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

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

#171

Post by vundercind »

openrisk wrote: post #64

There is this element of abstract mathematical thinking that many young people get exposed to at some point in the educational system but just never "get it" and they disconnect. This is where it goes awry as the gap only widens later on and its a pity. Working with symbols, equations etc. feels like it should be more widely accessible. Its almost a game-like pursuit, it should not be alienating. It might be a failur…

Lots of people seem to get permanently lost right around when operations on fractions are introduced. Other places, too, but that seems like the earliest one where a lot of people get lost and never really find their way back.

Factoring was another that lost a lot of folks in my class. Lots of frustration around it seeming both totally pointless and the process involving lots of guessing, several classmates were like "well, fuck math forever I guess" at that point, like if they'd been asked to dig a ditch with a spoon and then fill it back in.

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

#172

Post by vundercind »

sethammons wrote: post #111
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…

One size doesn't fit all is what I believe Common Core math is attempting. The part that it misses is that a student should probably be fine demonstrating one modality instead of having to demonstrate them all

> The part that it misses is that a student should probably be fine demonstrating one modality instead of having to demonstrate them all

I cannot overstate enough how consistently and extremely this has turned my kids off from math. 3-for-3 on absolutely hating this. Having to solve the same thing five different ways just pisses them off, and, like... yeah, of course it does. They want to finish the work and go play and it feels like you're just fucking with them and disrespecting their time by making them solve the same problem several times, even if that's not the intent.

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

#174

Post by vacuity »

bloqs wrote: post #154
tgv wrote: post #121

Earlier quoted context omitted.

I cannot agree. It's just "feel-good thinking." "Everybody can do everything." Well, that's simply not true. I'm fairly sure you (yes, you in particular) can't run the 100m in less than 10s, no matter how hard you trained. And the biological underpinning of our capabilities doesn't magically stop at the brain-blood barrier. We all do have different brains. I've taught math to psychology students, and they just don't…

This is mostly correct. Working memory plays a huge component in grokking more complicated mathematical components, and IQ itself is separated into performance and verbal IQ (which together constitute your IQ score) and its demonstrably robust. Some people find this easier than others and that is OK. I dont disagree with the premise that mathematical thinking can benefit anybody, but its absurd notion that everything…

I think most people can become fairly skilled in useful fields if educated properly, and the people who can't are a small group that can be cared for. I agree that even in a better education system, people aren't all going to be equally skilled in the same fields, just that most people can contribute something of value.

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

#175

Post by ai4eva »

DiscourseFan wrote: post #71
block_dagger wrote: post #34

Statistical (Bayesian) thinking is an extremely underrated way of thinking of almost everything.

Frankly, its overrated. Now you can adjust your priors.

lol yea.

bayesian thinking doesnt come to me naturally.. i have no intuition for it. seems forced. believe me - i have tried. but there are those who are swearing by it.

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

#176

Post by macintux »

trialAccount wrote: post #173

The author: Would love to participate but account creation seems to be broken on Hacker News https://x.com/davidbessis/status/1859561768915173466

If someone still on X could send them the hn@ycombinator.com support address, that'd be useful.

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

#177

Post by vundercind »

limit499karma wrote: post #4

> the provocative claim Leibniz made that claim centuries ago in his critical remarks on John Locke's Essay on Human Understanding . Leibniz specifically said that Locke's lack of mathematical knowledge led him to (per Leibniz) his philosophical errors regarding the nature of 'substance'. https://www.earlymoderntexts.com/assets/pdfs/leibniz1705book...

I haven't read his Human Understanding, but his Second Treatise is really weak in ways that can't really be blamed on lack of mathematical training (unless we're going with "all rigorous thinking is math") so there may be more to it in his case than just "he didn't study math enough".

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

#178

Post by crispyambulance »

penguin_booze wrote: post #139

To my mind, the premature formalization of the math is the principal contributor to gas lighting and alienation of people from maths. The reduction of concepts to symbols and manipulation thereof, is an afterthought. It's misguided for them to be introduced to people right at the outset. People need to speak in plain English [0]. To some mathematicians' assertion that English is not precise enough, I say, take a hike…

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 thus find new truths. It's a way of thinking and that can be very exciting.

Tragically, many students disengage before this can happen because of sheer boredom and the tedium of endless math drills. Once they develop a gap in their knowledge it becomes difficult to progress unless those gaps are addressed. For lots of students, it all ends with fractions. You'd be surprised how many adults don't really understand fractions. For others it ends with algebra, and for the college bound it ends with calculus.

Only math majors and a minority of engineering/science/CS folks get past the "standard sequence" of math courses in college and gain an appreciation for the really interesting stuff that comes AFTER all that.

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

#179

Post by vundercind »

DiscourseFan wrote: post #71
block_dagger wrote: post #34

Statistical (Bayesian) thinking is an extremely underrated way of thinking of almost everything.

Frankly, its overrated. Now you can adjust your priors.

I'm pretty down on it just by association. So many people who are super-into it seem to be doing a lot of that rigorously-wrong engineer-brain thing.

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

#180

Post by mbbbackus »

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, he inspired me to relearn a lot of fundamental math on MathAcademy.com which has been super fun and stressful. I feel like I have the tetris effect but with polynomials now.

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