Problem solving is a key concept used to cope with the demands of a rapidly changing world. It is regarded both as a cross-curricular competence that is related to, but not identical to, general cognitive abilities, and as a domain-specific competence (e.g., in mathematics). Based on results of the Programme for International Student Assessment (PISA) 2003 and a connected repeated measurement study in Germany (PISA-I-Plus), the cognitive potential exploitation hypothesis postulates that crosscurricular analytical problem solving competence can be regarded as a resource for improving domainspecific problem solving competence in mathematics. The paper presents results from a 15-week field experimental training study (N= 173 students in Grade 9) investigating aspects of this hypothesis by addressing this research question: can broad training in cross-curricular analytical problem solving with a focus on conditional knowledge, procedural knowledge, and planning skills enhance (1) cross-curricular analytical problem solving and (2) mathematical problem solving? The results show an interactive effect between treatment and prior cross-curricular problem solving competence indicating an effect of transfer for low-achieving problem-solvers on mathematical problem solving competence. The results are discussed from both an educational research and an instructional perspective.