Why Do Americans Stink at Math? (opens in new tab)

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 lowest University of Tokyo graduate is considered higher than the top grad of any other school - so getting in there is the hard part)

2 - In the US we invest more in higher ed than K-12 relative to the rest of the world on a per-pupil basis - especially at the top schools. (Look at the Harvard or Yale endowment on a per-student basis)

3 - In the US, college professors are at the top of their peer group academically. It's a mixed bad in K-12.

The best American student mathematicians are the equal of anywhere in the world. But when people talk about poor math performance in the US, they're talking about the average—average math performance is terrible. This is because the U.S., more than any other advanced country, tolerates a high level of poverty and economic inequality. This inequality is reproduced within the educational system, and brings down our averages.

The average is lower not because the U.S. has lower performance across the board, but because so many more students lack the most basic numeracy. Too many students are going to school hungry, come from families torn apart by joblessness, abuse, and addiction, or where the single breadwinner has to work 80 hours/week in order to achieve a higher level of poverty, and simply doesn't have time to help the kids with their school work or ensure they are disciplined students, much less ferry them to all sorts of enrichment activities.

The bad effects of such societal level bias against math can be seen in public spending in schools also. Enormous amounts of money are spent on football coaches/teams[2] in schools whereas not enough money for math teachers/students.

The society seems to equate success only with one's ability to earn money. Then you can see that many such popular public figures "getting successful" without math as they can be seen to earn large amounts of money.

This is sad as such people even if are successful on money front, cannot understand any of the complex aspects of modern societal/business/political structures (be it, things like privacy issues, or many public policy issues like taxes) and of course cannot understand any of the modern technological/scientific discussions (be it discussions regarding global warming or genetically modified food or statistical significance of some tests).

[1] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1968613

[2] http://www.theatlantic.com/magazine/archive/2013/10/the-case...

Relative to the US population, the primary and secondary education do not produce a high level of capability.

Looking at the fields medals per capita[1] you can see that the US doesn't have as much as the UK, Russia, or France. You can also see that the university with Fields medals recipients [2] for more details, and indeed you can see that of the mathematicians associated with Princeton are not Americans.

As a specific example, in [1] you can see that France is generating more than 4 times more fields medalists per capita than the U.S. Why is that?

It probably has to do with the more rigorous Math education. Look for instance at this translated Math final[3] exam for French high school students. This is for the "Literary" students, those who focus more with the worst level of Math. You can see examples of the "Scientific" math test here [4]. It's in French, but it's Math, just by looking at the symbols it's possible to understand. It has some differential equations solving, probabilities, geometry with vectors/planes in 3D spaces, Series analysis, etc. Integrals and derivatives are also part of the program. In Physics these concepts are applied to calculate velocity/speed/radioactive decay etc.

[1] http://stats.areppim.com/stats/stats_fieldsxcapita.htm

[2] http://mathworld.wolfram.com/FieldsMedal.html

[3] https://gfbrandenburg.wordpress.com/2011/06/19/a-look-at-one...

[4] http://www.letudiant.fr/bac/bac-s/corriges-et-sujets-du-bac-...

You can see this especially strongly in graduate programs, where US citizens can often get a sort of "affirmative action" because they are the only ones eligible for NSF student fellowships (incentivizing universities to admit them). There's just very little domestic interest in math and physics, despite both feeding into rather favorable job markets (as long as you aren't dead set on being in academia long-term).

As for your second question, it's an extension of US universities' preeminent standing in most fields (on average, there are of course exceptions). I don't think there are really any math specific effects going on there.

The US does have the richest mathematics knowledge in the world because the US can buy it.

For example, maybe if you are a very good mathematician in the US you can get high-paying jobs for intelligence agencies, data analytics, that sort of thing. But if you are a mathematical genius in another country, maybe they don't have the same job opportunities so you have to go into math teaching.

That would cause the US to have very good mathematicians and at the same time terrible math teachers.

It's a fallacy. US is a large country, so those talented students concentrate in fewer universities. In Europe for instance, due to language and culture barriers, talented students from Czech Republic do not very often go to Cambridge. You need to look at mean or median if you want accurate assessment.

The European Allied soldiers were so disciplined that they just kept climbing up the ladders and getting killed one by one, following their orders to their deaths. The Americans saw this and said, "fuck that, I'm not climbing up there."

I think most Americans are pragmatic and they won't do something unless it makes sense. And to be honest, most people don't need to study math. Or at least it's not obvious that they do. I think most of the math professors I've talked to would agree. They view math, as it's taught in core curricula, more as an art than as having vocational value.

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 American and Asian American 'testing scores' are actually pretty good - and have been holding steady for a very long time. (Asians do a little better). Nothing has changed.

+ Latino American and African Americans fare poorly, but having been getting better since we've been measuring by standards (i.e. 1950's-1970's).

Here's the trick:

+ 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.

The key correlating factor here is 'ethnicity'. 'Ethnicity' is the broad, generalist predictor of educational outcomes. This definitely not 'race' and it's not even 'IQ' (those things are plausible but controversial) - it's a series of behaviours, social norms, examples, attitudes towards work, success, access to services, social networks, mentors, role models, etc. etc. etc..

Educational outcomes (and crime stats, income stats) break down along ethnic lines. In a manner of speaking - America can be thought of as 'four nations' - White, Black, Asian and Latino. Obviously - it's very crude and generalist, and policy based on this would probably be racist - nevertheless - you pretty much have to look at the data given this.

In the end: American test score results have more to do with the changing ethnic composition of the American population than they do anything else. Again: White people and Asians in America have performed consistently he same for decades. Teaching methods haven't changed much, students habits haven't changed much - so the outcome is naturally consistent.

More economic prosperity, access to services and different attitudes + deeper integration have meant Latino A. and African A.'s are doing a little bit better - but because there are so many more Americans of those groups - particularly Latino Americans - it changes the outcome of the 'average american test score'.

Analyzing educational results does not make sense until you break it down along ethnic lines. Once you do - it becomes crystal clear. It's the absolute #1 most important thing about the educational data that turns 'paradox' about educational investment (teaching has remained largely the same) and outcomes into 'perfect sense'.

Unfortunately, it's so sensitive few will want to talk about it - for fear that the general public equates educational outcomes to 'intelligence' and try to strongly correlate ethnicity + race to this, which would be fodder for racist/KKK types, which wouldn't really help the overall social situation in America.

Anyhow - America is actually doing pretty well overall.

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

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

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 analysis or Fourier transform just by reading about it

Very few 8 year olds are grappling with fourier transforms.

A.) For the obvious not everyone learns the same way

B.)Drills and practice are important, but being able to actually apply your math skills is also important. I remember in high school when there were math word problems so many people HATED them. These were people in honors/college level classes and they struggled to actually apply the math to situations. Find how fast the train is moving, how long the ladder is, and Geometry proofs all made many of them get confused. They didn't understand the point of the math they knew.

Personally, I got SO bored with drills/memorization. And personally for me, that if that's the -only- method of learning used it's awful for long term retention. The math skills that I've retained the longest were taught in several different ways-- a mix of drills/practice, visualization, mixing it with other types of problems so that I could see how the puzzle pieces fit together, etc. I understand the point of what I'm doing, it's not just some abstracted concept that I happened to write 50 times.

I agree that past a certain point you'll have to accept abstraction, but especially in early years up until probably Algebra, it's a useful skill to be able to use math in the real world. Seriously, I've met so many people who can't calculate a tip, understand fractions enough for simple cooking, do their budgeting, or begin to understand economics and taxes enough to be even decently informed citizens.

However, I do think that examples and applications help a great deal. Sometimes, a mere description of first principles doesn't do it for me, and then, when I see an actual example, I suddenly understand it and the theory along with it.

But i agree that the key is practice. At university, where the pace picks up dramatically, you figure out that going to the lecture is not as important as finishing the assignments. Always finish the assignments.

In talking about how Japanese teaching methods are better than American teaching methods, it states: "Similarly, 96 percent of American students’ work fell into the category of “practice,” while Japanese students spent only 41 percent of their time practicing."

They might try something that looks similar with word problems, but that is a far cry from the majesty of investigating the world with simple arithmetic. The problems they come up are contrived and students are no fools. Problems must come from within, not be handed to people.

Drilling vs understanding is not an either..or. Most learning starts with messing around, trying to figure something out. It is slow and will be painful if the interest is not there. At some point, understanding is sufficient with a foundation in place and then drilling comes in to get a mastery, but what "drilling" is and needs to be will vary from person to person. Too little, and the speed fails to materialize inhibiting understanding of higher level concepts. Too much and it gets boring shutting off critical interest.

All of this suggests that teaching mathematics in a one-size-fits-all is difficult. Also, imagine trying to grade 120 guesstimations for weeks on questions the students come up with. This is the essential difficulty of our current teaching mindset, namely the single authoritarian figure blessing or cursing the work of others.

The key to true learning is excitement and motivation and little external judgement. Interested people will largely self-correct with a few subtle pointers here and there.

Even at the level of Fourier transforms, most students probably fail to understand the problem. So how can it possibly make sense? Math is about working around hard problems, but the teaching of mathematics leads one to believe that there are simple algorithms to apply and we are done.

A lower level example of this is Newton's method. Solving f(x) = 0 in their experience (quadratic formula) is easy and graphing shows the zeros anyway. What is the problem it solves? But what if you just give them a graphical piece of the curve and ask where they think a zero is? Then the problem becomes clear and the solution can make sense. Then it gets translated into steps (draw a line that fits well, find its root, find out what it looks like around there, repeat). And then to master it, one can do a number of drills.

Good luck doing this, however, with people who do not care one iota about it and live in a culture where the majority of Americans have disdain for math (probably born out of a mixture of shame of how poorly they did in math class and bitterness that this most wonderfully human tool for exploring the world has been denied them).

That's probably the most accurate description of HN comments I've seen. People see a headline related to something they already have pre-existing beliefs about, they read a few paragraphs just to make sure they're on point, and then they jump straight to the comments to argue in favor of what they already know to be true.

I'm willing to wager $10000 that a significant majority of HN commenters in any thread do not read the article in full, and even among those who do, a smaller minority actually post comments addressing the meat of what the article is saying.

Jim, this is seems like a crazy generalization. I assume you haven't tried to quantify this and it's just anecdotal opinion right? No problem, let's continue:

1). All my beliefs are falsifiable. Since your claim includes "everybody", I guess this counterexample alone proves your conjecture false.

2). If the most open minded community on the Internet scores 100, what score would you give HN? Can you name a single one that's better? I'd like to check it out.

3). How often does a response here randomly adopt the retort "Its Obama's fault" or an ad hominem attack? When it does happen it's almost immediately killed or downvoted off.

On a separate note, the article plays up how bad Americans are at math. Is this data controlled for household income and education level of parents? The factors are so significant it's hard to accept the data without them.

Lastly, my personal experience mostly matches the article. So many math classes were rote, boring, and uninspiring. I first learned it didn't have to be this way during discrete math because it required less algorithms, more creativity in proofs, and pulled back the curtain on what really made things tick.

Americans stink at reading, too.

- It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. …The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them.

- American institutions charged with training teachers in new approaches to math have proved largely unable to do it. At most education schools, the professors with the research budgets and deanships have little interest in the science of teaching.

- Without the right training, most teachers do not understand math well enough to teach it the way Lampert does. “Remember,” Lampert says, “American teachers are only a subset of Americans.” As graduates of American schools, they are no more likely to display numeracy than the rest of us.

- Left to their own devices, teachers are once again trying to incorporate new ideas into old scripts, often botching them in the process.

- In Japan, teachers had always depended on jugyokenkyu, which translates literally as “lesson study,” a set of practices that Japanese teachers use to hone their craft. A teacher first plans lessons, then teaches in front of an audience of students and other teachers along with at least one university observer. Then the observers talk with the teacher about what has just taken place. Each public lesson poses a hypothesis, a new idea about how to help children learn. And each discussion offers a chance to determine whether it worked. Without jugyokenkyu, it was no wonder the American teachers’ work fell short of the model set by their best thinkers.

And the most important two paragraphs:

The other shift Americans will have to make extends beyond just math. Across all school subjects, teachers receive a pale imitation of the preparation, support and tools they need. And across all subjects, the neglect shows in students’ work. In addition to misunderstanding math, American students also, on average, write weakly, read poorly, think unscientifically and grasp history only superficially. Examining nearly 3,000 teachers in six school districts, the Bill & Melinda Gates Foundation recently found that nearly two-thirds scored less than “proficient” in the areas of “intellectual challenge” and “classroom discourse.” Odds-defying individual teachers can be found in every state, but the overall picture is of a profession struggling to make the best of an impossible hand.

Most policies aimed at improving teaching conceive of the job not as a craft that needs to be taught but as a natural-born talent that teachers either decide to muster or don’t possess. Instead of acknowledging that changes like the new math are something teachers must learn over time, we mandate them as “standards” that teachers are expected to simply “adopt.” We shouldn’t be surprised, then, that their students don’t improve.

But this isn't news (even if the article is from 2014). I've linked to this report from 2007 many times before and I'll do so again:

http://mckinseyonsociety.com/how-the-worlds-best-performing-...

To find out why some schools succeed where others do not, McKinsey studied 25 of the world’s school systems, including 10 of the top performers. The experience of these top school systems suggest that three things matter most:

Getting the right people to become teachers; Developing them into effective instructors; and Ensuring the system is available to deliver the best possible instruction for every child.

In the US, we fall down on all three of these points.

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

(just kidding)

I know people will throw stones at me for this, but the reason teachers are not the top 1% of the society is because functionally their job is a commodity. (We're talking about elementary/middle/high school teachers, not professors here).

It is not hard to find someone who knows high school math, for example. I'm not discounting the fact that there are sometimes really outstanding teachers, but the thing is, it's hard to objectively measure their performance since their teaching talent is not directly related to how well their students do. On the other hand, the "teachers" at universities are well respected since their talent is not only limited to how well they teach but the quality of their own research--the value is much easier to quantify.

I used to think so too, but I don't think that is exactly the case. School districts usually span many neighborhoods, rich and poor. Within school districts, there are school zones (school boundaries), or mappings of residential addresses to assigned schools. While it's true that richer neighborhoods tend to have better schools, the property tax money is collected centrally at school district level, and then distributed across schools, both rich and poor. I haven't seen evidence that districts distribute more money to schools in richer neighborhoods.

If anyone is more knowledgeable on this, I would love to learn more.

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.

Teaching in Canada is along the lines of nursing or something: it's professional, requires a degree of competence and certification, there is social value. It's not exactly 'doctor' but it's respected for what it is, as it is in most nations.

I think it's because people assume American teachers are not paid much, but the one's I know are paid reasonably.

Don't the countries that rank better use the rote method even more?

But students are never told why they should care about abstractions in the first place, which is unfortunate. Many high schools simply refuse to speak the students' language.

I suspect this will change in this century. IMO, if a high school really wanted to be progressive, they would totally reform their math curriculum to include more exposure to applied math and computer sciences. Young folks should be using math to build their own Instagram or Minecraft clones that they can deploy to their devices that VERY DAY - using the concepts they've been introduced to in mathematics.

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!

Leave the program execution to the computers, give the children critical thinking skills.

Most people "in the trenches" writing tools that would make use of the fundamentals in their field (either in the physical sciences or engineering disciplines) tend to agree that linear algebra has disproportionately little representation compared to calculus. To be fair, that is somewhat of a downstream problem from mathematics departments, and speaks more about the possibility of stagnation in the undergraduate science and engineering curricula.

fair caveat though: my PhD is in numerical linear algebra...

Everyone? I love math.

It just doesn't add up.

Finding a good math teacher in America is difficult because the good math students rarely become teachers.

Mind sharing what some of these ideas are?

http://marginalrevolution.com/marginalrevolution/2015/01/no-...

https://youtu.be/XnVcaHMsYqM

Chinese Tsinghua Univ beats MIT to take the top seat at USNews for engineering. I think this is the second time in a row.

As far as I know, Chinese universities took the best students without considerations of gender at all. They do have AA for races but it is minimal.

USA is moving towards to AA-for-school-and-workplace, I hope this will make more people happier with high self-esteem, in the meantime you lose your competitiveness quickly.