I rather see functions as transformations, in the mathematical sense. A function receives an input and produces an output, according to some logic that only the function is responsible for. A small logical block that can be reused into somehow bigger logical blocks (i.e. programs). I think it is much more realistic, lead you to good programming practice, and also much more fun.

I have tried to teach that and students have always (seem) to like & understand this approach. It was for student at university level, so maybe more able to understand this 'functional' view of functions.