Quite often "root learning versus understanding" is the difference between being able to show and demonstrate you know your stuff ("root learning") and not being able to show or demonstrate it, but you think you kinda know it ("understanding").
[1] http://math.berkeley.edu/~wu/wu1999.pdf
[2] http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf
The challenge is that simply getting the right answer, especially in terms of arithmetic (one small piece of math), can mask how well a student understands the underlying concepts and whether s/he can flexibly apply the concepts.
Here's a great video on that topic:
https://www.youtube.com/watch?v=_ofQ_WnQiZ4
https://www.youtube.com/watch?v=BlvKWEvKSi8Perhaps I missed something or misread it, but that wasn't my takeaway. Rather, it seemed he was expressing that mechanics doesn't, on its own, directly lead to understanding (measurable by ability to apply the tools to novel, to the student, problems/situations). Given that he also endorsed Khan Academy in this same article it seems he has no problem with it developing mechanical understanding as a complement to the understanding needed by practitioners (scientists, mathematicians, engineers, etc.).