The triad mechanism consists in three stages, referred to as intra, inter, and trans, in the development of the connections an individual can make between particular constructs within the schema, as well as the coherence of these connections. The Intra stage of schema development is characterized by a focus on individual actions, processes, and objects in isolation from other cognitive items of a similar nature. For example, in the function concept, an individual at the Intra level, would tend to focus on a single function and the various activities that he or she could perform with it. The Inter stage is characterized by the construction of relationships and transformations among these cognitive entities. At this stage, an individual may begin to group items together and even call them by the same name. In the case of functions, the individual might think about adding functions, composing them, etc. and even begin to think of all of these individual operations as instances of the same sort of activity: transformation of functions. Finally, at the Trans stage the individual constructs an implicit or explicit underlying structure through which the relationships developed in the Inter stage are understood and which gives the schema a coherence by which the individual can decide what is in the scope of the schema and what is not. For example, an individual at the Trans stage for the function concept could construct various systems of transformations of functions such as rings of functions, infinite dimensional vector spaces of functions, together with the operations included in such mathematical structures.