Studies on design, show that problem formulation plays a major role in creative design. We plan to construct an interactive computer system that aids problem formulation. In the current stage, to improve our understanding of problem formulation, we have conducted exploratory protocol studies of novice designers and collected data from an expert designer in the form of a depositional interview. A formal representation of the design problem is needed to improve our empirical investigation. We propose a preliminary framework for such a model and we call it a problem map. It provides a basis for comparing how different designers perceive a problem. Our study is based on the design of a model aircraft for the AIAA student design competition. This preliminary analysis shows the evolution of the problem and the solution spaces in the elaboration of the problem maps through time. The problem maps also show a richer representation of attended attributes and relations for the expert and more attributes left in vacuum for the novices.