Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Proof you can do hard things

blog.nateliason.com

Post reply on HN
Print view View original

51–60 of 330 posts

Re: Proof you can do hard things

#51

Post by roflyear »

Medh_Suk wrote: post #21
ethanbond wrote: post #11

Self-image really is important, especially on the dimension of self-efficacy. There are compounding effects in both the positive and negative direction though. I’ve used this same idea to dig myself out of ruts. When things are fucked up I’ll start paying attention to small things and deliberately “defer” progress on a few bigger things that are harder to do and more costly to fail. Each small win helps build momentu…

"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've never gotten anything out of discipline itself.

Re: Proof you can do hard things

#52

Post by maxwin »

I think the better way is to come out with a lot of interesting real world scenarios that require calculus or other math. Math doesn't get created out of a vacuum. It was created for a reason. I think if we can avoid diving into abstractions too quickly and focus on specific real world problems and lead the kids step by step to the solutions , that would be more interesting.

Re: Proof you can do hard things

#53

Post by bee_rider »

jimmydddd wrote: post #42
wwarner wrote: post #31

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…

I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.

Calculus is needed to understand, like, basic sophomore and junior year engineering stuff. You can maybe pass the tests without understanding where the models came from if your professors are just really lazy and only give you canned problems, but that isn’t a goal we should strive for.

And engineers should usually be using battle-tested models rather than coming up with their own derivations, so to some extent using the calculus day-to-day shouldn’t be necessary in many cases. But it is necessary in order to understand where the models came from. This is what separates engineers from tech-priests.

Re: Proof you can do hard things

#54

Post by owenpalmer »

jimmydddd wrote: post #42
wwarner wrote: post #31

I like the idea, but I’m gonna say that (a) calculus is more than a good challenge and (b) math is actually easy. To understand how things actually work, you need math, especially calculus. Deep learning? Calculus. Statistics? Calculus. Finance? Calculus. Physics? Calculus. Mech E, robotics, earth science, econ? Calculus. Second, calculus, like all math, is easy. Like that’s the point, it’s the science of simple thin…

I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.

One time I asked an engineer if he used calculus and he said no, so it must not be useful.

Re: Proof you can do hard things

#55

Post by wwarner »

roflyear wrote: post #49
wwarner wrote: post #45

Earlier quoted context omitted.

How you can use R without knowing calculus? Why would you even turn to R if you didn’t have a calculus problem to solve?

You don't use calc much when you use R, unless you're working on a problem that involves calculus, which isn't many problems, usually? R is usually used to do data stuffs in my experience. Like, "take in this data from this CSV, and do these manipulations" which may involve math but not often calculus.

I am totally for software assisted math. Math isn’t just pencil on paper, and it isn’t only proof, and it’s great to talk about over beers.

Re: Proof you can do hard things

#56

Post by Natsu »

WesleyJohnson wrote: post #46

I lost interest in school around the 10th or 11th grade. I never took any math classes beyond what was required to graduate way back in '96 in Florida. I also didn't go to college. I've been a professional web developer since 2005 and a development manager (who still codes) since 2017. I don't understand the first thing about Calculus or even logarithms. I'm sure if I did, I'd probably be a better developer. I've had…

A lot of math is cumulative, i.e. built on top of the prior concepts/tools. There are some things that are effectively the start of their own branches, but a lot of them then go back into a tangle of general mathematics that's all deeply interrelated, and also a subject onto itself when you get into ways to convert problems into totally different representations to use other mathematical tools on them.

In your case, follow something like Khan academy through the normal grade school programs to pick up where you left off and work backwards on picking up any concepts you're weak on then pursue whatever threads interest you. Wolfram can also help you look up specific things or find necessary formulas if, e.g. you just need the formula for a cone or to know how to integrate sin().

Re: Proof you can do hard things

#57

Post by cameldrv »

bee_rider wrote: post #53
jimmydddd wrote: post #42

Earlier quoted context omitted.

I saw an article where they asked a bunch of scientists and engineers if they actually used calculus in their professions. None of them did. They used Excel and the R programming language.

Calculus is needed to understand, like, basic sophomore and junior year engineering stuff. You can maybe pass the tests without understanding where the models came from if your professors are just really lazy and only give you canned problems, but that isn’t a goal we should strive for. And engineers should usually be using battle-tested models rather than coming up with their own derivations, so to some extent using…

I wonder if there’s a way to teach Calculus in a more practical way. I use the principles of Calculus constantly in many aspects of my job, but I don’t think I’ve ever done say, integration by parts professionally. Understanding deeply what an integral and a derivative are is a very useful skill though.

Re: Proof you can do hard things

#58

Post by savingsPossible »

paddw wrote: post #12

There are infinitely many hard things. It is hard to learn Japanese. We don't require that every high school student attain basic proficiency in it though. The reason we learn calculus in high school is because it is foundational for many advanced STEM fields, and we will yield better results during university for the small percentage of students who go into those fields by forcing everyone to learn it in high school…

> and we will yield better results during university for the small percentage of students who go into those fields by forcing everyone to learn it in high school

I fear that you might be right about this

Re: Proof you can do hard things

#59

Post by bee_rider »

andruc wrote: post #9

Everyone commenting so far seems to be missing the forest for the trees. Doing hard things, and the proof that comes with it, is empowering.

The issue is that one tree—calculus is pretty important and fundamental to lots of fields of study—is covered in tinsel and lights, and also for some unfortunate reason some folks have gotten it into their heads that they’ll never need it and might as well light it on fire.

Re: Proof you can do hard things

#60

Post by batman-farts »

It's a bit sad that calculus remains the stereotypical example of difficulty in most curriculums. Throughout childhood, I remember it seeming like some sort of complex, inscrutable, untouchable phantom hanging in the distance at the far end of the high school math course progression.

If somebody had told me that calculus is how you transition between dimensions, or that techniques of integration would enable me to generate 3D shapes from 2D lines, I think I would have been much more motivated to progress rapidly in math, and much less discouraged when I hit the "hard parts." Those are the answers I tend to give today when somebody asks me, "why take calculus?" Demystifying it doesn't even have to be a wholly practical explanation, like deriving acceleration from velocity.

Segregating out the "hard stuff" doesn't even necessarily lead to great learning outcomes, either. At my high school, and it seems many others, the honors kids were put on the track leading to calculus while everyone else ended up in a dedicated statistics class. The honors kids were expected to pick up statistics through supplementary assignments in their laboratory science classes, and this same approach carried over into lower-division undergrad. As an adult, I feel like that approach has only given me cause to go back and seek out a firmer grounding in statistics.

Post reply on HN