From: James Wetterau (jwjr@ignition.name.net)
Date: Wed Apr 19 2000 - 10:12:00 MDT
"Michael S. Lorrey" says:
...
> > As it happens, this particular topic has been rather well researched. Mike
> > is exaggerating a bit, but it is certainly true that in the first half of
> > the 20th century American high schools taught many subjects that are now
> > considered advanced college fare. My favorite example is the fact that the
....
> few well worn phrases. I just received a message from a girl on a
> newsgroup who
> is a senior in college and is so happy she came out in the top of
> her class in
> linear algebra...
...
And your point is?
Linear algebra is not simple algebra. It's typically taught after
calculus, around the same time as the study of ordinary differential
equations, but before more advanced topics such as modern algebra,
real and complex analysis, number theory, partial differential
equations, topology, and so on. Glancing back at the Springer-Verlag
volume "Linear Algebra", by Klaus Janich, from their "Undergraduate
Texts in Mathematics", I see that they describe the study of linear
algebra as concerning sets, maps, groups, vector spaces, including
complex and Euclidean spaces, bases, matrices and their
classification, eigenvalues and eigenvectors, endomorphism and the
characteristic polynomial. This is not the stuff one typically covers
in high school algebra, but rather an advanced application of the type
of tools that such courses provide to topics that extend beyond the
purview of a basic algebra class. While a very well prepared student
-- say, someone with a perfect calculus advanced placement score --
studying math for a BA at a reasonable college in the U.S. would
typically encounter linear algebra in the first or second year of
study, as I did back in 1987, a person who had only had a good high
school mathematics education and who wished to study math as a
supplementary topic might well wait another year or two for ODE or
Linear Algebra. This is in no way a sign of a deficiency in high
school or higher education standards.
...
> The year I graduated from high school, 1986, NH had the highest average SAT
> scores in the nation, while it had spent the least per capita on education fo
r
> many years, and is still one of the five lowest funding states... Our state
> Supreme Court is, at the moment, being dismembered by the Governor, the AG, a
nd
> the legislature (ostensibly for other reasons, but we all know the real reaso
n)
> all because the good 'ol boys couldn't seem to make the connection that money
> doesn't equal quality education, despite our history.
The United States Senator from New York Daniel Patrick Moynihan
famously observed some years back that he had learned from the Federal
government's own statistics people upon comissioning a review that the
distance from a state capital to Canada had several times the
statistical correlation with results on standardized tests in that
state than did the amount of money spent per pupil. (Specifically,
the closer to Canada, the better the scores.) He joked that the thing
to do was move the state capitals to the northern border of each
state.
Clearly many other factors are at work.
All the best!
James Wetterau
This archive was generated by hypermail 2.1.5 : Fri Nov 01 2002 - 15:28:07 MST