Much study has been done on many aspects of design. Although problem formulation is believed to play a major role in a creative design of high quality, it has gained less attention. In our larger study, we are investigating the role of problem formulation on design creativity. In order to conduct such studies, a formal representation of design problems is needed. In this paper, a taxonomy for representing the design problem space is proposed. We call this static representation the problem map. It can provide a basis for comparing how different designers perceive a problem and help demonstrate the co-evolution of problem and solution. Our preliminary study was based on the design of a model aircraft by an expert and two groups of novice designers. The examples of the problem maps showed that the expert had a richer set of attributes of design entities and relations among them, which the novices missed.