Ben's consolidation of knowledge structures about infinite sets

According to a recently proposed model for processes of abstraction in context, the construction of a new structure is to be followed by a consolidation phase. In this paper, we develop an empirically based, theoretical analysis of consolidation that emerges from a sequence of interviews about the comparison of infinite sets with a talented student. We take for granted that construction has occurred in the first interview and analyze the second one. Our analysis shows that consolidation can be identified by means of the psychological and cognitive characteristics of self-evidence, confidence, immediacy, flexibility and awareness. We also found three modes of thinking conducive to consolidation, one related to problem solving, one to reflective activity and an intermediate one.