Studying the change mechanisms rather than the things that are changed is the study of functions. An algorithm describes how one thing is transformed into another. It is an algebraic creature. A dependence concentrates on how one thing is affected by another. It is an analytic creature.
Mappings are useful in counting.
A typical use of mappings is to take a well known set or structure, define a correspondence between its elements and the elements of a less well known set, and then to estimate how far away the function is from being a 1-1 correspondence between the sets. In this sense, mappings are combinatorial creatures. But the real way to study the complex numbers is to use all these approaches at once. Some reformers insist that students no longer need to establish their conjectures with deductive proof. This is especially true about conjectures that can be easily checked in thousands of cases with appropriate computational environments.