Mathematical interactive content: what, why and how

The real challenge of e-Learning is to produce content that brings a general improvement in the way students learn and teachers teach. For that, “intelligent” interactivity is the single most important feature that such content should have. But the design and production of content with this kind of interactivity has turned out to be harder than expected, the main reason being that it requires the convergence of many kinds of experts in parallel to the convergence of the several technologies involved. In the case of mathematics, the least amount of expertise asks for the presence of professional mathematicians, software engineers, publishers, and perhaps learning theorists, that can productively talk to each other. In this paper we want to examine afresh, with a view to the future, what is (or can be) meant by interactivity; the reasons why interactivity should play a role in optimizing general mathematical learning and in making possible, and viable, that mathematics teachers at large embrace a role that is congruent with their present day mission. Finally we propose a check list for desirable features that advanced mathematical learning systems should have, state some guiding principles for their design, and describe what is involved in their production.