What do people mean when they say people are taught to memorize math not understand it?

What do people mean when they say people are taught to memorize math not understand it?

Learning is pretty much 99% memorization, you can't understand something if you are unable to remember what it even is.

I fell for the "understanding" meme and avoided math because i thought it was something i couldn't do, but since i started looking at math like every other thing I've learned it's mostly just memorization.

People probably mean connecting emotionally to the information as opposed to just sucking it up and trying to retain it. Who gives a fuck how you got from A to B as long as you make it to B amirite?

The more you understand, the less you need to memorize. The less you need to memorize, the less you can forget.

Mathfags are extremely insecure and will always do whatever they can to insult other fields. It makes them feel better about their miserable selves.

Here's an example from personal experience. Suppose I have a quiz coming up on polar coordinates, and I need to know the formula [eqn] \int r^2(\theta)\text{d}\theta [/eqn] Sure, I could just brute-force memorize it, but I could also remember where it comes from, which would give me more insight into the math. In this case, I remebered that triangles approximating the area have areas of approximately r*(rθ), using arc length to approximate the base of the triangle.

From Lockhart's Lament, you're taught to have faith in the fact that the Pythagorean Theorem is true. Then you're taught applications of it and even more applications of it. But you never explore how it was created in depth unless you do it on your own time or wait until you take a proofing class. You're taught to take theorems then compute. Alternatively, you can teach yourself to derive this stuff from scratch and all of a sudden you find that it's much easier to memorize a few rules instead of a list of formulas

>What do people mean when they say people are taught to memorize math not understand it?
Are you retarded? Open a dictionary and see the difference for yourself.

Tell me the difference.

Deep.

A lot of mathfags are just huge database of problems/exercises pattern looking machines.

you missed a factor of half

>What do people mean when they say people are taught to memorize math not understand it?
Having a child memorize 7 * 5 = 35 doesn't give them the ability to tell you what 7 * 6 is. Memorizing gives you one answer, understanding gives you a tool for deriving answers to an entire set of problems without having seen each particular problem's answer in advance.

An education is what you know after you've forgotten everything.

I've seen students taught to memorize the distance formula without realizing that its basically just the Pythagorean theorem.

If you understand the Pythagorean theorem you can derive the distance formula effortlessly.

A simple example, but I think its what people are referring to

You have a very narrow definition of what memorization is. you wouldn't teach a child to memorize a specific multiplication, you what have them memorize what it means to multiply, for instance, 2*3 is two groups of 3 or 3 groups of two.

you can memorize an idea that has a wide scope.

Memorizing here is just a verb for being a brainfucker to yourself, just memorizing math, without understanding it.

>You have a very narrow definition of what memorization is.
No, you just have an autistically literal definition of what memorization is.
>you what have them memorize what it means to multiply
That's not memorizing, that's understanding. The fact you need remember what you understood has nothing to do with what memorizing means in the context of "memory vs. understanding." The "memory vs. understanding" distinction is whether you teach a kid to memorize answers vs. teaching them how to derive answers on their own to questions they've never seen before.

Only those that learn to understand have the ability to make it to C, or potentially create a C.

You're right, honestly.
STEM, but Math to a lesser extent, are all about memorization and """understanding""". I unironically find Philosophy courses more difficult, as they're much more involved. This also shows in the disparity in IQs. (where philosophy majors have the highest IQs, following physics majors and math majors.)

t. 4.0 senior math/philo double major

followed by*, rather

rote memorisation = disconnected facts that you barely remember or correlate half the time
critical thought and actual comprehension = a web of connected facts and associations that you can move around within and apply dynamically

So the difference between memorization and understanding depends on what you remember?

On the most basic level, elementary school math, the memorization approach is handing kids a multiplication table and asking them to memorize the product of all integers up to 10

This is how my school did it, and a lot of kids got very quick at it. Those same kids then struggled immensely when asked to multiply anything else, because they had no intuitive grasp of what a multiplication actually IS.

It's the difference between learning how to solve problems you've never seen before by generalizing a principle vs. memorizing an answer without having a method for getting there beyond "I was told this is the answer." I genuinely don't have any idea how you're still not getting this.

its when teacher just say
>here is y=2x+1, pass x to get y, pass y to get x
But kids are not going to know what function is, what was function foundations, why is it legit and other shit.

Majority of cs are clueless when it comes to calculus, they learn formulas and how to use them to pass exam, but what are those formulas, where it came from? why is it legit? how did they invent it?
nah

Do people who've memorized pemdas understand pemdas because of the fact that pemdas can be used in different situations?


When solving a problem with parenthesis, multiplication , and addition you'd proceed by using a piece of information you've memorized.

If your definition of understating is memorizing a piece of information which has a wide scope then we're going to have to agree to disagree because i call that memorization.

The person to discover it couldn't memorize it because no one new what it was to memorize. Understanding it is about understanding why it is true in the kind of way that would help someone to discover/invent it for themselves.

I have memorized the letters of the English language, with them i can construct an infinite number of words, all words i can construct are bounded by the letters i know, any word i produce is a product of a function whose domain is the set of letters i have memorized.

as i said 99% memorization.

You're using a definition of memorization based teaching that includes literally anything you could teach someone that they go on to use later, which makes it a retarded definition. You can't do anything without memory. That's doesn't mean you can't make a distinction between having someone remember an answer vs. teaching someone how to derive answers themselves. Just becase you use memory in the independent derivation cases doesn't mean you *only* use memory. It's the stuff you do in addition to just remembering something that makes it an act of applied understanding. You probably don't remember the answer to 523*327 and in fact might have never even dealt with that as a specific multipliction problem to solve before, so when you work out that the answer is 171021 you'll have done something more than just recall a fact. You learned a function rather than just a value. And the fact you can go further and teach someone a method for meta-deriving new methods for deriving answers doesn't disprove the concept of rote memorization vs. understanding. It just means there's a spectrum with varying degrees of understanding involved.

tahfhagohireh
did you like my word?

There's a lot more to language than the symbols used to represent it. You're doing the equivalent to claiming Leonardo da Vinci wasn't any better at painting than anyone else because he was limited to using images that are bound by the wavelengths of visible light, or that Jimi Hendrix wasn't better at guitar than anyone else because he only used the same 12 notes.

That's nothing, watch this.

tᴀHfHᴀGoHJReH

having the means to produce doesn't mean having the knowledge to create - simply having free access to stone and mortar doesn't make you a mason

Math is merely the penultimate step in understanding the universe.

For you see, even though all things can be reduced to math, all math can be reduced to Rap Music.

Rap Music is the ultimate science that, with practice, can be understood and not merely parroted.

I support this meme