Characteristics and dimensions of a competence model of theoretical computer science in secondary education

Guiding theme of the ongoing reformation movement of the education system in Germany catalyzed by the OECD Programme for International Student Assessment is standardization. Educational standards are developed for all grades of school up to university level with a focus on the core subjects, reading, mathematics and scientific literacy [1]. Starting basis for the elaboration of standards are competence models, where competence is conceived according to Weinert [2] as "a roughly specialized system of abilities, proficiencies, or individual dispositions to learn something successfully, to do something successfully, or to reach a specific goal." As for computer science education, most of the existing approaches to competence models are of pragmatical nature, based on years of teaching experience. Although plausible and well thought out most of these models neither are concerted nor verified. This research work introduces a methodology of constructing a competence model from exercise characteristics by means of empirical statistical analysis. Exemplified by theoretical computer science in secondary education, it is exposed how hypotheses on the dimensional structure of a competence model are theoretically founded and empirically verified.

The proceeding roughly breaks down into five steps. First step is the identification and classification of the characterizing attributes of task difficulty. "Characteristics" may be the closeness to the student?s realm of experience, the level of abstraction or complexity of the content, the level of formalization or redundancy of the task setting, or the level of cognitive process. Second step is the generation of hypotheses on the dimensional structure of a competence model, based on classification of the characteristics. For this purpose, the attributes are bundled to theoretically homogeneous groups according to criteria like "concerning the task setting, the curricular content or the learner activity". It is postulated that each competence dimension is composed of one group of characteristics, just as spectral colors are combined from primary colors. Step three is the implementation of an empirical study to gather empirical data on students? abilities along the characteristics. Step four is a statistical data analysis in order to verify the dimensional structure. Factor analysis appears to be an appropriate statistical technique for analyzing the correlations between the characteristics and bundle them to a small number of underlying dimensions, called factors. Since a factor shows, e.g., large correlation with the characteristic level of formalization and medium correlation with the characteristic redundancy of the task setting, it may be interpreted as their common factor, describing the portion of task difficulty emerging from the task setting. As step five it is proposed to cluster the competence profiles, referring to the factors. Typical competence profiles resulting from cluster analysis may be expressed in terms of characteristics to provide an individual competence diagnosis that is both meaningful and comprehensible. The following two examples are profiles of minimum and maximum competence level, to be fulfilled by every student (a) and to be attained only by high performing students (b) respectively: (a) The learners model a course of action close to their realm of experience (e.g., traffic lights) by using automata. If textually specified, algorithms are recalled and properly applied. (b) The learners model a problem beyond their experience (e.g., syntax check of arithmetic expressions) by using automata. Even if formally specified, problems are analyzed and appropriate algorithms are created.