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Abstraction in Context: Epistemic Actions

Rina Hershkowitz, Baruch B. Schwarz, Tommy Dreyfus 

March 2001, Volume 32, Issue 2, Page 195

Abstract:
We propose an approach to the theoretical and empirical identification processes of abstraction in context. Although our outlook is theoretical, our thinking about abstraction emerges from the analysis of interview data. We consider abstraction an activity of vertically reorganizing previously constructed mathematics into a new mathematical structure. We use the term activity to emphasize that abstraction is a process with a history; it may capitalize on tools and other artifacts, and it occurs in a particular social setting. We present the core of a model for the genesis of abstraction. The principal components of the model are three dynamically nested epistemic actions: constructing, recognizing, and building-with. To study abstraction is to identify these epistemic actions of students participating in an  activity of abstraction.

Keywords:
Research Studies
Article
Curriculum Developer
Calculus and Higher Level Mathematics
Conceptual Development
Higher Education
Grades 9-12
Higher Education
Curriculum
Geometry & Measurement
Teacher
Theory
Representation