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Five-Year-Olds Can Learn Calculus (2014)

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

#71

Post by roel_v »

sp332 wrote: post #64
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…

The map is not the territory - charts are just one way to represent an independent and a dependent variable.

True; but do you have anything in mind that is less abstract than a graph and still expresses the continuous (or not, depending on what you're looking at...) nature of a relationship between two variables? Because I don't know of any way that is easier and more intuitive to understand than that. But maybe I'm just projecting based on my own preferences.

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

#72

Post by Quarrelsome »

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 ... abstractions like the relationship between a value on an x and a y axis.

I don't think that's true. Its wholly dependent on what they've been focusing on thus far. To use the dismissive "they simply" is a misrepresentation of the plethora of candidates. Did you mean "most"? Also its not a question of brain matter but the current development of that matter towards these sorts of ideas.

Its also a completely different subject to emotion control which you brought up somewhere else. This is about understanding, not control.

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

#73

Post by [deleted] »

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.

[deleted]

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

#74

Post by Ntrails »

eecc wrote: post #65
Ntrails wrote: post #58

Earlier quoted context omitted.

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)…

No, you're straying away from the original point which was: there's no need to make rote memorization of arithmetic tricks and multiplication tables a hard prerequisite to everything else about math. Nobody claimed that arithmetic is absolutely useless

It is never hard blocked on arithmetic though (in the UK at least). A bunch of simple numerical solving will be harder without being able to do multiplication in your head - but certainly someone could get through without.

I'm honestly dubious of anyone who claims that the reason people hate maths is because of times tables.

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

#75

Post by roel_v »

Quarrelsome wrote: post #72
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 ... abstractions like the relationship between a value on an x and a y axis. I don't think that's true. Its wholly dependent on what they've been focusing on thus far. To use the dismissive "they simply" is a misrepresentation of the plethora of candidates. Did you mean "most"? Also its not a question of brain matter but the current development…

In order to bring our arguments to a common frame of reference, I think that I can reword my point as follows: to do the sort of abstract reasoning that is required for what is commonly (so not like the OP, who redefines calculus as 'abstract(ish) concepts that will be useful in real math later on') considered 'calculus', one needs a part of the brain that is not just 'grown' by training, but that actually needs to grow to a certain baseline before it can function at all - after which it can be further developed by training/practice.

So in other words, some brain functions just do not physically 'exist' (the matter needed for those functions) at very early ages. You can't take any 2 year old, or 3 or 5 year old, and practice until they get it. You have to wait until that part grows naturally. And growing (or maybe just 'activating') that part earlier doesn't say anything about overall intelligence, either.

And yes, it's different from emotion control, but not dissimilar - the mechanisms is the same.

All of this, of course, for the general population. I can't deny there are child prodigies who understand these things years before their peers; they exist, it's a simple observation. My point is: some things you cannot train in children. You have to wait for the brain to get there; and children not being there yet is not (necessarily) because of lack of training.

Hopefully this clears up my position, and contrasts it with yours. If it does in the way I think it does, it becomes a matter of the state of the art in neurology and neural development. My information comes from having read some popular literature (books, not the 'parenting' section of Marie Claire, but still...) on child development; not a very authoritative position, I'll freely admit. I never got the impression anywhere that this position is controversial or even just not universally accepted, but if it is, then our (apparent) disagreement can be reframed in these terms. (to preempt - at that point I don't have anything to add except the tried and proven 'trawl google scholar until I find something that I can bend into supporting my position, to make it appear that I have Science(TM) on my side although I don't really know anything about it'; but maybe I'm getting ahead of myself here :) )

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

#77

Post by ctlby »

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.

> There's plenty of research on the "entity theory" bias, mostly applied to gender.

Junk science if there ever was any. The effect sizes for these treatments are tiny, if they even replicate it all. It seems like every day now there's a new rebuttal of stereotype threat, implicit association tests, priming, etc.

Just from today: http://www.tandfonline.com/doi/abs/10.1080/09515089.2017.135... http://internal.psychology.illinois.edu/~acimpian/reprints/j...

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

#78

Post by tmaly »

It would be entirely possible to teach advanced math topics to younger using just pictures.

One example great example is the pythagorean theorem which can be demonstrated with a series of triangles and squares.

I do not know of any current books that has done this to a degree a five year old could learn from, but there is a huge opportunity here.

The book How to Teach Your Baby Math touches on some of the fundamental differences between using visualization and symbology.

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

#79

Post by tradotto »

tmaly wrote: post #78

It would be entirely possible to teach advanced math topics to younger using just pictures. One example great example is the pythagorean theorem which can be demonstrated with a series of triangles and squares. I do not know of any current books that has done this to a degree a five year old could learn from, but there is a huge opportunity here. The book How to Teach Your Baby Math touches on some of the fundamental…

How about a video? https://www.youtube.com/watch?v=U_ZHsk0-eF0

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

#80

Post by roceasta »

occultist_throw wrote: post #67
iovrthoughtthis wrote: post #60

Earlier quoted context omitted.

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 eno…

And you succinctly put why I despise "School". I love learning new areas and new techniques. And when Im teaching myself, I can fail and I go back a step or 2. Not the end of the world. If I do similar in a class, then I set myself further back with a slowly growing chance of doing badly (D or F). And in College, then its another 1-4 credit hours to pay for the privilege. They not only fail me, but demand more money.…

I think this also explains why driving tests aren't as bad as school: they are pass/fail and one can re-take as many times as wanted.
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