In this paper, we share major lessons we have learned in our curriculum analysis explorations and provide suggestions for future mathematics curriculum research. Specifically, we will discuss the successes and challenges of using comparative methods and developing analytical frameworks. Using an old Chinese saying, follow the vine to get the melon (顺藤摸瓜), our journey starts with getting a holistic picture of standards and moves to identifying a specific topic in the textbooks. We first conducted a study to compare the geometry standards of the Common Core State Standards for Mathematics (CCSSM) and the Chinese Compulsory Education Mathematics Curriculum Standards (CMCS); then we analyzed the presentation of a specific topic, triangle congruence, in multiple geometry textbooks. For each comparative study we conducted, developing the analytical framework that can be used to guide future investigations constituted a critical step in the research methodology. We have learned lessons from adapting the well-known van Hiele model, which was created for the development of geometric reasoning, into a lens for a detailed curriculum analysis. We have also learned lessons from elaborating on the key constructs from the “Mathematics Curriculum as Story” framework for coding and analysis. These lessons as well as our future directions serve as the primary focus of this paper.