
## 8 Conclusions And Future Work

Our main objective in this work was to identify requirements and research areas for planned research project. In retrospective, we think we have accomplished our goals in different forms and at different levels.  We have developed an architectural proposal that can be useful from different perspectives, both practical and theoretically perspectives. From a particular point of view, we have gained a much better understanding of the basic elements which are the important building blocks for programming learning material into an e-
Learning environment like ActiveMath (we specifically mean programming exercises). We identified the need for a formal reasoning framework as a fundamental issue. We justified the ideas on standard cognitive models and frameworks.  We think our proposal in this direction is compatible with the design principles of ActiveMath. We have identified the role that cognitive reasoning on programming can play in this context.

Summarizing, we believe that the following specific points are important to guide future work:

- A review of non-st and ard reasoning forms not covered by Bloom's Taxonomy in terms of our proposed model.

- A formal language for expressing programming plans and exercises taking into con-
sideration generative capabilities.

- A typing system for translating plans into adequate forms of dynamic logic-like lan-

gu ages.
- The precise identification of the primitive verbs and corresponding Bloom-complexity mappings (i.e.  Bloom's semantics).  This has to be accomplished in a cognitively

sound way.

- From a more practical perspective, the design of an extension of the ActiveMath OmDoc representation in order to be able to represent code at all the three layers
(Eval, DR, MDR).

## Acknowledgments

We gratefully thank the DAAD for the financial support that made possible this visit. My very special thanks go to Jörg Siekmann for having invited me, for the contacts and the material support. Very special thanks to ArtinSoft for the support and space to make this visit possible. To George Goguadze for the introduction and pointers to ActiveMath. And last but no least, I am particularly grateful to Serge Autexier, Dominik Dietrich, Marvin Schiller, Ewaryst Schulz and Marc Wagner for all the great help and the nice and friendly company.