This chapter focuses on using hypothetical learning trajectories, in particular how they can be compared with the observed learning of four case study students. It addresses the question of how insights from design research can be presented in a succinct form. The chapter explores whether a conjecture map would be useful for communicating the main insights from J. Smit's design research project. Design principles and conjecture maps are different things but can capture similar ideas. A major difference is that design principles in Van den Akker's format do not specify mediating processes, whereas they are explicit in conjecture maps. Furthermore, while design principles are formulated in practical advisory terms, conjecture maps are more research oriented. One could also use multiple conjecture maps to show progression. Sometimes people who read about hypothetical learning trajectories initially consider them to be linear
