the learning process for a student rarely involves consuming a precise, coherent definition,

But it should! I do make a point of embedding references to actual standards in my teaching, mostly in exercises like "what paragraph of the (e.g., Java) language spec. says that the following program is illegal". The intention is: students should a) get used to reading (semi-)formal specifications b) see that concepts from "theory" (lecture, papers) appear verbatim in actual "industrial" specs c) get scared of using software/language that has no specification

.. the nature of functional programming supported by a review of the theory upon which it is founded: at the very least, the lambda calculus, preferably along with some basic ideas from type theory.

That. And I do start my FP teaching with term rewriting, as a model of first-order programming. (gives you terms as a model of data, and rewrite rule application as a model of pattern matching) - J.W.