Unless you taught a long time ago or are in a very strange state, odds are those children were tested with standardized tests, probably multiple times. I live in Michigan, so I can guarantee that pretty much every child coming out of Detroit has been tested in a standardized manner by the state at least three times while in school (conservatively, I remember having more but I'm not sure what all they were), and they still come out with problems. You can't even get a real HS diploma without passing these tests. (At least when I graduated you would get a diploma from the school but it lacked some sort of state endorsement.)
I don't think total lack of standardized testing is the problem. The problem is they are either being cheated on or gamed, or nobody really knows how to solve the problems being identified.