In this article, I consider how cartographies have become a onto-methodological approach that seeks to produce, rather than represent, the world that they are enacting. Going beyond Alfred Korzybski's famous axiom that 'the map is not the territory,' my point is that the map can shake up the territory. This shift is discussed in relation to the…

"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…