Why Do Americans Stink at Math? • Hacker News Board

Re: Why Do Americans Stink at Math?

#121

Post by vixen99 » Fri, Oct 28, 2016, 11:32 AM UTC

DanBC wrote: post #103

atemerev wrote: post #97

The key to math education is practice. Even drilling, maybe. Other fields deal with concepts more or less mapped to the real world. Physics is about real world, more or less (right until you get to quants, then the level of abstraction rises dramatically). Same goes for biology, and even computer science in general. There, you can rely on words, which usually convey meaning. In math, you can't rely on words. You'll n…

> The key to math education is practice. Even drilling, maybe. Do you have any research to support that? Because from what I've seen we currently think that drilling does nothing to help with understanding, and that one of the problems people have with maths is applying the wrong technique to a problem because they don't understand the problem. > You'll never understand even relatively simple things like complex anal…

Whitehead and Russell famously took several hundred pages in Principia Mathematica to prove the validity of the proposition 1+1=2. What is it that kids are understanding that W&R took much pain over? Understanding equates to learning the rules and when and where they can be applied. That's where drilling comes in.

Re: Why Do Americans Stink at Math?

#122

Post by krmboya » Fri, Oct 28, 2016, 11:35 AM UTC

atemerev wrote: post #97

The key to math education is practice. Even drilling, maybe. Other fields deal with concepts more or less mapped to the real world. Physics is about real world, more or less (right until you get to quants, then the level of abstraction rises dramatically). Same goes for biology, and even computer science in general. There, you can rely on words, which usually convey meaning. In math, you can't rely on words. You'll n…

Reminds me of this interview by Knuth [1], where he says, because of his initial insecurity that he was not good enough, he started by out doing twice as many math exercises as his classmates.

He at first put in a lot of effort, but eventually he was just coasting through ahead of his classmates. He attributes it to the drilling he put in initially.

[1] http://www.webofstories.com/play/donald.knuth/9

Re: Why Do Americans Stink at Math?

#123

Post by eli_gottlieb » Fri, Oct 28, 2016, 11:43 AM UTC

Ended wrote: post #99

ctrlalt_g wrote: post #41

Earlier quoted context omitted.

I once heard an anecdote that might describe some of what's happening. In the trenches of WWI, when it was time to fight, soldiers would have to climb up a ladder onto a battlefield. The problem was that German snipers could see the tops of the ladders. The Germans would keep their rifles fixed on where they knew the enemy would emerge and simply shoot them down once they saw helmets appear. The European Allied soldi…

OTOH, the terrible truth is that it was necessary to order thousands of soldiers to their almost-certain deaths in order to win the war, and without a disciplined army this would not be possible. This says something about the value of discipline (in war or maths!) even when it's not obviously in your personal interest.

World War I was a stupid war over stupid pride-issues between imperialist powers.

Re: Why Do Americans Stink at Math?

#124

Post by slfnflctd » Fri, Oct 28, 2016, 11:43 AM UTC

rdtsc wrote: post #26

> Without the right training, most teachers do not understand math well enough to teach it the way Lampert does. My high school math teacher majored in math and then got a certificate in teaching. She wasn't a teacher who was told to teach math among other classes. She knew all the advanced stuff (beyond what a high school curriculum required), she was excited about it, she could explain things in various ways, give…

> She knew all the advanced stuff [...] was excited about it, could explain things in various ways, give analogies

I envy you this experience. I still remember telling a math teacher in 8th or 9th grade that I wanted more information on why a formula worked, how it was originally derived, or any different way of looking at it to better understand it. She essentially said, "you don't need to worry about all that, just memorize it." It was intensely frustrating for me, and contributed to me losing interest in academic pursuits. I don't know how you can train teachers to be more open to this kind of thing, but it sure would help.

Re: Why Do Americans Stink at Math?

#125

Post by ArkyBeagle » Fri, Oct 28, 2016, 11:44 AM UTC

It's an anecdote, but...

Guy I went thru undergrad with went to a high school where the 10th grade algebra class requires naming the principle to be applied for each step in a problem, as if it were a proof.

This is painful. But he'd learned algebra properly. I hadn't. His math grades were much better than mine for a long time.

Re: Why Do Americans Stink at Math?

#126

Post by ArkyBeagle » Fri, Oct 28, 2016, 11:47 AM UTC

atemerev wrote: post #97

The key to math education is practice. Even drilling, maybe. Other fields deal with concepts more or less mapped to the real world. Physics is about real world, more or less (right until you get to quants, then the level of abstraction rises dramatically). Same goes for biology, and even computer science in general. There, you can rely on words, which usually convey meaning. In math, you can't rely on words. You'll n…

I think they key is being able to jump between the narrative ( story ) domain and the formal symbols domain. At first, it is learning a language. Later, it is learning how to learn that language dynamically.

Re: Why Do Americans Stink at Math?

#127

Post by ArkyBeagle » Fri, Oct 28, 2016, 11:50 AM UTC

impendia wrote: post #120

ScottBurson wrote: post #24

Earlier quoted context omitted.

> It's a mixed bad in K-12 Your typo is very accurate :-) I would say that our problem in K-12 is a self-perpetuating one. The teachers were taught math badly and so never really learned it (and learned to hate it into the bargain). So then they teach it badly. I'm not sure there's any solution except for tuning the students in to Khan Academy and suchlike programs.

>The teachers were taught math badly I'm a college math professor, and I've talked to people who've taught the required "math for elementary ed majors" class. From everything I've heard, it's bleakly depressing. The students (i.e., the future teachers) show little aptitude, curiosity, or work ethic. They just want to be shown algorithms that will always lead them to the correct answer. I haven't taught such a course…

I went to a university that used to be a normal school. I am not sure the math ed. majors "showed little aptitude" ( they got better grades than I did ) nor curiosity, but they were quieter people.

Re: Why Do Americans Stink at Math?

#128

Post by ArkyBeagle » Fri, Oct 28, 2016, 11:53 AM UTC

sjg007 wrote: post #32

11thEarlOfMar wrote: post #3

It's an interesting question when you consider that in at least two university mathematics department rankings[1][2], the US holds 7 of the top 10 global spots. One could argue that for whatever reason, many of the professors, researchers and postdocs at those schools learned math in other countries, but, if these lists are to be believed, the US does have the richest mathematics knowledge in the world. So two questi…

Because they come here either as engineers or mathematicians in both academia and industry.

Bingo. I have worked with PhDs from overseas who lacked basic knowledge of things like hand tools.

Re: Why Do Americans Stink at Math?

#129

Post by ArkyBeagle » Fri, Oct 28, 2016, 11:55 AM UTC

JetSetWilly wrote: post #83

johncolanduoni wrote: post #51

Earlier quoted context omitted.

> European Americans actually do better than Europeans - on average. + Asian Americans to better than Asians - on average. + Latino Americans do better than Central/South American Latinos + African Americans do better than Africans. I've always heard this explained as a sort of "selection bias". Since immigration to the US (particularly for university education) is often seen as desirable, the people who manage to pu…

> I've always heard this explained as a sort of "selection bias". Since immigration to the US (particularly for university education) is often seen as desirable, the people who manage to pull it off tend to be above the mean. I think this is an explanation that could only be come up with by the descendants of those who have emigrated. Thinking here in Scotland, the people who emigrated were not necessarily the most a…

It's not clear that capability was that much of a factor. As the scion of Scots emigrants from the 19th Century, at least the 20h century version of my family was made up of bright capable people but hardly brilliant.

Re: Why Do Americans Stink at Math?

#130

Post by jacquesm » Fri, Oct 28, 2016, 12:04 PM UTC

icebraining wrote: post #119

jacquesm wrote: post #90

Earlier quoted context omitted.

> In the trenches of WWI, when it was time to fight, soldiers would have to climb up a ladder onto a battlefield. The problem was that German snipers could see the tops of the ladders. The Germans would keep their rifles fixed on where they knew the enemy would emerge and simply shoot them down once they saw helmets appear. > The European Allied soldiers were so disciplined that they just kept climbing up the ladders…

I don't know about any americans, but isn't the Souain affair pretty much a CO ordering his soldiers to keep going despite an ever mounting heap of corpses?

Sure, but that's not structural and there are definitely parallels in the American civil war.

war is an exercise in stupidity to begin with, it shouldn't be surprising there are pockets of even worse. But to claim that structurally Americans refused to get out of the trenches in a certain way in order not to get killed whereas docile Europeans were led like lambs to the slaughter is not something I've found in any history of World War I (or II for that matter).

Both wars had extremely heavy casualties on both sides, and in both wars there were quite a few instances of CO's treating their men like disposables. The Christmas Truce is a beautiful story about such behavior. Even so, both sides were desperately trying to win the war and the rule would have been to not take action hastening the demise of the men on one's own side.

I've yet to come across any substantiation of the anecdote related above, if it was structurally true you'd think it would be more than a mere anecdote.