chapter  1
31 Pages

The nested epistemic actions model for abstraction in context


In this chapter we study mathematical abstraction in educational contexts. Our purpose is to observe the act of abstracting throughout successive activities in mathematics classrooms. To do so, we operationally define abstraction in a way which is general enough to encompass empirical and theoretical aspects, we elaborate a methodological tool for observing the emergence of abstraction in successive activities, and we refine the theory of abstraction through empirical analyses in classrooms. The tool was originally inspired by Freudenthal’s idea of vertical mathematization, as was our preliminary, vague definition of mathematical abstraction. This definition stirred the design of activities with potential for abstraction but needed to be refined. The nested epistemic actions model constitutes such a refinement, based on our empirical studies as well as theoretical considerations on mathematical abstraction by others. We show that the model is adequate to identify and trace abstraction and its consolidation in successive activities in numerous contexts, including work by individuals, small and large groups in unguided and guided activities with and without technological tools.