Personally I'm a huge advocate for the fact that what one might call "wisdom" is not unique to our age and may indeed be getting a bit lost in the shuffle, but nevertheless, there's no way that we can go back to covering everything that took 12 years to learn in 1869 and cover all the things that take 12 years to learn today. When you push an hour into the curriculum to cover, say, the basic functioning of electricity, to name just one thing that I think one should not be able to escape from modern schooling without having gotten exposed to at some point, an hour has to come out of it somewhere else.
It's exactly like learning scheme. Seriously who fucking cares about scheme?
I see latin and greek in a Harvard test as a part of distinguishing highly educated kids from the others.
I'm a CS student at the University of Waterloo, where most early CS courses and many advanced courses here use scheme. There are thousands of students taking CS courses here so in fact there is a generation of grads being produced where a significant number (thousands at least) of them base much of their CS knowledge on scheme. That makes it very relevant.
Err... This website is written in Arc (a cousin of Scheme), which itself is implemented in MzScheme. So by extension, you care about scheme, and so does everyone else here.
I can see how Latin will probably not help with English much (and with French I couldn't see it either) but in comparison German has a LOT more grammatical possibilities and rules and they are very much like Latin except for maybe 2 cases and a few other Latin oddities. This probably makes German comparatively harder for a native English speaker..
The way we had to study Latin was very analytical, never like a spoken language but like dissecting word by word until you could finally understand the sentence. So through studying Latin vocabulary and grammar like that, you got a different and actually excellent insight into your own German mother tongue. And a lot of words, vocabulary and expressions (also in English) at least have Latin (if not Greek) roots.
Some university degrees used to require you to have had Latin in school, medicine was one of those.
The more interesting part of Latin, however, is reading all the great writers and learning about the times they lived in. In a modern Latin class, this should get much more emphasis, even if it happens at the expense of pure language analytical skills.
As a math professor, I think this is a great question. Students learn that math is about manipulating formulas and equations, or about excessive formalities. But being able to explain simple arithmetic facts in clear and plain English is often neglected, and is of the utmost value.
http://dictionary.reference.com/browse/reason
1. a basis or cause, as for some belief, action, fact, event, etc. ...
3. the mental powers concerned with forming conclusions, judgments, or inferences.
So, its the difference between "reasoning", which we do in math and logic all the time, and "belief" or "motive". That is "reason" did indeed have a specific mathematical meaning at that time, and it still does today.
One might also google "mathematical reasoning"...
I feel like anybody with a basic understanding of what an exponent represents should be able to explain why you add exponents.
=
(a*a*a*a*a) * (a*a*a*a*a*a*a)
^ ^
n times m times
X^N * X^M
= N copies of X, multiplied by M copies of X
= N+M copies of X multiplied together
= X^(N+M)x^n = exp((log x)n). By definition, exp(n+m)=exp(n)exp(m). By definition, a(b+c) = ab + ac (for the log x thing). QED.
By the way, (the infamous calculus book) Baby Rudin has the poor reader show this property holds in exponentiation for reals, starting with integers and via rationals, as an exercise on its first chapter. Insane difficulty for me, even though the author practically holds your hand along the way! Cool read, though.
a^(n+1)=a^n * a
a^(n+2)=a^n * a^2
a^(n+3)=a^n * a^3
a^(n+0)=a^n * a^0
therefore
a^(n+m)=a^n * a^m
Now the students who do math contests and are AIME/USAMO level could probably do the geometry section here without a lot of trouble, but they are the exception.
There's 2 trigonometric proofs, and a number of less than obvious geometric proofs, especially the latter ones pertaining to the circle. The rational equation in #8 on algebra going to involve solving a cubic. And although #7 in arithmetic wouldn't be too hard if you worked entirely in pence, it is still a trickier problem in the days before decimalization.
Granted, it's weird in this day of students taking 5+ AP classes to see no calculus, but the math isn't weak at all. Remember, there's no calculators here. Maybe a slide rule and a table of trig values/logarithms. But that's still a lot of work by hand.
In terms of proofs, they are pretty basic, and I learned that stuff in third grade. I mean, I went in and out of gifted programs, but I think the better question is how long does it take to get people to add integers correctly? Ten years?
I drove myself a lot as a child, and drove enough teachers crazy to have to switch schools about ten times before middle school, but I would be surprised if my experience is no longer strictly atypical for people seeking a world-class education.
Note: I didn't attend an Ivy-League, but I did end up skipping a few grades. All those were after elementary school, so it's likely I was ahead of students at the time -- ahead of average, not ahead of the expectations we should have for first class minds seeking a higher education in an age when this is exceptionally uncommon.
There are communities of people who would indeed consider this an easy test but they tend to delve even more deeply into classics than a typical contemporary of the test.
Hell, this makes the SATs, with its ragged edges and sloppy Times New Roman straight out of MS Word, look like carelessly produced junk.
Which makes it all the more impressive--each page took considerable craft and attention to detail.
For more information on this, you'd have to get a book like this one--I can't find anything more online: http://www.worldcat.org/title/printing-of-mathematics-aids-f...
In fact, reading that sort of makes me curious about what pedagogical approach was taken to teach pre-limit calculus.
Worse, this test doesn't call for much analysis; it's mainly regurgitation of memorized trivia and the most mechanical arithmetical techniques.
To be fair though, at least now you can rote learn the right things to pass the tests in any country, not just a few wealthy western schools that teach latin and greek....
I also have a very close friend who is now an elementary school teacher (4th grade), and says this as well (they don't just teach with rote memorization). Recently, she was telling me about the subjects she was teaching and the different learning tools they were employing in the class room, and we were having a discussion about how great it was that they are focusing on problem solving and knowledge discovery and not just on rote memorization.
I can't even comprehend what is being asked on most of these questions let alone what it's about, at least if I knew what they were asking I'd be halfway there.
Charles W. Eliot, president 1869–1909, eliminated the favored position of Christianity from the curriculum while opening it to student self-direction.
I really want to know how you concluded that this has something to do with religion...
I studied ancient Greek too for several years. I hadn't heard of this 'General Supposition' as a way to describe conditional clauses. Apparently -- just looked it up some -- it was an older way of describing the categories we use now (which are mostly temporal based -- future less-vivid, etc.). So there are two spheres for classifying conditional clauses.
If you look up the Goodwin grammar reference for 'General Suppositions', the vast majority are from NT Greek. So that's what made think it was mostly used in NT Greek.
So in a way, thinking about conditionals as 'General Suppositions' is sort of biased in that direction.
But you're right, could apply to Classical Greek too. I should've remembered that Classical Greek is mostly a superset of NT Greek, so there would be examples there too, etc.
But it's actually a rather deep question. Classifying conditions as 'general' asks for a kind of aphoristic understanding of things (talking only about the very general case). I would hazard a guess that the majority of this is in NT Greek. But I suppose some historians and philosophers also generalized (Thucydides, Plato) in this way and could have their protases classified as such. But it is sort of a different way of thinking. Bad to generalize ;-) -- but it may go quite to the heart of certain differences between aspects of NT and ancient Greek.
In practice, the requirement for the classics was no impediment to elites; one could be admitted on the condition that shortcomings would be remediated. Once admitted, you could easily purchase the services of a tutor or cheat your way through.
Heck, I learned Latin in high school in the late 90s. I hated it when I took it, but it certainly made learning other things a lot easier.
Nice, reminds me of
> Find 7th root of 0.9999 to four places of decimals
:)
Rather than in the current education system where very very few people want to proceed working in these pure sciences and majority of them want to become leaders and thanks to Univs of US in which leaders are "annointed" by dishing out MBA's based on GMAT / CAT scores.
[1] See today's links.