The introduction of inquiry-based instructional formats at secondary and tertiary levels reveals some difficulties related to missing teaching praxeologies. Indeed, the paradigm of visiting works is dominant in those institutions where a “teacher pedagogy” is widespread: managing inquiry-based activities requires a “pedagogy of inquiry” which is based on distinct teaching praxeologies. The aim of this chapter is to present two research studies presenting didactic analyses of the exploration of different teaching types of tasks related to the implementation of study and research paths, paying special attention to the exchanges between teachers and researchers working in the same team.