

Phillips Exeter Academy Mathematics Course Materials - tokenadult
http://math.exeter.edu/dept/materials/index.html

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hga
Well, I guess it's no surprise that the rot has set in even at Exeter. In many
ways, my below average public school in the late '70s was more rigorous than
this dog's breakfast, at least prior to the calculus (where I don't like the
emphasis on "Working within contexts whenever possible...").

Note that the word "proof" doesn't appear until the very highest specific
class; traditionally the geometry class after the first algebra class was
where that was introduced.

Then again, if they're preparing students for Harvard, as of the late '80s the
only math requirement there was to prove you could do algebra, according to a
friend who took their honors calculus.

~~~
tokenadult
So you think these are easy problems? What would be an example of a secondary
math curriculum that is better?

~~~
hga
Well, for starters, the old traditional one that focused on _math_ and not
calculators (beyond graphing; being able to quickly turn an equation into a
graph is useful, particularly for the calculus).

I personally found the Algebra I, Geometry and Algebra II sequence to be good.
Algebra I teaches you symbolic math. Geometry teaches you geometry, analogs to
algebra (the algebraic discoveries of the Greeks were done with geometry) and
introduces you to formal math including proofs. Algebra II brings it all
together with serious analytic geometry and more algebra (and hopefully
includes matrices); you need a really strong foundation in both to master the
calculus.

After that, _briefly_ do enough trig to be prepared for calculus (see related
comment below) and finish up your pre-calculus ending with limits.

At that point I draw an arbitrary line ending secondary math, although of
course that's not how it's done, especially in the rest of the world.

Things NOT to do:

Avoiding "drill and practice".

"hands-on labs that require [ Algebra I students ] to collect data, make
conjectures, and draw conclusions"

Actually, their "ADVANCED INTEGRATED MATHEMATICS" doesn't sound at all bad,
except that the binomial theorem is something you should have learned early in
Algebra I. It probably is a _much_ better way to introduce trig, which it
deadly dry and apparently pointless in the traditional sequence.

Back to the things that set off warning bells:

An "inductive approach to calculus".

"Working within contexts whenever possible" (the emphasis suggests to me that
they aren't just doing the standard physics applications).

~~~
tokenadult
_I personally found the Algebra I, Geometry and Algebra II sequence to be
good._

What textbooks did you use to learn those subjects? If I remember correctly
from other comments of yours, you went on to a rigorous quantitative major in
college, right?

~~~
hga
I'm sorry, but that was in the period of 1975-8, so there's not a chance in
the world I could remember them. And I went on to be a Chemistry major at MIT
... but _everyone_ at MIT must pass the first four classes listed here:
<http://news.ycombinator.com/item?id=1107911> (the calculus plus physics as of
the 19th century).

My advice is to find older textbooks (used is cheap). Pre-calculator is good
(cheap non-graphing calculators were available long before the graphing ones
were), avoid New Math and all that like the plague (yes, set theory _is_
tremendously useful (and multiple bases even more for people like us), and I'm
_very_ glad I started learning it in elementary school, but for 99% of
students it's going to be a totally unmotivated distraction then (I was lucky
I found it "neat" and simple to learn)).

Rainforest Math is _right out_ , as it anything that doesn't assume you've
drilled your arithmetic tables until you know them cold.

People have said good things about the Singapore Math curriculum
(<http://www.singaporemath.com/>) but I haven't really looked at it. Others
like the Saxon math texts
([http://saxonpublishers.hmhco.com/en/saxonpublishers.htm;jses...](http://saxonpublishers.hmhco.com/en/saxonpublishers.htm;jsessionid=CDB48C7E0E7010591B28AE3BF45EE04F.ecom-
app-wk2)), which integrate geometry throughout. Avoid _anything_ with
manipulatives.

(Side note: _DO NOT_ try algebra based physics (generally taught as a US
senior class); it's cargo cult science and _no one_ does it but "educators"
and their victims. There's a reason Newton invented the integral calculus to
figure out his system of mechanics.)

I've procured some texts to someday _relearn_ my math starting with Algebra; I
can only vouch for the beginning of the first ones _and not for someone
learning this for the first time_ ; I haven't touched in detail any beyond
those two. If you're interested, just ask and I'll supply the list with ISBNs.

~~~
tokenadult
_If you're interested, just ask and I'll supply the list with ISBNs._

I am interested, so I am asking here. I'm always interested in recommendations
of math learning materials, because I am a math teacher by occupation now.

~~~
hga
I'm working on the list (the annotations will take a while, and I'll probably
post it section by section); watch this space, and I'll email you a copy as
well.

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quant18
All of the links on that page give me a "system cannot find the file
specified" error, except the Harkness one. I assume they were working four
hours ago, based on the comments here ... (must resist urge to spout
conspiracy theories). They were also working 18 months ago, for anyone who
still wants to see them:

[http://web.archive.org/web/20080610161827/http://math.exeter...](http://web.archive.org/web/20080610161827/http://math.exeter.edu/dept/materials/index.html)

Anyway, based on the dates, I'm guessing this may be some kind of
summer/remedial course, rather than their regular curriculum.

~~~
tokenadult
I'm encountering the same error in not finding the files, which I had
previously downloaded. Thanks for the helpful archive link.

As of the last revision date, those problem sets were the usual study
materials for the main school year math courses at Exeter. Even very advanced
students took the courses shown (depending on entry grade) before going on to
other courses.

