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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

#321

Post by red75prime »

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 belief that some people have an innate skill that they are born with is deeply unhelpful.

In practice your views result in stinting access of non-existent (in your opinion) talented children to a faster education track. They don't exist therefore they don't need different treatment (finer points get lost when the idea disseminates). Quite a hot theme in American education two (or so) years ago.

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

#322

Post by tptacek »

samatman wrote: post #319
tptacek wrote: post #318

Earlier quoted context omitted.

When you write a comment here, you're talking not simply (or even primarily) to the person you're responding to, but also to the rest of the community. Have you considered what value there might be, or not be, in a comment like this? We are extraordinarily fortunate to be taken seriously enough as a community for the primary sources on stories like this to come talk to us directly. I'd ask, as a neighbor of yours in…

That's a fair ask, that post was not one of my better moments. As much as I dislike the rhetorical tactic wielded with "everyone who doesn't agree with me is simply confused", a one-sentence tell off does nothing to counter it, and just makes me look like a jerk. Which I was.

No problem! You'd be doing me a favor if you noted any time you see me in the same situation. Thanks for hearing me out!

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

#323

Post by kamaal »

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,…

>>It's like an imagination sport.

Honestly speaking I think this is a wrong way to teach people to think about Math. Math is just one of those things which feels hard because people struggle to hold long trials of manipulations in their head. Especially if they are manipulations to something very large, evolved slowly over hundreds of steps. People are not coming short, its just how the human mind works.

IMO, the right way to teach Math is to teach people that its just base axioms, manipulation rules. And after that its how you evolve the base axiom using rules. People need to be taught how to make one valid change at a time. Of course this means tons of paper work and patience. But that is what Math actually is. Its taking truth and rules, to make new ones.

Im teaching this to my kid, and she often goes like this is it?? its really just laborious paper work??

Im using this method and LLM help at times these days to learn Algorithms and Data Structures. When you start working things from base conditions and build from there. A lot of Algos that otherwise seem like the domain of novel inventions just seem to follow from the manual steps you just worked, and then translated into a program.

When you remove all the fluff, Patience and Paper work is all there is to Math.

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

#324

Post by defrost »

quus wrote: post #304
defrost wrote: post #53

Earlier quoted context omitted.

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.

> If the benefits really just amount to a few units of pre-algebra content, that would be disappointing.

They don't though - there are benefits all the way up.

Giving a few examples of benefits from low order mathematical thinking (understanding concepts of compounding, etc) does not equal a statement that these are the only benefits.

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

#325

Post by scubbo »

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…

> 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 see you're familiar with Ryan North.

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

#326

Post by diffeomorphism »

notepad0x90 wrote: post #300
diffeomorphism wrote: post #242

Earlier quoted context omitted.

> I don't think UBI is feasible, it is anathema to the human condition to be content with the bare minimum. Hm? That is exactly why UBI works, no? As the name indicates, the bare minimum is taken care so that you can work towards "the best life possible for our loved ones" without worrying about starving, sickness or homelessness. In contrast, if you were wrong and people would be content with the bare minimum, then…

I posted a more detailed sibling comment on this thread, but that's not why UBI works. it just shifts what the "bare minimum" is. Most Americans aren't fighting to get the best tent spot while out on the streets because they can't afford housing or begging for food on the streets. UBI isn't solving that, except as a welfare replacement for a small percentage of the population (and not a great replacement either). may…

> In short, it is silly to expect UBI to be a means by which people would work only if they want to work

I think it is misleading to call that scenario UBI and that the rest of your post also shares barely any resemblance to actual UBI plans, goals or side effects.

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

#327

Post by fluoridation »

margorczynski wrote: post #316
fluoridation wrote: post #264

Earlier quoted context omitted.

Where's the data backing up what you said? >You probably have a narrow definition of “most people” (probably some motivated high school or undergraduate student) I was thinking "3-4 out of 5 people you pick on the street at random". >too loose with what it means to “understand mathematical concepts abstractly”. Enough that they could recognize whether a mathematical concept is applied correctly (e.g. if I have a 2% m…

> Where's the data backing up what you said? What he is saying is the default hypothesis based on our understanding of biology and psychology. If you have variability in genes you'll get variability in characteristics that are connected to them - height, bone structure, mental capacity, etc. It is on you to prove that there is an arbitrary cut-off when it comes to this variance from which point it doesn't matter in r…

>If you have variability in genes you'll get variability in characteristics that are connected to them - height, bone structure, mental capacity, etc.

Then you're agreeing with me. The thing all of those have in common is that they follow normal distributions. The shortest recorded adult and the tallest recorded adult are quite far apart, yet the vast majority of adults are between 150-200 cm tall. That's precisely what I was saying; the outliers of mathematical skill are very very far apart, but most people are roughly equally capable.

>I think you're living in a bubble of at least average-smart people and don't get that probably millions if not billions of people around the globe (based on average IQs) won't really get that concept.

What I'm saying it that it even someone with below-average IQ could do it, if taught properly. Mathematics is less about being smart and more about being rigorous.

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

#328

Post by elbear »

Retric wrote: post #187
kdfjgbdfkjgb wrote: post #170

Earlier quoted context omitted.

> You're saying that the curiosity is "natural" hence one is either born with it or not. Why does curiosity being natural necessarily mean some people are born without it? It could also mean everyone (or every average human) is born with it, and overtime it gets pushed out of people.

Some infants explore vastly more than others. So the minimum might not be zero, but it isn’t some fixed quantity.

That's not because it doesn't exist, it's because it's restrained

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

#329

Post by elbear »

air7 wrote: post #92
elbear wrote: post #41

Earlier quoted context omitted.

Not even that. It depends on the learned ability to stop pushing yourself when your focus is wavering. That's how you develop aversion towards the topic. Let your natural curiosity draw you to particular topics (that's why you might have a winding road through the subject).

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.

I was talking about curiosity in general not curiosity about something in particular. We are naturally inquisitive to the point we have to be restrained by our parents. The problem is some of the restraints are based on the fears of our parents and not on actual dangers. Also, it's hard to develop an appreciation for something when it's forced fed to you.

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

#330

Post by heisenzombie »

kamaal wrote: post #323
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,…

>>It's like an imagination sport. Honestly speaking I think this is a wrong way to teach people to think about Math. Math is just one of those things which feels hard because people struggle to hold long trials of manipulations in their head. Especially if they are manipulations to something very large, evolved slowly over hundreds of steps. People are not coming short, its just how the human mind works. IMO, the rig…

The author (and Grothendieck, liberally quoted in the book) disagree with you.

I think the reason you disagree is that it sounds like you’re teaching your child to be good at math class (a perfectly valid and good thing to do). Being good at math class requires being good at rational/logical thinking and computation. It also has only glancing similarities to anything that the author would recognise as mathematics.

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