My early school math involved memorising multiplication tables. Later on, there was rote memorisation of other aspects of math that I just never understood - you just "had to", and none of the teachers could explain why.
It was for this reason that I hated math, and it wasn't until I started understanding some of the more fundamental relationships many many years after school that I finally got it.
While this is but one anecdote, and having heard similar stories from others is just more anecdotes - there does seem to be research backing up that a lot of people don't understand the fundamental relationships between numbers and how math works.
I see Common Core math trying to teach relationships between numbers - showing that by being able to break down large unwieldy numbers you can get something that while it might have a bunch more steps, they're at least feasable without counting on fingers/toes or trying to remember times tables.