After retiring from USAF, I decided to teach mostly math plus some physics and chemistry at WOSC junior college. WOSC has a nursing program and I got a lot of nursing students who landed about 5th grade level on the math placement test and had to start with "zero level" remedial math (arithmetic), then beginning algebra (8th grade), then intermediate algebra (high school), then College Algebra to meet the associate degree requirements. In other words, two years of math classes.I get what you are saying, but you are assuming algebra is taught for the purpose of learning math. But, what about the kid that wants to become a nurse, do you offer a specific math course for that student too? vocational schools and universitys are there to teach those skill specific courses, public schools establish schemas for you to use in your career training.
I saw how ingrained this "math ain't good fur nuthin'" was ingrained in the poor students, so I started putting an offer into the orientation for each class:
"If you can't read, then you have to depend on the skills and honesty of other people to read everything to you. If you can't do math, you have to rely on the skills and honesty of other people that you aren't being cheated. For any part of this course, if I can't tell you what it is good for, then we'll just skip it. I have spent decades making a good living using advanced math every day, and not knowing basic math skills is like not knowing how to read. And learning math is a skill you develop, not something you can memorize for the final. Think of a tennis or weightlifting class. If you sit and watch tennis for a semester, you still can't play. You only learn math by doing it."
I had one EMT, wanting to be a nurse, in my remedial math class, and she was adamant that math was pointless for a nurse. Finally I pointed out that a nurse was the last person to check that an injection was correct in type and size and if she could not calculate and recognize how much 10cc was and gave 100cc, she could kill somebody. She complained to the head of the nursing program, who informed her that I was correct, and if she did not pass her math classes, including college algebra, she would be dropped from the nursing program. The ed majors and jocks kept whining they wanted special math classes just for them, but the nurse program was solid.
I considered the question "what is this for?" fair game, and we did fun problems like ordering concrete for swimming pools, figuring carpet for houses, and calculating the note lot had really charged us 40% interest on that used mustang. Parabola? Well, that's the curve a bullet or baseball follows...