You’d think it would be simpler to give a test to the candidates, so obvious louses would get filtered out (and the rest would know that their competency was being honored). I cannot grok a graduate not being able to use BOOK FORMULAS, and as for not being able to follow the evaluation logic of nested parentheses — even with calculators which can reproduce this with open and close paren keys — good grief.
As for remedials — when I entered engineering school I had the opposite situation. I was able to test out of English rhetoric altogether. I had mastered that in high school. And I did just fine in college papers. They did have me go through calculus again, no test-out being possible, but that was pretty much an easy coast as, once more, I had mastered a year’s worth of it in high school.
The policy for grading was pretty much bell curve, though the policy often was that if there were one or two stellar students well above the grouping they would not be counted in the curve, but just awarded the A. I was often one of those stellar students. It did ease relations with my classmates who didn’t feel so antagonistic towards the “curve raiser.” I didn’t really care a lot about there being no A+, the normal A being enough to open just about any door during that era.
Not sure that there is a test you could give to “filter” those out - because a degree in Engineering is to a great extent a demonstration that “I have learned to learn”.
For example, my High School was exceptionally poor at most technical classes. Our “Math” teachers were hired based upon their ability to coach sports. Often, the students would have to teach the teacher in subjects like Algebra - forget Calculus. Our bone-headed high school teachers couldn’t master basic Algebra, Geometry or Trig.
Naturally, I paid dearly for their incompetence; but they apparently were really good at coaching basketball - you know, the important stuff.
Me, I’m happy to learn - and I’m a quick study. Being able to grasp complex subjects quickly and move on has served me well. I do wish I understood the higher level maths better - but I put my head down, passed the course and haven’t used the course material in my 25 yrs as an engineer.
What matters is the aptitude, the attitude and the ability to break a complex problem down into a hierarchy of simple challenges. Everything else can be learned, as needed.