Ideally, how would math be taught?

Rather than "memorize formula, solve problems, tommorow add more to formula, solve more problems, repeat," how should math ideally by taught?  What kind of teacher would you need?  What kind of student interaction would there be?  And are there any close examples from other countries or societies, past or present?

Kids need to learn how math works, not be told how it works.  Maybe they could group kids into different classes based on mathematical aptitude.  It seems rather stupid to just lump them into classes randomly, when you could do it in a way that would create some kind of benefit.

>Ideally, how would math be taught?

each page from the math book would be put on the teachers penis....
he would then pound the days lesson into all available holes of each classmember

Math shouldn't be taught at all.  Guidance should be available to help people who need a certain amount of math to learn it by themselves and also for the few people who like it to learn as much as they like, again for themselves on the topics they prefer.  Stop wasting resources on the fuck ups who will never use what's being forced down their throats and things will go much better.

Well, countries that tend to have high scores in mathematics and science typically teach the practical applications of math rather than concentrating on theorems and whatnot, or, even worse, dumbing down mathematics by completley ignoring material that students may find difficult, such as "word problems" or irrational numbers.  In fact, I occasionally voulunteer at my local community center as a math tutor, tutoring 7-10th grade math, and I consistently find that very important subject matter is often skipped, or at the very least simply glanced over.  Word problems are very rare until 10th grade algebra, in the 8th grade remedial math class, 471/23 is 20, remainder 11, not 20.47826086956522..., (and remains so until the end of the year) and in practically every algebra class, students cover material such as polynomials, rational expressions, etc, without being explained even the first thing about what they are, or what they are for.  Analytic Geometry is only discussed by students taking the honors algebra course (about 20 kids out of 500 a semester), so while these kids might be able to factor (x+2)(x+3) into a second-degree polynomial, they wouldn't be able to tell you the characteristics of its graph.  When I tutor these kids, I try to cover this material for them as best as I can, and I often see marked improvements in the few kids who are willing to listen to me talk about it, but for the majority of them, they're simply victims of the typical American school district.

>>4
Then the same should be true for reading. If we're going to say that it's ok to be innumerate, then the same should apply to illiteracy.

>>5
Is correct.

Anyway, ideally, all humans would have a USB cord that extends from their brain. They could plug in and learn everything that way.

Sometimes I wonder if at this time I should go back and learn what I missed, just because I don't like being behind 99% of the HS grads in Korea. Other times, I just think it's all crap, because nobody teaches practical stuff in the USA.

I think it should be explained from a practical standpoint, and I would sacrify depth in favor of proper background support (using formulas = not as useful as understanding them). Formulas shouldn't be asked to be memorized either, that's moronic. And geometry is often overlooked, when it can be great to help understand the base for a lot of things.

A teacher should provide a proof for every theorem he gives you and if you don't get the proof, don't believe the theorem until get the proof. I don't know why anyone would use a formula and not care why it works, but thats what kids do everyday, especially in physics where the teacher will just give them a list of derived formulas to plug numbers into. The won't learn anything that way.

Test scores are not what change the world, creative ideas are.

I believe that at a young age those who are creative should be taught analytical/abstract math, and those who are not should be taught applied math. 

And how will you determine this "creativity"?

There is a general issue in that the goals of education are not what they ostensibly should be, and they will likely never be such. "There is no power but power over other people." True mass education is undesirable to those who would have to arrange for it.

The manifest goals are several. The first appears to be training children to obey orders, in particular to remain sedentary. The second appears to be indoctrination. The third is to confine persons of the relevant age group to remove them from potential criminal activity. The fourth is to remove them from competition with older persons in the workforce in order to artificially inflate wages.

There are probably other ways of phrasing all this to make it more palatable or perhaps less controversial; however, the root cause of the math (and indeed, general) education issue is that the actual "motive forces" propelling it are contrary to the goals of actually educating people.

If the goals were such, different overall behavior would be observed. For example, progressively higher standards would be put into place, attempts to significantly advance the amount of content delivered in a given period of education, and the like would be observed. Instead, the focus is on capturing larger numbers of students, dealing with "problem students", and the like, and the standards degrade over time to reduce the rates of withdrawal from the compulsory education program. Those are all advancements toward more complete control of the society, not higher-quality education.

I'm largely unconvinced there is a "solution" as such. While I could review proposed solutions and try to anticipate their effects, my overall assessment is that this cause is far beyond futile and will remain so in the absence of extremely powerful external influences on global society. One of the only ones I suspect would suffice is an impending natural disaster for which the entire population of the planet must be recruited to devise the technology to avert. Another would be if economics became so heavily reliant on technology that countries engaged in "technological arms races" to recruit as many creators of technology for economic purposes as possible, which is far from the case now. It does not appear plausible that either of these situations will occur in the near future.

>>12
in the absence of absolute theistic controls... culture and 'civil'ization are all that remain as a control mechanism for secular societies

in the broadest sense, the goal of education was never to comb the population for exceptional intellectual potentiality; but rather to increase the average level of the general population, though in doing so, allowing a possible avenue of advancement to the pinnacle of current erudition

once you have entered the system, if you are sufficiently capable and sufficiently willing.. you can reach any level of knowledge currently known to institution, perhaps you may even contribute to this institutional knowledge yourself

in the least, you will be educated to a level of complacent realization which you accurately stated as the primary goal

socioeconomic class is the largest determining factor. public education is highly general and largely delivered apathetically and often incompetently. capitalism states gradation of quality relates to value and therefore "you pay for what you get". government subsidized scholarship programs are what allow highly dedicated and equally capable individuals to advance beyond their class; but it is statistically unlikely for an individual to start their education in a squalid under-funded public school and through sheer will, utilizing self-study, form a comparable knowledge base to privately educated individuals of equal intellect, though certainly it does happen in a minority of cases...

ultimately, if the entire population of earth was equally educated the competition would become unyielding...
long-established disproportionate power, financially or otherwise, would steadily erode and eventually cease to exist. status quo forces are trying to keep such a scenario from occurring within their lifetimes, it is most certainly contrary to their interests

>>13
Unless you claim otherwise, I'll take this as largely agreement with a different emphasis. At least I largely agree with your assessment as a description of other aspects of the same situation.

One of the closest points to disagreement appears to be over whether education is used as a method of controlling society. My claims are significantly limited in this regard, specifically to omission of information portraying the country in a negative role (e.g. outright failure to mention or downplaying of various genocides and embarrassing political missteps), control over youth labor and mischief, and conditioning for sedentary lifestyles.

I'm relatively confident in those claims, as they're relatively minor and halfhearted sorts of controls compared to the legal/penal system and the routine raiding, gassing, gunning down, plea bargain charades in lieu of trials on pain of disproportionate prosecutory efforts and longer sentences ("revenge" for the expense of a trial to discourage anyone from insisting on having one), and dumping into industrialized rape camps (a.k.a. "prisons") the government responds to any sort of dissent with. By and large what we've ended up with is the government volunteering to be a mass babysitter and throwing some educational window dressing and government propaganda atop it.

The second is the unyielding competition claim. Such a state of affairs as "equal education" would be unstable, like an inverted pendulum. It would quickly evolve to a state of unequal education such as exists now as self-reinforcing advantages are achieved by other aspects of chance, circumstance, and so on. Access to information is an asset like any other, and the upper classes will collect disproportionate amounts of that just as they do all other assets.

>>14
yes, i agree with your initial post. it is airtight in its logic, i just wanted to point out a specific dynamic outside of the scope you addressed

absolutely the theoretical concept of "equal education" would be near impossible to apply in any realistic sense. i should have included a caveat to stress the speculatively theoretical nature of that last paragraph

since we are all in agreement, i'm sure we realize there is no better proposition for a pragmatic realistic solution than the ones already posed by modern culture. can one really offer a unique solution previously unconsidered by this late stage

FLOOD

wow this thead was boring

and a load of blah blah blah as well