I know I'm biased. Geek is as geek does, but $deity almighty am I tired of that line. If simple math isn't valuable to your profession, it might at least be worth a think about how valuable your "profession" might be in the first place.
Some of the huge systemic problems we are facing right now may have something to do with the fact that we have entirely too many professions where it really doesn't matter if one could master simple math.
I've made this point before, but people often conflate the two, and are unable to separate them in their minds.
What this person is saying is "these things do not train a person to perform these specific sets of tasks". That's vocational training, and there's nothing wrong with that. Academic education, on the other hand, is about learning to think, about history, rhetoric, science, and all sorts of things that aren't directly applicable to a particular job, but provide a necessary foundation for critical thinking and enlightenment, so to speak.
What our system really needs is two streams. An academic stream, for those who choose, and a vocational stream, which is what a large proportion of students and seemingly educators like this guy want.
This way, everyone gets what they want. Students truly interested in learning things not directly related to performing a job will have the benefit of a more supportive learning environment, and students who just want to get a job will also attain the required vocational training.
It's really win-win.
As a disclaimer to all of this, I was the type that had fun proving stuff in seventh grade and had already read through Spivak's Calculus by Grade 10.
This makes your earlier claim of never having seen most of the concepts rather dubious.
Just because basic calculus (or other math) isn't used in our everyday life, doesn't mean it is wasteful to learn it. So yeah, I'm tired of that line too.
In 10th grade most kids have done a year of algebra and are doing plane geometry along with simple proofs.
That must be it: the scientific sample of people he described the test contents too did not use proofs in their work. Therefore, introducing mathematical logic in 10th grade is not going to prepare students for the high-tech jobs of the future.
From what I've seen the biggest problems my sibs had with higher math wasn't the higher math, it was the algebra underlying it. They get one year of Algebra in 8th grade and the move on to Geometry assuming they have mastered it, but they havent.
There is a strong resistance from the kids because its either boring, too hard or not explained in a way that is relevant to them to see how it can be applied. This is among the main reasons why in the US the number of SMT college/uni graduates has not increased since 1980, while humanities has more than doubled.
Similarly, electricians need very little math at all. We clearly need electricians. Should we just not educate the students we think are likely to be electricians? Or should we have a real discussion about what topics are most likely to enrich the lives of the most students?
We just yesterday had an article posted about the 1850's Harvard entrance exam. Surely, if they had a time machine, there'd be quite a few antebellum Harvard freshman willing to tell us all how important it is to memorize Thucydides in the original Greek.
For instance, a large number of doctors tested (in a study I can't locate the citation for) fell prey to Base Rate Neglect when doing a mock diagnosis. This seriously affects the amount of money wasted and the amount of illnesses cured in medicine. Along with a wide swath of related problems, it could be cured with an intuitive understanding of basic probability theory.
If you fail to recognize the importance of understanding math in your profession, then yes: http://www.ted.com/talks/peter_donnelly_shows_how_stats_fool....
Whether one uses specific knowledge directly in their profession is irrelevant. The knowledge is required to teach the concepts and skills. There is also more to life than one's profession.
The other day I was building something and realized that I hadn't done a trig problem in at least 10 years. I felt pretty sad when I had to look up how to solve it. I still remembered the general concept, but the details were lost on me. Yet, it was important that I knew how to do it.
I'm trying to go through Khan Academy in my spare time to learn and relearn the math that has slid out of my memory.
At least in this case you know what things to look up; imagine never having learned those things in the first place.
I try to quickly learn about every concept I come across to the point that I understand when and why you would want to use it, but not the point that I understand how to implement it. When I encounter a problem that fits the concept, then I can look it up and learn how to do it fully.
I don't know, I feel it has served me well anyway. I like to jump on problems in all kinds of industries, so it is impossible to study everything ahead of time.
You know what is even funnier? That after learning the logic behind programming I was able to perceive mathematical concepts under a whole different view and had so many fulfilling "oh that!" moments so far!
I agree that everyone should learn math in school, but that's so they can learn how to think and analyze. If the skills have atrophied through disuse I would conclude that they have found other ways to achieve the same goals.
Graphics designers often use a lot of math directly when working out layout's and things. An intuitive understanding and lot's of effort can help compensate but it's a significant loss if they can't do simple math on how tall / wide things are when you scale them.
I apologize if English is not your native tongue.
Then I guess he won't be using his comment history on HN as a reference for his next interview.
"Managers, salespeople, and lawyers with [a] poor understanding of math as basic as adding fractions are very risky. It's not that they can't perform most job functions, it's that they are extremely likely to make costly mistakes. 'When should I add one more person to keep people from charging as much overtime?' Or, the old: 'Should I offer overtime or comp time?' etc. As [for] salespeople and lawyers, effective negotiation require[s] them to be able to say: 'I can't drop the price any more but I can do X' (which costs us less), etc.
"Graphic[...] designers often use a lot of math directly when working out layouts and things. An intuitive understanding and lots of effort can help compensate, but it's a significant loss if they can't do simple math on how tall / wide things are when you scale them."
Is that written poorly enough to take the time to passive-aggressively call someone stupid on the internet?
Maybe someone should start working on a text-to-speech app for HN with built-in meaning detection, then? Without one, onemoreact's posts unfortunately were not read out loud to me, and I had to do double-takes for "vary", "preform", and "incite" (all real words pronounced differently than what was intended). The missing punctuation also made it difficult to parse the text given the absence of verbal pauses or tone changes.
It'd be different if the argument was incoherent, or took a huge amount of effort to understand.
English is my second language, and I sorta know a couple more and could have a nice rant about English orthography and phoneticity or lack thereof and the root causes of this unfortunate situation. English as a second language issues might cause one to confuse "vary" and "very" but will not be the cause of pluralizing with an apostrophe. The lack of quotation marks is also at best a laziness issue, not a dyslexia issue.
I really struggle to see why someone would go to the effort of posting a comment and not bother to correct at least the spellcheck-catchable typo "extreamly."
Pluralizing with an apostrophe or not using quotation marks are even common with people who have English as a first language, and are signs of discomfort or lack of practice with English writing, which could be the result of dyslexia, English as an eighth language, or any other reason. Could even be stupidity, but when the ideas are coherent, to jump to that just seems to be a way to feel superior to someone.
Seemed like an intelligent enough comment to me, even though I would extend it to the reading comprehension that the author of the subject of this thread must lack to fail a 10th grade reading test with 62%, then further extend it to become a belligerent attack on management in general. The school boards in America are still debating evolution every single year. I add, of course, that school boards have nothing to do with teacher's unions, and break them more often than they support them.
I wish you luck in your struggle.
For salespeople, sums, differences, multiplication and division of fractions might not be the best example; calculus might be more appropriate. Some of the best salespeople I've ever worked with could effortlessly modify the deal numbers in their head on the fly during a negotiation. For example, it could entail working out a seemingly big "cash discount" number and offering it on the spot, knowing full well that it won't take so many points off the margin that the pricing team will throw a fit nor impact their commission such that they care. These are fairly simplistic one or two decimal place fractional arithmetic that are only moderately more complex for the layperson than tallying up the tip at a meal, but it puts a lot of pressure on the customers when they are told, "if I have to walk out of this meeting without closing, I won't ever get the authority to offer that discount again".
Take a look around and I think you'll find many, many incredible things that were done and made without the aid of trig and algebra. Specialization is pretty much the foundation of modern economics after all.
> If simple math isn't valuable to your profession, it might at least be worth a think about how valuable your "profession" might be in the first place
I don't think the requirement for maths is a way to judge the value of a profession. I think it's essential for every day life, but not necessarily for work.
There's more to life than knowing how to do math. And the people ruining the world are generally not the ones that suck at math.
Also while I can think of several jobs you might be able to conduct without knowing maths, performance in most of them could nevertheless improved a lot by knowing maths. I imagine running your own business without knowing maths is also a recipe for disaster, so by deciding against maths, you automatically settle for loan slavery for your life.
I regularly end up doing simple math for people who cannot, including those in management. And that's not even counting the programs I have written.
Apparently, a lot of people have forgotten how to deal with simple fractions, to say nothing of simple 2D geometry. Most of you probably have no idea how many windows have ended up screwed up or back ordered because of this...
The test-taker seems to be making excuses.
The point probably is your and other people's definition of what "simple math" is and should be...
Close to none of the history, RE, French, geography, music, phys ed, or even science (heck, nearly every subject) I took in high school has proven directly necessary for my profession. But the standardized tests aren't for adults, they're for students. (Should we expect to pass their agility/phys-ed tests too? :-))
Being able to learn these things, and developing the skills necessary to learn them, is a worthwhile experience and hopefully provides a lot of the inspiration, brain-shaping, and knowledge exposure necessary to get by as an educated adult, even if you can't pass the tests to some arbitrary standard.
I barely remember any of the French I learnt, but I can't help but feel the exposure has given me a better insight into, and a better ear for, my own language. It's a similar story for most of those other subjects.
Students are correct and so is this board member, math education as it stands today really is worthless. It is of no value. It has no practical value and it has no theoretical value. And if you think otherwise it is likely because you managed to escape from the system, possibly with a four-year degree in computer science or other relevant field, with little more than a glancing introduction to actual mathematics, which are arguably one of the most valuable things mankind has ever produced.
There's no need for the cognitive dissonance necessary to insist that math as learned in school is incredibly value even as you, if you search your heart, know better. All you've got in its favor is that you've been told its valuable, so by golly it must be. It's not. It's taught terribly and all the value has been sucked out of it.
If you did not take multiple classes that consisted almost entirely of writing many proofs per week, you never took mathematics. If all you did was problems 6-32 evens due next Tuesday, that's not math.
Moreover it's necessary to teach kids the basics before you teach them advanced concepts. Despite what the article might have you think, we do teach musical notation first. Kids learn that as they are first learning to play. Composition is reserved for the university.
Also, the inefficiency of math education in schools does not mean that what they teach is worthless. Certainly they could do better. And maybe making teenagers do hundreds of proofs would be better. But at the end of they day, the student who took calculus in high school is better prepared for college (and a scientific career) than a student who did not.
Assuming your high school was like mine, when you learned algebra, trig, and calculus, you were probably taught a few of the whats, some of the hows, but almost none of the whys. It's only in upper-level undergrad and graduate courses that the beauty really starts to be taught in earnest.
You're absolutely right to say that putting kids through years of proofs would probably make them hate math even more. Again, that's largely due to the way proofs are taught, especially at the secondary school level. They're all just a bunch of rules listed one after another, "doing a proof" is basically like explaining all the rules of chess to someone who's never played before, and then asking them to put the board in a particular state, thirty-two moves into a game. It ends up as a bunch of trial-and-error guessing... it's frustrating and it's boring. Sure, there are a few savants or folks whose brains are wired in such a way that it's either easy or interesting, but it's just painful for most folks, because there's no intrigue.
It's not until three or four years into college that most people are exposed to proofs as an intellectually stimulating game, where intuition plays an even bigger role than "looking at a list of rules and deciding which one fits".
But we don't get that in high school. We're not taught how to intuit something and then map the rules to our intuition. In fact, we're usually taught that this is wrong!
The fact is that we can't convince someone to find programming (or math) beautiful. So we teach them enough that they can hopefully 1) pass the tests, and 2) absorb enough to be useful. We do that through repetition and exercises. This is why beginning CS classes are often so tedious. They are aimed at a fairly general audience. In contrast, later classes are aimed at students who are specifically interested in CS, so the teaching methods are different, and better for those students.
If we were talking about music, would you let me get away with saying "The average student doesn't like music, in any form whatsoever"? Music is something human beings just like. We're wired to like it. Certainly there are forms of music we prefer, but I think you'd have a hard time finding someone who didn't like any music.
Math, numbers especially, can resonate in the soul in the same way that music does. It's more abstract and much less visceral, but just as beautiful, once you've really learned how to comprehend it.
I think your argument about math classes being tedious is orthogonal to whether or not math can be beautiful for everyone. Entry level music classes can be tedious, too. No one repeatedly hammering out "Frère Jacques" on the piano would say that it was beautiful, but they could hear someone playing some Chopin and easily acknowledge the beauty. Again, I maintain that this is due in large part to music being much more visceral -- you don't have to understand it to appreciate it, while in math you often do.
Early in high school (late 1980's mind you), I decided to take up percussion to play in our award-winning marching band. I started out on cymbals, but that was too simple. Then, I worked on the rudiments of percussion/snare drum. I had to work hard on the "math" of the musical notation, but I soon realized that I had a feel, an "ear" for complex percussion rhythms. And it jived with my already attuned ability in singing. There was something natural that "just clicked."
I see this same pattern in African spiritual music performed by people with no formal education. There's a natural mathematically knowledge they possess without any formal math education.
To me, music is just a higher abstraction of math. One that people with no math education can appreciate without even knowing why.
It's only when educated in math, that the "resonation of the soul" takes place. And I'll superficially agree with the reasons of the other commenters about why the education is lacking.
My point is that we don't have to teach them to feel anything about math. Some people will grok it at a deeper level than others and come to that realization on their own. But I think the overall analogy to music is pretty good. Mozart grokked music theory better than anyone alive today, but that doesn't mean I can't appreciate his genius (given no formal training). And I couldn't integrate an equation today (15 years out of college), but that doesn't mean I can't appreciate math in my life.
This is kind of a ridiculous comparison. As you said, "Music is something human beings just like. We're wired to like it." On the other hand, we are not wired to like math. We don't go to math concerts. We don't listen to math when we drive. We don't typically do math in the shower.
And sure, some people feel that math "can resonate in the soul", but most do not. We certainly don't teach people to feel that way about music. On what basis do you claim we can teach them to feel that way about math?
To refute this, we either have to come up with a way of measuring whether streaming students based on their scores is a benefit, or we have to come clean and say it's arbitrary.
Saying that high school doesn't teach you anything vocational but you learn how to learn is interesting, but to answer the OP directly we need some evidence showing that students are indeed learning to learn. Otherwise, it's just faith.
We should be especially wary of survivor bias hre. Most folks here are educated and pleased with their career arc. It's easy to assume from n=1 that our education is the reason. But many who took the same classes aren't doing so well. Maybe our education isn't the reason for our success.
One criticism of IQ tests is that they measure the ability to pass IQ tests. Do we have the data to refute the accusation that standardized tests measure only the ability to pass standardized tests?
Yes, we should confirm our biases with studies, but at an even more basic level, we don't even know what we're arguing about here.
"How useful is this in the professional world" is a pretty crappy metric for deciding what to teach, because the common set of useful topics is pretty small. We could easily stop public education at junior high or earlier if that's the goal. I've never, not once, needed anything from history class, or biology class, or social studies, or literature class in my professional life. Most people have probably never needed algebra, geometry, or trigonometry. But I'm pretty certain I would be worse off if school stopped at age 10, or if I just repeated the same stuff for 8 years after that.
This is a false dichotomy. You could also come up with a good reason/argument/explanation of why the test would be effective, which no sees a refuting criticism of.
It's not just evidential measurements or arbitrariness. Ideas matter too!
(And in fact you need ideas to interpret measurements or evidence. Is your attempt to measure itself correct? You could try to measure that, too, but you'll immediately face the same problem again. At some point you'll have to do something other than measure.)
With particular relevance to this article, "I am successful and well-credentialed, ergo, if a test suggests that I am not educated or intelligent, that test must be faulty" is not by itself very persuasive to me.
If he's capable of defending that degree then he theoretically should have a grasp on the kind of mathematics are being thrown in Grade 10. If the grade 10 mathematics are some odd-ball thing that has no real relevance (and thus the last time he saw it was grade 10) it points at a bigger issue.
If my memory serves me, grade 10 was algebra almost exclusively. It wasn't until my grade 11/12 courses that other topics like limits and matrices came into play (and those are still simple by my terms).
What I'm trying to say is, although intelligence and success are separate entities the test should be somewhat correlated with his university education. If what high schools are doing is NOT preparing students for real world or post secondary life then what are they doing?
I don't remember the definition of "congruent". I graduated with honors in Computer Science, and took many math classes along the way and did very well, and the topic of "congruency" never came up beyond high school mathematics.
There's definitely something weird going on here. I imagine that it will be tempting for people on Hacker News to argue that they know the definition of "congruent" and it's not a difficult question and I should turn in my degree, but whatever.
Also, when we did the "congruent triangles" stuff in school, it was actually the most "graphical" way of conducting mathematical proofs. It was a very fun way to practice doing proofs. I don't even remember how much we continued to prove stuff in other parts of math. And again I think knowing about conducting proofs is useful/essential for CS.
Could it be that you never had the congruent stuff at school? Our teachers mentioned that there are alternative ways to do geometrical proofs (I think with mirroring and projections?), so your teacher might have chosen another route. Because the congruency stuff is really easy to remember imho, it seems likely you never actually heard about it.
Summary of "the congruency stuff" off the top of my head: two triangles are congruent if the have either three equal edges, or two equal edges with an equal angle between them, or one equal edge and two equal angles. (equal meaning same length for edges). I think that's it :-/ (it's late...).
If we rely on the average state of mind of a population to guide education, we will quickly end up teaching nothing. We should instead strive to teach as much as possible with the understanding that some information will be forgotten. We don't want our children to be as good as us. We want them to be better than us.
In order to perform well on a math test you don't always have to really understand the fundamental principles behind what you're doing. Sometimes you can get away with wrote memorization. e.g. You can come up with equations for a lot of things yourself if you understand Gaussian distributions but, if you're being prepped for an exam by teachers who know roughly what's on it, they might just give you equations to memorize for the things that are likely to be asked. You may perform nearly as well as someone with deep understanding of the material, but you are unlikely to remember those equations long after you've taken the test!
It is quite likely that the person who took and failed this test was the sort of math student who was able to get by memorizing what he was told to without really understanding things. If he had written the same test in high-school he likely would have done much better because he would have been prepared for it with memorized methods and equations that he never understood and has long since forgotten.
On teaching methods:
When teachers teach students to pass tests, short-cuts like wrote memorization tend to happen. The useful knowledge learned from this kind of teaching is minimal. Unfortunately, many teachers are unable to teach the deep meaning behind mathematics because they were taught by wrote memorization themselves. When they were assigned to teach math class they probably had to look everything up themselves since, like our test-taker, they never understood the basis behind it and have forgotten most of what they memorized.
It seems that we must overcome the problem of educating teachers before they can overcome the problem of educating students.
I think the more damaging thing about this article was his (and the author's) insistence that the math is not required for the majority of professions, and therefore, should not be required in high school. Basic education is liberal arts education, and, setting aside barista jokes, liberal arts education is about understanding a wide breadth of subjects. It is not, nor has it ever been, vocational training. Moreover, this type of math is absolutely imperative to some of our most needed (and oldest) professions, like engineering and construction, and some of the newer ones, like software engineering.
That aside, I agree with your point, and what you highlight is a problem with standardized test per se. People will always optimize for the variables by which they are measured. The trick is to align those incentives with the desired outcome of education.
As a postscript, the word you're looking for is "rote," not "wrote"--the former means learning by repetition, while the latter is the past tense of write. Since we're talking about education, this paragraph seemed appropriate.
A) Our current evaluation methods don't tell us whether a student is simply memorizing steps or learning the subject matter.
B) When your primary evaluation critera is to pass a standardized test, the system will optimize to achieve that goal. Since we know that standardized tests don't really evaluate understanding, we have a vicious cycle on our hands.
I'm pretty sure I was guilty of that sort of rote learning more than once, and it seems to be the first thing that disappears once exams are over.
Until 8th grade or so (pre-algebra), students learn math that (I think) everyone should know. After that, it can be hard to give a good answer. Why does someone who is not interested in studying math after high school need to know the quadratic formula? Why does someone studying for the GMAT need to know anything at all about geometry? Math curricula simply cover the wrong things (and as a result math tests test the wrong things).
Take a look at these two sample 10th grade math tests (the level taken by the guy in the article): http://www.doe.mass.edu/mcas/2011/release/g10math.pdf http://ritter.tea.state.tx.us/student.assessment/resources/o...
There is TONS of focus on geometry and coordinate geometry. There is NO focus on math concepts that are much more important (in my view), like basic finance, basic statistics, basic probability. These are things people need to know in order to be informed citizens, understand policy, process things in the news, rent/buy a home, take on college loans, etc.
None of this means that tests are bad of course. I think tests are, generally, a good way to understand what people know (in math).
Finally, the guy says: "The math section had 60 questions. I knew the answers to none of them, but managed to guess ten out of the 60 correctly."
If he really knew the answers to NONE of them, I have a hard time taking him seriously. I love how he gives himself credit for managing to guess 10 correctly. These tests are mostly multiple choice!
But definitely for personal finance I think quadratic stuff might pop up now and then. Exponential stuff definitely pops up...
Well he obviously is really bad in maths, so he might not have realized he was due to have some random hits :-)
Here's a novel idea: publicly commented and curated testing system. Wikipedia-like. People write questions, other people can take the test, leave comments, suggestions, etc and those can be factored in to build a smarter and better test.
My personal axe to grind is that number theory and basic finance, rather than calculus, should be taught to teenagers.
And in my own US public schooling, I found the teachers completely unable to provide any intuition whatsoever behind calculus. It wasn't until two decades later, when I was studying computational finance for fun, that I actually really understood integration as something other than symbol manipulation. Seriously, this whole "teach to the test" mentality may get kids to answer correctly by rote over the short term, but doesn't help them to learn much in the long run -- at least if they're intuitive learners.
I agree with you fully, kids need to be taught based on what they want to do. I've wanted to be an entrepreneur for a while now and the only class that interests me in school is journalism (I enjoy writing). The math class is a joke, English is boring, and the rest of the classes are boring.
Virgina releases their tests every year (most states don't; it's expensive), and since this is the WaPo, it could be a VA test. Here's a link to their 2010 exam: http://www.doe.virginia.gov/testing/sol/released_tests/2010/...
edit: It's unlikely he's from VA, though, because VA doesn't do a standardized 10th grade math test. They give End-of-Course tests instead; statewide finals, essentially.
How old would most 8th Grade students be? And how long would they have to complete the test?
Multiple choice questions are not widely used within the exam system in the UK. There are 'Skills for Life' qualifications aimed at adults who missed out at school in Literacy and Numeracy that are MCQ based. The link below will take you to some practice tests (both pdf paper based and tests designed to be completed on screen). What do you think of those?
I don't teach in VA, but according to the implementer's guide, it's un-timed. From my experience, I'd say probably 2 or 3 hours for the 50 math questions, depending on the student's skill.
I haven't worked enough (at all) in adult ed to comment in depth on these, but they look like they'd cover a lot of the important stuff for a basic job and your general day-to-day numeracy and literacy.
But that's the thing, what I got out of my education was HOW TO LEARN a subject.
I'm confident that you could pick nearly any subject that I know little about and, with a proper amount of time, I could become somewhat proficient at it. The level of my ability will, of course, depend upon the subject and various factors to do with me as a person.
Standardized tests are a tricky thing, they are needed to determine a student's progress but at the same time they assume that all students are the same. To me that's the problem with education systems in the US, they assume that they can teach all kids the same thing the same way with the same results.
As a father of two children with completely different personalities, attitudes and interests, I can tell you treating kids as emotionless puppets to force-feed information to is a path to failure.
Wouldn't it be fair to say that is basic human nature, not a result of your schooling? I remember already successfully jumping in and picking up new subjects on my own before I even entered high school, and I imagine much of the HN crowd were too.
Though, I admit I may come with some bias. I grew up on a farm where I was out there at a young age trying to solve real problems alongside my father and grandfather. They valued my insight into the problems as much as their own. If learning how to learn is a skill that is taught, that is where I learned it.
But, as a human, you do have the ability to learn but a proper education does go a long way in helping you discover how to learn a subject. Instead of goofing around on a subject for ten years when you finally figure it out, a proper education lets you learn the subject much quicker and more efficiently.
After all, as a basic example, it would be rather difficult to learn physics if you can't read the papers written by the smart people who came before you.
This is hindsight bias. Knowing math helps cure you of the affliction of hindsight bias. The fact is, you don't know what career a person will end up choosing, and math is important (as is art, music, philosophy, chemistry, physics) in a subset of them. Therefore, if you want ANYONE to be able to do the math for you later on, you need to expose everyone to it to find the future mathematicians.
Not everyone grows up to be a writer, but we all read Shakespeare. Is that a waste of time? Only in hindsight.
And maybe, just maybe, this guy isn't all that smart and the test is valid. But of course, the article doesn't address that, as it's more interesting to write about anecdotal evidence and drama for the innumerate audience.
Oh, well, that's the problem. He is on a public school school board. School boards have been known to have adverse selection for dullness for more than a century. Here is Mark Twain's harsh comment on that: "In the first place God made idiots. This was for practice. Then He made School Boards." -- Mark Twain, Following the Equator (1903) 2:295
Other than that, the author of the submitted article simply describes the school board member as a "success" who makes money. The genius of the American political and economic system is that people who desire money more than they desire deep understanding can often achieve that goal. America is a wealthy country, and by world standards a lot of Americans are more successful than what you would expect if you look at the success of people in developing countries who know more and who work harder.
The submitted article is by a guest author, but it is part of a regular column series in the Washington Post that takes the consistent line that criticisms of the United States school system for inefficiency and waste of resources are misplaced. As an American who has lived overseas, spending the first part of the 1980s in a developing country, I can't agree with that party line. United States schools could do a LOT better, particularly in teaching mathematics in elementary school,
and while it may be that many current United States standardized tests in core subjects have poor validity (being designed by state governments more for political than for educational purposes), the answer is NOT to throw away reality checks on how the school system is doing. Rather, the answer is to align reality checks on United States schools more closely with testing programs that identify the most successful countries,
and to look to the practices of the most successful countries for policy guidance on how to reform United States schools.
It is still possible for United States school to improve a lot simply by bringing in better management practices,
and efforts to improve United States education shouldn't be sidetracked by a single anecdote about the occasional well-off school board member who has limited academic ability.
I've done more analysis on a similar test called PISA, but I think it's worth bringing up in the context of this debate. In standardized testing there are often significant underlying factors that have nothing to do with the schools themselves. From the executive summary of PISA: "[In the United States], after accounting for socio-economic
background, the performance difference between students from single-parent families and those from other types of
families stands at 23 score points.... Parents’ engagement with their children’s reading life has a positive impact on their children’s reading performance." Consider that the divorce rate in the US is one of the highest in the world, 5 times that of China. This problem along with any others is one that needs to be considered in the context of education.
Also, PISA was not done on China, but rather on two specific cities: Shanghai and Hong Kong (similarly, TIMSS was done in Hong Kong). Along with Beijing, these are the most advantaged areas in China in terms of both money and education. The US administers PISA to a wide range of schools across the country. I imagine we would see much different results if PISA only tested Boston and some other advantaged city. The PISA study itself even notes that scores were much higher in urban schools. Other countries are either testing exclusively urban schools or urban schools at a higher rate than the US.
There are serious, serious problems with education in the US. But it's important to look at these studies with a critical eye and avoid the temptation to go off on a rant on how the US is bad at math. Data doesn't lie, but analysis is often wrong and/or exaggerated. In sum, problems with education in the US are deeply rooted in racial, social, and geographic issues. Better management practices and policy reform, while good, doesn't change the fact that the US isn't Singapore.
Canada was consistently ranked approximately fourth, a fact that seems to have been largely ignored.
I agree with some points in your reply. I don't think China as a whole is well represented by the schools in its most developed urban areas. The results from Shanghai in the most recently announced test to include Shanghai surely don't reflect what students from rural areas in China would do on the same test. But even agreeing with that point, I wonder if you've had a chance to take a look at what Ma's book
says about differing classroom practices and differing lesson content between the United States and China. China is very, very, very much poorer than the United States because of the lousy policies it had in the 1950s and 1960s. But its educational policies since the 1970s have been on an increasingly sound basis, and seem to be producing admirable results in economic growth with remarkably low school budgets. But please note that I never appeal to China as a country with country-wide results that are uniformly better than those of the United States. China is especially doing well on a resources-adjusted basis, while Singapore, Taiwan, and some other countries are just plain doing well nationwide, period. (I am most familiar with Taiwan, from much time living there.)
I also agree with the idea that it's important to look at education studies "with a critical eye" and it was with that in mind that I referred fellow participants on HN on several earlier occasions to the studies showing that United States schools are underserving the most able learners,
missing opportunities to reach the top end of mathematics achievement reached by other countries. "Data doesn't lie, but analysis is often wrong and/or exaggerated," I agree, and what I find is that some forms of analysis are not even attempted by many commentators on education policy. I think writings that are good examples of good analysis
are food for thought for those of us participating on Hacker News who seek ways to improve education wherever we live.
"The methodology of the blog post [comparing aggregate TIMSS scores] you point to repeatedly is laughable."
Incidentally, the data tokenadult links to suggests that differences in TIMSS scores are due to differences in ethnicity of the student body, not management practices. He deliberately ignores this data but the rest of us should not.
you could learn something new that could help you better understand the other countries in the world and what the United States might learn from them.
The only data I've cited is TIMSS data which is published and presumably peer reviewed. It's true that Tino Sanandaji PhD (note: he graduated, not that it matters) pointed this data in a blog post. So what? It's the same data you cite.
The data says the groups of people with top math performance worldwide (circa 2007) are:
1) Taiwan 598
2) South Korea 597
3) Singapore 593
4) Asian Americans 582
5) Hong Kong 572
I'm not asking if you speak Chinese or whether "hundreds upon hundreds" of your Chinese buddies agree with you. That is irrelevant to the topic at hand.
I'm asking you for a logical argument, based on data (in particular the data that you cited), that concludes American schools underperform. Any such argument needs to control for the quality of students, since student test scores are obviously a function of both the school and the students.
If you believe the dead tree books you hint have such an argument, please tell me which book and which pages.
Or feel free to continue making logical fallacies. I'm not really posting for the purpose of arguing with you, I don't expect to learn anything from that. I'm just trying to make sure others reading your posts are not misled by vague assertions that hundreds of unnamed authorities might agree with Chinese speakers like you.
P.S. To make myself appear smart, while providing absolutely no facts, I'll cite dead trees also:
Some more irrelevant facts: I have a PhD, I lived in Asia, I often have sex with Asian women, and I'm a good cook.
But even Asian Americans reliably outperform other ethnicities in American schools, placing in the top 5 in math performance worldwide despite American schools, it does not necessarily follow that American schools are performing adequately.
For instance, Asian families can obviously be supplementing education through private tutors, additional study and demands at home, &c.
It also doesn't follow that just because this system "works" for Asian Americans that it's a reasonable system to apply nationwide. Perhaps Asian families manage this because they're economically advantaged. Perhaps Asian families make unreasonable sacrifices in other areas of their life (by a measure of "reasonableness" along the lines of "benefit to child ends up being worth the cost to the family").
Also worth mentioning, but perhaps not worth dwelling on, that TIMSS includes private schools. How much more likely are Asian Americans to attend private schools than (say) Latino Americans?
Finally, I think this particular debate may be besides the point. We have the ethnic and socioeconomic mix that we have. We do not have the option of being South Korea. So the question is, does the education system we have serve the best interests of mix of students we have today? That's the question this WaPo story is addressing.
I have no doubt that Asian families (in the US, Singapore, Japan, etc) send their kids to Kumon and are terrorized by tiger mothers. Net result: in all these nations, the children of tiger mothers score about 570-600 on TIMSS. So US schools systems educate Asian students pretty much the same as Asian schools.
There is not enough data to compare the results for non-Asian students, since we lack data on (Asian School, Black/Hispanic/White student).
Similarly, people of European descent tend to get scores of about 470-530, with Finland being an outlier at 546. Among this group, Americans of European descent are #6 (at 524). Again, data on (European school, Asian/Black/Hispanic student) student is lacking.
So the data suggests US schools do not significantly underperform either Asian or European schools, at least for the categories of student we have data on.
I.e., if US schools are inadequate, then so are the schools of most of the world.
Still, somewhat ironically, you are both right. Underperforming ethnic groups in the US bring the average down, and the US educational Prime Directive of making sure the high-performing groups don't get ahead brings it down even farther. While Asian schools work hard to push Asian kids ahead, US schools refuse to do so, because that would just widen "the achievement gap" they're trying so hard to close. So US schools, first in spending, are last in effectiveness for ethnic Asian kids. That "doing the least with most" is school underperformance. The only reason Asian-American kids do as well as they do is that, like their cousins in Asia, they get a lot of their education outside of school.
 2007 TIMSS results:
Asian scores are on p. 3, Asian-American scores on p. 15
I do agree with you that US schools are not cost effective - I've long been a proponent of cost cutting. In my view, the biggest problem we have with US schools is cost, not quality, and we should focus our efforts on making school cheaper.
You field logical fallacies of your own on a regular basis. Indeed, your gratuitous rudeness and sexism borders on ad hominem and is inappropriate here.
From this data, how do you conclude that American schools underperform?
If American schools with heterogenous student bodies* are preparing only one ethnic group to be competitive in international math comparisons, then they are certainly coming up short in other areas. The 'melting pot' is not a new concept in American education and while disparities in language ability, cultural mores, and economic condition present an additional challenge for American educators, addressing these disparities has long been a part of their mission and resources are allocated appropriate.
* It's reasonable to say that American schools serve a more ethnically and culturally diverse student body than the other examples cited here, notwithstanding the relative diversity of Singapore and Hong Kong by regional standards.
Now I'm jealous!
It seems that tokenadult believes there's a mimicable or replicable non-genetic factor, and you believe there's a genetic or otherwise 'unique' factor that indicates a gap that can't be closed. It's probably some combination of the two, but it'd be nice if we could talk about that instead of this other stuff.
I made no argument as to whether that factor is genetics, tiger mothers, Kumon, etc.
If you don't give a wheelchair to someone who can't walk, of course they can't get around...
Since Singaporean schools have a student body that is roughly 100% Asian, we have no data on whether or not they perform that trick.
A different straw argument - we don't send dogs to preschool, we send them to obedience school, because we recognize certain things need to be different to achieve the same goal - not biting or urinating on everything.
edit: I'm realizing this might just be about effort/actions vs. results. I'm decidedly on the side that results are what we need to compare.
The US has some 'great' public schools, and some 'terrible' ones. But, the difference has a lot more to do with the students than people are comfortable admitting. The private / public gap in education is also a lot less than you might expect.
Argument from authority (also known as appeal to authority or argumentum ad verecundiam) is a special type of inductive argument which often takes the form of a statistical syllogism.
Although certain classes of argument from authority do on occasion constitute strong inductive arguments, arguments from authority are commonly used in a fallacious manner.
Since I'm not logically proving anything, I'll refer to an authority, Strunk and White, who say:
"Avoid foreign languages: the writer will occasionally find it convenient or necessary to borrow from other languages. Some writers, however, from sheer exuberance or desire to show off, sprinkle their work liberally with foreign expressions, with no regard for the reader's comfort. It is a bad habit. Write in English"
The person was described in somewhat more detail than that:
He continued, “It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate. “I help oversee an organization with 22,000 employees and a $3 billion operations and capital budget, and am able to make sense of complex data related to those responsibilities.
I'm in favor of standardized testing and am as annoyed as you by the shallowness of this article, but you're undermining your own argument here.
Now, I completely agree that a single anecdote isn't cause for policy overhaul. But if a guy who has been successful in college can't pass a test designed to weed out students who shouldn't go to college, that's a clue that maybe something, somewhere isn't working right.
That does not bode well for him having a lick of intelligence
Did you read the article? Sounded like a pretty smart guy. I've served in local office, there are plenty of idiots on school boards but there are smart people too.
Even more entertaining is all of the discussions of those who have 'real' degrees and who are 'not like this man'. They believe he must be a ignorant bureaucrat who lucked his way to the top. They believe it's inconceivable that schools are to blame, even though many are sold a bill of goods from schools that degrees set the social classes apart from others and they really are more human than others. While in fact, schools have become one of the most clever profit centers ever created. While there, you are indoctrinated to believe only those going through here are human. So, when you go out to the world, only hire those from here (plug for more school business!)
Remember, some of the most financial successful people in the US, in the world, do not/did not have degrees > Steve Jobs, Bill Gates, Mark Zuck, the list goes on. Although, my personal believe is financial success is not the true success (even stated by Gates recently)
This belief that you must be part of academia to be innovative and this near prejudice of non-academia citizens is appalling.
Learn what this man is saying rather that trying to prove him wrong and self-justifying. Yes, we can count, read, apply studied principles learned from books and media. His point is, are we the principle authors? Are we the ones innovating, improving society by our ideas, helping our fellow man/woman by our work? If not, perhaps something IS missing from our schools. Perhaps that is part of the problem. Let's fix it and make our world a better place.
That one man rose to power in government and obtained degrees, despite poor math and reading skills, doesn't surprise me much less outrage me.
Why can I understand the math difficulties? Well, I too forget stuff that I don't use very often. I'd have to go look up the all the trig identities if I needed them. But, I wouldn't take this test blind without any refresher.
The advantage "kids" have when they take these standardized tests is that it's very close to fresh in their minds, or at least relatively fresh. That has to count for something.
These days kids are taught from kindergarten on how to take standardized tests. My sixth grader can look at a test question and narrow it down to two answers before even reading the question. And for math, he doesn't solve the problem, he plugs the two answers in to see which is right.
I teach math at a community college and it is common to have students test into math classes that they don't have the basic prerequisites for - just because they test well.
This will change with the continuing revolution in data and the data driven decision making it makes possible. Eventually corporations that reward politics and personality will become weaker and those that reward data driven decision making will become stronger (except in cases where the corporation can depend on government handouts, e.g. Wall Street).
No matter what kind of business you run, the seller knows almost all the time more about the product/service/etc than the buyer. And as long as you don't have perfectly comparable products markets are far from ideal. Therefore the individual relationships between people matter because you can never fully quantify human relationships.
This statement is suggestive of where the problem lies. A doctoral thesis is supposed to be an original piece of work. The idea of assigning credit hours towards it is meaningless. We don't honour creative people for the number of hours they put in but for the works they leave behind.
Modern education systems in North America focus on the wrong things.
And more specifically what it is supposed to tell us with regards to children's education? So, let's assume he is a highly trained expert in 1 or 2 fields and then the doctorate is like putting a needle-like focus on one (comparatively) tiny area of those fields and going in deep all the way. This, again, has nothing to do with children's education... it's like complaining that a brain surgeon cannot even pass basic school-level French grammar.
All this is flying too close to the "why do kids have to learn all this crap like math, art, music, history?? all they wanna do is become rich managers and bankers or CEOs anyway!" argument.
I blame the US for this hideous dilution of the title, and qualification of Doctor. While being a young curmudgeon I will also condemn the practice of M.D.s being called Doctor.
I saw a 8th grade textbook that explained how compute square roots by hand - but the algorithm was wrong. It only worked for examples in the book.
Suppose that this man is correct - that the material being taught/tested is useless and unnecessary for a successful career. In that case, shouldn't we stop teaching it, remove the material from the curriculum, allow students to graduate a year or two earlier and fire a bunch of useless teachers?
If not, why not?
It doesn't follow from the fact that we're imparting only two useful years worth of knowledge in (say) 4 years of high school that students are only capable of benefiting from 2 years of high school.
Perhaps most importantly, we live in a democracy. This means that people vote for the direction of our government. When doing so, many different issues are considered. Of these, most are probably outside the area of ones expertise. How can we expect good decisions made by people ignorant of the subjects in question? So we teach basic science, basic math, history, english, and the arts to everyone. This way our population has at least a small amount of knowledge to fall back on when needed.
On a less concrete topic, there is much speculation about the effects of learning on brain structure. Despite not remembering much mathematics, for instance, how do we know that learning mathematical concepts did not leave a lasting effect on the brain? What about the lessons we learn from history class? We might not directly associate with them when making everyday decisions, but is it not possible that learning those lessons contributed to our current thought processes?
In summary, it is very difficult to quantify exactly what you retain from education and even harder to identify specific ways in which it helps you or helped to shape your mind. Thus, it is best to err on the side of caution and teach as much as we can.
Modern schools explicitly aren't vocational, they don't even claim to strive to teach skills that can be directly applied to jobs, the point is that it is useful to understand how to learn and think about things well. They also provide exposure and opportunity; there are plenty of jobs that do require these skills (or more accurately, require skills for which learning these skills is a prerequisite), and if we didn't teach them to everyone then the children of laborers would end up as laborers even when they are capable and interested in being rocket scientists.
But I'm asking people who agree with the premise whether they also agree with the logical conclusion - if the tested skills are unnecessary for most/all, why not stop teaching them, fire teachers and reduce spending on education commensurately?
I understood the claim to be "the skills being measure are not necessary" to mean "you don't need the skills to be successful" which I do agree with. That is a completely different claim than the idea that that the skills are useless, the skills are only useful to some (significant) subset of the population, and I argue that we should teach them even to people that they will be useless for to force feed them an opportunity that they might otherwise have ignored as a possibility.
If you don't use that knowledge for your profession, then yes you will forget it. However, if you don't use it for your profession, it doesn't mean learning it was useless. I would be more worried if he still sucked at math after preparing for the test for a semester or two.
I have a degree in Chemistry and yes, that knowledge is slowly slipping out of my mind. However, the skills I learned while learning chemistry - logical thinking, ability to memorize and recall, building a mental model of abstract concepts - these stay with me.
His role today is one of management, and he has no need for anything beyond basic maths. However, there would have been a time when mastery of things technical meant a promotion, or an opportunity to supervise younger graduates. I know of many brilliant managers who no longer have their technical chops.
For all we may know, his degrees may be in Biology and Marine Science. It means that his profession would be one that doesn't have to worry about differential equations, or chemical reactions, or American History.
However, there is an interesting point whether too much irrelevant material is taught at school. I hear this in universities too, that professors keep adding material to the curriculum. I don't have an answer for that. I think schools focus too much on abstract thinking, and too little on effectual thinking.
You shouldn't be able to just guess the answers one-out-of-four. When I was in school (not in US) there never was such a thing. You simply solve the problem and write an answer, which usually is a simple number.
I don't think any of my classmates or teachers ever figured that out. They just thought I was smart for finishing early with 100% correct. Which, in a way, I guess I was, but not the way they thought.
I'm sure if the man actually prepared for the test, he would have done much better. Hell, I've taken standardized tests, gotten very good scores, but if I had to take them RIGHT NOW without any preparation, I'd probably fail them.
It doesn't mean that you're dumb, it just means that you haven't flexed that particular muscle for long enough now that you may simply have to re-learn those things or you will have to invent them on the spot from first principles.
The brain is great at throwing out unused (unreferenced) memories.
Given proper preparation (like the ones students go through), say a couple of years of relevant re-education I'm sure the author could pass the test.
Most people forget 90% of things they've learnt in school after 5-10 years after finishing.
If you take a look at the things you were learning in college, you'd be amazed how much of even interesting and seemingly useful things somewhat associated with what you currently do, you can't even remember learning.
Successful man fails 10th grade standardized test, concludes that success is not correlated with being able to do math.
Aside from the obvious logical/statistical falacy of making an overreaching conclusion from a sample size of one, and various other illogical claims("if this guy doesn't need math, why does anyone??") this article assumes that the purpose of education is developing vocational skills.
Why should that be? Kids should learn to appreciate the world, get exposure to different things. There's no reason to make them hunker down at age 5 and start preparing for their future careers. If they don't like math, that's fine. Likewise for history, science, whatever. But it's a shame for anyone to miss out on the beauty inherent in all of these subjects.
Situation: I have three children, current ages 11, 10 and 5, parents are University educated and engaged in the children's learning.
The progression of learning for each child has been:
Age 3: Starting to learn to read at home. Enjoying being read to, and discovering that letters and words have meaning. Starting to understand counting, and a one to one relationship between a number and a quantity of objects. Learning that numbers of objects can be added and subtracted. Really excited to learn, and will try new things if they give a chance to learn.
Age 5: Starting formal schooling, with pre-school/prep. Getting readers to take home, very excited at the time that is being spent being presented with new words. Fully understanding numbers and how to count things. fascinated by the idea of infinity and zero. Learning the concept of fractions (of apple). Loves learning.
Age 5.5; half a year into formal schooling.... I'm board at school...
Parents still introducing new ideas at home and encouraging reading of material to extend ability... Trying to introduce new maths concepts to encourage interest.
Age 6: Bringing home standard worksheets for maths and literacy, some conflict to get homework completed... Not really interested in school. Loves reading, not interested in maths.
Age 8: Don't want to go to school, Don't want to do homework... What is going on? Just wants to spend time reading. Loves an argument about the physical world.
Age 10: Discipline problems at school, no interest. Loves reading, loves computer games.. Still loves a good argument...
Age 11: OK We have a problem, High school in one year... he's missing a bunch of the basics What happened? Looks like lots of remedial work over the Christmas Holidays.
How is it that kids who are engaged and excited to be learning at five years old can so quickly have this interest buried when confronted by formal learning? How am I to prevent this from happening to my youngest (currently 5yrs) as well? She is very bright, some would say "gifted", I don't want here to start to hate learning as well. There has to be a better way!
Digging deeper and talking to the older kids it quickly becomes obvious that they do enjoy learning, they just can't be stuffed doing the boring repetitive stuff once they have grasped the concept being covered. We go over maths concepts at home... They get it, they are interested in it, they just don't want to do it at school.
Looking through the kids school books it becomes obvious that what they have been doing all year is not "learning", but more "drilling". Now I'm not an education expert, but I do understand the value of repetitive drill when practising to become an expert at a particular procedure or action, it has great value if you are a dancer, gymnast or swimmer... I'm just not sure at how good it is at instilling enthusiasm for learning and an ability to take what has been learnt and apply it to new situations.
My understanding is that the current methods of education came about shortly after the industrial revolution in Europe, and were a way of training people in a standard way that would make them suitable for employment as workers in factories and offices. We are no longer living in industrial Europe c1850, surly we should be looking at better ways of educating our young.
The real tragedy is that this man was able to rise as high as he did, and our current system supports it.
My guess is that the test had a lot of algebra 2 material, which requires some memorization of formulas. It's not hard math, it's just sort of plug and play, but it's hard to remember what to plug the numbers into if you haven't had a recent refresher, or you're not teaching it.
As far as getting a 62% on the reading portion, well that's just pathetic.
For all we know, the reading test was either testing for a different kind of plug-and-play (“the author of the above paragraph is using (a) apostrophe; (b) synechdoche; (c) both; (d) neither”) or is testing mastery of a certain kind of teaching-to-the-test in the guise of “reading comprehension”.
You can't possibly be implying that most people are in their current jobs because of skill or training?! Bwaahaaahaaahaaah! Such naivete! Where have you been hiding?
edit: add link & proper version titles.
It would be a fabulous retort if you were this fellow and you actually did happen to know. "Short or long" would be almost as good a come-back as "African or European" when asked about unladen swallows.
Life lesson: If it sounds too easy for the money he's making, it's probably not.
...which all requires a completely different skill-set than what kids are being taught in school. Politics, opportunism, cold-blooded back stabbing if necessary and clever PR being just a few of those.
Also, when he actually was in school, the curriculum was probably (at least somewhat) different, different tests and questions. He cannot really base an educated opinion on the school system and standardized tests from just that alone - leaving what you personally feel about the school system out of the equation for a second.
Sounds more like a disaster from the rest of the biosphere's POV.
The God of math has spoken: obey, conform or be cast out...There is nothing other than Me. All other gods require Me to make them whole - in fact you can't even think without Me... Now go forth and preach my wisdom because there is no other wisdom other than Me.