Carsten Ullrich

Knowledge Representation and Management in ACTIVEMATH

ACTIVEMATH is an open web-based learning environment for mathematics. It dynamically generates interactive mathematical courses adapted to the students goals, preferences, capabilities, and knowledge. The content authored for ACTIVEMATH is represented in an extended OMDoc which in turn is an extension of the OpenMath XML-language. ACTIVEMATH is the first system that uses OMDoc. It makes use of this knowledge representation in several knowledge management tasks, among them the web-presentation of mathematical text including formulæ, the communication with the integrated mathematical systems, the user-adaptive composition of a course, the dynamic generation of learning suggestions, and the dictionary facility. This article describes the knowledge representation and management in ACTIVEMATH and emphasizes its bias toward mathematics.

Combining ITS and elearning technologies: opportunities and challenges

The development of Intelligent Tutoring Systems (ITS) and eLearning systems has been progressing largely independently over the past several years. Both types of systems have strengths and weaknesses – ITSs are typically domain specific and rely on concise knowledge modeling and learner modeling, while eLearning systems are deployable in a wide range of circumstances and focus on connecting learners both to content and to one another. This paper provides possibilities for convergence of these two areas, and describes two of our experiences in providing an ITS-style approach to eLearning systems.

Authoring presentation for OpenMath

Some mathematical objects can have more than one notation. When a system compiles mathematical material from multiple sources, a management effort to maintain uniform and appropriate notations becomes necessary. Additionally, the need arises to facilitate the notations editing of the mathematical objects with authoring tools. In this paper, we present our work towards those needs. We have designed a framework that defines an authoring cycle supported by series of tools, which eases the creation of notations for the symbols in the process of publishing mathematics for the web.

A flexible and efficient presentation-architecture for adaptive hypermedia: description and technical evaluation

Means of achieving personalization in the Web are adaptive hypermedia techniques and the flexible composition of learning content from individual learning objects. If the objects are represented in a format different from the presentation format (e.g. as XML as opposed to HTML), a potentially expensive transformation process is required. Furthermore, caching becomes impractical depending on the degree of personalization, as the dynamic information is available at presentation time only and varies for each user. In this paper we present a flexible and efficient presentation pipeline based on a model-view-controller architecture, which overcomes performance problems and couples caching and personalization. It transforms single learning objects and uses a view-layer for adaptive presentation and navigation support that provides additional advantages such as incremental rendering and the easy adaption to different layout styles. Both theoretical and simulation results prove the efficiency of this architecture.

Integrating learning object repositories using a mediator architecture

We propose a mediator architecture that allows a learning system to retrieve learning objects from heterogeneous repositories. 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, a novel ontology-based query-rewriting method has been developed. The architecture has been realized in the Web-based, user-adaptive and interactive e-learning environment ActiveMath. Currently, it enables the ActiveMaths course planner to access four heterogeneous learning object repositories.

Assistance- and knowledge-services for smart production

The transformation towards Smart Manufacturing results in machines that are increasingly complex to use and to maintain, as well as in ever-complicated production processes. Coupled with a continuing reduction of staff, this leads to an increasing demand for information needs and work expertise. At the same time, these challenges offer the opportunity to enhance the employees leeway with respect to designing and organizing their work. The project APPsist focuses on how this transformation can be supported technically and organizationally. This paper presents the technical approach: an architecture for intelligent-adaptive assistance and knowledge services. The paper describes how process mapping identified the requirements of the APPsist system, and presents the identified services and their communication, as well as the intelligent-adaptive functionality of the services.

Using Computer Algebra Systems as Cognitive Tools

We describe how Computer Algebra Systems (CASs) can be used as cognitive tools in a learning environment. In particular, we show howa CAS is employed in ACTIVEMATH, how different types of CAS-exercises are designed, and how feedback can be produced with the help of the very same CAS. We report the results of a first preliminary formative evaluation of ACTIVEMATH CAS-exercises in a university course and some modifications of ACTIVEMATH caused by this evaluation.

Problems and Solutions for Markup for Mathematical Examples and Exercises

This paper reports some deficiencies of the current status of the markup for mathematical documents, OMDoc, and proposes extensions. The observations described arose from trying to represent mathematical knowledge with the goal to present it according to several well-established teaching strategies for mathematics through the learning environment ACTIVEMATH. The main concern here is with examples, exercises, and proofs.

Querying Heterogeneous and Distributed Learning Object Repositories via Ontology-Based Mediation

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.

SafeChild: An Intelligent Virtual Reality Environment for Training Pedestrian Safety Skills

Training children safe behavior in traffic situations is both important and challenging. One of the problems is children’s limited perceptual-motor abilities and associated difficulties with important cognitive skills required to be safe pedestrians. Existing traffic education programs focus more on theoretical knowledge, while training practical skills in the real world is dangerous, expensive and hard to organize. This paper presents a promising alternative – an intelligent virtual reality training environment that allows children to practice their pedestrian skills. It describes the interface and architecture of the system, as well as the skill model of the pedestrian safety domain. The results of the conducted pilot study show that children of the target age group rarely have problems with applying (and acquiring) “basic” pedestrian skills in the developed virtual environment. However, when applying and learning “advanced” skills, they require additional support.