22 June 2004 Technologies involved in the teaching of undergraduate mathematics on the web Johann Engelbrecht and Ansie Harding University of Pretoria, South Africa Abstract In this paper an overview is given of technologies involved in the teaching of undergraduate mathematics on the web. A diagrammatic view of technologies involved in symbolic presentation of mathematics is discussed, positioning HTML within the family of Mark-up languages. An exposition is given of technologies involved when moving from a WYSIWYG or from a TeX, LateX environment to the web. Virtual learning environments in which to host a mathematics course on the web are discussed as well as assessment packages, software packages and wireless learning devices. 1. Online teaching and learning The internet offers the possibility of providing a stimulating learning environment to engage learners in meaningful learning through reflection, application and interaction (Macdonald et al, 2001). For this and other reasons the number of web-based or online courses has increased rapidly over then past few years to become a significant constituent of educational pedagogy worldwide. Online learning or e-Learning is stimulated primarily through the use of telecommunication technologies epitomised by the world wide web and includes electronic mail, bulletin board systems, electronic whiteboards, inter relay chat rooms and desktop video conferencing (Suanpang et al, 2003). Where does mathematics stand in the shift towards online learning? Although mathematics courses have not been at the pioneering front of internet course development the current presence of mathematics courses on the internet bears testimony to the subject’s increasing participation in this new mode of education. Indeed the visual facilities and exploratory opportunities offered by well-designed mathematics material on the web often supplant the talk and chalk paradigm by far. Yet, it would also be audacious to say that mathematics teachers embrace the internet with overwhelming enthusiasm. One reason for this perceived reluctance is that mathematics is a conceptual subject and the common opinion is that face-to-face contact is necessary for conveying these concepts. Another and perhaps more valid reason is because of the problems surrounding symbol presentation in the HyperText Markup Language (HTML), the language commonly used for internet presentation. The technology itself seems to be a hampering factor. Lately, however, mathematics courses on the internet do not appear to be a rarity any longer, whether these are fully or partially web-based. Indeed the visual facilities and exploratory opportunities offered by well-designed mathematics material on the web often supplant the talk and chalk paradigm by far. Quoting Bookbinder (2000) Enhancing the mathematics curriculum with web-based technology takes time and effort, but the effort is well worth it. The authors have done a comprehensive overview of the current status of undergraduate teaching of mathematics on the web (Engelbrecht and Harding, 2004a, 2004b). In the following section we give an exposition of technologies involved in the teaching of undergraduate mathematics on the web. We give a diagrammatic view of technologies that makes symbolic presentation of mathematics possible followed by a discussion on the scope of virtual learning