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

quantamagazine.org

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

#51

Post by quus »

defrost wrote: post #50
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'll second guerrilla - you can absolutely benefit from mathematical thinking without pushing into territory higher than undergaduate studies. You can even benefit from the thinking taught in good high school coursework (or studying online). At an arithmetic, bookkeeping level you can better appreciate handling finances and the seductive pitfalls surrounding wagers (gambling, betting, risk taking).

My claim isn’t really that there’s no benefit or utility to math — that’s obviously false — but that maybe its benefits to regular people are more modest than the cheerleaders want to admit.

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

#53

Post by defrost »

quus wrote: post #51
defrost wrote: post #50

Earlier quoted context omitted.

I'll second guerrilla - you can absolutely benefit from mathematical thinking without pushing into territory higher than undergaduate studies. You can even benefit from the thinking taught in good high school coursework (or studying online). At an arithmetic, bookkeeping level you can better appreciate handling finances and the seductive pitfalls surrounding wagers (gambling, betting, risk taking).

My claim isn’t really that there’s no benefit or utility to math — that’s obviously false — but that maybe its benefits to regular people are more modest than the cheerleaders want to admit.

What are the costs (in your estimation at least) to "regular people" (regular by your metric) of not engaging in easy bake low level "mathematical thinking".

* How many have a lower return on { X } through not understanding compound interest, tax brackets, leveraging assets, etc.

* How many have steady net losses through "magical thinking" wrt gambling, betting, hot stock tips.

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

#54

Post by khafra »

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; especially for those of us who were last in school decades ago.

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

#55

Post by benreesman »

cchi_co wrote: post #32
benreesman wrote: post #2

I’m far from being any kind of serious mathematician, but I’ve learned more in the last couple years of taking that seriously as an ambition than in decades of relegating myself to inferiority on it. One of the highly generous mentors who dragged me kicking and screaming into the world of even making an attempt told me: “There are no bad math students. There are only bad math teachers who themselves had bad math teac…

How much of math aversion stems from a chain reaction of ineffective instruction

According to an excellent mentor: all of it minus epsilon.

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

#57

Post by graemep »

junto wrote: post #23
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 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…

> 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.

My first thought when the article got to the dialog between logic and intuition bit was that the same is true for school level physics.

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

#58

Post by ajuc »

shrubhub wrote: post #40
ponderings wrote: post #33

Earlier quoted context omitted.

I've had some success converting people by telling them others had convinced them they were stupid. They usually have one or two things they are actually good at, like a domain they flee to. I simply point out how everything else is exactly like [say] playing the guitar. Eventually you will be good enough to sing at the same time. Clearly you already are a genius. I cant even remember the most basic cords or lyrics b…

But also, some people are stupid, right?

The inborn part is how quickly you get results (good or bad). Stupidity is the results.

If we spent 50% of time thinking productively - inborn thinking speed would matter. But in my estimate even 5% is generous.

So it matters far more what kind of feedback you have to filter out the wrong results, and how much time you spend thinking - than how quickly you can do it.

Also practice helps with speed.

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

#59

Post by barrenko »

tracerbulletx wrote: post #9

A nice sentiment but clearly a large % of people never do learn even basic mathematical thinking and seem very confused by it. So is there some scientific study backing up the claim that all these people could easily learn it or are we just making it up because its a nice egalitarian thesis for a math popularization book?

We are not really taught (thought) to think, we are taught to memorize. Until one actually tries to think, you really can't tell if they're able to do it.

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

#60

Post by hehehheh »

chipdart wrote: post #42
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 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 would argue something different. The "skill" angle is just thinly veiled ladder-pulling. Sure, math is hard work, and there's a degree of prerequisites that need to be met to have things click, but to the mindset embodied by the…

I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed.
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