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Why Do Americans Stink at Math?

nytimes.com

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Re: Why Do Americans Stink at Math?

#151

Post by dylanfw »

vixen99 wrote: post #121
DanBC wrote: post #103

Earlier quoted context omitted.

> 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.

> 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?

W&R proved 1+1=2 in their axiomatic system. It wasn't done to prove once and for all that 1+1 is in fact 2, but to show that their system produced mathematical truths. The truth of 1+1=2 was already assumed and understood since they were kids, and that's why it was necessary that their system also produce it.

Of course PM was obliterated by Godel shortly after.

Re: Why Do Americans Stink at Math?

#152

Post by qntty »

jimhefferon wrote: post #147

I teach math. I am impressed that when you read these comments, very few of them show evidence of having read the article. The article is about experience with actual students, with ones who have a real knack for the subject and would learn it despite what any teacher did, and with ones who waver. There proves to be a better way, which the article describes in various ways, including as "sense-making." One of the pro…

Do you have an opinion on math-circle inspired schools like Proof School[1]? To me it seems obvious that this is the direction that math education should go in for kids who are passionate about math.

[1] https://en.wikipedia.org/wiki/Proof_School

Re: Why Do Americans Stink at Math?

#153

Post by HarryHirsch »

Since no one has brought up "Nix the Tricks" yet, here's the link to the ebook: http://nixthetricks.com/

Foreigners are likely unaware that these are the algorithms routinely taught to US students in math class. There are no formal proofs, no emphasis on making sense - the only purpose is to have something memorizeable to have students pass the next test (and possibly the No-Child-Left-Behind test at the end of the year). There is no generalization, no focus on understanding. When you tell an American kid at university level "this is why concept XY makes sense" they don't understand why you might say this, they are only interested in the algorithm and the solution (and passing the next test, of course).

Small wonder that anyone exposed to that curriculum sucks at math and on top of that us turned off the subject. It's like Feynman in Brasil!

Re: Why Do Americans Stink at Math?

#154

Post by Fluid_Mechanics »

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…

Not so sure about that; the act of thinking about math is a form of "practice", so in my experience reading about it was sufficient for most concepts.

Re: Why Do Americans Stink at Math?

#155

Post by yanjuk »

I taught my two kids long division in about ten 40-minute sessions spread over 5 days. I sat with each child as we learnt the procedure. To begin with I held the pencil and asked questions, then the child took over the writing and I monitored to fix mistakes until finally the task could be performed/practiced solo.

In this one-on-one practice approach misconceptions are eliminated quickly at the start. It could not easily be replicated in a large group. Instead the approach in the article seems to be about groups of people identifying each other's misconceptions. Either way the effectiveness lies in avoiding bad habit formation.

If you look at YouTube each method of arithmetic has variants and you can pick the one that looks best. e.g. I chose a method of multiplication with consistent placing for the carries which reduced error considerably over what I was taught at school.

Re: Why Do Americans Stink at Math?

#156

Post by johan_larson »

vog wrote: post #109

In contrast to this, note that in International Mathematics Olympiads, pupils/students from the USA are quite good: http://www.imo-official.org/

Oh sure. The best education in the US is awesome, possibly the best anywhere. But the average is pretty sad, particularly compared to the rest of the first world.

Re: Why Do Americans Stink at Math?

#157

Post by libeclipse »

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 disagree with this. I remember when I was in primary school and I was confused about how to multiply decimals. At that level I didn't even know what it would mean to multiply a decimal: how can you have 5, 0.2 times? I asked the teacher and instead of explaining the concept properly, i.e. 0.5 is half etc., I was just told to multiply the other way around, by adding up 0.2, 5 times - and do drills with that.

It's this kind of teaching that makes good robots and terrible mathematicians. (Thankfully I'm neither the former not the latter.)

Re: Why Do Americans Stink at Math?

#159

Post by madengr »

Americans who need to be good at math, are good at math. If you don't use it, you lose it.

Hell, I'm an EE, so I'm probably one of those who would be considered "good at math" (at least by layman opinion), yet I may do at most a couple of integrals a year. I'm mostly just doing basic algebra on an RPN calculator. Though I did ace all that EM theory, random proceses, etc in grad school; do I use the math behind it? Rarely.

Re: Why Do Americans Stink at Math?

#160

Post by aswanson »

libeclipse wrote: post #157
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 disagree with this. I remember when I was in primary school and I was confused about how to multiply decimals. At that level I didn't even know what it would mean to multiply a decimal: how can you have 5, 0.2 times? I asked the teacher and instead of explaining the concept properly, i.e. 0.5 is half etc., I was just told to multiply the other way around, by adding up 0.2, 5 times - and do drills with that. It's th…

That was a good way to teach you commutativity, though.
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