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

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231–240 of 419 posts

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

#231
post #121
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 cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't…

> Or let's try other topics, e.g. music. Conservatory students study quite hard, but some are better than others, and a select few really shine. "Everyone is capable of playing Rachmaninov"? I don't think so.

Bad example, it's much more likely to create a musical prodigy by providing early and appropriate guidance. Of course this is not easy as it assumes already ideal teaching methods and adequate motivation to the youngling, but even those with some learning difficulties have the potential to excel. The subtypes of intellect required to play complex music and absord advanced abstract math subjects are quite different, former requiring strong short-term memory (sightreading) the latter fluid intelligence -I think almost everyone is familiar with these terms by now and knows that one can score high/low on certain subtypes of an IQ test affecting the total score-.

BTW IDK if the Rachmaninoff choice was deliberate to imply that even the most capable who lack the hand size won't be able to perform his works well yeah, but there are like 1000s of others composers accessible that the audiences appreciate even more. Attempting to equate music with sports in such manner is heavily Americanized and therefore completely absurd. Tons of great pianists who didn't have the hand size to interpret his most majestic works and of others. Tons of others who could but never bothered. There have been winners of large competitions who barely played any of his works during all stages of audition or generally music requiring immense bodily advantage. Besides, it's almost 100% not a hand size issue when there are 5 year old kids playing La Campanella with remarkable fluidity.

And even in this case this isn't even the point. Most conservatory alumni today are 100x skilled than the pianists of previous generations... yet they all sound the exact same, their playing lacks character/variability, deepness, elegance to the point where the composers ideas end up distorted. And those can be very skilled but just have poor understanding of the art, which is what music is, not the fast trills/runs, clean arpeggios, very strict metronomic pulse.

> So no, unless you've placed the bar for "mathetical skill" pretty low, or can show me proper evidence, I'm not going to believe it. "Everyone is capable of..." reeks of bullshit.

Well the vast majority of people in the Soviet Union were very math literate, regardless of what they ended up working as (although indeed most became engineers) and in quite advanced subjects. This is obviously a product of the extensive focus of primary and secondary education on the sciences back then.

So the point isn't to make everyone have PhD level math background and I heavily dislike the dork undertones/culture that everyone should love doing abstract math on their freetime or have to have some mathematical temperament' . But let's not go the other way and claim that those not coming close to achieving the knowledge those in the top % of the fields possess, they are chumps.

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

#232
post #154

Earlier quoted context omitted.

This is mostly correct. Working memory plays a huge component in grokking more complicated mathematical components, and IQ itself is separated into performance and verbal IQ (which together constitute your IQ score) and its demonstrably robust. Some people find this easier than others and that is OK. I dont disagree with the premise that mathematical thinking can benefit anybody, but its absurd notion that everything…

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 calculus was she'd likely have been perplexed and probably have guessed it to be some kind of growth on one's foot.

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

#233
post #210

Earlier quoted context omitted.

Most NBA players are under 2 meters tall. The average height is 1.99 meters. https://www.lines.com/guides/average-height-nba-players/1519

Since we are being pedantic, your statement may be true but it is unsupported by the data you presented. To make it simple, let's talk about the imaginary basketball league with four players, of unit less heights of 4, 4, 4, and 1. The average height is 3.25, yet 3/4 the players are taller than average. A paid promotion of International Median is not Average Association.

Most people have an above-average number of legs.

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

#234
post #69

I want to say yes, but I have two counters. One is that math nerds at school insisted on intimidating for the win and I just hated it. The second is notation. I had a snob teacher who insisted on using Newton not Leibniz and at school in the 1970s this is just fucked. One term of weirdness contradicting what everyone else in the field did. Likewise failure to explain notation, it's hazing behaviour. So yes, everyone…

> One is that math nerds at school insisted on intimidating for the win and I just hated it.

For me the worst part was the teachers that encouraged that behavior and did the same.

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

#235
post #23
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 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 strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. The author of the book has picked out mathematics because that was what he was interested in. The r…

"What we should be teaching children is HOW to learn."

Absolutely correct. And that begins with getting their interest, thus their attention; and that's a whole subject in and of itself.

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

#236

Earlier quoted context omitted.

Wouldn't it then follow that all students of the same teachers end up with the same skill level in math? Not sure that's the case.

Doesn't follow. Bell curve in, shifted bell curve out. Ideally this also tweaks the variance a bit. In other words: Some students flourish despite their teachers, some flourish because of them.

And how would you call the students in the left tail of the Bell curve if not bad students?

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

#237
post #23
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 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 strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus. The author of the book has picked out mathematics because that was what he was interested in. The r…

I don’t know if I agree. Grad school was profoundly humbling to me because it really showed me that there are a LOT of people out there that are just much much better than me at math. There are different levels of innate talent.

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

#238

> the provocative claim Leibniz made that claim centuries ago in his critical remarks on John Locke's Essay on Human Understanding . Leibniz specifically said that Locke's lack of mathematical knowledge led him to (per Leibniz) his philosophical errors regarding the nature of 'substance'. https://www.earlymoderntexts.com/assets/pdfs/leibniz1705book...

I haven't read his Human Understanding , but his Second Treatise is really weak in ways that can't really be blamed on lack of mathematical training (unless we're going with "all rigorous thinking is math") so there may be more to it in his case than just "he didn't study math enough".

Leibniz wasn't saying that "rigorous thinking" is only available to mathematically trained or that Locke's reasoning was not "rigorous".

His critique of Locke was that one can not have a correct model of human understanding (or world model) based on purely philosophical means, and that the lack of exposure to certain aspects of modern mathematics (that was emerging at that time) was the basis of Locke's misunderstandings.

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

#239
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

I think that's also a trap. Even professional athletes spend a little bit of their time doing simple drills: shooting free throws, fielding fly balls, hitting easy groundstrokes.

Sometimes your daily work keeps up the "easy" skills, but if you haven't used a skill in a while, it's not a bad idea to do some easy reps before you try to combine it with other skills in difficult ways.

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

#240

Earlier quoted context omitted.

Bobby Fisher won his first US Championships at 14 against people who had been playing chess longer than he had been alive. Suggesting they didn't want it more, or practice more than some kid is silly. "We can't on one hand believe in the plasticity and retrainability of the mind, while simultaneously believing that speed is something only a few are born with." Sure we can, the initial orientation of neurons differs b…

I think there's a probabalistic argument I'm making that's more in line with the article. Yes - there will be 10x-ers. And that group will have a 10x-er iside it, and so on given exponential dropoff of frequency of talent. Bobby Fisher is a few std dev above even the best, perhaps. Generally speaking, "You can do anything you want, but wanting (enough, and naturally) is the hardest part" might need a three standard d…

I agree with you. I don’t think I’m naturally gifted at much (I’m just average), but I was taught stubborn hard work pretty early on. Unfortunately it took me until my 20s to figure out I could be athletic if I applied that hard work. I could also be good at programming doing the same. I’ve met people who are truly gifted and it’s amazing, but I’m pretty decent at the things I worked hard at.
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