In this paper we present three cases of instructional design that illustrates both horizontal didactising, the activity of using already established principles to design instruction, and vertical didactising the activity of developing new tools and principles for instructional design. The first case illustrates horizontal didactising by elaborating how the constructs chains of signification and models were used to design an instructional sequence involving linear growth. The second and third cases illustrate vertical didactising by developing argumentation analyses and generative listening, respectively, as instructional design tools. In the second case, argumentation analyses emerge as a tool that other designers can use to anticipate the quality of conversations that can occur as students engage in tasks prior to implementing the instructional sequence. The third case develops the notion of generative listening as a conceptual tool within the context of designing differential equations instruction to gain insights into what are, for students, experientially-real starting points that are mathematical in nature and to provide inspirations for revisions to instructional sequences.