Although mathematical practice has traditionally valued two distinct kinds of mathematical work--referred to by Gowers (2000) as theory building and problem solving--activity in classrooms appears to be organized largely around the latter, rather than the former. This study takes up the question of whether there is a customary role for theory building in the secondary geometry course and to what extent teachers of geometry hold students accountable for that disposition. We analyze records from study groups composed of experienced geometry teachers in the USA, and ask to what extent the disposition towards theory building is visible in those records, and how teachers react to the suggestion that it could play a larger role in their practice. Among our findings, we report that participants consistently attached a higher value to work organized around problem solving, rejecting the idea that they might hold their students accountable for theory building.