Real analysis students’ understanding of pointwise convergence of function sequences in a DGS assisted learning environment

Abstract

The purpose of this research study is to understand how math majors conceptualize and make sense of pointwise convergence of sequence of functions in a series of in-depth qualitative interviews. Framed in APOS (Dubinsky & McDonald, 2002) and VA (visual-analytic) strategy coordination (Zazkis, Dubinsky & Dautermann, 1996) theoretical perspectives, the analysis showed that students demonstrated a diversity of mathematical behaviors associated mostly with the process level of understanding in APOS model. Yet a complete understanding of pointwise convergence at object level did not take place, students still also exhibited significant achievements in progression from process to object. The VA coordination also proved a beneficial mechanism in students’ making sense of pointwise convergence in a dynamic geometry environment.