Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Five-Year-Olds Can Learn Calculus (2014)

theatlantic.com

Post reply on HN
Print view View original

51–60 of 128 posts

Re: Five-Year-Olds Can Learn Calculus (2014)

#51

Post by throwawayjava »

roel_v wrote: post #31

Anyone commenting on this (whether saying 'yes' or 'no'), please first read the article. What it considers 'calculus', none of us here would consider calculus. Because very few 5 year olds are capable of understanding even something as basic as a line plot (or '2d graph' or however you want to call it). They simple do not have the neural matter to comprehend fairly advanced (from an evolutionary point of view) abstra…

TBF "what calculus is" -- i.e., the level of rigor at which topics are taught -- varies a lot even among college courses called "calculus"...

In particular, IMO the distance between AP calculus and honors calculus at an ivy is larger than the difference between this material and AP calculus.

Re: Five-Year-Olds Can Learn Calculus (2014)

#52

Post by porsager »

roel_v wrote: post #31

Anyone commenting on this (whether saying 'yes' or 'no'), please first read the article. What it considers 'calculus', none of us here would consider calculus. Because very few 5 year olds are capable of understanding even something as basic as a line plot (or '2d graph' or however you want to call it). They simple do not have the neural matter to comprehend fairly advanced (from an evolutionary point of view) abstra…

> They simple do not have the neural matter to comprehend fairly advanced (from an evolutionary point of view)

Do you have some links to research on this? Sounds interesting.

Re: Five-Year-Olds Can Learn Calculus (2014)

#53

Post by jacobolus »

chii wrote: post #26
roceasta wrote: post #21

Earlier quoted context omitted.

The fact that school math is thought to be 'scary' and 'hard' is not the issue. Plenty of video games are known to be scary and hard. For instance, they contain monsters and are difficult to complete. They even have objective grades (scores). What makes the difference is that video games aren't compulsory. So they represent true play . Which is what makes them educational, unlike a school curriculum, however much it…

There are some aspects of doing math that isn't fun, because it is grinding. Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that. Just like in sports, where you must also do a lot of basic practise to get good. Making the practise like a game can be done to done degree, but ultimately, a kid is going to see through that after a while, since it ge…

> Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that.

The way around is to just not do that.

Students get huge amounts of practice with basic multiplication if they are assigned more interesting problems/projects that use multiplication as one step, and will inevitably memorize all of the same basic facts, assuming they actually do the work.

Memorizing multiplication facts for their own sake is a soul-sucking waste of time that turns kids off from math for good.

Similarly, the way to get good at spelling is by reading engrossing books for hours every day and writing about subjects of personal interest. Studying lists of spelling words in school is beyond pointless.

These are not skills like sports or playing musical instruments, where there is a particular physical technique involving fine muscle coordination, where practicing incorrectly will establish wrong movements. Instead we’re talking about simple verbal/linguistic recall of previously seen information.

Re: Five-Year-Olds Can Learn Calculus (2014)

#54

Post by pamqzl »

userbinator wrote: post #48
monsieurbanana wrote: post #47

Earlier quoted context omitted.

Completely baseless comment. You can both learn calculus and play with toys. And if calculus is presented as a fun group activity, like suggested in the article, I don't see why it would hinder the kids growth. It's the other way, really.

There's also nothing stopping toys from being calculus-related either, although at the moment I can't think of any examples of such.

Imagine a toy truck that, as you drive it back and forth, plots the first and second derivatives of its position with respect to time on a little screen on the side.

Hmm, that's not the worst idea...

Re: Five-Year-Olds Can Learn Calculus (2014)

#55

Post by pbhjpbhj »

erispoe wrote: post #33
pishpash wrote: post #30

Earlier quoted context omitted.

They bypass conditioning because they are smarter and are good at it. Who do you think are the people who espouse anti-intellectual drivel like "math is scary" or "math is uncool"? Hint: not the smart people.

There's plenty of research on the "entity theory" bias, mostly applied to gender. I.e. if you tell girls that they're bad at math, on average, they will act as if they are. Unfortunately, framing math as hard or scary only serves to reinforce stereotypes and bar people who do not have the keys to defuse that framing from advancing. It's not the rich male kids who are told math is hard and scary.

Does the "if you tell girls they're bad at maths ..." work differently with boys?

In UK girls get the better results on average. In part I think this might be because they're taught as they are generally quieter and less desirous of rough-and-tumble (in primary school, by the predominantly female teachers, say) that girls are more studious. Generalising further: boys are thus modelled as either boring swots or good for manual labour (they don't sit still, which for some reason seems to make many female teachers think means they're not intelligent).

[I'm pressing the point probably a bit much I know].

Re: Five-Year-Olds Can Learn Calculus (2014)

#56

Post by zimpenfish »

userbinator wrote: post #49
gremlinsinc wrote: post #3

I'm not even sure.. arithmetic really needs learned as much anymore... as a dev I rarely use my times table... if I need to calculate something I'll pull up a console and go into a repl and just ask php or ruby to calculate it for me... I know HOW the calculation works and why, but I don't need to know and remember times tables. I like the idea of thinking outside the box on how to teach math and science, as I feel m…

if I need to calculate something I'll pull up a console and go into a repl and just ask php or ruby to calculate it for me I'm guessing you don't spend 100% of your time in front of a computer, and even if you do, in the time it takes you to do that, someone who can actually do mental arithmetic will have approximately calculated that problem and several more, because they can stay in the "flow" of thinking about the…

Being able to perform mental arithmetic even approximately is a very helpful skill - buy 6 items at £12.80 and get charged £110? Easily catchable with a quick "6x10+25%" mental approximation.

(I'm fairly sure there's a famous book about this kind of thing but for some reason my brain is stuck on "How To Solve It" by Polya which I don't think is correct.)

Re: Five-Year-Olds Can Learn Calculus (2014)

#57

Post by tttt5 »

zaptheimpaler wrote: post #41
chii wrote: post #26

Earlier quoted context omitted.

There are some aspects of doing math that isn't fun, because it is grinding. Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that. Just like in sports, where you must also do a lot of basic practise to get good. Making the practise like a game can be done to done degree, but ultimately, a kid is going to see through that after a while, since it ge…

Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization? Its kind of dumb how arithmetic is seen as a precursor to math when its really not. You could do an ENTIRE college-level course in linear algebra or calculus or graph…

Being able to recognize that 11 * 15 = 10*15 + 15 may be related to success in higher level math courses like linear algebra and calculus.

Re: Five-Year-Olds Can Learn Calculus (2014)

#58

Post by Ntrails »

zaptheimpaler wrote: post #41
chii wrote: post #26

Earlier quoted context omitted.

There are some aspects of doing math that isn't fun, because it is grinding. Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that. Just like in sports, where you must also do a lot of basic practise to get good. Making the practise like a game can be done to done degree, but ultimately, a kid is going to see through that after a while, since it ge…

Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization? Its kind of dumb how arithmetic is seen as a precursor to math when its really not. You could do an ENTIRE college-level course in linear algebra or calculus or graph…

Of course understanding fourier transforms isn't reliant on my ability to do 6x7 - but arithmetic as a lifeskill is actually valuable. It's like saying that grammar and spelling aren't important because spellcheck will sort it out.

Splitting out arithmetic from "Maths" doesn't seem terribly sensible to me. Times tables aren't really problematic, and they do provide opportunities to teach valuable concepts (5x6 = 6x5).

Re: Five-Year-Olds Can Learn Calculus (2014)

#59

Post by jamesrcole »

jonnybgood wrote: post #2

I have no doubt they can. There's so much negative cultural conditioning towards mathematics by eliciting negative emotions that it's ridiculous (i.e. math is scary, math is hard, math is for smart people, etc.). I believe kids who excel at math is not due to them being smarter but due to the bypassing of the cultural conditioning. The bypassing can be due to the parents, teachers, some mentor, or their particular fa…

> cultural conditioning

I suspect that mathematics being poorly taught is also a major contributor.

Re: Five-Year-Olds Can Learn Calculus (2014)

#60

Post by iovrthoughtthis »

roceasta wrote: post #21
jonnybgood wrote: post #2

I have no doubt they can. There's so much negative cultural conditioning towards mathematics by eliciting negative emotions that it's ridiculous (i.e. math is scary, math is hard, math is for smart people, etc.). I believe kids who excel at math is not due to them being smarter but due to the bypassing of the cultural conditioning. The bypassing can be due to the parents, teachers, some mentor, or their particular fa…

The fact that school math is thought to be 'scary' and 'hard' is not the issue. Plenty of video games are known to be scary and hard. For instance, they contain monsters and are difficult to complete. They even have objective grades (scores). What makes the difference is that video games aren't compulsory. So they represent true play . Which is what makes them educational, unlike a school curriculum, however much it…

Hard and scary carry differently meanings in those contexts though, surely?

Video games are safe e.g you can always try again, you can do incrementally well.

Video games are scary in an exhilarating way, you blood will pump and your pupils will dilate but at the end you can put it down, turn the lights on and watch funny cat videos to recover.

Math (at school) is hard because you get one shot. Finite lives. After enough retries society says "nope, you're done". It's hard because you can't test yourself when ever you want and your study is not directly related to your tests.

Math is scary like anxious scary. Like stay up at night dreading your exam or don't sleep for a weekend to finish your report scary. You can't watch cat videos and hope it goes away because it won't. You can't buy a new math or try it again in a few years.

You get one shot. You get little to no feed back.

That's hard and scary.

Post reply on HN