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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

#331

Post by LoganDark »

tartoran wrote: post #201
LoganDark wrote: post #77

I have an autistic friend with dyscalculia. They see numeric digits as individual characters (as in a story), each with their own personalities. Each digit has its own color, its own feelings. But they are not quantities; they don't make up quantities. Numbers are very nearly opaque to them. I wonder how this theory would apply to them. Do they still perform mathematical thinking? They're still capable of nearly all…

I don't have dyscalculia but behind the numbers I have my own intuitive system(s) that I jump to sometimes when doing arithmetic. I think we all do since the early days arithmetic in school or what not, perhaps the dyscalculia folk missed making some connection at some point. I feel that arithmetic with numbers without that intuitive system is rote memory..

Indeed, I do also have an intuitive system for this; that's what I mean by "make up a quantity". When something makes up a quantity for me, then I can perform math on it. I have to wonder if my friend with dyscalculia doesn't have a "quantity" system like I do. They can't really perform multiplication or division but can technically perform basic addition and subtraction, though it takes them a while. I think it may be the rote memory you mention doing that for them.

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

#332

Post by kamaal »

heisenzombie wrote: post #330
kamaal wrote: post #323

Earlier quoted context omitted.

>>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 .

>>It also has only glancing similarities to anything that the author would recognise as mathematics.

Nah, these are the same things. Trying to make Math look like is for people who are 'geniuses' i.e people with massive capabilities of holding large thought trials and changelogs in their head is how you arrive at making people look stupid doing math and eventually make them hate the subject.

Math is paper work. Approach it that way and all of a sudden doing a 100 page proof is within everyones reach. If you ask people to hold a 100 page proof in their head, and more importantly make changes to that in random places and fix the entire changelog trial, probably 2 - 3 people on earth will be able to do it, and you will just convince everyone else its not for them.

I have a hunch that big mathematical breakthroughs in history have happened around and after renaissance era due to paper getting cheap and ubiquitous. There is only that much you can do in your brain alone.

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

#333

Post by red75prime »

crispyambulance wrote: post #178
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 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?

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

#334

Post by notepad0x90 »

diffeomorphism wrote: post #326
notepad0x90 wrote: post #300

Earlier quoted context omitted.

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.

if that is the case, then I must apologize for my ignorance.

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

#335

Post by Retric »

elbear wrote: post #328
Retric wrote: post #187

Earlier quoted context omitted.

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

How?

People do studies on weeks old babies, it seems unlikely curiosity has been restrained at that point.

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