This study aimed to investigate the evolution of students’ written argumentation on socioscientific issues (SSIs) during a sequence combining two teaching strategies: debate practice on SSIs and reflective activities on the argumentation produced by students. The quality of their argumentation was assessed considering a set of norms characterizing argumentation practice on SSIs: three generic norms (i.e., justification, others, and questioning norms) and three specific norms (i.e., complexity, uncertainties, and open-endedness norms). The 2-year sequence was implemented by teachers from different disciplines in two classes with students aged 16–18. In total, it consisted of four debates on different SSIs and involved four reflective activities following a progression, allowing for the discussion of the generic and specific norms of argumentation on SSIs. The debates were all computer mediated and held synchronously in the classroom. They involved students developing their argumentation in a written form. Overall, the results showed positive changes, even if limited, regarding the appropriation of both the generic and specific norms of argumentation on SSIs. The more pronounced changes were observed considering the initial level of the quality of student argumentation in the debates: Students whose initial level was low tended to justify their arguments more frequently, while those with a higher initial level tended to question the claims and arguments more often. Furthermore, at the end of the sequence, students easily coordinated several aspects of the debated SSI, but rarely mentioned knowledge uncertainties and stakeholders of the SSI. These findings imply that combining debates on SSIs with reflective activities is an effective teaching strategy deserving to be disseminated in classroom practices, although two specific norms (i.e., uncertainties and open-endedness norms) require a more in-depth treatment.