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Why Do Americans Stink at Math?

nytimes.com

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Re: Why Do Americans Stink at Math?

#61

Post by jomamaxx »

johncolanduoni wrote: post #51
jomamaxx wrote: post #39

Earlier quoted context omitted.

"Why doesn't the preeminence of the US math knowledge appear to seep into the primary and secondary school education?" Because preeminence of top tier institutions (which are kind of global centres anyhow) - has absolutely nothing to do with teaching math to the commons. Here's a hint: +++ Americans don't suck at Math +++ There's a very un-PC but very large elephant in the room that people won't discuss. + European A…

> 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…

That could very well be true, and I'm not stating it as proof of anything, other than to claim that Europeans score 'ballpark the same' on either side of the Atlantic.

I suggest your theory is probably very true for Asian Americans - the one's who came here are 'la creme do la creme'.

But not for Europeans. Europeans that came here were the poorest, the least educated, criminals, fringe religious types etc.. Europe was 100x more civilized than America during early history - why would anyone with any social status leave London in 1800 - to go and live a million miles away, a very, very hard, back-breaking life?

Well - those tenant farmers who could get cheap land and get out from under the thumb of their landlords etc..

But it's a good point.

Re: Why Do Americans Stink at Math?

#62

Post by sjg007 »

increment_i wrote: post #29
tomc1985 wrote: post #18

If they would teach kids to play with math (or any form of knowledge, for that matter), and not just run through 10,000 rote problems, maybe we'd rank better. Especially word problems -- most of them felt like they were written for students wearing intellectual blinders... if you had any modicum of relevant knowledge outside of the lesson oftentimes word problems were impossible to solve

Could not agree with you more. Another thing I've noticed anecdotally is that many of the math teachers in the secondary system in North America do not have a broad understanding of math themselves. Math is given the most rote treatment of all the subjects, and I suppose this is understandable given the abstract nature of math. But students are never told why they should care about abstractions in the first place, wh…

Not sure how math helps you deploy instagram clones. I mean set theory, logic, computable functions but that's a big stretch.

Re: Why Do Americans Stink at Math?

#63

Post by saint_fiasco »

Frogolocalypse wrote: post #20
tomc1985 wrote: post #18

If they would teach kids to play with math (or any form of knowledge, for that matter), and not just run through 10,000 rote problems, maybe we'd rank better. Especially word problems -- most of them felt like they were written for students wearing intellectual blinders... if you had any modicum of relevant knowledge outside of the lesson oftentimes word problems were impossible to solve

> If they would teach kids to play with math (or any form of knowledge, for that matter), and not just run through 10,000 rote problems, maybe we'd rank better. Don't the countries that rank better use the rote method even more?

From the article:

>Though lesson study is pervasive in elementary and middle school, it is less so in high school, where the emphasis is on cramming for college entrance exams

I think the implication is that kids are supposed to be taught to play with math in addition to the rote memorization, not that rote memorization is evil.

Many of the more "fun" math techniques rely on knowledge acquired through rote memorization, just like dynamic programming uses the results of inefficient calculations to speed up subsequent calculations.

Re: Why Do Americans Stink at Math?

#64

Post by Frogolocalypse »

anexprogrammer wrote: post #48
Frogolocalypse wrote: post #27

Earlier quoted context omitted.

Not really. You still go to the shops and buy things in litres and kilograms, and their entire construction industry is in metric. The only commercial product that isn't in metric, funnily enough, is beer and cider. I guess getting pissed people to change proved harder than everything else.

...and milk is always pints. An awful lot of products come in imperial sizes but metric labelling - 454g jars of jam etc. Timber sometimes gets called 2x4 even though it's 50x100, but that seems less common now. Oddly just about everyone still uses feet and inches for their height. I hear kilos more and more often for weight, I don't think I've ever heard cm for height in the UK.

> ...and milk is always pints.

Returned milk is (you know, in dem bottles). But milk you buy in the store is 1L, 2L, etc.

> Oddly just about everyone still uses feet and inches for their height.

True. Probably because of the recognition of the 6' centering measurement. People know that if you're 6', that's kind of the cut-off for what is referred to as 'tall enough'. Over that, you're generally 'tall'. Under that, and you're average height.

Re: Why Do Americans Stink at Math?

#65

Post by mrcactu5 »

mathattack wrote: post #14
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…

We do a great job with the extreme students. The top 5% of private and public schools in the country produce more than enough folks capable in mathematics. It's the rest of the country that struggles. There are a lot of reasons why the US does well in Universities and poorer up until then relative to the rest of the world: 1 - In much of the world, the school you get into matters more than what you did there. (The lo…

our best students to really well. our average students are doing poorly / lagging behind. the US also has an anti-intellectual bent to it. You can be smart, but you can't be too curious or question anything.

Re: Why Do Americans Stink at Math?

#66

Post by Frogolocalypse »

saint_fiasco wrote: post #63
Frogolocalypse wrote: post #20

Earlier quoted context omitted.

> If they would teach kids to play with math (or any form of knowledge, for that matter), and not just run through 10,000 rote problems, maybe we'd rank better. Don't the countries that rank better use the rote method even more?

From the article: >Though lesson study is pervasive in elementary and middle school, it is less so in high school, where the emphasis is on cramming for college entrance exams I think the implication is that kids are supposed to be taught to play with math in addition to the rote memorization, not that rote memorization is evil. Many of the more "fun" math techniques rely on knowledge acquired through rote memorizati…

I think rote learning is a really really important thing, perhaps the most important thing, in math. Math is like any sport... you get good at it by practice practice practice. Check check check check. You have to train your brain to be good at it, and it can be hard, just like anything you train at.

> Many of the more "fun" math techniques rely on knowledge acquired through rote memorization

I wasn't aware of this. I have a nine-year-old. Are there any examples of this?

Re: Why Do Americans Stink at Math?

#67

Post by sssilver »

droithomme wrote: post #55

People keep saying Americans stink at math, americans don't understand science, americans are ignorant, etc. And yet at the same time we have these sorts of track records: http://www.popsci.com/us-dominates-at-sending-stuff-to-mars It's not just Mars or the moon, or decades ago, the US also is where most operating systems and software and CPUS are conceived of and designed. As well as countless other things that peop…

How many of the people involved in those accomplishments are boasting American middle school education?

Re: Why Do Americans Stink at Math?

#68

Post by nemo44x »

yazaddaruvala wrote: post #58
nemo44x wrote: post #47

Math is hard work. I was bad at math. I went to college a couple years after I graduated high school where I made little effort to challenge myself. But after figuring things out, at 20 I decided I wanted to do computer science as I enjoyed some of the programming skills I picked up (C++ of all things!). I was very unprepared for the math part of it and it was hard. I tested into a remedial math level and when I look…

Congratulations! I'm always disappointed when people say "some people just can't learn X". It isn't that they cannot learn X, they just cannot learn it in the same time frame, and they shouldn't be expected to!

I mean that's really the problem. For some reason we think things will just make sense once we are taught the lesson and we try an exercise. But that's so often not the case. Accept you'll never be the genius who creates new things - maybe you will but put that aside. Focus on trying hard and committing yourself. It doesn't matter if it's math or cooking food, the more you try it and think of it and accept failure the better you'll be. Accept your limits as a creator but never accept that you can't understand a concept if you spend the time you personally need at it.

Re: Why Do Americans Stink at Math?

#69

Post by danharaj »

yorwba wrote: post #33
danharaj wrote: post #12

Put 100 mathematicians, math educators, and policy makers into a room and ask them to come up with a good mathematics curriculum. They'll come out with 101 proposals. That's not a problem, really. Mathematics is not merely about mathematical substance, but also mathematical process (the two are intimately related), and not just process, but the process of discovering processes. Curricula, standards, directives, are a…

> (and I get to apply some really high powered ideas to programming once in a while which grants a satisfaction that lingers) Mind sharing what some of these ideas are?

Lately I've been experimenting with comonads to structure stateful code. The idea is that a comonad describes the interface for a state machine, and you can convert any comonad in Haskell into a monad transformer which acts as a restricted form of the state monad. The state monad describes expressions that can arbitrarily manipulate a state of some type. The monad you derive from a comonad does not have direct access to its state, the comonad describes all the allowed manipulations and queries.

This is all described and implemented here: https://hackage.haskell.org/package/kan-extensions-5.0.1/doc...

In particular, the type:

  data CoT w m a = CoT { runCoT :: forall r. w (a -> m r) -> m r }
Let's unpack this. The following type represents a state machine whose nodes are labeled with a continuation demanding an `a` and executing an effect:

  w (a -> m r)
The forall quantification in CoT means that it does not care what the result value is. It will take a state machine, manipulate it for a bit, produce an `a`, pick a continuation from the state machine and execute it.

That's a lot going on! I don't have time or space to explain how this is actually useful but here's a handy approximation:

- `w` is an interface

- `w s` is a model labeled with a value of `s` for each state it can occupy. These labels are a sort of view.

- `CoT w m a` is a controller that can manipulate a model and compute in some effectful context.

High powered MVC. The upshot is that because we're leaning on Functors, Monads, and Comonads there are extremely well behaved and natural composition operations. For example, `fmap` allows us to change the view of a model by applying a pure function. The fact that `CoT` is a monad means that we can run controllers in serial, as well as combine our controller languages in sensible ways. The fact that `w` is a comonad means we can reason about the behavior of models equationally. This lets us transform, compose, and compare models with mathematical precision.

This is a project I only seldom work on in my spare time. I have already applied it to writing GUI's and game logic to good effect but I'm still exploring the design space regarding reactivity and temporal behavior. This has led me to reading the mathematical literature pertaining to products of comonads/sums of monads (they're dual).

Re: Why Do Americans Stink at Math?

#70

Post by mathattack »

eatbitseveryday wrote: post #44
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.

> tuning the students in to Khan Academy and suchlike programs I think parents have an enormous role to play in the effectiveness of K-12 education. If they are not very much involved (e.g., enforcing, participating, encouraging) then school isn't valued or prioritized, nor will the average student see how fun many subjects can be to learn (assuming the teacher may not be effective at this). > were taught math badly…

Just an aside, wouldn't this be expressed as "taught poorly"?

Blame the English teacher who thunk it badly. :-)

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