A notation for sets, sequences and series : possible benefits for understanding and use

Abstract

The use of a well-designed and uniform notational system is imperative to improve communication and understanding. Currently, a fairly consistent notational system is used to notate the elements of sets, but the notations for sequences, series and other quantifications often vary from one author to another. The most widely used notation for sets has limitations and cannot easily be generalised to sequences and series. Furthermore, the well-known sigma notation for series is ambiguous and difficult to grasp. This article proposes a clear notation that can be used for all of the above. We aim to test the hypothesis that this notation could aid an understanding of concepts which build on the use of this notation. As a first step, we conducted a pilot study to inform the design of an experiment to evaluate the effect of the proposed notation on understanding. Secondary-school learners who had never been exposed to the sigma notation participated in the pilot study.