The computer, the new media, reaches out and influences the behaviour of design as it does almost every facet of life. In recent years, much research into the development of computer-aided design has looked at the concept generation stage of the design process. Most of these applied studies have focused on the testing of computer systems. On the other hand, there are also many studies on the visual thinking and cognitive behaviour of designers while sketching or drawing in the stage of concept generation. From the synthesis of the two aforementioned disciplines, we can find that there exists a point of deficiency. That is, the cognitive research about designers using computers as sketching media is absent. It is this area that is discussed in the current paper. The fundamental analytic data of this research is the visual process chronicled from the sketching of subjects. The analytic data is the verbal data from the questions that the subjects are asked after sketching. The data is analyzed using three coding schemes. The cognitive appearance while designers generating concepts with computers or conventional media are propounded and discussed in this research.