I can understand the frustration in this posting. I suspect that most of
this list shares it to some degree.
I don't believe there are any teaching methods that "guarantee" success.
That includes the "new" pc ones.
A good teacher is probably the single most important variable in student
suceess.
Math should be relevant to students if possible. The two persons cited,
Newton and Einstein, worked on problems which were very relevant to them,
not on abstract mathematics. And neither was a tenured university professor
when they did their work. And Newton at least was a very good communicator,
judging by the non physics/math portion of his life - the majority of it.
And Einstein wrote letters to Presidents and others on the nuclear bomb. So
I suspect they could both communicate.
Most students just don't need tons of algebraic skills. And learning about
investment planning would teach critical thinking - whatever that means -
as well as or better than most, if not all, math word problems. And the
mathematics of investment can form the basis to study tons of algebra,
as well as the exponential and log functions.
So some educators now want to do away with the core subjects. I'm not sure
there isn't a happy middle ground, probably under the rubric of inter-
disciplinary studies.
Of course I'm talking about the 85% of our students (that figure is a guess)
that don't go into the hard sciences or graduate level soft sciences.
As far as future engineers and scientists... I'd like to see a curriculum
that nourished these types too. But society has chosen to ignore this problem
since the trauma of sputnik wore off. If we need more engineers and
scientists we don't try to reach out to minorities or women, or more males -
we import them. Much cheaper and easier. (I'm not advocating this social
policy! I'm just recognizing it.)
I do think we may see a reaction against those who want every student to
study precalc and trigonometry.
One last thought - math teachers don't always set the standard for how
much math to teach. It's the med schools and business schools that
demanded calculus of their applicants!
Phil Mahler