This paper concerns an empirical study carried out with a group of high school physics teachers engaged in the Module on relativity of a Master course on the teaching of modern physics. The study is framed within the general research issue of how to promote innovation in school via teachers’ education and how to foster fruitful interactions between research and school practice via the construction of networks of researchers and teachers. In the paper, the problems related to innovation are addressed by focusing on the phase during which teachers analyze an innovative teaching proposal in the perspective of designing their own paths for the class work. The proposal analyzed in this study is Taylor and Wheeler’s approach for teaching special relativity. The paper aims to show that the roots of problems known in the research literature about teachers’ difficulties in coping with innovative proposals, and usually related to the implementation process, can be found and addressed already when teachers approach the proposal and try to appropriate it. The study is heuristic and has been carried out in order to trace the “appropriation path,” followed by the group of teachers, in terms of the main steps and factors triggering the progressive evolution of teachers’ attitudes and competences.