Measuring individual learning progress the combinatorial way

Measuring human aptitude and learning processes has a very long tradition and the research community established well-elaborated test theories. Since the advent of learning analytics, a new community is contributing to the theories and methodologies of measuring learning. In this paper we introduce Competence-based Knowledge Space Theory as a combinatorial, multi-dimensional framework for modelling and assessing competencies and competence development over time. A particular strength of the approach is the conceptual and methodological separation of latent aptitude (competencies, knowledge) and observable performance as indicators for aptitude. In the Lea´s Box project, the approach has been realized and deployed as online learning analytics platform tailored to the needs of conventional classroom settings (i.e., only little, heterogeneous, and incomplete data as basis for analytics). The paper illustrates the potential strengths of the approach and gives and outlook for future developments.