<< I suggest that a proof of the quadratic formula does not increase one's
understanding of it, or one's ability to use it. >>
I agree that learning the proof is independent of one's ability to use it.
That's probably true for everyone.
But you also say:
<<data tells us they will probably not reach the promised land of calculus>>
I agree that there are at least 2 kinds of students in my intermediate
algebra class: those who intend to take further math and those who will
complete this minimum graduation requirement, never to worry about math
again.
Students who appreciate mathematics WILL appreciate seeing the proof and
derivation of the QF. But as for the rest of the students, it has been and
will always be just a formula to be used and not understood. The proof will
not help their understanding.
That's my 2 bits...
Mark Harbison
Whittier, CA