As lesson study becomes more prevalent, there is a need to continuously develop theoretical and methodological infrastructure to support and refine its use. In this article, we present a critical methodological analysis of the challenges and benefits of using Toulmin's argumentation model in mathematics education to assess the debriefing phase of lesson study. During debriefing sessions, teachers offer arguments about how to improve teaching that are grounded in observations of students' learning. Toulmin's model provides a means to analyze the structure of such arguments. Using an empirical example, we illustrate challenges of using the model, such as determining appropriate grain sizes for data and claims, evaluating qualifiers, recognizing multiple categories of backing, identifying implicit warrants, and deciding between the individual or the group as a unit of analysis. We also discuss benefits such as being able to systematically compare mathematics teachers' pedagogical arguments against one another, assess attainment of debriefing session goals, and characterize group discursive dynamics. Despite the challenges of using the Toulmin model, we conclude that it provides a useful framework for systematic analysis of lesson study debriefing sessions. The present article can help researchers anticipate and address challenges of conducting Toulmin-based qualitative analyses of debriefing session discourse.