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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#191

Post by butterNaN »

constantcrying wrote: post #189
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…

What I specifically dislike is the question "what am I ever going to use this for" or versions of it. Which I only ever hear about mathematics, but which can be asked about every other subject as well. Yes, math is hard and definitely not for everyone, which I think is perfectly fine. But arguing that something has no use to you, because the first time in your life you actually have to engage in complex logical think…

I feel your complaint is valid, but I your ire should be directed towards people who are supposed to answer this question, not the people who are asking it.

My guess is that answering "what am I ever going to use this for" is easier for other subjects, sometimes almost intuitive. For Maths, it needs to be defined as soon as it starts getting abstract.

"what am I ever going to use this for" is a perfectly valid question. People who are supposed to answer it should do a better job of doing so, writing good curriculum, and overall communication.

Re: Proof you can do hard things

#193

Post by yakubin »

__MatrixMan__ wrote: post #171
nottorp wrote: post #161

Earlier quoted context omitted.

I believe it was called "mathematical analysis" in my corner of the world. In high school and uni. It's the continuity/limits/integrals stuff. Also it was never optional. Either in high school or CS at uni.

In the US we'd reserve "mathematical analysis" (or more specifically, Real analysis) to the college level classes which involve writing proofs about the continuity of functions between sets of real numbers. You'd probably end up with a lecture on the mean value theorem here, and leave with the ability to prove it, among other things "Calculus" is the application of that theory without argument. It's an advanced high…

> In the US, you can probably pass calculus without writing a proof, but you can't pass mathematical analysis without at least understanding epsilon/delta proofs.

In Poland we do those in high school. :)

Re: Proof you can do hard things

#194

Post by smeej »

travisjungroth wrote: post #83
smeej wrote: post #47

Earlier quoted context omitted.

I hate the framing of problems and domains as hard because I found it so confusing when they turned out to be easy for me. It gave me a false sense of competence and superiority. Because I found calculus (and everything else in school people said was hard) easy, I thought I was just exceptionally capable and other people were incompetent and/or stupid. I didn't find out until much later (and it still feels like much…

> I think learning how to learn things that are hard FOR YOU is quite possibly the most important skill in life. I’d certainly agree it’s extremely valuable. There are some failure modes from taking it too far (like anything). People tend to be happier when they’re very good at things. You also contribute more to the world. If you’re always doing things that are hard for you, you won’t do as much or as well, really b…

I agree that it wouldn't be a good idea to spend your life focused on things that are hard for you, but since, as you said, there will be hard parts no matter what you do, learning how to learn the things that are hard is the critical skill.

You don't really have to learn how to learn things that are easy for you. That's what gets them classified as "easy." But you'll never accomplish anything unless you learn how to work through those inevitable hard parts, and the sooner you can learn that, the better.

Re: Proof you can do hard things

#195

Post by butterNaN »

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 can only speak for myself here, but my journey with Maths did start with concrete, practical relationship between concepts and usage. I still remember fascinated by Geometry and Trigonometry, because how it can be used to create graphics and video games is obvious.

The more abstract it gets, the more it warrants an introduction with "here's how it's used in real life".

I can recall the point when it started becoming mechanical - it was when I started doing Derivatives and Integrations. I was 'just solving puzzles' until I hit a chapter, tucked away way back in the syllabus, almost at the end of the 2 year arc - a chapter about Applied Differential Calculus. I still remember the feeling of "Oh... I get it now" euphoria, with a tinge of sadness - why wasn't this covered early on?

Same thing would have happened in Engineering as well, but at the time my teacher was good. They started by explaining the applications of Fourier Transform before we actually got to learn the mechanics of it.

Re: Proof you can do hard things

#196

Post by toyg »

hardware2win wrote: post #174
toyg wrote: post #170

Earlier quoted context omitted.

So what I'm hearing is that math is only good when there is no GPS / no phone. Let's be honest: advanced math is useful in programming contexts. Everywhere else, in 2023 you're using computer programs that will do the hard math for you.

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.

Which is basically never, if you're not a developer or statistician.

Re: Proof you can do hard things

#197

Post by zephyr9 »

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…

Hello mathematics, meet philosophy.

Re: Proof you can do hard things

#198

Post by rhaway84773 »

constantcrying wrote: post #189
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…

What I specifically dislike is the question "what am I ever going to use this for" or versions of it. Which I only ever hear about mathematics, but which can be asked about every other subject as well. Yes, math is hard and definitely not for everyone, which I think is perfectly fine. But arguing that something has no use to you, because the first time in your life you actually have to engage in complex logical think…

Math is abstract. Very few to no other school level subjects are abstract.

That’s why you hear discussions about pushing algebra out, but not about pushing arithmetic out.

That’s why some schools replaced algebra with “data science”.

Abstraction isn’t easy.

But that’s precisely why math, especially algebra and the like, is so essential. It’s the only path to building abstract reasoning among students.

Re: Proof you can do hard things

#199

Post by smeej »

nine_k wrote: post #91
smeej wrote: post #47

Earlier quoted context omitted.

I hate the framing of problems and domains as hard because I found it so confusing when they turned out to be easy for me. It gave me a false sense of competence and superiority. Because I found calculus (and everything else in school people said was hard) easy, I thought I was just exceptionally capable and other people were incompetent and/or stupid. I didn't find out until much later (and it still feels like much…

Ah, the trap of the gifted student! When everything other students find somehow hard is easy for you, you get a delusion that nothing is hard, and that putting in some effort is not necessary. A rude awakening may come at high school, or at college. Those who kept toiling just keep toiling, and overtake you, because.you're not used to pushing through. I think it's important to learn early enough that things are usual…

I was always told that at the next level of school, I would finally meet a challenge. I got through a master's degree without its happening, and unfortunately that just drove the initial point deeper, that I was somehow fundamentally different from other people rather than just very luckily in an environment exceptionally well-suited to my aptitude (even though the rest of the world is not).

Re: Proof you can do hard things

#200

Post by paulcole »

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…

> The question is never asked about any other school subject

Are you kidding? Every tech-bro on the planet makes their disdain for literature, philosophy, etc. extremely well known.

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