Categorization of problems to assess and improve proficiency as teachers and learners

We describe how graduate students categorize introductory mechanics problems based on the similarity of their solutions. Graduate students were asked at the end of a teaching assistant training class to categorize problems from their own perspective and from the perspective of typical introductory physics students whom they were teaching. We compare their categorizations with the categorizations by introductory physics students and physics faculty who categorized the same problems. The utility of categorization as a tool for teaching assistant training and faculty development workshops is discussed.