Issues with Notation at the Interface Between Technologies

Abstract

Mathematics is underpinned by the notation in which we write it. Traditional notation is not free of ambiguity, but on the whole the conventions we use to write mathematics on paper are flexible and visually clear. It is important, though, to view this as the product of a particular technology. When we wish to transfer our mathematics from one technology to another, the interface between the systems of notation becomes paramount. The problem is highlighted particularly when students are introduced to computer algebra systems (CAS). In this paper we highlight the differences between pencil-and-paper and electronic (linear) notation, some well-recognized and others not, particularly noting certain points at which students often encounter difficulties. The solution to these problems is not intuitive or obvious, and students encountering the interface between traditional and CAS technologies need specific intervention to assist them in overcoming the many difficulties they encounter.