Leading whole-class discussions in mathematics instruction in a productive way is identified as a core practice. However, productive discussions are rarely seen in classrooms. Thus, we need more knowledge about how different teacher actions in response to students' comments can affect the students' learning. If research is to be able to produce such knowledge, detailed analytical frameworks and concepts are required. Thus, this study sought to propose concepts and refine definitions of existing categories of teacher actions to help develop Drageset's framework ([2014]. Redirecting, progressing, and focusing actions - a framework for describing how teachers use students' comments to work with mathematics. Educational Studies in Mathematics, 85(2), 281-304.). This was done by analysing 35 mathematical whole-class discussions, generated from multiple-choice tasks supported by classroom response systems, in secondary schools in Sweden and the UK. The results suggest five new categories of teacher actions and enrichments of two existing categories in Drageset's framework.