Ubiquitous e-Learning: Designing Web Systems for Economics and Business Mathematics

In this paper we survey some of the developments with regards to technology-enhanced support of mathematics learning and teaching. Coverage is especially given on how to design systems that work effectively on the Web, particularly in the fields of economics and business studies. This is a rapidly evolving landscape in which general trends in e-learning have raised expectations of the electronic tools to go beyond merely providing mechanical functions: nowadays the teacher expects them to help organise their teaching and even enhance their teaching methods. For the student, there is increasing focus on the learner experience, which seeks a wider range and availability of e-learning support tools together with greater ease of use. Advances in technology mean that options keep changing, setting many challenges for system developers, so this paper seeks to indicate the broad features in these changes, with particular regard to future planning. These general considerations are subsequently brought into focus in later sections of this paper by addressing the question of how e-learning systems may provide judicious support for the uniquely human abilities of solving problems. In this case visualisation is an excellent aid, but any tools provided need to draw on a wide range of online resources that are readily available so as to properly establish the learning context. Finally, we briefly introduce into this context two new systems for teaching mathematics: VisualEconoMath, an integrated environment comprising automated tools for deriving solutions to prescribed mathematical problems and How2SolveIt, which supports the quintessential human learning processes surrounding questions and answers, in this case between students and lecturers.