Recent studies on school achievement such as the OECD-program PISA do not aim at curricular fields of achievement alone, but also at transdisciplinary competences such as problem-solving. The concept of a transdisciplinary competence leads to basic theoretical and methodological questions: selection and operationalization of competences in school studies, delimitation from specific disciplinary achievements and basic cognitive competences as well as the question of the significance of the school context for the development of competences. These questions are dealt with empirically within the framework of a construct-validation study by employing several paper-and-pencil and computer-supported procedures. As was to be expected, the problem-solving competence proved to be a multidimensional construct. The analytic ability to solve problems, analyzed by means of a paper-and-pencil test, is closely connected with basic cognitive competences, while computer-supported strategy measures seem to constitute a specific factor.