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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#211

Post by alpaca128 »

constantcrying wrote: post #179

I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much m…

> I see no reason why it should have to justify itself in any way

If you cannot justify to children why you force them to sit in school for hours every day you shouldn't be surprised by the consequences. Though weirdly schools tend to be very surprised in my experience. And yes, this question is absolutely asked in other subjects too, but less often as they're not as abstract and usually related to things people encounter every day.

> Justifying mathematics is easy

And thus left as exercise to the reader?

Re: Proof you can do hard things

#212

Post by BiteCode_dev »

DarkNova6 wrote: post #206
BiteCode_dev wrote: post #186

Earlier quoted context omitted.

That's because math is harder for most people. There is no difference between learning a name in history or in biology, or some workflow. But math reasoning really filters out people in a way nothing else does. All other topics just require memory and basic reasoning. Even physics mostly is hard because of math. And philosophy, mostly because of jargon and references. Otherwise, if you break it down, it's not that co…

> math reasoning really filter out people in a way nothing else does. Disagree. I say: Bad math teachers really filter out people in a way nothing else does. "Here is a list of rules which can be used in specific circumstances. I am not going to tell you why you would need them and the exam will feature several corner cases. Also, I will not provide any examples or detailed explanations because what would other peopl…

True.

But even with the best teachers for every field, math or sport will filter out people way more harshly, and sooner, than any other field.

You can smooth things out with quality teaching, but there is a human hardware limit, and you reach it sooner with those two.

Many people don't like to hear it because their ego is bruised or because it goes against the idea that "everybody can do anything".

This is wrong. Birds fly, fishes swim. There is nothing bad about either.

Re: Proof you can do hard things

#213

Post by roel_v »

keerthiko wrote: post #149
hardware2win wrote: post #141

>You know they will never use it in adulthood, outside of certain career choices. If somebody says stuff like this, then they do not understand math, imo. Im a little bit sad whenever somebody argues for math by using "no phone available at the moment" argument. Math is insanely powerful world modeling tool. Starting from calculating right amount of fence for your garden, to estimation of 500km route arrival time whi…

IME a big part of this misdirection stems from school focusing on the mechanics of math, rather than the intuition of math. In the long run, the mechanics of math (how to do long division, or differentiate an expression, or expand a geometric series) are important only insofar as to help us model and predict and analyze the world, intuitively. However, students who do not intuitively see the power of mathematical int…

I've never taught mathematics but I think it's much harder to teach the intuition, and I also think that more people are capable of learning the mechanics than the intuition. So from the point of view of someone designing a methodology and curriculum - you have to design for scale.

I have the same thing with learning languages: I despise focusing on the rules of conjugation and word order and rote memorizing rules, exceptions to them and exceptions to exceptions. I much prefer to bootstrap with some vocab and then acquire by immersion, even if that means I get the conjugations wrong in the beginning. But I also find myself in the minority by far, to the extent that pretty much all language teachers I ever had (except my high school French teacher - she was awesome letting me translate MC Solaar lyrics for grades) didn't even really seem to believe that there are other ways of learning other than studying rules.

Re: Proof you can do hard things

#214

Post by nicbou »

constantcrying wrote: post #179

I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much m…

This drove me nuts when I was a student. No one gave me a solid reason, even though it was right there.

Math is a language that is required to describe how the world works. It's the official language of certain spheres of society that seriously impact your life. If you don't speak it, other people will make decisions for you that you can't understand.

It's also really useful if you deal with finance, engineering, computers, statistics etc. If you don't speak math, these doors are closed to you.

This would be a lot more evident if they had us solve real world problems with math.

Re: Proof you can do hard things

#215

Post by constantcrying »

alpaca128 wrote: post #211
constantcrying wrote: post #179

I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much m…

> I see no reason why it should have to justify itself in any way If you cannot justify to children why you force them to sit in school for hours every day you shouldn't be surprised by the consequences. Though weirdly schools tend to be very surprised in my experience. And yes, this question is absolutely asked in other subjects too, but less often as they're not as abstract and usually related to things people enco…

>If you cannot justify to children why you force them to sit in school for hours every day you shouldn't be surprised by the consequences.

Nobody told me why I should learn about ancient history or 20th century literature.

>usually related to things people encounter every day.

Basically nothing I did in school had anything at all to do with things I encountered every day. I played video games and hung out with friends. I didn't study European art history in my time away from school.

>And thus left as exercise to the reader?

Yes. I assumed that most people on this website understand the inherent value in abstract thiking and broadly applicable problem solving techniques.

Re: Proof you can do hard things

#216

Post by BiteCode_dev »

DC-3 wrote: post #210
BiteCode_dev wrote: post #207

Earlier quoted context omitted.

They are not defeated by literature, they are just not that interested in it, and therefore never practiced, and dislike working on it. It's not a matter of the field being too difficult. It's a matter of personality. > Quite the claim. Yes. I've discussed this claim with people defending the opposite idea, and I've yet to find anybody making a good demonstration that philosophy is hard in itself. They point that the…

As I read it, your argument boils down to: > When a student who likes literature does poorly in mathematics, it is because he is not clever enough. > When a student who likes mathematics does poorly in literature, it is because it is boring. If you truly believe this I have nothing more to say to you. I will not respond to your comments on philosophy, though I think they are wrongheaded, because I think your position…

> If you truly believe this

Well, I've tried sincerely to find out what was difficult about philosophy for many years. Have you done the same with math?

> because I think your position to discuss such things is made untenable by the obvious contempt in which you hold the humanities.

You assume I was a math head, and that I have disdain from humanities.

That's a total projection which tells me you are not being objective in this discussion. So you are right, it's a good thing we stop there.

But for the record I actually like humanities.

Just because you think a topic is harder than another doesn't mean you prefer one.

I don't even particularly like math, and I'm very bad at it.

I'm probably better than the average Joe, but I'm way better at writing than at calculating.

And I enjoy reading philosophy and sociology.

It's ironic that someone in humanities can be so judgmental of its fellow human, and in a very black and white way.

Re: Proof you can do hard things

#217

Post by l__l »

throwbadubadu wrote: post #181
l__l wrote: post #155

Earlier quoted context omitted.

This is my field :) Category theory is about connecting the dots between different areas of maths. The "general application" is to allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details. It arose when geometers and topologists realised they were working on the same problems, dressed up in different ways. I think the utility for technical people, from…

Don't need to convince me ;), but I mean this is for the very average person who argues like "why do I need more math than adding two numbers"... and even just "allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details" and "learning to do abstractions correctly" would not seem more approachable to them than the calculus description I gave above? imo. Is…

I honestly don't know. This might be a skill issue on my part (very much not an educator), but I think of it as a language for thinking about structural abstraction, so to me the question is akin to "is there a real-life problem that German relates to?"; I can certainly think of lots of problems that would be made much much easier by understanding the language (e.g., getting around Germany, i.e. noticing abstractions), but it's tough to point to anything for this explicit question other than "conversing with someone in German".

I guess to try and mirror your calculus example, I'd try and motivate why someone should care about abstraction itself, perhaps with examples like 'calculating my taxes each year is exactly the same problem, except the raw numbers have changed'.

Alternatively it might go over better to say something like: "Imagine you have a map with a bunch of points, and paths which you can walk between them. CT is the study of the paths themselves, the impact of walking down them in various routes: for mathematicians, this means looking at things like turning sentences such as 'think of a number, add 4 to it then divide by 2 then add 6 then subtract 1' into 'think of a number and add 7'. Once you've spotted this shortcut on this silly toy map, you'll recognise the same paths and the same shortcut when you see on your tax form 'take your income, add £400 to it, divide by 2, add £600 and subtract £100"

Re: Proof you can do hard things

#218

Post by hardware2win »

lovelyviking wrote: post #202
hardware2win wrote: post #174

Earlier quoted context omitted.

You didnt understand my message. Math is not about calculators or computers. It is about modeling (e.g real world) It is useful whenever non-standard, already modeled in your calculator problem apprears.

>You didnt understand my message. Perhaps he didn’t and isn’t it a part of the problem to apply math? >Then you basically not only get better tools to operate (model) in real world, day2day life, but also it opens you doors to highly paid careers. can you elaborate on how “it opens you doors to highly paid careers”?

>can you elaborate on how “it opens you doors to highly paid careers”?

Depends on the level of proficiency

Examples can be engineering or fancy financial related companies like Jane Street

Re: Proof you can do hard things

#219

Post by _lvbh »

alpaca128 wrote: post #211
constantcrying wrote: post #179

I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much m…

> I see no reason why it should have to justify itself in any way If you cannot justify to children why you force them to sit in school for hours every day you shouldn't be surprised by the consequences. Though weirdly schools tend to be very surprised in my experience. And yes, this question is absolutely asked in other subjects too, but less often as they're not as abstract and usually related to things people enco…

I think it’s useful to justify math at a young age. I fell into the “math doesn’t matter” group and regret it since stepping into software engineering

Re: Proof you can do hard things

#220

Post by trinovantes »

BiteCode_dev wrote: post #186
constantcrying wrote: post #179

I really despise all the "why you should care about math" takes. The question is never asked about any other school subject and only mathematics has to justify itself that way. I had to learn about categories of plants and animals, interpret 20th century literature, learn about events from a thousand years ago, I did presentations on the demographics of European countries, how certain chemicals react and much, much m…

That's because math is harder for most people. There is no difference between learning a name in history or in biology, or some workflow. But math reasoning really filters out people in a way nothing else does. All other topics just require memory and basic reasoning. Even physics mostly is hard because of math. And philosophy, mostly because of jargon and references. Otherwise, if you break it down, it's not that co…

Math as a field of study might be hard but in my experience math pre grad-school is just memorization as much as any other subject. I studied for my exams by simply doing countless exercises and memorizing every problem pattern to the point where I'm just plugging numbers into a series of formulas, even if I don't fully know why I'm doing so.
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