In this chapter, two studies are presented that investigate aspects of the cognitive potential exploitation hypothesis. This hypothesis states that students in Germany have cognitive potentials they do not use when solving subject-specific problems but that they do use when solving cross-curricular problems. This theory has been used to explain how students in Germany achieved relatively well on cross-curricular problem solving but relatively weakly on mathematical problem solving in the Programme for International Student Assessment (PISA) 2003. Our main research question in this chapter is: Can specific aspects of cross-curricular problem-solving competence (that is, conditional knowledge, procedural knowledge, and planning skills) be taught, and if so, would training in this area also transfer to mathematical problem solving? We investigated this question in a computer-based training experiment and a field-experimental training study. The results showed only limited effects in the laboratory experiment, although an interaction effect of treatment and prior problem-solving competence in the field-experiment indicated positive effects of training as well as a transfer to mathematical problem-solving for low-achieving problem-solvers. The results are discussed from a theoretical and a pedagogical perspective.