Formation of Mathematical Objects as Decision Making

When taken literally, mathematical texts are concerned with objects of a specific kind and learning mathematics, among other things, requires students to make sense of those mathematical objects. Understanding mathematical objects is commonly described as a cognitive construction. It is proposed and substantiated that for those objects to emerge for the individual, the construction processes have to be supplemented by a deliberate decision to view, treat, use, and investigate a structure or a collection of items as a unified object. This decision strongly depends on the mediation by symbols, diagrams, and notational systems.