One line of the article stood out for me: "College admissions officers value calculus, almost as a proxy for intelligence." I think what lack of Calculus signals is more lack of facility with Mathematics generally.
When I speak with students who have weak (or missing) Calculus backgrounds, I usually find that they are uncomfortable with something much more basic: they simply do not understand what it means to use a symbol for a quantity. Not understanding that, they don't see how manipulating symbols (e.g. subtracting something from both sides of an equation to move a term to the other side) makes any sense. It's as though they had a mental block on the day when a teacher said "let x be the unknown". They usually bluffed their way through that class, and the next and the next, as they proceeded through middle school. But they never really got their heads around the ideas. And this, not intelligence, is the problem with their later success in STEM fields.
Helping such students is a real challenge. It's a matter of establishing a connection and a trust that will let you probe back into their past until you find the place where the problem arose. This is like psychotherapy. It takes one-to-one work and it takes a long time to build trust, before the probing can begin. None of this is practical in a traditional college teaching framework, and that is why college admissions offers key on Calculus.
As for the discussion of Statistics, I agree that this is more important for general students. STEM students need to add Calculus as well.
> (e.g. subtracting something from both sides of an equation to move a term to the other side)
You mention that as if it was a trivial operation, but it only works because subtracting a constant is total and injective. In general if a=b then f(a)=f(b) [the substitution property for equality] for any total function f - but the converse is not true in general.
When I speak with students who have weak (or missing) Calculus backgrounds, I usually find that they are uncomfortable with something much more basic: they simply do not understand what it means to use a symbol for a quantity. Not understanding that, they don't see how manipulating symbols (e.g. subtracting something from both sides of an equation to move a term to the other side) makes any sense. It's as though they had a mental block on the day when a teacher said "let x be the unknown". They usually bluffed their way through that class, and the next and the next, as they proceeded through middle school. But they never really got their heads around the ideas. And this, not intelligence, is the problem with their later success in STEM fields.
Helping such students is a real challenge. It's a matter of establishing a connection and a trust that will let you probe back into their past until you find the place where the problem arose. This is like psychotherapy. It takes one-to-one work and it takes a long time to build trust, before the probing can begin. None of this is practical in a traditional college teaching framework, and that is why college admissions offers key on Calculus.
As for the discussion of Statistics, I agree that this is more important for general students. STEM students need to add Calculus as well.