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US 'in denial' over poor maths standards (bbc.co.uk)
60 points by NickPollard on May 21, 2014 | hide | past | favorite | 97 comments


In the US, the quality of your math education is determined by where you live on the community level, usually by property value. Within 10 miles, you can have both a school that performs on par with Sweden and another that performs on par with Turkey.

What does this mean? Things are way worse for the poor here than this study even acknowledges. If you're poor in America, your best chance at a good education is by raffle.


Could this be explained in part by people who are good at math tending to make more money than people who are bad at math?

http://media.collegeboard.com/digitalServices/pdf/research/2...


If that's a component, it's a relatively insignificant one. Regression to the mean would likely take care of that advantage across generations.


It has nothing to do with that. Wealth in this country is in no way correlated to math ability.


Do you have any direct evidence of this?

I ask because it is well known that math ability is correlated with educational achievement, and level of education is known to be correlated with income. Putting these two together, I would suppose that math ability is correlated with income.


I'm not saying that greater math ability doesn't correlate to greater wealth. That could very well be true (and it probably is). What I meant was that the public school system is funded by tax dollars. Wealthier neighborhoods contribute more tax money and have better public schools. I obviously don't have any direct evidence, but I would sat there's almost no correlation to wealthy neighborhoods and their residents being good at math. If you don't believe me, we could go knock on every door in my parents' neighborhood and ask them what they got on their SAT math section :P

Joking aside, I'm basing that on the fact that not every high-paying job requires math skills, and not every rich person got rich because of math.


Well, I think you're hitting on something.

1. I think you're wrong about the lack of correlation and, as nickff points out, better math ability is correlated with higher income, but

2. Math ability does not affect income.

Correlation is not causation. The better math ability is a side effect of higher income in my opinion, not vise-versa.



What an annoying response. You link me an 18 page PDF and call it direct evidence? Did you even read what I said? I'm not arguing that greater math ability doesn't correlate to greater wealth! This issue boils down to wealthier neighborhoods getting more money to invest in better math education for their students. That's it! Are you claiming that all rich people are good at math? Or that only people good at math are rich? In your world, can there exist a neighborhood of wealthy people who are not good at math? I have no clue and frankly I'm done explaining myself here.


Your belief is wrong. All research on the subject tells us that spending has at most a small impact on test scores. I'd link you to PDFs but I know how you feel about that.


I think you're wrong, and that spending does have a huge impact on test scores; the PDF you link even supports that higher family income correlates with higher test scores. My argument assumes that wealthier families spend more than less wealthier ones.


The evidence is not on your side.

http://washington.cbslocal.com/2014/04/07/study-no-link-betw...

You can downvote me but you still have no evidence for your beliefs.


I actually can't downvote you. And I wouldn't. Downvoting without responding is cowardly, or at least not conducive to the aim of a civilized discussion. Its the Hacker News equivalent to anonymous hate mail. They are like rumors, and lead to distrust and aversion to frank debate, everything we should try and avoid. If someone downvotes a comment that is ultimately upvoted, the downvotes should be reassessed against themselves or something. If Wikipedia had such a mechanism the whole community would break down. Its a bad feature.

School spending is not the only spending involved. A large cost, roughly equivalent to spending, of the family is that which is spent on providing a loving, supportive, positive, non-absent relationship within the family. This costs time away from work. This costs money cultivating relationships with intelligent people. This provides affluent children with more positive influences, positive role models, and less stress that lends to more focus on learning. They tend to invest more in their children, but its not to say that a wealthy family will invest as much as a poor family with more of a focus on education. The list goes on and on. Its not as if you need to be affluent to provide or invest in these things, its just more conducive.


I don't mean to be uncivil.

The claim that low-income students suffer because they are less likely to have families that enrich them is probably not as true as you seem to think.

http://econlog.econlib.org/archives/2010/11/the_science_of.h...


Incidentally, both Sweden and Turkey are ranked below the US average. Swedish education is in a sorry state at the moment, dropping fast in the rankings and already well below the level of any other nordic country.


Having gone to school in MA, I know educational spending ($/student) here is inversely correlated with performance.

But I'm not really worried about national average, state average, even school average: there just needs to be the opportunity to succeed for individual students, wherever they're located.


I think it is very much worth caring where the average is. This average person will grow up to become a voter and taxpayer and we need intelligent citizens to vote in competent representatives. Philosopher kings never happened, otherwise, just making sure the smartest get smarter would be okay; we have a democracy and the only way to make it work is to have informed citizens.


Arbitrary education standards and comparisons to other countries aren't going to change the way people think.

(Implicit in the above is the opinion that for loads of national political issues, the biggest thing stopping "the masses" from being informed is that they simply don't care.)


I think the interesting thing was even middle class kids demonstrated poor performance too. The problem us spread wider across the distribution rather than abysmal performance by a minority such so that it pulled down the average (to me, that never really made sense in my intuition).


I definitely agree. There are some high-performing schools but they're a minority. There's also a minority of very, very low performing schools.

What makes us unusual is how wide the spectrum is, even if the average is bad.


I totally agree and am depressed that places like inner cities have such a hard time getting more charter schools and competition that would give these kids and their families a shot at a decent education.

Is it politics? Teachers unions? Getting good admin people? What's holding back these places from getting ahead?

As a comparison, my sister lives on the outskirts of a large metro area and their school has been teaching STEM for almost 10 years now.


All of the above.

Politics is involved through school boards where an understanding of education is not really considered a job requirement. And at state and national levels it's difficult to fix problems that are uniquely local.

Teachers Unions can create the wrong incentives in a district.

Good Admin people are hard to find and bad ones make the working environment unplatable for good teachers.

Add in money as well for some districts.


Honestly, the problem is a collection of so many problems that it's very difficult to really even assess the situation properly. It could be the overemphasis on standardized testing. It could be the lack of support teachers get in inner cities and the fact that they have to babysit 50% of the time. It could be the public school system's unwillingness to adapt. It could be the unions fighting tooth and nail to prevent more charter schools from opening. It could even be the charter schools not actually working!

Personally, I think the problem is that the public school system can't work well enough in poor areas. I think those children need a completely different education system to work for them (longer hours, after school programs, school uniforms!, etc).


>What's holding back these places from getting ahead?

There is no motivation for someone to teach in inner cities beyond a sense of civic duty. I live in a city with terrible (unaccredited) schools. Students in those schools are often openly hostile to teachers and faculty. Administration is often on the verge of a breakdown due to the pressure to "turn things around." Why would anyone want to teach there? I know I didn't want to.

If you think it's a travesty that talented and bright teachers want to avoid inner cities then you should do it yourself. That's what I say to anyone who brings this up. Often I will be told, "But that's where you're needed!"

"So are you," is my response.


This is probably one of the main things I did leave out, which is the socioeconomic toll of broken families, absentee parents and the lure of drugs and gang culture.

>>> If you think it's a travesty that talented and bright teachers want to avoid inner cities then you should do it yourself.

I can't argue with you there.


I'm curious what you mean by "teaching STEM", do you mean a particular emphasis on STEM? Because most schools at least cover the science and math part, with varying degrees on the technology and engineering (often limited by teacher availability and financial resources). If they don't cover those things then they aren't really covering any state's high school curriculum.


Sorry, bad wording on my part. Yes, they have an emphasis on STEM. My niece is in 4th grade and they're already learning algebra, something I didn't start learning until 3-4 years later.

They also are learning about programming and other really technical stuff I was surprised to hear about. The other thing which was nice to hear is how they foster kids to learn and enjoy math - something I missed out on until I was in college and had a professor who really gave me a sense of how wonderful mathematics can be, not just a means to an end.


Yeah, let's robo-blame the unions, that will inject some magic Ayn Rand juice into things and make everything better real quick. Sure.


I taught high school physics for a semester and the math abilities of these students (many considered top students) were abysmal. Somehow several of these students had received As and Bs in Algebra 2 but were unable to transform f = ma into a = f/m. They also had a very flawed understanding of how to solve quadratics.

I later realized that the issue is that mathematics is often taught as procedural. Students are taught a process (a set of steps to follow) that will take you from A to B. This works very well when you can remember all of the steps but if you forget one step you will always get the wrong answer. Almost none of these students could reason abstractly about the nature of the equations they were looking at. They could only refer to prior experiences following a sort of algebra recipe.


I remember when I 'got' algebra. I was in 10th grade in Chem class. We were using mols = (mols/Volume)*Volume. For weeks, I had no idea what was going on. I just plain did not understand algebra whatsoever. But finally, at the end of a lab class where we actually mixed things and then found the concentrations and volumes, I finally figured out that these algebraic equations actually tied back into the real world. This was not for lack of trying on my part, my teacher's part, or the schools. I just plain did not understand. I think it was a developmental issue for me. I wasn't ready to chemo-mentally, therefore I just muddeled along frustrating everyone including myself.

I say this because I went on to get a BS in physics from a UC. Obviously I learned math very well later on. But in 9th grade, I was unable to learn anything harder than long division. I was a 'left-behind' child due to my brain. Nothing, I believe, could have helped me. Not all the tutoring in the world. My brain wasn't old enough then.


I was also a very poor math student in HS that went on to get a physics degree. I can say that it was the method of instruction as well as my own lack of motivation. Classes were boring and easy to pass even if you did not know the material. In my state you needed a 2.0 GPA to get into a state school. This is generally doable for even the worst students.

The lack of real consequences for not studying and doing homework played a huge role in my childhood academic experiences. I am often baffled when I hear reports of students who are over stressed by the requirements of high school academics. The standards seem now to be even lower than when I was in school yet students constantly complain that they can't keep up. It's mind boggling.


I believe it may have to do with a reverse bell-curve that seems to be prevalent in some areas. My High School was public and pretty good overall. However, we had basically 2 classes of people. The over-achievers and the under-achievers. The overs were on 3 varsity teams, had perfect grades, were on church youth group, Eagle scouts, etc all at once. The unders were high or drunk most classes. You pretty much were in AP classes or were getting D's; a reverse bell-curve. Now granted, this was a decade or more ago, but my little brother says its still the same mostly. But from this, I can understand the confusing narratives. You have some kids killing themselves [0](produced by one of the moms from the high school a hill over) and some kids with no future and they know it. Overs don't take classes with, play on teams with (due to GPA requirements), or hang out (if at all) with the Unders. Its tough to tease out a single statement because there are possibly 2 schools sandwiched on the same grounds.

[0]https://en.wikipedia.org/wiki/Race_to_Nowhere


Well, surely more standardized testing will fix that right up.


If there is a better way to evaluate educational systems and educators, then it should become the minimum standard. I.e., it would still be "standardized testing". I don't know why that phrase became a thought-terminating cliché.


Standardized testing isn't a meant to teach skills. It is meant to assess skills. No one is proposing that more standardized testing will teach students how to do mathematics.


I think the thing that distresses me the most is that any attempt that has been made to alleviate the situation (like the common core) has been stamped "big government" by people who seem to _not_ understand the urgency of this situation.

I'm out of ideas. What do we do?

EDIT: added a not. Wow did that change what I meant to say.


It'll really require a culture shift, starting with the parents. I don't know much about school systems in other parts of the country, but going to school in Maryland there wasn't a lack of mathematical support and teaching. The kids who excelled and wanted to push themselves got all the support they needed. And usually it was kids with intelligent parents that pushed the importance of education and mathematics on them that did well. I'd bet the top performers in American schools are basically on par with top performers in other countries. The will and determination to push kids into that top performer bracket isn't there, even amongst the well-off.

You can force stricter math curriculum onto students, but all it will accomplish is more students failing and their parents complaining that they are pushing the kids too hard. And a lot of those parents have good paying jobs that don't require them to even remember algebra... so they probably don't have any respect for the subject. That type of mentality is endemic in America. Naturally it's going to get passed on to the kids.


It depends on when you start to force it down their throats :) The earlier in their education that they are pushed to reason more rigorously (again, within reason) the easier it will be for them to accept mire rigorous education earlier. Still, I really agree with you though that a cultural shift will be best, but I'm not sure how this ever will happen.


Part of the problem is that a subset of the right wing wants privatization. In order to encourage privatization, you actually want the public sector to be as bad as possible so there's greater outcry for subsidized privately-run alternatives.


A fair-sized proportion of the right wing (loosely defined to include libertarians also) favors privatization. It is fair to say that some of them want to believe that the public sector is as bad as possible. It is unlikely that any are deliberately making it worse.


Have you read through common core? That crap is confusing.


What? I just looked it up[1]. The common core math standard looks very readable and reasonable, and it’s not even very big (93 pages). Is there anything in particular that you found confusing, inappropriate, or overly prescriptive?

For example, in Grade 7, there are about 50 requirements, one of which is “Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.” That sounds like an appropriate thing to learn in 7th grade.

Edit: In fact, most of the time when I am reading the standard I just nod and think “yep, that’s probably about when I learned that concept” when I grew up in California, although in a few cases (e.g. using scatterplots and proving Pythagorean theorem in 8th grade) I don’t think I learned them until high school.

[1] http://www.corestandards.org/Math/


Common core invents new arithmetic techniques that no one knows. It's the worst idiocy of reinventing the world.


Citation needed.

As far as I can see common core defines standards of ability, rather than teaching methods. There are a bunch of awful, dreadful textbooks that claim 'common core compatibility' but which ignorant people conflate with being part of a common core syllabus, as if they are approved/endorsed by the same people who drafted the Common Core standards, whereas in reality textbook approval seems to be a an extremely politicized and corrupt process carried out by the individual states. I wish there were a single federalized syllabus, because it's not like Math works one way in Connecticut or Rhode Island and another in Texas or Arkansas.

Your argument is like saying Windows is terrible because you can find some poorly-programmed Windows software. Flaws in an individual textbook or exam paper are not the same thing as flaws in the standard they claim to adhere to. Perhaps you would like to use the link to the common core standard in the grandparent post to point out examples of what you are talking about.


> I wish there were a single federalized syllabus, because it's not like Math works one way in Connecticut or Rhode Island and another in Texas or Arkansas.

So we can replace 50 extremely politicized and corrupt processes with one massive, impenetrable, extremely politicized, and corrupt process?

Otherwise, I agree. The problems are with implementation, not the standards themselves.


It might be more efficient, and has proven to be so for a bunch of other things. The nature of grade school math is not changing so fast, for example, that we need to constantly rewrite our textbooks.


Is that anywhere in the standard itself, or are you criticizing a particular textbook?


It sounds like the complaints my colleagues keep levelling against common core. And to a one, every example they found came from textbooks or blog posts, not the standard.


[Citation needed]


Common Core is much more legible than the prior standards. That being said, it is a framework and not a solution that should be applied blindly at any opportunity.


One size fits all is surely the answer.


The whole point of the common core, from my understanding was to be vague enough to let local governments decide how best to implement it. They were trying to avoid "one size fits all."

Having everyone in the same page with regards to an overall standard seems good in my book.


Mathematics is one of those few areas where there is only one right answer to most problems. You can have different methods of arriving at that answer, but in many cases one method is optimal and can be proven as such.

Mathematics isn't cultural. Numbers and the laws that govern them aren't going to change in response to how people feel about them or who is teaching them. I fail to see the benefit of working without objective criteria in this domain.


This standard isn't one size, its a system of measuring sizes. The size or sizes chosen to fit the particular purpose is an implementation detail. Your argument is like calling all shoe sizes "one size" because there is a standardized, limited range of choices.


"One size fits all" is the only possible answer when you have multiple, mutually contradictory goals.

The idea that even just one child out of millions might be left out means no answer that treats the problem on an individual, child-by-child basis can ever be considered.

It also rules out anything where one child might get "more" than another. (Never mind that many people are perfectly happy and comfortable despite having gotten less than others.)


Objective standards that come down from on high probably create perverse incentives and do more harm than good.


I think its our job to teach our own kids, if the govt cant do anything because of all the naysayers and doubters then its left to upon the parents.

My parents challenged me in Math at a young age and I was always a step ahead in school.

Also as a nation we need to stop putting everyone on the same playing field. Students will always be left behind lets start focusing on programs that will help the smart and the challenged, not one program for all.


> not one program for all.

It wasn't "one program for all" in any of the public schools I attended in the US. Admittedly, we send everyone to high school (well, offer it, some students fail out early, some are failed by their teachers, others by their family). But once in high school, all 4 states (VA, NC, GA, NV) I'm familiar with (admittedly dated, 90s) had different tracks and graduation requirements. At least two tracks, usually 3 (college prep, honors, vocational; the first two could be considered the same track with honors as a specialization given the overlap in courses).


I dont think common core was around in the 90s. Besides the tracks still share common math requirements. I believe at my school the only difference was you didnt have to take Math your senior year for vocational. (Of course honors/AP would be taking advanced courses).

I was trying to say common core was "one program for all".


That's not helpful for any kids whose parents are bad at math. You're condemning them to a lifetime of ignorance because of their parents' deficiencies.


Tutors, I used them in college once I left my parents house. You can find free tutors on most college campuses for challenging subjects, Math Chemistry etc.

If you are still in high school you can find many online resources to help, Youtube Kahn Academy etc...

Just because you are bad at something doesn't mean you cant find someone to help your kid whether its a relative, neighbor, tutor or old teacher.


Any parent can give encouragement and demand their kid work hard, but a parent without knowledge has no way of assessing whether a tutor or other pedagogical assistant is any good. Try thinking about this in the context of something that you're not good at.


>something that you're not good at.

This was kinda my message but it didnt come out that way. There are resources out there that are sometimes freely available you can use to get better at something you arent good at.


While I am fully aware that the American public education system is far from excellent, I am always skeptical of reports that laud China, Korea, and Japan as paragons of math and science instruction. What exactly is being measured here? Arithmetic and the ability to solve word problems of a few known formats is not mathematics. I do not want my future children to be calculators, I want them to be thinkers. There is creativity and beauty in math, and what worries me is not that it does not exist in the current implementation, but that it does not exist in the ideal implementation.

Of course, I'm also one of those people who doesn't particularly care whether a college education prepares me for a job, because that's really not the point.

See also: Lockhart's Lament (pdf at http://www.maa.org/sites/default/files/pdf/devlin/LockhartsL...)


This report is based on PISA test results, and you can find some sample questions here: http://www.oecd.org/pisa/test/

I think these questions are quite fair at testing the mathematical abilities of students. These questions don't simply test mechanical calculations, but also require applications of mathematical knowledge and insight towards problem solving.

If you disagree, then can you provide examples for better questions to test students at their mathematical skill level?


There are some major issues with this article, the more I look at it. The general tone is quite prejudiced--using Turkey, Chile, and Mexico as obviously terrible comparisons we should be ashamed of. The article also fails to mention that the two countries the US is ranked between are Sweden and Spain.

There's also no indication of the variation between #1 and #34 on the country rankings. Are the kids in Mexico 50% dumber than South Koreans? Or 5%?

Finally, is it a shock that there's variation in test results between US states? To whom?

There's plenty that can be critiqued about American education, but this article shows a lot of good ways not to do it.


Its a news article, not a research paper. And just because it lacks the depth of a research article does not necessarily impeach it. A better question would be "would this information be included in, or be reasonably drawn from, a good article?"

I think this information would be conclusions that could be reasonably drawn from a good research article, and therefore I disagree that "this article shows a lot of good ways not to do it."

And while I agree the general tone is quite prejudiced (using the South as representative of the US is akin to using Eastern Europe as representative of the EU) those countries are not terrible comparisons. Most Americans would admit those countries are not good to be similar to in way of education achievements, and yet the author does make a good argument that America is similar to them, and in doing so impeaches Americans view of the success of their educational achievements.


Education is not under Federal control, I live one of those "high performing" states. Painting this as a US issue is as silly as painting an issue solely controlled at the national level as an EU issue. I think the BBC's choice of portraying the US as a rusty bus is offensive as, again, this regional not a national issue.

I also think the areas named of poor performance often have poor performance across the board, that is not limited to the subject of mathematics specificity.


I disagree that the article painted the issue as a national issue. To the contrary, this is the rare occasion that I see a recognition on the part of Europeans that the US is composed of 50 states, and that making conclusions about the EU based only upon information from Romania, Croatia and Poland is probably ill-advised. It recognizes that states like California are big (being more populous than all of of Canada). And it recognizes what many Americans already know: the South is America's Eastern Europe.


I think US education system is basically broken. Instead of fixing problems you are arguing who is more privileged. Texas versus California illustrates it well.


According to this article it doesn't sound broken in the north. I'm opposed to nationwide changes as I am fearful it will just mess of the good things we have going on here.


I'd be curious to see what others think about this question:

There are so many articles that preach the wonders of international math education in Asian countries, and just as many that attempt to mortify with the Asian system of rote memorization that kills any creativity or true problem-solving. Which effect do we think is greater?

Because if the latter, then perhaps focusing just on math is as myopic as focusing within a country.


What percentage of the current US workforce actually draws on advanced (even intermediate) mathematical skills on a day-to-day basis?

I'd wager a guess that most developers on HN don't even touch the stuff.


Not very many. You might enjoy the essay "What is Mathematics For?" by Underwood Dudley [1].

[1] http://www.ams.org/notices/201005/rtx100500608p.pdf


don't confuse math skills with arithmetic skills. maths teaches you to think and reason about what you've got. arithmetic is just a way to apply your reasoning.

unless of course you're taught to follow steps without thinking and use a calculator all the time so your working memory isn't trained enough to reason about more complex problems.


I read all the comments kindly posted here before mine, and then I read the fine submitted article. Here I will link to the study "Not Just the Problems of Other People's Children: U.S. Student Performance in Global Perspective"[1] that underlies the news report submitted here. The full study report will of course give you details that a brief news report has no space to provide. It's good to read a news report from British journalists about education issues here in the United States, as the British journalists are less likely to hand-wave away concerns about United States educational performance.

As a response to some comments here, I'll note that I have lived in east Asia (I am a proficient speaker and reader of Chinese as a second language, and have lived in Taiwan during two three-year stays since I became an adult) and can verify that the schools there generally do a better job teaching mathematics (and also second languages) than the schools in the United States, at less expense per student. That efficiency in primary and secondary education lets both students who go on to higher education and students enter the workforce after secondary education achieve more in their adult pursuits than many Americans. Children there have childhoods with play and fun, but then they get to grow up to be adults with actual skills for advancing themselves.

For comparative rankings of different countries, showing how many more students in some countries reach high levels of mathematics achievement by eighth grade, see the very well constructed data chart "Distribution of Mathematics Achievement" for eighth graders in Exhibit 1.2 of Chapter 1 of the TIMSS report from the 2011 testing round.[2]

This issue is familiar to Americans like me who have lived overseas and have learned the local language of another country and have read the math textbooks available there. Better instruction can produce better educational results--and for less money besides. The top student issue is illustrated also by results from the International Mathematical Olympiad[3] and other international academic competitions. The United States has a huge population base, and it has many families in which the children are brought up by parents who are first-generation immigrants who received their own primary and secondary educations in other countries. (Such children do conspicuously well in academic competitions in the United States.) And the United States is wealthy, a heritage from the good governance structure set up by the United States federal Constitution. But even at that, the United States national team can be beat at the International Mathematical Olympiad by countries that have many fewer people and much poorer economies. Some countries have a very impressive group of top students.

[1] http://www.hks.harvard.edu/pepg/PDF/Papers/PEPG14-01_NotJust...

[2] http://timssandpirls.bc.edu/timss2011/downloads/T11_IR_M_Cha...

[3] http://www.imo-official.org/


[deleted]


Computation is what computers do best. There's so much more to mathematics than computation. Computers aren't anywhere near humans at discovering properties and proving them (in other words, proving theorems).


I'm pretty sure a computer could be used to solve most International Mathematical Olympiad problems quicker and more reliably. Its not an argument that computers are better at creating the theory that is used to solve the problems.

In essence, I'm saying the International Mathematical Olympiad is not a competition about forming or proving theorems. Correct me if I'm wrong, but isn't the competition essentially determining who makes a better computer? I'm arguing the utility of such skills is limited by the existence of computers.

Although I admit formulating and modeling problems would be a useful skill set not easily replicated by a computer, I'm not sure this is what most testing regimes actually test for.


I'm saying the International Mathematical Olympiad is not a competition about forming or proving theorems.

This statement shows you have utterly no familiarity with the content of most International Mathematical Olympiad problems, which are typically posed as open-ended problems for which the contestants must provide written solutions with proof.

Correct me if I'm wrong

This is one of the rare cases where I can recommend a Wikipedia article for more reading on the topic.

https://en.wikipedia.org/wiki/International_Mathematical_Oly...


Your petty insult is matched only by your willful ignorance of and refusal to address the substance of my argument:

> I'm pretty sure a computer could be used to solve most International Mathematical Olympiad problems quicker and more reliably.

Case in point:

http://www.imo-official.org/problems/IMO2010SL.pdf

> A1. Determine all functions f : R -> R such that the equality f([x]y) = f(x)[f(y)] holds for all x,y in R. Here, by [x] we denote the greatest integer not exceeding x.

Can Mathematica or another computer program solve that? I am betting it can. And very quickly. And I also reject that such a problem is open ended.

The most that the Wikipedia article speaks on the topic related to the above mentioned partial quote is

> extensive knowledge of theorems

Which does not mention actually proving any theorems. Although I may misunderstand the difference between proving a theorem and proving a solution to a given problem.

I await your lack of substantive response.


Perhaps it suffices to say that persons who know the item content of the IMO contests intimately are very happy to hire (or recruit as students) young people who have demonstrated ability to solve the contest problems. They don't think they are gaining access to people who can be replaced by a computer program.


UK 'in denial' over pluralization of the word 'math'.


It's not a plural, it's a contraction of mathematics.

Curiously I think Americas still say they study physics.


Apparently physics comes from the Greek φυσικός (phusikos) [1] so it's not an abbreviation at all. Compare to math and maths which are abbreviations of mathematics which comes from the Greek μαθηματικός (mathematikos) [2]. We do still say mathematics in the US, the difference is just in the abbreviation.

(I copy/pasted the Greek versions, so hopefully they're correct. They look correct to my inexperienced eye.)

[1] http://en.wiktionary.org/wiki/physics

[2] http://en.wiktionary.org/wiki/mathematics


Do you take Econ 101 in England or Econs 101?


I was racking my brain trying to think of an another example. It would be Econ and Home Economics is "Home Ec".


Once again, over again, one more time, beat up on the US over its "rotten" 'education'. Graduate/professional school? Nope. They're talking K-12. Then they are talking 'averages'. Yup.

This beating up on the US is mostly just fun from public flogging, a scam, a way to get headlines.

The US tried hard, poured in lots of money, bricks, mortar, etc., and it didn't work. Details:

Frontline video on efforts of Michelle Rhee in the DC public schools:

     http://www.pbs.org/wgbh/pages/frontline/education-of-michelle-rhee/
Transcript

     http://www.pbs.org/wgbh/pages/frontline/education/education-of-michelle-rhee/transcript-35/
If the Asians are so good at teaching math, then let them fix the DC public schools. Wait: Rhee is Asian. Oh, well, try the backup plan.

Okay: 'Control'. Control on country of origin.

I'll put it to you in blunt terms: Essentially the worst schools in the US do better than the schools in west Africa and Mexico. Some people won't like that point.

So, I'll give another point: How do the students in Minnesota of Norwegian descent do compared with the students in Norway?

That is, are we talking "US schools" or country of origin?

Next, for "US math", I have a right to be torqued and offended and I am: I'm a native born US citizen educated only in the US and hold a Ph.D. in engineering from one of the best research universities in the world for my research accomplishments in applied math, complete with theorems and proofs. I've done just fine in "math", thank you.

For math in Asia? From nearly all I've seen, math in Asia is not so good. I can think of some good work from Japan, but otherwise, no. For South Korea, one of their better college math majors came to the US for math grad school and right away had to conclude that they had learned no 'math' at all in college in South Korea and, instead, had just done some rote memorization with zero understanding. Then as a grad student they had to start over essentially as a freshman college math major.

But articles like the OP keep talking about K-12 'math' where likely they mean mostly just simple arithmetic; not a biggie.


Only slightly related to the article actually but when did the pluralized term maths become a thing. I feel like it had to be recent but I've been noticing it everywhere lately.


Commonwealth people generally say maths.

http://www.word-detective.com/2011/05/math-vs-maths/


Not in Canada.


Looks like it's more accurate to say that the English-speaking world generally says maths, excepting North Americans.


It's a british thing.


It's not a British thing, it's a standard English thing. I understand it's a difficult language but sometimes we contract words rather than lopping parts off.

It's interesting that you guys chose to keep Physics, did Physic sound too weird? :D


Physic is already a word, means medicine.

This side of the pond we use British to mean "not American, originating in United Kingdon". I say this as a Canadian. For parts of our English that differ from American, like colour, we say "it's British". Our dictionaries say the same thing too:

https://www.dropbox.com/s/hak6bs1hpnpu3rb/Screenshot%202014-...


Physics isn't a contraction or abbreviation, it's the entire word.

Mathematics is the entire word which all English speakers agree on. The difference is that British-English decided to abbreviate the word to 'maths', while American-English decided to abbreviate it just as 'math'.


I don't dispute the general findings of the study summarized by the article, but who's choosing the images that go along? The article opens with a mention of the "deep South" and is accompanied by a photo of a rusted bus in a field?

The middle picture with the caption "There is a complacency about mainstream US education standards" shows an anonymous residential street. And the final picture captioned "Massachusetts has high results by international standards" shows a gleaming, gated, gold-domed building [Update: turns out its the Massachusetts State House--that's a fair comparison with a rusty bus in a Mississippi field].

So kids in Mississippi attend school in rusty old buses, whild kids in Massachussetts go to pristine palatial academies, I guess? Also, it turns out there are streets with houses in the US.


I think your comment is a case of rational irrationality.

The theory of rational irrationality holds that people often choose—rationally—to adopt irrational beliefs because the costs of rational beliefs exceed their benefits. In this case, the cost of admitting (including to yourself) that the article's surmise makes a valid point is greater than you are willing to accept. (Likely related to the denial that the article discusses.) So you are being irrational, attempting to impeach the article by drawing ludicrous conclusions from its incidental and irrelevant choice of picture aids.

Simply: you are being absurd.




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