I may have an interesting take on all of this. I grew up in a poor area and am only 23 y/o now so my experience is pretty fresh still.
Our school system sucked. We didn't even have homework in HS b/c we couldn't take the books home...but we had security guards in every hallway...everyone acted out all the time. There were 3 stabbings in my 4 years there. It was ridiculous.
In 10th grade I got into the voc that was a part of this school. It completely changed my life. The ONLY kids who had any drive were the kids in voc. I did go to college after a year of partying and I wanted to be a nurse but the waiting list was 4 YEARS LONG so I gave up...I did general studies for a year and then got pregnant and had DD. I decided she needed me more than I needed to work or go to school. When we are done having kids and they are all in school (if we don't end up homeschooling) I want to be a MW..
The rest of the people in my voc class went to college only one dropped out besides me and even though there were only like 16 of us in the class I think that is pretty good considering...
Edited to add: 6 of the girls in my class were already mothers and 2 were pregnant by the time we graduated. So that is obviously not ideal either.
For me, I think the problem in public education is in the first few years of elementary where kids aren't getting a good foundation in the basics.
I'd agree that it is problematic when people are taking remedial math after they graduate from high school. Why is that though? Perhaps they weren't being steered to take math throughout high school. This recently changed in our areas but at one time you only had to take two years of math in high school.
I'm not against vocational training, but what happens if someone changes their mind, and they haven't received the type of education that will prepare them for college.