As a programmer when solving a problem, a number of conscious and unconscious cognitive operations are being performed. Problem-solving is a gradual and cyclic activity; as the mind is adjusting the problem to its schemas formed by its previous experiences, the programmer gets closer and closer to understanding and defining the problem. The primary cognitive operations the programmer uses to set up refining models are: language abstraction, analogy, algorithmic abstraction, decomposition-superposition, conversion, intuition, and variation. In our paper we are shedding new light on algorithmic abstraction, while explaining the essence of decomposition-superposition, a key element-pair in the cognitive toolkit of programming.