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We expand upon previous research that looked at the question: \Can graduating students design software systems?" Specifically we want to examine students' understanding of the phenomenon\produce a design." What does this instruction mean to them? In order to investigate student understandings, we examined their designs using a phenomenographic approach. Our outcome space includes six understandings: (0) the design a layman might produce; (1) a design with some formal notation; (2) a design that uses formal notations to express the static relationships among the parts; (3) a design that uses formal notation to express sequential (dynamic) information, but does not relate that to the static system parts; (4) a design that includes and relates multiple artifacts, both static and dynamic; and (5) a design that relaxes the notations and includes only essential artifacts. The last understanding was found only in our expert's design, and we do not expect it from undergraduates.