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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

#301

Post by ericd »

card_zero wrote: post #131
air7 wrote: post #92

Earlier quoted context omitted.

parent comment was a bit tounge-in-cheek but I'll continue the sentiment: You're saying that the curiosity is "natural" hence one is either born with it or not. I think that there is no way around the fact that it will be hard and uncomfortable to mimic the progress of someone that has an innate inclination towards a subject (be it talent or focus or curiosity) artificially.

Hey, that doesn't have to be what "natural curiosity" means. Besides which it makes no sense to say people are born with complex interests. I mean, OK, your genes might incline you a certain way, but that's not the same thing. Being interested in a subject is massively helpful to learning it. But interest arises circumstantially, it's an emotion. The grim reality that it would be really useful to you to learn a certa…

I think there is some natural inclination towards abstract thinking versus more grounded in reality, just judging based on kids I know. Some of them really enjoy playing with ideas in their heads, some enjoy playing with things they can touch more. It seems likely that those different attractions would express themselves in how much they practice different things as time goes on.

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

#302

Post by tnias23 »

davidbessis wrote: post #189
tgv wrote: post #161

Earlier quoted context omitted.

> Not really. There's nothing inherently special about people who dedicated enough time to learn a subject. "You didn't work hard enough." People really blame you for that, not for lacking talent. > So far in human history there were less than 200 people who ran 100m in less than 10s. And many millions have tried. There may be 200 people who can run it under 10s, but there are thousands that can run it under 11s, and…

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-…

[dead]

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

#303

Post by mncharity »

I've lately been struck by people having a life difficulty due to "missing a clue" absent some experience. The person poorly conceptualizing and executing physical therapy, for lack of athletic experiences. The person poorly handling cognitive decline, for lack of a grasp of work processes. The person variously failing from having physical discomfort as an abort criteria, for lack of experiences normalizing its deferral.

"I have this clue at hand" can have broad impacts. Software development's emphasis on clarity, naming, and communication protocols, helped me a lot with infant conversation. Math done well, can be a rich source of clues, especially around thinking clearly.

There's an idea that education should provide more life skills (like personal finance). And another, that education should have a punch list (as in construction), of "everyone at least leaves with these". Now AIish personalized instruction will perhaps permit delivering a massive implicit curriculum, far larger than we usually think of as a reasonable set of learning objectives. Just as a story can teach far more than the obstensible moral/punchline of the story, so too might each description, example, question and problem, dynamically tuned in concert. So perhaps it's time to start exploring how to use that? In the past, we worked by indirection - "do literary criticism, and probabilisticly obtain various skills". And here, from math. Perhaps there's a near-term opportunity to be more explicit, and thorough, about the cluefulnesses we'd like to provide?

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

#304

Post by quus »

defrost wrote: post #53
quus wrote: post #51

Earlier quoted context omitted.

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.

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.

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

#305

Post by edanm »

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 actually heard about this book very recently, and it's coming up soon on my (never-ending) reading list.

Happy to hear you're enjoying it, makes me even more confident that I should read it :)

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

#306

Post by llm_trw »

Tainnor wrote: post #191
llm_trw wrote: post #148

Earlier quoted context omitted.

There's a difference between being able to memorize what a square root is and being able to do math - which to mathematicians means being able to organize a proof. I've found that the people who most believe in math being a genetic ability are the ones who do not work in the symbolic world of modern math, but in the semantic world of whatever the field the math describes is. The two are rather different.

Square roots are not some "mathematical trivia", they're amongst the most fundamental operations in mathematics.

In arithmetic. There is a lot more to math than arithmetic.

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

#307

Post by cutemonster »

Jensson wrote: post #96
thefaux wrote: post #17

Earlier quoted context omitted.

Sadly, when I was a postdoc, an eminent mathematician I was working under once shared a story that he found amusing that one of his colleagues was once asked a question in the form: "This might be a stupid question, but..." and the response was "There are no stupid questions, only stupid people." Run into too many people like that, who I daresay are common in the field, and it's easy to see how people become dispirit…

Isn't that a positive statement, that you can ask questions without worry since they aren't stupid?

Maybe, I guess it's easily misinterpreted though O.O

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

#308

Post by lifter3101 »

itissid wrote: post #196

"It's the economy stupid" is what I would say. Mental capacity is capacity. Most of us don't study math not because we don't want to but because we can't. I bet if you asked in a survey of people that if you were given a UBI that covered all your expenses and needs what would you do? It would be perfection of the self or art. Both of these are what is practicing and learning math.

Didn’t we have that experiment during Covid? A bunch of people got paid to stay at home, sometimes for 2 years. How many Grammy nominations since then have gotten to musicians that came out of that? A new face at the Oscars? MOMA exhibiting an artist that was a barista before the pandemic?

At least anecdotally, many people around me now have more children, on the other hand.

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

#309

Post by gmays »

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,…

+1 for Math Academy. I’ve been using it daily for over a year now (started October 2023). I summarized my experiences after 100 days here in case it helps anyone: https://gmays.com/math

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

#310

Post by sonabinu »

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,…

Thanks for sharing this. I was debating buying the book.
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