The development of problem-solving competence is both a goal of learning at school and a prerequisite for further learning. The PISA study 2003 revealed surprising results: Students in Germany seem to possess cognitive potential that becomes visible when solving cross-curricular problems. However, this potential is not effectively used in schools for developing curricular competencies. In order to test this potential-utilization hypothesis, analyses of cognitive demands of PISA problems as well as studies on the structures of required competencies are needed. Two studies on solving analytical problems and dynamic problems are reported, the results of which suggest a three-dimensional competence structure for both competency domains. Substantial correlations of these dimensions with curricular competencies, especially in the domains of mathematics and science, give rise to the expectation that training of single dimensions might transfer on curricular learning in those domains.