Representation is essential to design work. While there is a multitude of research on, for example, gesture, prototyping, and sketching, there is a critical need for a more general account of design representation, able to explain diverse results across representation modes and design tasks. We address this need by experimentally testing dual-process theory hypotheses regarding the impact of gesture and sketching on a range of design tasks, including reproduction, evaluation, elaboration, ideation, and selection. Central to this is the (mis)match between representation mode at input/response, and the interaction between Type 1 and Type 2 processing. These findings support a novel dual-process explanation of design representation, suggest resolutions to previously contradictory findings, and provide implications for design theory, education, and practice.