Newsgroups: alt.callahans
Date: Sun, 20 Dec 92 19:21:52 EST
From: korz@cs.columbia.edu (Frederick Korz)
Subject: Re: Spheres and Calculus [Re: Cyber (was Introduction was Eh?)]
Organization: Columbia University Department of Computer Science
Distribution: world

In article <1992Dec19.234517.5334@ucc.su.OZ.AU> DM writes:
>
[deletia]
>
>DM is surprised. "Don't you folks in the US learn calculus in high
>school? What _do_ you learn in high school mathematics? (To clarify
>my point - Australian high school students do learn calculus. Not too
>advanced, but enough to solve reasonably tricky problems.)"


  My turn to have a hot button pushed.  Not that I'm seriously angry 16
years later, but I've got a slow simmer going on education in general
that I have personal knowledge of for mathematics and science.  To
your specific question the answer is "no".  In general, learning much
of anything, on average I'm inclined to say, "no" too.

[[Patrons who've "been there, done it" might want to skim or skip the rest...]]


  There are no national standards (and I'm not suggesting there should
be - not having decided whether it would be worse or much worse :-).
Instead each state (state != nation-state) is free to set its own
standards and potentially each local school or school district within
these states has further defining and interpretive powers.  This
results in at least 50+1(the District of Columbia) standards and all
sorts of flavors in the USA.

Broad, biased, generalities:
  In general one starts with a gaussian of abilities of any and all
sorts of measures.  Then the system seems happy if they can reach the
middle 50% of the measures they think important.  The laws want to
give all "equal opportunity" so they provide for forced redistribution
of teaching effort & materials.  So, if you're having trouble there is
help.  Then, with X percent of resources devoted by law to the bottom
of the curve*, the general approach is 100 - X goes to the middle 50%.
If one shows promise, then gal/guy, you're on your own not to be bored
to death.

*(No, if you think I am disagreeing with those laws, I only seem to be.)

Specifics:
  As of at least 2 years ago the basic track for the state of New York
was unchanged since the 1970's when I was a HS student.  I have not
heard of any radical changes in the past 2 years.

  The ruling body for NY is "The Regents of the State of New York"
which sets the curricula and standards for the granting of a "Regents
Diploma" (in contrast to a general HS diploma).  In addition to 4
years each (8-12) of english and social studies (e.g. history, anthro,
economics), and 3 years of any language, if hazy memory serves:

	mathematics	science			history
	-----------	-------			-------
8	algebra		???			NY state
9	algebra		earth science		world (non european) cultures
10	geometry	biology			european
11	algebra & trig	chemistry		US
12	precalc(opt.)	physics (optional)	electives

(I just don't recall the english.  At the time I loathed it because,
although I was an avid reader of Sci-Fi and fantasy, english was
inflicted rather than explained.  Nobody gave that one clue that was
the handle to have it make sense.  It took me until 10 years later, in
graduate school for hind-sight and some purely optional German
Literature courses to receive the key that would have made "english"
any clearer than mud!)


Demographics:
  Suburbia, low to medium affluence, school district having 3 high
schools (years 10,11,12 then) of about 1000-1200 pupils each.


Now if you showed promise this is what they did:

  For social studies and english they formed "advanced class" section
or two that did the same curriculum as the middle 50% with whatever
enrichment the instructor threw in.  The sole exception to this is
that there were 12th year electives taught at a freshman college level
in both US history and economics.

  For the mathematics and the sciences, they compressed 2 years into 1
and thereafter simply threw you in with people a year ahead of you.

	mathematics	science
	-----------	-------
8	algebra x 2	??? + earth science
9	geometry	biology
10	algebra & trig	chemistry
11	precalc(opt.)	physics (optional)
12	calculus**	Freshman level chemistry or biology***

** Either the equivalent of non-major's or major's 1st year calc.
*** one at one school and one at the other.  A bus commute.  We tried
to get a physics but met with no success.

Perhaps you can see now what I meant about being bored to death.  Once
a year ahead, you were not strongly challenged.  This was silly since
to get a year "ahead" you had already proven the ability to proceed at
twice the pace of the curriculum.  Bah!

I got really bored in mathematics and, rather than flunk out, did the
algebra & trig in one semester and precalculus in the second semester.
This was unusual and only the result of my earnest request and a
sympathetic chairman.


I suspect that school districts axe even these sorts of things when
faced with budget crunches or wasting the money they have or whatever.


Hindsight:

  Hindsight of undergraduate work, 5 years as an officer in the
submarine fleet and then nearly 6 years as a graduate student is:

	your education is your own and what you make of it

	to make the best of it, you *must* take an active part.

	standards alone cannot impart education

	the standards are mediocre and, because they are applied
	across the board and because most HS students of my
	acquaintance**** are passive about their education, standards
	are unlikely to change to _ensure_ one gets a solid education.

(****) and my father's acquaintance too, a teacher of 32 years
experience having a sample size on the order of 5 to 10 thousand if
not higher.

[And folks wonder why a college degree seems more and more a
requirement.  I wonder to what extent it is just years 5,... of high
school.]

 Of course around here, The Place, I'm probably preaching to the choir.

>>My only question now is whether the decay will go progressively
>>backwards, so that in a few years I'll be struggling to remember what
>>8 times 5 is.  :-)"
>
>:-) "Why, it's 42, isn't it?"
>
>- Danger Mouse.

"Why yes, that is 'The Answer', but what was 'The Question'?"  :-)

	my opinion, fraught with errors, for whatever it's worth,
	frood/fred
Newsgroups: alt.callahans