Computer science educators expect their students to develop a scientific design discipline with programs and proofs. Established acquisition of a scientific discipline encapsulates rich cognitive representation, which is reflected by competent non-specific transfer. Do computer science graduates demonstrate non-specific transfer of fundamental design notions? The study presented here reveals some undesired findings. Computer science graduates, who are engaged in teaching, showed rather limited competence with task representation and the heuristic of decomposition and (re-)composition, as well as with progression through ordered design stages. Many followed a rather unordered and unconvincing solution plan, which yielded only partial outcomes, and no conviction of exploitation. We describe our findings and offer suggestions for explicitly elaborating (sometime implicit) design notions.