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Proof you can do hard things

blog.nateliason.com

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Re: Proof you can do hard things

#291

Post by Izkata »

foofoo4u wrote: post #245
trinovantes wrote: post #220

Earlier quoted context omitted.

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.

This is my experience as well. And unfortunately, many of my teachers feed into this. "Ok kids, today we're going to learn this new formula. You put a number in, do some arithmetic, and you get an answer out. I am not going to bother explaining the importance of this formula, how it came into existence, nor its practical application — likely because even I don't know. But what I do know is it's important because ever…

> Ok kids, today we're going to learn this new formula. You put a number in, do some arithmetic, and you get an answer out. I am not going to bother explaining the importance of this formula, how it came into existence

Short story time: I never could memorize various geometry equations, like surface area or volume of basic shapes. Then one day while bored at my part time job, I found a paper and pencil and decided to use what I'd just learned in calculus to see if I could derive one of those equations, by leaving variables in instead of using concrete numbers.

It totally worked, I reinvented the volume of a sphere equation and ever since that day I've never forgotten it because now every part of the equation has meaning. I know why it is the way it is, and it makes sense.

Re: Proof you can do hard things

#292

Post by derangedHorse »

rhaway84773 wrote: post #198
constantcrying wrote: post #189

Earlier quoted context omitted.

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.

I don’t think it’s the abstraction, I think it’s the perceived lack of usefulness. I’ve known many individuals who are bad at math but can understand the abstraction of most programming constructs. I think it’s mainly because the pay off of learning programming has a higher immediate value (it can be used for a variety of tasks and can even help score a high paying job).

Re: Proof you can do hard things

#293

Post by foofoo4u »

Izkata wrote: post #291
foofoo4u wrote: post #245

Earlier quoted context omitted.

This is my experience as well. And unfortunately, many of my teachers feed into this. "Ok kids, today we're going to learn this new formula. You put a number in, do some arithmetic, and you get an answer out. I am not going to bother explaining the importance of this formula, how it came into existence, nor its practical application — likely because even I don't know. But what I do know is it's important because ever…

> Ok kids, today we're going to learn this new formula. You put a number in, do some arithmetic, and you get an answer out. I am not going to bother explaining the importance of this formula, how it came into existence Short story time: I never could memorize various geometry equations, like surface area or volume of basic shapes. Then one day while bored at my part time job, I found a paper and pencil and decided to…

This gets to the heart of what math class needs. Which is a process of learning how to re-invent formulas, constants, and other concepts. Through this, students will come to appreciate why such things exist. And they will appreciate it further if students are first challenged to solve such problems in the absence of it.

Re: Proof you can do hard things

#294

Post by CodeSgt »

BiteCode_dev wrote: post #248
CodeSgt wrote: post #239

Earlier quoted context omitted.

> This is wrong. Birds fly, fishes swim. There is nothing bad about either. I have a hard time with this mentality. I would have agreed a few years ago perhaps, and do still agree that we all have our own aptitudes, but the level of absolution in a statement like this just isn’t really quite as applicable to humans in my opinion. There are things I never thought I’d be capable of that I’ve recently begun to excel at.…

> I believe that any perceived immutable barriers or obstacles are almost entirely psychological. Laws of physics are laws of physics. And biology is applied physics. People in sport have known that for a long time. You can train as much as Usain Bolt, he still has a huge advantage. Thinking the other human characteristics are not affected by this is weird. You will never be Von Neumann, no matter how much you spend…

> Obviously at the extreme end’s of the spectrum, the human hardware limit is very real.

Re: Proof you can do hard things

#295

Post by inanutshellus »

ethanbond wrote: post #27
Medh_Suk wrote: post #21

Earlier quoted context omitted.

"It costs you nothing to believe in yourself. But it will cost you everything if you don't." Discipline is a muscle. Go Build it. Key is to understand different activities require different muscles. Be mindful of picking your activities, but dont keep on waiting.

I am discussing a way to be disciplined, which is with decent flexion deliberately built into your self-image. E.g. I know many people who go through bouts of intense fitness or diet fixations, take a lot of well-deserved pride in their discipline, and then hit a major event that temporarily precludes the fixation. They really struggle to get back on the train. One major factor, IMO, is that they’re daunted by the in…

Sounds like your friends are "goal oriented" rather than "process oriented".

Goal Mindset = "reach difficult state of fitness"

Process Mindset = "Time to do my gym routine, just with lighter weights bc I'm temporarily weakened"

Re: Proof you can do hard things

#296

Post by fatnoah »

fsmv wrote: post #6

You take calculus to understand the nature of change over time, which is the foundation of physics. The formulas to do integrals aren't important but the concept of integrals is. Honestly I think we should try to focus on differential equations instead but maybe it's necessary to do calculus first.

When I studied Calculus in high school, it was taught via mathematical proofs and concepts. I didn't really "get it" and struggled to keep a C average...until that one day I was working on a problem in the library about water draining from a pool it hit me that "it's about rate of change!". That was it...that concept changed Calculus from some weird math thing to something I could understand and get my head around.

It also underscored the poor teaching methods at my school. I was somewhat vindicated by being the only person in my class to get a 5 on the AP test. I also ended up in a major where I did almost nothing but calculus for undergrad and grad work.

Re: Proof you can do hard things

#297

Post by riialist »

I thought "doing hard things" would be something like a running Marathon, studying or working while having toddlers, learning to be a pro coder as an adult, taking care of your close ones while they are sick.. But it was about doing basic math.

Proving to yourself or anyone else that "you can do hard things" since you did more or less math in school/collage/university will leave you trainwreck at the first real hard thing that bumps your way.

And why some people don't do the math? I guess, because they are told its boring and/or hard, but they should do it anyway. And people don't like to be told what to do.

Re: Proof you can do hard things

#298

Post by TRiG_Ireland »

Sodman wrote: post #246
TRiG_Ireland wrote: post #235

Earlier quoted context omitted.

> 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. I've often heard it asked of languages, specifically Irish.

I always disliked Irish (and languages, in general) in school. However, now that I'm over a decade out of college I find it to be one of the few subjects I wish I'd paid more attention to when I'd had the chance... Sure, it's not particularly useful in adult life, but neither is organic chemistry, for most folks. The main difference for me is that it's relatively easy to "fill in the gaps" for any other subject we le…

I asked that question in school (strange to look back on, as I'm now fascinated by languages), and the only answer the teacher could give was that doing well in Irish would give extra Leaving Cert points. That struck me at the time as depressing.

Re: Proof you can do hard things

#299

Post by jdmn73 »

__MatrixMan__ wrote: post #238
yakubin wrote: post #193

Earlier quoted context omitted.

> 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. :)

In the US, our education system kind of sucks (:

I also did these in my good but non-elite American public high school.

Re: Proof you can do hard things

#300

Post by blitz_skull »

greatwave1 wrote: post #275
blitz_skull wrote: post #241

Earlier quoted context omitted.

You didn't go to the high school I went to. Some people, fundamentally, just cannot do math.

Was it a good school in a wealthy area? If not, what makes you confident that your peers were falling behind due to some sort of innate inability, instead of as a result of compounding poor teaching or other environmental factors?

Do factors matter?

Unless you can mass edit all the factors, then it remains that some people simply cannot do math past a certain level.

But for what it’s worth, it was a very small school in a VERY poor area. (Median income probably at or below $20k / year) The teaching was actually above-average for the area, but probably below average over a national rating.

I do think factors matter in my personal anecdote of my particular high school. However my LIFE has reinforced my observations: most people are profoundly bad at math, from a seemingly fundamental level.

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