The Abstraction in Context framework and the Dynamically Nested Epistemic Actions model

Leading team

Dr. Rina Hershkowitz

Prof. Tommy Dreyfus

Prof. Baruch Schwarz

Summary

Understanding how students construct abstract mathematical knowledge is a central concern of research in mathematics education. Abstraction in Context (AiC) is a theoretical framework for studying students’ processes of constructing abstract mathematical knowledge as the processes occur in a context that includes specific mathematical, curricular and social components as well as a particular learning environment. Inspired by Freudenthal, abstracting is taken as human activity of mathematization, namely the reorganization of previous math-ematical constructs within mathematics and by mathematical means, interweaving them into one process of mathematical thinking with the purpose of constructing a new (to the learner) mathematical construct. The emergence of constructs that are new to a student is described and analyzed, according to AiC, by means of a model with three observable epistemic actions: Recognizing, Building-with and Constructing-the RBC-model. While being part of the theoretical framework, the RBC-model serves as the main methodological tool of AiC.

Related Publications

Dreyfus, T., Hershkowitz, R., & Schwarz, B. (In press). The nested epistemic actions model for abstraction in context – Theory as methodological tool and methodological tool as theory. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to Qualitative Research in Mathematics Education: Examples of Methodology and Methods. Springer: Advances in Mathematics Education Series.