In RME, mathematics is understood as both an activity and as the product of that activity. In other words, it's a unidirectional relationship: activity produces products. Often, the activity is understood as private, mental activity, and the product is understood as mental objects:
In this talk, I argued for a cultural perspective, in which activity produces artifacts,
but also, those artifacts mediate and transform activity. The upshot is that activity and artifacts become intertwined:
From this perspective, mathematics artifacts are not private mental objects, but rather they are things in the world. They are durable and shared, and they exist across people and time (within a social group). Furthermore, activity is not private mental activity, but rather it is the accomplishment of a
system composed of both persons and artifacts.
As I detail in the paper, adopting such a perspective resolves some internal tensions in RME. It also has implications for the activity principle, reality principle, and interaction principle. Finally, it leads to a new principle: the
producer principle, which states that people
are produced as particular kinds of people as they engage in activity with artifacts:
