Abstraction in context: Epistemic actions

Rina Hershkowitz, Baruch B. Schwarz, Tommy Dreyfus

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)195-222
Number of pages28
JournalJournal for Research in Mathematics Education
Volume32
Issue number2
DOIs
StatePublished - Mar 2001
Externally publishedYes

Keywords

  • Abstraction
  • Activity
  • Construction of knowledge
  • Context

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