Generative and evaluative approaches are two different ways of diagnosing students’ input that have been realized in a number of intelligent tutoring systems. We describe how ActiveMath’s exercise subsystem realizes both types of diagnosis and how it can combine them. A framework for distribution of diagnostic services is extending the existing web-service approach to mathematical services with the notion of context. In addition to an appropriate diagnosis, a goal is the interoperability of diagnosis services.

This paper describes a new student model technology that combines evidences and knowledge about pedagogical and domain structure. Its structure is generated from the metadata available in the content representation of the adaptive web-based learning platform ACTIVEMATH (or other contents). The evidences are processed with Item Response Theory and Transferable Belief Model uncertainty methodologies. We summarize evaluation results for this student model.

1We propose a mediator architecture that allows a learning system to retrieve learning objects (LOs) from heterogeneous repositories of LOs and not exclusively from its proprietary repository. A mediating component accepts queries formulated in a uniform query language, translates them into repository specific queries and passes them to each connected repository. For the translation of queries, an ontology-based queryrewriting method has been developed which uses the specified knowledge representation of the repository and an ontology mapping to compute the rewriting steps for translating. For distributing queries we realized a mediating architecture, which passes the translated queries to the repositories. This architecture has been integrated in the Web-based, user-adaptive and interactive e-learning environment Active Math.

Abstract. The capabilities of a automated theorem prover's interface are essential for the effective use of (interactive) proof systems. L Ω UI is the multi-modal interface that combines several features: a graphical display of information in a proof graph, a selective term browser with hypertext facilities, proof and proof plan presentation in natural language, and an editor for adding and maintaining the knowledge base. L Ω UI is realized in an agent-based client-server architecture and implemented in the concurrent constraint programming language Oz.