Everyone is capable of, and can benefit from, mathematical thinking • Hacker News Board

Re: Everyone is capable of, and can benefit from, mathematical thinking

#381

Post by sn9 » Sat, Nov 23, 2024, 9:06 PM UTC

aleden wrote: post #286

In my high school we were basically only instructed to get good at applied math. Calculus. Which more often than not was simply "plugging it in". Most of that work is trivially automatible through Mathematica. When I reached a university, I took number theory and abstract algebra and it blew my mind that math was actually so beautiful in a way that defied explanation. When I took real analysis I finally saw the side…

Calculus isn't on the standard SAT or even the Math Subject II tests [0], at least not in the early 2000s.

They taught us calculus because it's a prereq for engineering and physics and that's been important since the space race.

[0] https://en.wikipedia.org/wiki/SAT_Subject_Tests

Re: Everyone is capable of, and can benefit from, mathematical thinking

#382

Post by sn9 » Sat, Nov 23, 2024, 9:22 PM UTC

tgv wrote: post #355

davidbessis wrote: post #189

Earlier quoted context omitted.

I'm the author of what you've just described as clickbait. Interestingly, the 100m metaphor is extensively discussed in my book, where I explain why it should rather lead to the exact opposite of your conclusion. The situation with math isn't that there's a bunch of people who run under 10s. It's more like the best people run in 1 nanosecond, while the majority of the population never gets to the finish line. Highly-…

So, for starters: you don't have any evidence, if I understood it properly. None whatsoever. That's really not the basis for arguing "become 1000x better." If only because your operationalization is missing. If you can't measure someone math's skills, how can you say they can become 1000x better? I think the whole article manages not to even speak about what "math" actually is supposed to be. Symbol manipulation acco…

You'll want to get your daughter to start using Math Academy for at least 30 minutes per day [0].

New solutions exist for old problems.

[0] https://www.justinmath.com/books/#the-math-academy-way

Re: Everyone is capable of, and can benefit from, mathematical thinking

#383

Post by sn9 » Sat, Nov 23, 2024, 9:25 PM UTC

hilbert42 wrote: post #232

sourcepluck wrote: post #193

Earlier quoted context omitted.

Imagine our world was extremely similar to how it is now in any way you'd care to imagine, except two things were different. 1. Everyone (young, old, poor, rich) thinks that maths is interesting and fun and beautiful and important. Not important "to get a good job" or "to go to a good college" or "to be an impressive person", but rather important because it's fun and interesting. And maybe it also helps you think cle…

"Kids are told week in week out that maths is stupid, that they are stupid. …." Come on, how often are kids exposed to such stupid talk? I suspect very infrequently. My grandmother, who wasn't stupid by any means but who knew only basic arithmetic, would never have uttered such nonsense. And I'd stress, like many of her generation and background, her knowledge of mathematics was minimal, if she'd been ask what calcul…

In math classrooms filled with 30 students on average for 12 years? With usually all 30 of those students having mathematically illiterate parents who can't help with their homework?

Every student hears it enough for it to be a widespread sentiment. It spreads like an infection.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#384

Post by sn9 » Sat, Nov 23, 2024, 9:30 PM UTC

khafra wrote: post #54

gsabo wrote: post #15

I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

> If it's easy, then it means you already know this material, and you're wasting your time. One thing I'm anticipating from LLM-based tutoring is an adaptive test that locates someone's frontier of knowledge, and plots an efficient route toward any capability goal through the required intermediate skills. Trying to find the places where math starts getting difficult by skimming through textbooks takes too long; espec…

LLMs hallucinate and are completely the wrong tool for this. People need to learn about the history of AI.

Expert-systems using techniques from the 80s are doing this right now [0].

[0] https://www.mathacademy.com/how-our-ai-works

Re: Everyone is capable of, and can benefit from, mathematical thinking

#385

Post by quus » Sat, Nov 23, 2024, 9:36 PM UTC

defrost wrote: post #324

quus wrote: post #304

Earlier quoted context omitted.

You’re sort of making my point — there are people out there who think math education sets the mind free and opens the gates of higher cognition, and then others talking about hum drum stuff like tax brackets and compound interest. If the benefits really just amount to a few units of pre-algebra content, that would be disappointing.

> If the benefits really just amount to a few units of pre-algebra content, that would be disappointing. They don't though - there are benefits all the way up. Giving a few examples of benefits from low order mathematical thinking (understanding concepts of compounding, etc) does not equal a statement that these are the only benefits.

Great, so what are those benefits all the way up?

Re: Everyone is capable of, and can benefit from, mathematical thinking

#386

Post by sn9 » Sat, Nov 23, 2024, 9:37 PM UTC

beezlewax wrote: post #378

gsabo wrote: post #15

I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

I'd like to improve my mathematical knowledge (which has degraded to basically zero). Can you talk about the path or resources you are using to improve here?

If you know how to multiply and divide, Math Academy will take you to college level math pretty quickly.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#387

Post by sn9 » Sat, Nov 23, 2024, 9:37 PM UTC

bamboozled wrote: post #90

gsabo wrote: post #15

I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…

How have you been working on it? Asking for a friend ;)

I'd strongly recommend Math Academy for at least 30 minutes per day.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#388

Post by quus » Sat, Nov 23, 2024, 9:40 PM UTC

pokerface_86 wrote: post #343

quus wrote: post #44

I’m actually interested in the “can benefit from” claim in this title. I don’t particularly doubt that most people could become reasonably good at math, but I wonder how much of the juice is worth the squeeze, and how juicy it is on the scale from basic arithmetic up to the point where you’re reading papers by June Huh or Terry Tao. As anti-intellectual as it sounds, you could imagine someone asking, is it worth devo…

i’ve always found that mathematical thinkers do better, no matter the role. it’s difficult to express how, it’s kind of intangible, but it’s just a mental process that helps break down tasks and come up with unique solutions. that being said, my marketing pitch for math was always, nothing else is even close to as intellectually stimulating as math.

yeah, I wish we could be more specific here. Like I appreciate the things you’re saying, and I don’t doubt the truth or sincerity of that opinion — but I feel like I’ve encountered some math PhD students who were surprisingly inflexible in the way they thought, and very parochial in their intellectual interests. I guess I just haven’t (anecdotally) found the transference of math training to other domains as much as others seem to.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#389

Post by sn9 » Sat, Nov 23, 2024, 9:41 PM UTC

gravypod wrote: post #253

mbbbackus wrote: post #180

I've been reading the author's book, Mathematica, and it's awesome. The title of this post doesn't do it justice. He shows that math skill is almost more like a sports talent than it is knowledge talent. He claims this based on the way people have to learn how to manipulate different math objects in their heads, whether treating them as rotated shapes, slot machines, or origami. It's like an imagination sport. Also,…

I really want to try MathAcademy.com. How quickly do you think someone doing light study could move from a Calc 1 -> advanced stuff using that site? In my case I could put in at least 30 minutes to an hour a day.

Hard to say but this should give you an idea [0].

At that rate, less than a year is reasonable.

[0] https://www.justinmath.com/what-is-the-highest-sustainable-d...

Re: Everyone is capable of, and can benefit from, mathematical thinking

#390

Post by pokerface_86 » Sat, Nov 23, 2024, 9:44 PM UTC

quus wrote: post #388

pokerface_86 wrote: post #343

Earlier quoted context omitted.

i’ve always found that mathematical thinkers do better, no matter the role. it’s difficult to express how, it’s kind of intangible, but it’s just a mental process that helps break down tasks and come up with unique solutions. that being said, my marketing pitch for math was always, nothing else is even close to as intellectually stimulating as math.

yeah, I wish we could be more specific here. Like I appreciate the things you’re saying, and I don’t doubt the truth or sincerity of that opinion — but I feel like I’ve encountered some math PhD students who were surprisingly inflexible in the way they thought, and very parochial in their intellectual interests. I guess I just haven’t (anecdotally) found the transference of math training to other domains as much as o…

i think that’s a characteristic of a lot of PhD’s though - they become so specialized they become inflexible. i’m more talking about applied math into industry types. in insurance, tech, etc, i always tend to find the mathy people are faster, come up with unique solutions, and are more self motivated.