编者按数学思想、数学方法、数学思想方法，是近十年来中数界的热门话题．其内涵是什么？如何界定？在各种中数研讨会上，大家一直在研讨，甚至争论．蔡老师对此进行了全面、系统、深人的研究．本文无论是在理论研究上，还是在教学指导的意义上，都很值得一读，特此发表，以飨 The editors are mathematics ideas, mathematics methods, mathematics ideas and methods, and they are hot topics in the Chinese number field in the past decade. What is its connotation? How to define? At various medium-scale seminars, people have been discussing and even arguing. Teacher Tsai has conducted a comprehensive, systematic, and in-depth study on this subject. This article is worth reading both theoretically and teachingly. It is hereby published.