本文主要通过对求数列的通项的特征根法的建构过程的教学来展示数学知识和技能的发生、发展的过程,让学生提出从特殊情形到一般结论的猜想,让学生提出猜想后学会严格的论证,让学生在深刻认识数学对象的同时,也提高自身的数学能力. In this paper, we mainly demonstrate the process of the occurrence and development of mathematical knowledge and skills by teaching the process of constructing the eigenvalues ​​of general terms of the sequence of numbers, and let the students make the conjecture from the special case to the general conclusion that students should be strict after their conjecture Of the argument, so that students have a profound understanding of mathematical objects, but also improve their mathematical ability.