Sequence of partial sums as an infinite iterative process: a step towards the understanding of numerical series from an APOS perspective

Abstract

Learning infinite series entails many difficulties. In this paper, we focus on how students learn one aspect of the concept of infinite series: the sequence of partial sums as an infinite iterative process. The learning process of two groups of first-year university students was analysed using the genetic decomposition of the sequence of partial sums as an infinite iterative process. Different manifestations of action and process conceptions were observed in both groups. The differences in the ways the students grasped the sequence of partial sums reveal the importance of some key mathematical elements for understanding infinite series.