Abstract
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 it occurs in a context that includes specific mathematical, curricular and social components as well as a particular learning environment. 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 also serves as the main methodological tool of AiC.
In the first section of this chapter, we give an outline of the theoretical aspects of AiC as background to the description of the elements of our methodology in the second section, and their application to a specific example in the third section. In the concluding section, we close the circle by exhibiting the strong relationship of theory and methodology in AiC as it is mediated by the RBC-model.
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Dreyfus, T., Hershkowitz, R., Schwarz, B. (2015). The Nested Epistemic Actions Model for Abstraction in Context: Theory as Methodological Tool and Methodological Tool as Theory. In: Bikner-Ahsbahs, A., Knipping, C., Presmeg, N. (eds) Approaches to Qualitative Research in Mathematics Education. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_8
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