In scientific arguments, claims must have meaning that extends beyond the immediate circumstances of an investigation. That is, claims must be generalised in some way. Therefore, teachers facilitating classroom argumentation must be prepared to support students' efforts to construct or criticise generalised claims. However, widely used argumentation support tools, for instance, the claim-evidence-reasoning (CER) framework, tend not to address generalisation. Accordingly, teachers using these kinds of tools may not be prepared to help their students negotiate issues of generalisation in arguments. We investigated this possibility in a study of professional development activities of 18 middle school teachers using CER. We compared the teachers' approach to generalisation when using a published version of CER to their approach when using an alternate form of CER that increased support for generalisation. In several different sessions, the teachers: (1) responded to survey questions when using CER, (2) critiqued student arguments, (3) used both CER and alternate CER to construct arguments, and (4) discussed the experience of using CER and alternate CER. When using the standard CER, the teachers did not explicitly attend to generalisation in student arguments or in their own arguments. With alternate CER, the teachers generalised their own arguments, and they acknowledged the need for generalisation in student arguments. We concluded that teachers using frameworks for supporting scientific argumentation could benefit from more explicit support for generalisation than CER provides. More broadly, we concluded that generalisation deserves increased attention as a pedagogical challenge within classroom scientific argumentation.