This paper explores a major theoretical framework from psychology, Dual Process Theory (DPT), which has received surprisingly little attention in the computing education literature. DPT postulates the existence of two qualitatively different kinds of cognitive systems, a fast, intuitive "System 1" and a slow, reflective "System 2". System 1 is associated with cognitive factors such as crystallized intelligence, long-term memory and associative learning; System 2 with fluid intelligence, working memory, and rule learning. This paper summarizes DPT and the way it has been expressed and explored in literatures relating to intelligence, memory, learning, attention, cognitive load, and more. It proposes a summary model, the Dual Process Cycle (DPC). It then considers example concepts from computing education within the context of this model. Examples include programming expertise, mental models of programs, the notional machine, code reading and code writing, and the theory of Learning Edge Momentum (LEM). In conclusion, it is argued that the DPC (and the framework of DPTs in general) provides a useful context for defining such concepts more richly and exactly, and for generating interesting questions about them.