Experienced provers employ a host of skills when assessing the validity of a justification, often without names for those skills. This paper offers an introduction to a lens called Toulmin analysis that can help make sense of this process. Then this paper describes both an in-class module to help students learn to apply Toulmin analysis and multiple ways this module can be integrated into courses for mathematics majors and non-majors. Toulmin analysis has helped us bring human dimensions of proving to the surface in our classrooms, and it helps us build stronger and more inclusive entryways for students into mathematical communities. Learning about Toulmin analysis helps our students connect mathematical reasoning to other thinking, supporting transfer in both directions, and it has changed our thinking about the teaching and learning of mathematics even in contexts where we do not devote class time to this model overtly.