The Abstraction in Context framework and the Dynamically Nested Epistemic Actions model
Dr. Rina Hershkowitz
Prof. Tommy Dreyfus
Prof. Baruch Schwarz
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.
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.