US 'in denial' over poor maths standards
bbc.co.uk
bbc.co.uk
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...
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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.
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...
> 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.
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.
http://media.collegeboard.com/digitalServices/pdf/research/2...
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.
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.
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.
http://media.collegeboard.com/digitalServices/pdf/research/2...
http://washington.cbslocal.com/2014/04/07/study-no-link-betw...
You can downvote me but you still have no evidence for your beliefs.
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.
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...
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.
(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.)
What makes us unusual is how wide the spectrum is, even if the average is bad.
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.
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.
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).
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.
>>> 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.
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.
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 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.
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'm out of ideas. What do we do?
EDIT: added a not. Wow did that change what I meant to say.
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.
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.
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.
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.
Having everyone in the same page with regards to an overall standard seems good in my book.
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.
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.)
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.
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 was trying to say common core was "one program for all".
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.
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.
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...)
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'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.
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.
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.
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.
I'd wager a guess that most developers on HN don't even touch the stuff.
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.
Curiously I think Americas still say they study physics.
(I copy/pasted the Greek versions, so hopefully they're correct. They look correct to my inexperienced eye.)
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/
http://www.pbs.org/wgbh/pages/frontline/education/education-of-michelle-rhee/transcript-35/
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.
It's interesting that you guys chose to keep Physics, did Physic sound too weird? :D
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-...
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'.
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.
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.