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

(www.quantamagazine.org)
260 points sonabinu | 4 comments | 21 Nov 24 01:45 UTC | HN request time: 0s | source
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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.

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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”.

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1. diffeomorphism ◴[21 Nov 24 07:52 UTC] No.42202066{3}[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.

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2. drbig ◴[21 Nov 24 08:29 UTC] No.42202253[source]▶
Thank you for the insight that academic (in a very broad sense) bulk-fixed-time approach does in fact produce both of the cycles, and the gap indeed only widens with time (speaking from personal experience, especially from my life as an undergrad student).

Reminds me of my personal peeve that "studying" should not be "being taught", studying is pursuit of understanding, "being taught" is what happens in primary school (and I'm aware I'm simplifying here).

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3. blackbear_ ◴[21 Nov 24 10:34 UTC] No.42202877[source]▶
I would say that you could generalize this even further outside of education. A few early successes in life can greatly accelerate one's trajectory, while early failures could set one many years back. And this happens independently of whether those events are due to skill or luck.
4. 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...