A digital-friendly mathematical notation for series

Abstract

Mathematics in the South African Secondary School context is a subject under a lot of scrutiny and discussion. Enrollment figures for Mathematics in Secondary Schools are declining and qualified teachers that produce learners with good results are hard to find. In this climate, the use of on-line tools and portals could be a solution for teacher self-education and a useful and cheap supplementary source of material to learners of mathematics.

We conducted a survey to establish the usage of on-line portals by Secondary School Mathematics teachers in the province of Gauteng in South Africa. The survey showed that the use of on-line portals is very low for a variety of reasons. One of the reasons, after the more obvious ones such as training, access and infrastructure, was the difficulty that non IT-literate people have in using the tools, and in particular entering mathematical expressions electronically. '' In a parallel activity to present a possible improvement to the problem stated, we proposed a new notation for the well-known sigma notation for series. The sigma notation is one of the first complex and multidimensional notations that learners encounter in the final secondary school mathematics curriculum. Research showed that the use of a well-designed and uniform notation is imperative to improve communication and understanding in the field of mathematics. Currently, a fairly consistent notation is used to notate the elements of sets, but the notations for sequences, series and other equations often vary from one author to another. Furthermore, the currently used sigma notation for series is ambiguous. The notation proposed by us involves a modification of the traditional set notation because the most widely used notation for sets has limitations and cannot easily be generalized to sequences and series. The proposed modification addresses these limitations and provides an elegant extension of the set notation to denote sequences and series more uniformly. The proposed notation has the additional benefit not using any special character or symbol. It is also a linear notation and therefore simpler to use electronically.

We tested the comprehension of the proposed notation in a live school study for improved understanding. The outcome of the study did not show that the new notation brings any improvement in the learners’ ability to grasp the underlying concept, but it highlighted issues with the writing of the traditional notation that might benefit from a shift towards a more explicit notation using familiar symbols, such as the one proposed.

The survey results and the school experiment indicated that notations that use familiar and easy-to-write symbols, and are simple to input electronically using a standard keyboard, could lower the barrier to entry towards wider use of on-line portals for mathematics education. For wide-scale and general benefit, all mathematical notations will need to be adapted to adhere to the principal of one-dimensional, standard keyboard symbols. This is an ambitious goal but we hope that this dissertation can instigate thinking and experimenting in this area to slowly migrate mathematical notations to digital on-line friendly formats.