Ateyeh, KhaldounKlein, MichaelKönig-Ries, BirgittaMülle, JuttaReimer, UlrichAbecker, AndreasStaab, SteffenStumme, Gerd2019-11-142019-11-1420033-88579-357-1https://dl.gi.de/handle/20.500.12116/29964Repository 'Instance' concrete Module Repository Module Module Module Atom Atom Use U Repository UI I 'Course' = adapted (1) Course Module (1.1) Course Module (1.2) Course Module (1.3) Atom isPrerequisiteFor Figure 1: Concepts and relationships of the formal model to organize learning objects the system helps him by displaying the prerequisites laid down in the ontology. For some subtopics, Chuck may not find appropriate material in the repository. In this case, he will switch back into his role as author, develop the appropriate material, and add it to the repository for future use. 3 A Formal Model This section introduces a formal model defining the basic concepts needed in the process of courseware modularization. Special emphasis lies on how to operationalize the introduced concepts in order to help authors to construct reusable, extensible, and maintainable repositories for their learning objects. An overview of the concepts and their relationships is given in Figure 1. As described in Section 2, in order to modularize teaching and learning material on a subject, the authors have to agree on a collection of terms that describe the subject and on relationships between these terms [9]: Definition 3.1 (Domain Specific Ontology) A domain specific ontology is a directed graph with domain specific terms as nodes. The edges between the terms are typed. There exist two types of edges: $\bullet $isSubtopicOf: An edge from term t1 to term t2 is of type isSubtopicOf iff. t2 deals with a more generic topic than t1. Edges 237 of this type are unique and mandatory for inner terms, i.e. each term (except for the root of the graph) is subtopic of exactly one other term. Therefore, the terms form a tree when regarding the isSuptopicOf edges only. $\bullet $isPrerequisiteFor: An edge from term t1 to term t2 is of type isPrerequisiteFor, iff. t1 needs to be understood by a learner before he is able to learn t2. The isPrequisiteFor relationship builds an acyclic graph. In the following, we will sometimes talk about layers or leaves of the ontology. In these cases, we are always referring to the graph with respect to the isSubtopicOf edges. Learning objects are characterized by their content (described by the terms of the ontology) and by their intended usage. For instance, a certain learning object can be used asenText/Conference Paper1617-5468