时的思辨过程，这应当有益于培养学生从基本的方法论入手解决问题的能力.

Taking the solution of the eigenvalue problem of the Legendre equation as an example, this paper shows the simple scientific idea that "the solution to a simple problem is often the basis for solving a complex problem, and complex problems can often be transformed into simple problems to solve". On the basis of the relatively simple eigenvalue problem of the Legendre equation, the solution of the associated Legendre equation eigenvalue problem, the associated Legendre polynomial, is constructed, avoiding knowledge points that may exceed the class. Call for more demonstration of the critical thinking process when attempting to solve problems in future textbook development, which should be beneficial for cultivating students ability to solve problems from the perspective of basic methodology.