Learning and Teaching Mathematics on-Line: Which are the Main Difficulties?

Why has the full potential of Internet for learning and teaching Mathematics not been exploited? In the present paper we outline the main problems put into evidence by our experience in using e-Learning instruments for teaching Calculus in a Computer Science Degree course and describe some possible solutions. There is no doubt that learning Mathematics is effective only when students are actively involved: this means that practice has a relevant role. We wondered which kinds of exercises are more effective in teaching Mathematics on-line. Surely, practicing in a virtual environment is quite different from attending classroom lessons and there are several further difficulties in designing and implementing exercises for on-line use; therefore, we try to make some conjectures about features that make exercises attractive and, at the same time, instructive. Integrating Virtual Learning Environment (VLE) with Computer Algebra System (CAS) partially solves problems about authoring mathematical questions. Unfortunately, some questions about interoperability and reusability arise; consequently we took into consideration IMS Question & Test Interoperability (QTI), discussing the difficulties encountered in following the lines of its specifications for setting mathematical questions.