In earlier researches on freehand sketching, the cognitive behaviour of designers was studied. In recent years, some researchers began to look into this area from the design media aspect. The pen-based system, developed by Gross, Landay and other researchers, used the pen as an input device, allowing sketches to be freely drawn in a computer environment. The importance of the freehand sketch lies in its ability to freely represent various drawing projections using ambiguous sketches. However, as for the various drawing projections, such as diagrams, symbols, plans, elevations, sections, perspectives, etc., how are they interrelated to a designeris thinking process and the cognitive behaviour? Different media have different abilities to represent different projections. Would they affect the designeris design thinking as well? Targeting different media, i.e., conventional freehand sketches vs. the computer pen-based system, this research uses case studies and think-aloud protocol analysis to present an analysis and discussion. Research results show that there is a relationship of gradual embodiment that is mutually complementary, going from a whole perspective to being the dissected into sections between the different projections. In addition, these projections restrict the designeris various design thinking processes, while the use of different media may somewhat change the actual design thinking of the designer