Interoperable Competencies Characterizing Learning Objects in Mathematics

Cognitive task analysis has been used in ITSs to predict students' performance, improve curricula and to determine appropriate feedback. Typically, the learning factors/knowledge components have been determined only for the use in oneITS or curriculum and therefore, general frameworks were not applied. Moreover, the result is sometimes rather unsystematic and not reusable across domains. However, for making learning environments interoperable and comparable and to be able to reuse learning objects, the competency hierarchies have to be usable for different learning environments and across domains. In this paper, we propose an approach to competencies represented as pairs of knowledge and cognitive process whose ontologies extend and revise existing taxonomies. A goal is to make these competencies a quasi-standard that enables interoperability and reuse. Moreover, we briefly describe, how the competency ontology can be employed for different purposes.