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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

#341

Post by myworkinisgood »

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…

Math is a stepping stone to critical thinking skills. And while one can probably learn those skills in any way, math forces you to learn those skills by learning the method of writing proofs. No other field forces you to push your critical thinking skills to the limit that math does.

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

#342

Post by pokerface_86 »

gammalost wrote: post #85
magicalhippo wrote: post #36

Earlier quoted context omitted.

It sounds like trivial insight, but at least in my experience many adults and even teachers have this "it's hard so it's ok to not want to do it" attitude towards math. And I think that is very detrimental.

Well, isn't that a summary of most things? Most things worth learning are hard, but many things not worth learning are also hard. So we have to prioritize what hard things are worth learning. Math is low on the list for many people for (I think) understandable reasons.

math is low on the list then they bitch that they’re unemployable with a soft skill degree doing middle school level work. i get this is ironic as a pure math student is also fairly unemployable without extraneous skills, but they also tend to shine the brightest once they make it in.

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

#343

Post by pokerface_86 »

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’ve always found that mathematical thinkers do better, no matter the role. it’s difficult to express how, it’s kind of intangible, but it’s just a mental process that helps break down tasks and come up with unique solutions.

that being said, my marketing pitch for math was always, nothing else is even close to as intellectually stimulating as math.

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

#344

Post by o_nate »

magicalhippo wrote: post #25

I'm not a math teacher, but I do enjoy math, and I have helped several family members and friends with math courses. I've long thought that almost all have the capability to learn roughly high school level math, though it will take more effort for some than for others. And a key factor to keep up a sustained effort is motivation. A lot of people who end up hating math or think they're terrible at it just haven't had…

I also have long felt that anyone who has the ability to read and write at a high-school level in their primary language also has the mental capacity to learn to do math at a high school level. As a pedagogical challenge, I think the main stumbling block for most people with math is not the complexity of it but rather the dryness of how its taught. The rules of language are at least as complex, but many more people learn language at a high-school level than math. There are lots of reasons for that, most obviously language is used more in people's every day lives.

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

#345

Post by crazygringo »

brodo wrote: post #211
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?

The same goes for language skills, by the way. In the US, 21% of adults are illiterate, and 54% of adults have literacy below sixth-grade level.[1] This is higher than in other developed countries. For example, in Germany, 10% are illiterate, and 32% have literacy below fifth-grade level.[2] General intelligence also seems to have been trending downward since the 1970s (the reverse Flynn Effect)[3]. It has been measu…

The idea that 21% of US adults are "illiterate" doesn't mean they can't read, by the way:

> English literacy test results from 2014 suggest that 21% of U.S. adults ages 16 to 65 score at or below PIAAC literacy level 1, meaning they have difficulty "[completing] tasks that require comparing and contrasting information, paraphrasing, or making low-level inferences." Included in that 21% is the 4.2% of respondents who were unable to be assessed due to language barriers, cognitive disability, or physical disability.

https://en.wikipedia.org/wiki/Literacy_in_the_United_States

A lot of people aren't aware that the academic definition of "literacy" was changed around 1950 to no longer refer to "alphabetical literacy", which is still what most people think literacy means (in lay usage).

https://en.wikipedia.org/wiki/Literacy

And this particular survey ignored people who didn't speak English but were entirely literate in their native language. Which obviously has nothing to do with the educational system or people's intelligence.

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

#346

Post by wholinator2 »

hilbert42 wrote: post #232
sourcepluck wrote: post #193

Earlier quoted context omitted.

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 calcul…

I see it a lot on the internet, mostly I'm the young people places. People talk shit on math all the time, just like they do in person. Just slights and jabs that they've never needed the pythagorean theorem or to do an integral, and thus it was all wasted time and effort. You might just not hang around young people much, or at least their online congregations (i don't blame you). The idea that math education is dumb and useless is very much alive in the young adult to preteen tiktokified spaces online

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

#347

Post by metalman »

To use an absolutist statement about human well bieng tied to the authors pet ideals,is a classic example of magical thinking, and a lack of understanding in general,tied to a character assination of the many many excellent non numerative humans living and thriving everywhere. Not nice at all.

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

#348

Post by wholinator2 »

tgv wrote: post #223
llm_trw wrote: post #164

Earlier quoted context omitted.

You'd also be hard pressed to find one who doesn't know how to flush a toilet. Neither trivia has anything to do with being good at mathematics as done by mathematicians.

Are you an LLM? You brought up the point of mathematicians not knowing what a square root is yourself. Anyway, the square root is is so many levels below maths as done by mathematicians, it's laughable.

It certainly is suspicious that their name starts, "llm"

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

#349

Post by crispyambulance »

red75prime wrote: post #333
crispyambulance wrote: post #178

Earlier quoted context omitted.

I feel the opposite. Before high school, math is just a grind of memorization and unmotivated manipulation of numbers. Many students (ok, me, but I expect the same was true of others), get turned on to math for the first time when they encounter proofs in high school geometry and also actual applications in high school physics. It's a revelation to students that math can be a way to go from one truth to another and t…

> Tragically, many students disengage before this can happen because of sheer boredom and the tedium of endless math drills It's tragic and all, but were there attempts to teach non-preselected children/adolescents interesting stuff first? What are the results?

I don't know.

There is a certain amount of drudgery that unavoidable in learning mathematics, IMHO. Moreover, looking at the math textbooks of my niece and the students that I've tutored over the years, there's no effort spared in trying to make math "fun". If anything there's perhaps too much distraction caused by attempting to make a connection with the students and a failure to clearly and logically explain the math.

I don't have the answers, but believe that it's incredibly helpful to track students, intervene when they show a lack of understanding and not let them slip through the cracks. I do agree with the OP that everyone is capable of math but it's a long journey and it takes a lot of practice.

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

#350

Post by hyperthesis »

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-…

This beats TFA. Interesting relation between cumulativeness and distribution ("Yule process"). But how does this explain variation is how quickly children pick up maths - would you argue it's due to prior exposure e.g. parental tutoring?

Any comments on the "10x programmer"?

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