Processes of Abstraction in Context

The nested epistemic actions model for abstraction in context has been developed with the purpose of analyzing processes of mathematical abstraction in context. We take a point of view influenced by activity theory and consider situations in which the learners’ motivation for a new construct, as well as their thinking mode, are mathematical. Abstraction is then defined as an activity of vertically reorganizing previous constructs that leads to the emergence of a new construct. Processes are considered as they occur along a sequence of activities in a learning environment with a curricular, social and historical context. The basic elements of the model are three epistemic actions: Recognizing, Building-with and Constructing. These epistemic actions are nested within each other. Different constructing actions may go on in parallel and interact with each other. The patterns of interaction may indicate events such as the justification of a mathematical relationship by the learner or learner’s relationship to contextual elements such as technological tools. The consolidation of new constructs along a sequence of activities forms an integral part of the model. Constructing and consolidating processes are considered in a variety of social contexts ranging from solitary learners to entire classrooms.