Re: Prolems in Mathematics Education
- From: Pubkeybreaker <pubkeybreaker@xxxxxxx>
- Date: Tue, 04 Sep 2007 08:26:23 -0700
porky_pig_jr@xxxxxxxxxxx wrote:
On Aug 28, 10:44 pm, Tim Norfolk <timsn...@xxxxxxx> wrote:
Yes, this is like a chain reaction. First it's a school which says
that kids don't really need to know math (or give them the inflated
grades so they can graduate), so the colleges are on the receiving
end. Then it's a college which says that students don't really need to
know math, unless they are doing some engineering or like. What's
next? Students engineers who don't really need to know math? Yes, I
already saw something of that kind.
think in case of exceptionally bright students, they probably can
attend pre-calculus, so in college they start with something like
'Honor Calculus' or 'Calculus with Theory',
I don't know about "exceptionally" bright, but when I took pre-
calculus in
High School the course covered symbolic logic, advanced topics in
trig,
vector algebra, induction, intro to linear algebra, theory of
limits with epsilon-delta proofs,
and tons of proofs, proofs, proofs. The previous class (Algebra II)
covered
intro to trig (w/ DeMoivre's Thm) , analytic geometric (with
extensive study of conics),
systems of equations, a brief into to the solution of the cubic, and
tons of
problem formulation (word problems) with proofs proofs proofs.....
The geometry course was nothing but proofs.....
Normally, the sequence was Algebra I (grade 8) Algebra II (grade
9) Geometry (10th)
Pre-calc (11), Calculus (12). I asked and was allowed to take
Geometry and Pre-calc
together, so I got to take Calculus in the 11'th. The school created
a 2nd year calculus
course for me and one other student. Subsequent to my graduation,
everything got moved
up a year and the school offered 2nd year Calc as a regular course.
Unfortunately, they
RETIRED that course several years ago when the teacher retired. None
of the schlubs that
are teaching currently have the ability to teach that course. And the
course material that is
offered no longer emphasizes proofs. I know from direct experience:
my oldest son just
graduated from the same high school. His math training was a joke.
These courses were (once upon a time) RIGOROUS.
The Calculus course used Apostol Vol I. The course included a lot
of proofs, proofs
proofs, etc. It included a proof of the intermediate value thm. It
included infinite
series etc. The 2nd year of Calculus used Apostol Vol II, as well
as Boyce & DiPrima
plus some advanced topics (e.g. intro to Stieltje's integration, Euler-
MacLauren summation
etc.)
Of course the two teachers who taught these courses were EXCELLENT
teachers.
This sort of curriculum CAN be taught in high school. But it takes
teachers who
understand the material and motivated students.
Today, most students just don't give a sh*t. It is impossible to
teach such students
and I argue that we shouldn't even bother to try.
Part of the problems with colleges today is that they are under
considerable financial
pressure to maintain enrollment. As a result they allow any piece of
cannon fodder to
attend, regardless of background. Today, many students attend
college who would not
have been admitted 30 years ago. I argue that there are too many
colleges, too many
enrollment slots, and too many students who attend. The result is not
surprising: many
students don't have the background or ability to do real college work.
My high school courses were honors courses, but I wouldn't call
everyone who took them
"exceptionally" bright.
.
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