←back to thread

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

(www.quantamagazine.org)
507 points sonabinu | 3 comments | 21 Nov 24 01:45 UTC | HN request time: 0.973s | source
Show context
gsabo ◴[21 Nov 24 05:19 UTC] No.42201370[source]▶
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 easy, then it means you already know this material, and you're wasting your time.

replies(17): >>42201667 #>>42201721 #>>42201729 #>>42201821 #>>42201915 #>>42202008 #>>42202194 #>>42202777 #>>42202780 #>>42202880 #>>42203292 #>>42203429 #>>42203649 #>>42204501 #>>42204671 #>>42206252 #>>42208029 #
junto ◴[21 Nov 24 06:25 UTC] No.42201667[source]▶
> 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 reality is that this rule applies to everything.

The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s.

I think we do our children a disservice by convincing them that some of their peers are just “born with it”, because it discourages them from continuing to try.

What we should be teaching children is HOW to learn. At the moment it’s a by-product of learning about some topic. If we look at the old adage “feed a man a fish”, the same is true of learning.

“Teach someone mathematics and they will learn mathematics. Teach someone to learn and they will learn anything”.

replies(11): >>42201771 #>>42201890 #>>42202066 #>>42202222 #>>42202483 #>>42202522 #>>42202629 #>>42203513 #>>42203813 #>>42206203 #>>42206220 #
diffeomorphism ◴[21 Nov 24 07:52 UTC] No.42202066[source]▶
Caveat here is that "talent" and "dedication" is linked to speed at least in the beginning. For instance, any student can learn calculus given enough time and advice even starting from scratch. However, the syllabus wants all this to happen in one semester.

This gives you vicious and virtuous cycles: Students' learning speed increases with time and past success. So "talented" students learn quickly and have extra time to further explore and improve, leading to further success. Students who struggle with the time constraint are forced to take shortcuts like memorizing "magic formulas" without having time to really understand. Trying to close that gap is very hard work.

replies(3): >>42202253 #>>42203770 #>>42205330 #
jvanderbot ◴[21 Nov 24 12:42 UTC] No.42203770[source]▶
Indeed, speed is often read as "smarts" whereas I would maintain it's much more often "preparation". 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. On the nature/nurture scale, I think it's 20/80 or so - but prodigies and geniuses have an interest that keeps them thinking and learning 10x or 100x more than other kids, and a little bump that lets them get started easier and therefore much earlier.

This sets them up for fantastic success very quickly. [1] shows a great example of this.

I'm fond of saying "You can do anything you want, but wanting is the hard part", because to truly be a grandmaster, genius-level mathematician, olympic athlete, etc, requires a dedication and amount of preparation that almost nobody can manage. Starting late, with emotional baggage, kids, and having to spend 5 years relearning how to learn? Forget it.

1. https://danielkarim.com/how-to-become-a-genius-the-polgar-ex...

replies(2): >>42205379 #>>42205802 #
1. NoMoreNicksLeft ◴[21 Nov 24 15:37 UTC] No.42205379[source]▶
> I'm fond of saying "You can do anything you want, but wanting is the hard part", because to truly be a grandmaster, genius-level mathematician, olympic athlete, etc, requires a dedication and

I was having a problem agreeing with this subthread, and I have you to thank for putting it into words that I can finally formulate my disagreement against.

Have you never met one of those people for whom they did not need to "want"? They could literally phone it in and still do better than anyone else, no matter how dedicated they were. Even should practice/study be necessary for them, they benefited from it to some absurd proportion that I couldn't even guess to quantify. I've known more than one of these people.

I think most believe they don't exist for two reasons. The first is the ridiculous number of television shows and movies that depict motivation as being the key to success. We're just inundated with the (unsupported by evidence) that this is the means to extraordinary genius. Second, I would say that this is the most comforting theory. "Why yes, I could have been a gifted whatever or a talented something-or-other if I had put the time in, but I chose this other thing instead."

Maybe some would say we all need to believe this, that a society that doesn't believe in it is harsher or more unkind.

replies(2): >>42205530 #>>42206596 #
2. jvanderbot ◴[21 Nov 24 15:51 UTC] No.42205530[source]▶
I think I have met those folks. Maybe not. And you're welcome!

They're just quick. But the ones I've met, at least, are quick to make associations. When I really dig and ask them to explain themselves or a concept, they usually make analogies to things they know, but I don't. Then I have to go learn that thing. Then they try the analogy again, but I haven't fully learned it from years of making analogies about it.

Years of grad school experience was painful like this, until I got to a point 10 years after grad school, after a PhD, and well into research, that I "just got" things (in my subfield) as well. It's these experiences that made me feel that it's 80% preparation and perspiration (both of which are dominated by time), and 20% "other" mythology. Don't get me wrong, that 20% is what makes a 2 year old read earlier than others, and getting started reading at 2 (and continuing it!) for 4 years before starting school will make you light years ahead of your peers. The same goes for chess, math, etc etc. There is something legendary about Oppenheimer learning enough dutch in 6 weeks to deliver a lecture. Or perhaps learning to translate his lecture and memorizing it. Who knows.

Do we really believe there's a magical "genius" such that they can do anything? No, so what are the limits to their genius? The limits are defined by what they are a genius at. This is a tautological definition.

I'm not saying "Anyone at any time can become a genius at anything". I'm saying "If you take a kid, start early, and cultivate them just right so that you have time to realize compounding effects, - you can let them grow into basically anything" (probablistically speaking - there are learning disabilities and physical issues etc).

3. StefanBatory ◴[21 Nov 24 17:32 UTC] No.42206596[source]▶
> I think most believe they don't exist for two reasons.

I add third (okay, 2b) - because the pain of coming up with the fact other people are better than you at a deep, fundamental level is too overwhelming.