Understanding vs Memorization

I took one math class that gave the quadratic formula as "memorize this and plug everything in."  I took another math class where the procedure for getting to the quadratic formula was actually done step by step, answering the question "why is this formula so HUGE?"

I prefer understanding over simple memorization.  I feel students would do better in math if they were made to understand every concept.  Being "bad" at math is actually not grasping the core concepts, or not having them explained well.  If each student can individually understand concepts, they will progress through a course just fine.  This may mean learning at their own pace, even if it takes twice as long as other students, but at least they "get it." 

Why can't all math be based on "understand it and apply it"?  Sure, test scores determie how well you know it to a point, but actually making sure each student understands would help even more.  Instead of "No Child Left Behind" that asks for only test scores to be high, why not have something that requires UNDERSTANDING to be high.  It's harder to measure, and takes more time, but its worth a lot more than being able to guess correctly on a test.

Issue nr 1.
Money

Many teachers hate testing. I've heard a professor say that testing sucks the life out of the subject matter. But they're forced to do it if they want to keep their jobs.

You might find this interesting:
http://www.johntaylorgatto.com/historytour/history1.htm
http://www.johntaylorgatto.com/underground/index.htm

because no one understands that crap anyway

Most people are dumb and incapable of understanding mathematics and must resort to memorising everything and praying to god the test will have shit they've already seen.

Learning what something actually means rather than something = something else makes everything a hell of a lot more enjoyable. I'm currently studying Chemistry and Biology and both teachers have completely different teaching methods.

The chemistry teacher will simply put premade sheets on a projector, tell us to copy them out and then give us questions, which is such a fucking dull way to teach things that I find it hard to remember everything.

The biology teacher, however, is completely different in that he will spend the majority of the lessons telling us not only about the stuff we are required to know, but also the things that are only slightly related to it, giving us plenty of things to link together with each other, making the course a lot more enjoyable and a lot easier to do well in, purely because you actually understand what's going on rather than memorizing things that, for all you know, might not mean a thing.

In a perfect world, all teachers would teach like that, but the thing is that not everyone can keep up with teaching like that. While some of us are excelling in biology, some people are struggling because they prefer to learn by drilling the same thing into their minds over and over until it sticks.

Because these people can't cope the learning way, but we can cope with the memorizing way, a lot of teachers will use the memorizing way over actually teaching why everything means what it means.

Of course, this could go all the way back to "what if people are taught like this throughout all their lives, so they never get used to memorizing things and will understand things a lot better?" It'd make chemistry a hell of a lot more interesting, that's for sure.

>>6
the teaching style your biology teacher uses is not time-effective, and takes a lot of effort from the teacher and the students, especially if the student delinquency is making a problem.

Therefore most teachers are simply telling to "memorize stuff" -> "get good marks in exams" -> "forget everything after that"
this takes very little effort to do.

>>7
Time-effectiveness shouldn't matter, we _should_ go to school to _learn_, not just go through a system of memorization where we become "well rounded". And by "well rounded" I mean we memorize a bunch of shit we don't need and spend a small amount of time with other things which we would need in our later career.

I've been in love with science since I was a child and I want to learn science, sure math is alright with science, but learning what day Abraham Lincoln died is completely unimportant information seeing as how I could just look it up in an encyclopedia.

>>8

Well, to kinda defend history,
The study of history starts to get intresting when you see how decisions made in the past affect how the future starts. Things like realizing Henry Clay's compromises kept us out of a Civil War for a good 40 years, or how Reconstruction of the North and South reverted back to an opression of the slaves, make us understand that the things we do know will affect the future.

So in history, understand that we do not study "When Lincoln died." We study, "Why did Lincoln die, and how did it shape history?"

>>8

In general, I agree with you in that time-effectiveness shouldn't matter.  In specific, though, I stick with >>9 in that a "well-rounded" perspective really is a necessary aspect of the maintenance of a generally functioning society.  I agree that the memorization of the precise date of Lincoln's assassination is not a particularly useful thing--- trivia, really.  But, as >>9 said, it's our responsibility to try to gain some historical perspective and to draw lessons from it that can be applied to current situations.

Remember that it's your responsibility to participate in your civic system, too.  Especially if you live in the States (which I think is a fair assumption in this case).

Keep in mind, however, that high-school and college curricula are generally written with an agenda in mind.  Don't believe everything you're told by rote--- that's as foolish as believing nothing you're told.  Rather, learn to distinguish the motivations of your teachers, and learn to filter their bias.  I, personally, consider a teacher to be relatively accomplished if I detect little-to-no bias in their teaching.  That's a very rare situation, though.

A well-rounded approach to problem solving is also frequently associated with innovations within a field.  Bizarre approaches to old problems using techniques that were developed for a different field can sometimes turn into beautifully elegant solutions.  (Usually not, but sometimes yes!) 

Japanese kids "learn" English. But they don't understand it.  They memorize it. So instead of learning English as any other person on the planet learns any language (that is, learning a lexicon, and a grammar), they memorize everything.  So instead of having, for example, the words "dog" "run" "car", and an adequate grammar, which can produce "The dog ran after the car.", they just memorize the phrase "The dog ran after the car.", and this is true of EVERY THING THEY LEARN for the most part.  Japanese teachers just don't get it, when you point this out to them.

Ugh, I have such bad memory I could never learn anything without understanding it and minimizing the information required to use it.

>>11
I don't think anyone understands English when they learn it. I spent my pre-college years being drilled with grammar and the stucture of the English language and it's still Greek to me.

>>13
But you can clearly create novel utterances.  These kids can't.
Whereas you may not think you understand it, it's clear that being drilled in grammar built a grammar in your mind, like the one for your first language.  These kids lack that totally, and thus, can only create novel utterances through fucking up.  If they never made a mistake, it would all be parroting of phrases they memorized in class.

I'm doing speaking tests.  One part involves the kid reading a card with a question on it to me, and me answering, and them asking a follow-up.  On their Q&A sheet that they've been learning from, one of the questions is "Do you enjoy swimming?", where "swimming" is underlined to show that it can be changed to other verbs.  Now, if a grammar was being built, they'd be able to change that sentence into several new ones with verbs they know.  They'd be able to read sentences in such a structure.

On one of the cards, I wrote "Do you enjoy writing?"
Every single one of the kids spews forth "Do you enjoy swimming? Ah, no, uh, writing!"  They're not learning shit, they're just memorizing.  It's a problem.

>>14
Crap. How about teaching them a dozen short sentences in the form of:

{Do you | does {he | she}} {enjoy | like | hate} {swimming | writing | posting on 2ch | ...}

I had little trouble learning German grammar, but I had no memory for the vocabulary; if it were a one-to-one correspondence of "English word" to "German word" I might've had an easier time, but adding in genders limits me to something like a kindergartener's vocabulary, at least when you're talking about getting it right :P

I think it comes down to learning styles and motivation; memorization, in whatever form it takes, is the lowest common denominator for learning. People always *know* things before they *understand* them. There is no exception on this; the difference lies in how one comes to know something(rote is one option; detail/interconnectedness is the other), and whether the knowledge interests them. This is how you end up with people knowing specialized trivia; their interest in a subject drives them to continually greater levels of depth.

The schooling system used in the U.S. and U.K. and a few other places generally avoids rote work in favor of developing a "theoretical foundation," but the disadvantage of this is that students end up confused on how to approach particular subjects; they lack a systemic approach to learning any given material and will either hit a wall at some point, or develop their own systems independently.

On the other hand, what is done in Japan, Germany, etc., is comfortingly formulaic. The main issue with it, of course, is that doing this prevents any one subject from being explored at full potential, since learning by rote is generally a more time-consuming and difficult process for the amount gained.

Internationally, even though the U.S. itself largely dislikes the state of its education, other nations seek to emulate parts of the system.

As a student, one has to be prepared to learn no matter how the material gets presented, though. It's just a good skill to have.

>>3 This is true. Texas, however....

when it all comes down to it, memory and understanding are very similiar

quadratic equation = COMPLETE THE SQUARE = REMEMBERRING HOW TO COMPLETE TEH SQUARE

Figuring out how things connect is pretty much the reason I enjoy mathematics. I figure most of that out because while my teachers are rambling on about stuff that I've already learned, I screw around. Figuring things out beats memorizing 95% of the time for me. I forgot long division, because I never quite got it, because it was taught in a memorization sort of fashion. I ended up relearning it on my own after learning how to factor equations by long division. It all makes more sense when I understand how things connect fundamentally.

how do you factor equations by long division?

You simply divide it and have the quotient x the divisor

what is a quotient?

Using integral variables and operators, dividend / divisor = quotient as in 10 / 4 = 2

What's up with factoring polynomials with a leading coefficient other than one? 

What is a quotient?
What is an integral?
What is an operator?
What is a dividend?
What is a divisor?
10/4 does not equal 2. 10/4 = 5/2 = 2.5

>>25

10/4, where / is the operator for integral division, is equal to 2.  >>23 is correct.  The unaccounted-for part of the dividend can be yielded by 10 mod 4, which is equal to 2.

Hey, that was an example, not an attempt to derail the conversation, jerks.

i memorized what to put in this field and understood that I was BUMPing

lawl, op thinks quadratic formula is HUGE!

>>29
I bet you think finding antiderivatives is tough work.

QUADRATIC FORUMULA WAS LONGCAT SRS

>>31
QUARTIC FORMULA WAS LONGCAT SRSLY
corrected for truth

>>32
If you think the quartic formula is bad, you should see the quintic formula!

>>32
Quartic formula makes my dick hard. Seriously.

Www.youtube.com/ryudecay
I laughed so hard at this kids videos, he's gonna be famous some day.

Ofc. Understanding > Memorization

>>36
That's taken for granted by most, but the problem is which should be implemented at school-level, given concepts like pragmatism and time-constraints.

>>35
Advertising yourself on a sci/math board won't make you famous; we're not stupid enough to care.

>>37
Lol , forget school-level!

There it is just about the strategy how to survive the easiest way.But yeah, you don't need to understand a bit to survive there and even get good degrees.
That's quite laughable, but whatever.

People who have the potential won't be restricted by any systems.

>>39

>>People who have the potential won't be restricted by any systems.

Yup.