Different moments in the participatory stage of the secondary school students’ abstraction of mathematical conceptions

Abstract

This study reports characteristics of participatory and anticipatory stages in the abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary school students to obtain evidence of constructed mathematical conceptions and how they were used. We could distinguish both stages in different mathematical conceptions and, furthermore, two cognitive moments in the participatory stage. We argue that (a) the capacity of perceiving regularities in sets of particular cases is characteristic of reflection on activity-effect, and (b) the coordination of information provides the opportunity for changing the attention focus from the particular results to the structure of properties.