When I talk to other research mathematicians, there is pretty uniform agreement that we want our (university) students to understand the maths we teach them rather than just memorise processes. As far as I can tell, we have a reasonably consistent idea of what that means (although much less agreement of what to expect of students in a given context).
However, in the context of curriculum discussions, I've found that non-mathematicians are unwilling to accept 'understanding' as a suitable word to describe the desired outcome. I've also read a couple of times that students don't necessarily share our view of the term, although I haven't had time to check out the references.
So my question is:
Are there alternative phrases that can be used to describe what we mean by mathematical 'understanding' (at undergraduate level) that are better at communicating the meaning to non-mathematicians?
I have come across the phrases 'relational understanding' and 'instrumental understanding', which I think are helpful, but would only be meaningful to the minority who have come across them before.