Simple the bottom 40% ,as tested for over say ten grades 1 to 10th, in mathematics and/or english skills should not go into any form of college prep - period. Murray in his work points these student will never earn any four year degree but higher end students in that group might earn a two year degree if career focused in areas they showed talent for - an A.S. in Accounting doesn't demand algebra with modern technology and software.
Besides what Oniya already said, in your examples, you are systematically denying otherwise-capable students of pursuing a higher education...because of what, exactly? People in the 'higher' group might
earn a degree, but then again, they're not guaranteed to, either. People in the lower group might not
earn a degree...but they might succeed, too. You're already squashing that chance before it even has a chance to manifest. And even if a student goes to college and decides it's not for them, so what? Are they ruined individuals? Hardly. Some of those "top level" kids might realize they don't want to do the work in college or can't keep up with it and some of those "bottom level" students might grow up and want to pursue more. Why would you deny them that except to say some piece of paper with filled in bubbles shows they're not good enough? Standardized testing has plenty of its own issues and I sincereely doubt that a piece of paper with some numbers on it speak truly to a person's potential to rise to learn or pursue opportunities.
Your apparent attitude towards furthering education is really puzzling -- I can't quite figure out where you're coming from. More education is never
detrimental. If your accountant knows more than just basic algebra (which, by the way, is practically a standard for anyone
to know to get by in 'the real world', which is why it's taught as early on as middle school. If your accountant doesn't know algebra, then there's an issue in of itself -- algebra is literally everywhere.) they are able to not only solve more complex issues that may arise, but they can also move up further in their career.
The rest could be offered some pre-college and trade education or just trade education in their last two years of High School (towards community college) and the top 30% pre-college but damn it teach them some way to make money a semester of some skills like cashiering, handling money, customer service so they have a practical skill group.
Its not that hard.
I'm curious...did you ever have a job in high school? I started working at the age of 15 and I was taught these skills on the job.
That's why they're entry-level positions and that's why places such as grocery stores hire teenagers -- because the work is simple enough that teenagers can grasp it. Most basic jobs are generally unskilled work and will show you what you need to know. I learned how to bag groceries in literally ten minutes. I learned how to cashier in the course of a few days. I moved on to a bakery and learned to decorate cakes in under a week. I was taught kitchen work in a week. I became a functioning bartender over the course of about two weeks (and some people go to a bartending school -- those people will likely land higher-level bartending jobs, something that would take me years of experience in order to attain the same level of knowledge).
Indeed, if you work enough, you realize you've started to develop an understanding of the job you're in-- I went from packaging bread someone else made to decorating cakes and assisting in baking simply because I had spent enough time at my job that I started to understand the more complex things required. Teaching these things in school I would dare say is redundant and ultimately a waste of time.