In this paper, we analyse how N = 31 in-service teachers study the question that could generate a Study and Research Path (SRP): How does a parabolic antenna work? We also consider how they design lessons based on this question, by adopting the pedagogy of questioning the world according to the Anthropological Theory of the Didactic (ATD). The teachers investigated the question individually and in groups during an on-line course on Mathematics Didactics. Then, we asked to the teachers to organize a possible instruction oriented to an institution known to them, based on the question they analysed before. Written texts produced by the teachers in both roles, studying the question and planning lessons are analysed using qualitative techniques and the concept of RSP. The results describe the main difficulties of in-service teachers to planning instruction according to the paradigm of research and questioning of the world proposed by the ATD.