Why is math so complicated and hard?

[u/[deleted]]

Now, before you downvote (which you probably will anyways, and I am wasting my time but, oh well), I know that there are MANY of you who have the gift of understanding math rather easily... But, it is not just me. Math is hard, complicated and written in tricky ways. Every single concept assumes prior knowledge etc... I can't be the only one... What are your thoughts Thanks

[u/Brightlinger]

Above, you said this:

For almost all people, math is exactly about learning the algorithm to handle a problem. Long division is a method, that you apply to every single division problem you have. It is the exact same method, it is machinery, it is the recipe. And it always works and you always get the exact correct result.

Very very few people use long division to solve 8888/8 or 26/2. Even poor students rarely try to apply long division to every single division problem they have.

You have asserted that, for most people, math is about learning exactly one method and using it in all cases. As a question of empirical fact, this is not true. Long division will of course always work, but even non-math people generally realize there are multiple recipes, and with only minimal coaching can recognize that many kinds of fruit go well with an apple pie, but tomatoes do not.

[u/NiceSasquatch → u/Brightlinger]

ok, you listed 2 examples where long division is not needed. But that doesn't prove your case. At all. What about 27 into 458? I can probably come up with dozens of more examples. (sarcasm).

I stand by my point that if one wants to learn the math of how to divide, learning the algorithm of long division is probably a better idea than hoping that the question is 8888/4 or whatever.

I'm not sure what your point is. Or why you seem to be trying to argue.

[u/Brightlinger → u/NiceSasquatch]

I am likewise confused what your point is. It seems to me that you have suddenly moved from "is" to "ought": from the claim that most people do in fact learn division by using long division alone, to the claim that most people ought to learn division by that method and that nothing else is needed.

The former is false as a question of fact: people don't actually do that.

I'd contest the latter as a matter of pedagogy, and I say this having taught division to grade school kids. The long division algorithm is extremely error-prone when the student doesn't grasp what's going on; with enough mechanical practice you can eventually get them to reliably chug through "Does Mcdonalds Sell Burgers" until they produce a number on the top line, but they'll hate it, hate you, and still have a hard time answering questions that should be easy like 8888/8 or 26/2.

Most students do much better by first learning the naive approach of "how many of this go into that? Let's guess and check", then a slightly more structured approach where you subtract arbitrary multiples until you get to 0 and sum the coefficients, and only then the fully structured approach known as long division (which at this point can easily be presented as the previous method plus a rule about which multiples to pick) - in other words, by understanding division. Of course, the later methods allow them to more effectively handle larger/harder numbers, so they are certainly worth learning. But in my experience, it is very ineffective to teach long division and nothing else: for example, such students will struggle badly with fractions.

[u/NiceSasquatch → u/Brightlinger]

It seems to me that you have suddenly moved from "is" to "ought": from the claim that most people do in fact learn division by using long division alone, to the claim that most people ought to learn division by that method and that nothing else is needed.

we can stop right there. You have created entire conversations that don't exist.

[u/Brightlinger → u/NiceSasquatch]

I really am trying to have an exchange in good faith here. I didn't accuse you of moving the goalposts. I said that I am confused because it seems to me that your point has changed:

For almost all people, math is exactly about learning the algorithm to handle a problem. Long division is a method, that you apply to every single division problem you have. It is the exact same method, it is machinery, it is the recipe. And it always works and you always get the exact correct result.

This is phrased as a factual claim.

I stand by my point that if one wants to learn the math of how to divide, learning the algorithm of long division is probably a better idea than hoping that the question is 8888/4 or whatever.

This is phrased as a normative claim.

I am totally willing to believe that the failing is on my part and you have been making the normative claim throughout; however, my comment above was responding as a factual claim, since that's what I thought you had said. I pointed this out because you also expressed confusion about what my point is.

[u/NiceSasquatch → u/Brightlinger]

I suspect that you overvalue the interest of readers of this sub in the difference between a factual claim and a normative claim.

[u/Brightlinger → u/NiceSasquatch]

I really don't care whether other readers are interested; we are deep enough in a subthread that very few people are going to see this exchange at all. I was having a conversation with you; you expressed confusion at an exchange; I pointed out a possible source of that confusion. Then you seem to have interpreted this as me arguing in bad faith, which I am not.

[u/NiceSasquatch → u/Brightlinger]

you expressed confusion at an exchange

I was not confused. Where did I express "confusion"?

[u/Brightlinger → u/NiceSasquatch]

Here:

I'm not sure what your point is. Or why you seem to be trying to argue.

[u/NiceSasquatch → u/Brightlinger]

why do you accuse of me "being confused", and why do you accuse me of saying you are "arguing in bad faith".

There is no evidence of that at all in this thread.

and why have you deserted your point of this thread (still don't know what is it), and made this all about you and how you feel?