  When teaching an elementary logic course to students who have a general
scientific background but have never been exposed to logic, we have to face the
problem that the notions of deduction rule and of derivation are completely new
to them, and are related to nothing they already know, unlike, for instance,
the notion of model, that can be seen as a generalization of the notion of
algebraic structure. In this note, we defend the idea that one strategy to
introduce these notions is to start with the notion of inductive definition
[1]. Then, the notion of derivation comes naturally. We also defend the idea
that derivations are pervasive in logic and that defining precisely this notion
at an early stage is a good investment to later define other notions in proof
theory, computability theory, automata theory, ... Finally, we defend the idea
that to define the notion of derivation precisely, we need to distinguish two
notions of derivation: labeled with elements and labeled with rule names. This
approach has been taken in [2].
