A Mathematician's Lament — an Indictment of US Math Education 677
Scott Aaronson recently had "A Mathematician's Lament" [PDF], Paul Lockhardt's indictment of K-12 math education in the US, pointed out to him and takes some time to examine the finer points. "Lockhardt says pretty much everything I've wanted to say about this subject since the age of twelve, and does so with the thunderous rage of an Old Testament prophet. If you like math, and more so if you think you don't like math, I implore you to read his essay with every atom of my being. Which is not to say I don't have a few quibbles [...] In the end, Lockhardt's lament is subversive, angry, and radical ... but if you know anything about math and anything about K-12 'education' (at least in the United States), I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth."
Cue the other subjects (Score:5, Insightful)
The problems with K-12 education go WAY BEYOND mathematics.
I Sympathize With Him But Too Idyllic (Score:4, Insightful)
From the blog:
I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth.
Very well, here is an excerpt from the PDF:
Mathematics is an art, and art should be taught by working artists, or if not, at least by people who appreciate the art form and can recognize it when they see it. It is not necessary that you learn music from a professional composer, but would you want yourself or your child to be taught by someone who doesn't even play an instrument, and has never listened to a piece of music in their lives? Would you accept as an art teacher someone who has never picked up a pencil or stepped foot in a museum? Why is it that we accept math teachers who have never produced an original piece of mathematics, know nothing of the history and philosophy of the subject, nothing about recent developments, nothing in fact beyond what they are expected to present to their unfortunate students? What kind of a teacher is that? How can someone teach something that they themselves don't do? I can't dance, and consequently I would never presume to think that I could teach a dance class (I could try, but it wouldn't be pretty). The difference is I know I can't dance. I don't have anyone telling me I'm good at dancing just because I know a bunch of dance words.
Now I'm not saying that math teachers need to be professional mathematicians--far from it. But shouldn't they at least understand what mathematics is, be good at it, and enjoy doing it?
Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?
... everywhere. That art teacher that actually made you think about what 'art' is? Not going to find many of them in the political science department, are you? Of course, for any subject, someone who puts their heart and soul into the subject is the best teacher! In this respect, math is not special.
I'm sorry man, you're asking for the perfect math teacher. You know Robin William's character from the movie The Dead Poet's Society? You want a guy like that for math
The paragraph I quote is not the truth, it's wishing for the impossible. I wish I had a math teacher like this all my life but come on. The public school system is more worried about getting someone that actualy cares about the students at all. They can't even find those people let alone people who care about the students and live/eat/sleep/bleed math.
I'm right their with you in wishing for this but the expectation is unrealistic. Passions come to people unexpectedly. We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science. It's just the reality of academia right now.
it's really bad (Score:5, Insightful)
High school students are forced to write proofs as part of geometry class. However, they are never taught the rules of logic before being asked to write these proofs. That is just one example of how horribly, horribly stupid the HS math curriculum is in the US.
True story .... (Score:5, Insightful)
In university, I was taking an intro philosophy course on critical reasoning.
We had covered the concept of statistical significance. The example we'd used was a case of "0.05" meaning we had 95% confidence in the statistical results. On the exam, the professor made a typo, and the question read "how much certainty with a statistical confidence of 0.5", to which the correct answer is 50%.
I was marked as wrong, and when I complained, the professor indicated that since we'd never covered that example, and only covered 0.05 in class, it was assumed that was what she meant.
I informed her for someone teaching critical reasoning, she wasn't demonstrating any. I also insisted I get the credit for giving the actual correct answer (which I and everyone who answered it correctly did).
If that's indicative of how math is taught nowadays, we're all hosed. :-P
Cheers
Oh give it a rest (Score:5, Insightful)
Instructors of just about every field at any level of compulsory education (K-12) have to battle against entrenched biases against their fields, and against education in general, that have been fostered for years before the student ever gets in their classroom. Further, their task is to teach the curriculum provided. If they inspire their kids to love the field, that's great, but if they spend so much time inspiring the kids that they don't have enough time to teach the kids what they need to pass the state-required tests, they're still going to lose their jobs.
Teaching math, science, or anything else is HARD. Teaching it to people who don't care and don't want to be there is even harder. Teaching kids to love the field when the only metric used to judge your performance is pass rates on a standardized test is harder still. It's all well and good for professional mathematicians to bitch and moan about the state of education, but until they're ready to step in with some realistic and implementable ideas that don't presuppose that all kids have some inherent interest in these things that just needs to be tapped into, it's not helpful in the least.
Re:I Sympathize With Him But Too Idyllic (Score:4, Insightful)
you don't have to be a PhD. to be interested in and passionate about math. there are some very elegant things in math, and if they are taught to kids in the spirit of a voyage of discovery rather than a trudge along the banks of the river Styx, then there's a chance more kids will catch the bug and like math. And at the rate we're losing engineering capability, particularly in the US, this ought to be a priority.
Re:Cue the other subjects (Score:5, Insightful)
and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education, and people refusing to see and treat education as what it is: an investment in the future national security and economic stability of the united states.
Comment removed (Score:5, Insightful)
Re:Cue the other subjects (Score:4, Insightful)
The problems with K-12 education go WAY BEYOND mathematics.
Amen to this.
I'd say the majority of the issues, though, start at home.
Too many families are stuck running a two-income home (for a variety of reasons) and simply can't/won't/don't spend the time needed with their children in the formative years.
A lot of the rest, IMO, can be traced to schools not teaching children how to think critically, just to memorize stuff.
And that sucks.
You can convince me (Score:5, Insightful)
that math is better taught as an art than as a pragmatic problem-solving toolset when you can convince me that Pablo Picasso should have been forced to paint the Golden Gate bridge.
Society needs math as a tool in far greater quantity than math as an art. Socially-funded education serves the greater need of society. QED.
I survived public school mathematics. I still appreciate the beauty of patterns, especially the relatedness of art, music, and math. (Godel, Escher, and Bach really resonated for me. But that didn't make me a mathematical artist, any more than a musical composer or a woodblock printer.)
Lockhart's essay is an interesting read, really, but on some level it boils down to "Those unworthy schlubs treating Mathematics as a tool don't deserve it. It belongs to the artists, the dreamers, the purists!"
It's a pretty common arrogation in the math culture, it seems. I dont' recall sculptors ever being pissed at concrete workers or ironworkers. And I've never heard of any artist painter getting mad at the other kind of painter for not employing good artistic composition principle while painting the side of the barn.
Seriously. Math is both an art and a tool. The best artists find their art by themselves; they're not turned out by artist factories. School mathematics is to turn out the mathematical equivalent of bridge painters and ironworkers, because society needs those more (in greater quantity).
Re:it's really bad (Score:5, Insightful)
I agree, but that's not my point. My point is that understanding the formal rules of logic is fundamental to being able to understand proofs. But the bureaucrats who came up with the US math curriculum just said "the kids should learn this and this and this" but never attempted to put those things in the right order so that it was even possible for them to learn all those things.
It's no wonder kids think they are bad at math or hate the subject--it is presented to them in an impossible form.
Re:Cue the other subjects (Score:5, Insightful)
Re:US School System compared to Europes School Sys (Score:4, Insightful)
You must have attended a very very small school. Most US schools have different courses based on skill level. Your conclusions about the US school system are therefore wrong. They are merely conclusions about very small schools.
Re:Several Proxies (Score:3, Insightful)
Next time link to a video of someone getting a baseball in the nuts, they'll love that..
Half Steps (Score:4, Insightful)
First, *use* math to solve real problems and explain real scientific principles. Radio Lab (THE official National Public Radio show for geeks everywhere) had a great little episode where some student "discovers" that the periodicity of a pendulum forms a parabola when charted on a graph. Wow! That's heady stuff. (It's the first story of this episode [wnyc.org].) Understanding the interaction of science and math -- the universe, really -- is something that we can teach. Integration of math and science gets us part of the way there.
Second, incorporate the history of math into math class. Math advances all occur because of some historical context. Combining the two is a half-step that will get students to understand "why" we created this math, even if they never quite get the quadratic formula down. Combine these two principles, and it would go a long way.
Re:Cue the other subjects (Score:3, Insightful)
If everyone was smart, who would work at mcdonalds?
There would always be people at the bottom, no matter how educated everyone was.
Lad: Would you like to discuss quantum mechanics? My thesis was about...
Me: Just get my fucking burger.
Lad: sorry sir, was this to go?
Re:tl;dr (Score:3, Insightful)
Re:The way math is structured is disconnected from (Score:3, Insightful)
so you want to teach math using base-1 ... that's... insane.
Re:Cue the other subjects (Score:5, Insightful)
If everyone was smart, who would work at mcdonalds?
Smart people. Wouldn't that be awesome?
Re:Eh. (Score:4, Insightful)
I read as much of the essay as I could before I realized that the guy doesn't understand that his experience doesn't apply to everyone else. I understand where he's coming from because I tell the worst stories imaginable. I will go on talking about little, highly interesting details, until I realize that I'm the only one who finds them interesting. It took me a long time to realize that, just because I find it interesting, that doesn't mean that other people will.
To say that mathematics should be taught in the way that he likes the most is silly, at best. Most people will be able to pass through life with a rudimentary, at best, understanding of mathematics. Most jobs in this world do not require 90% of the theorems and principles that people are forced to learn through high school. I agree with the essay 100% on that point.
The key to math education, though, is not memorizing these principles, but rather learning how to solve problems. If someone can logically plan their way through a calculus problem, almost anything that they have to figure out at their job would be well within reason.
I never have understood the concept of math as an art, yet I enjoy math. I enjoy solving problems, enough so that I earned my BS in Mathematics, but this guy takes it to a whole new level. If not even all mathematicians think like he does, why does he expect that the general population will?
Re:Oh give it a rest (Score:4, Insightful)
Specialists in every field complain that educators get their field wrong or don't stir the passions of kids for their field as much as they ought to. What they fail to understand is that they're coming at the whole problem from the perspective of someone who is obviously gifted at and highly passionate about the field. They don't seem to get that most people don't pick up their field as easily as they do, and don't care enough to put in the effort it would take to get even half as good at it as the specialist.
Do musicians complain that the typical high school band teachers don't understand the basics of music? This is a specific example from the TFA and it is very well chosen. People don't expect high school band teacher to world class musicians. They do however expect high school band teacher to have a feel for what music is. They expect high school band teacher to know the difference between in tune and out of tune. They expect high school band teachers to drill notation and teach counting different times, but the also expect to be connecting these things to actual music at every step of the way.
We expect this of high school band teacher because most people know what music is supposed to sound like. Most people have enough sense for how it actually works to recognize somebody who can't play, or who cannot teach how to play.
Teaching math, science, or anything else is HARD. Teaching it to people who don't care and don't want to be there is even harder. Teaching kids to love the field when the only metric used to judge your performance is pass rates on a standardized test is harder still. It's all well and good for professional mathematicians to bitch and moan about the state of education, but until they're ready to step in with some realistic and implementable ideas that don't presuppose that all kids have some inherent interest in these things that just needs to be tapped into, it's not helpful in the least.
If you tried to teach a music class based on transcribing notation and chord theory, rather than listening and/or playing you'd find it hard also. Teaching kids to love music using a such a curriculum wouldn't just be hard, it would border on the absurd. Even if a few people did enjoy the raw mindless diligence to do such a thing out of context, there is no particular reason to believe that this would produce great musicians.
I'd like to add that science education in the US seems to me to be much closer to math education than music education. I remember learning to play lip service to the scientific method, but I don't remember ever being asked to sit down with some lab equipment and figure out what some relationship is. If you are given the equation, and given the experiment to "test" some particular aspect of the equation, you've removed the science, you've removed what is important.
More money in death (Score:4, Insightful)
I have to comply with 300 pages of regulations for the school I started in Denver. The cost of compliance is at least half the total budget.
Although this article did not touch once upon the issue of wages, it is a very good article -- perhaps the best I've read all year on the subject of education. The need to introduce mathematical intuition at a young age is something the Montessori Method has done for a century. In a Montessori school, the child progresses from concrete to abstract, working first -- from very young at two years old -- with physical objects that embody length, area, or volume, and only later attaching the abstract symbols we call numbers. The physical manipulation leads to visualization of how addition, subtraction, multiplication, division, and fractions work. A child who goes through all three years of "Primary", which is age 3 to age 6, by the end of it, the child will be multiplying and dividing, and have worked with manipulative materials that demonstrate fractions and even binomials and trinomials from algebra.
In the face of competition from government schools, it is a challenge. I have learned that the competition isn't so much for students as it is for teachers. By using tax dollars, they can pay so much more, offer more benefits, and provide stability stemming from a legally-guaranteed funding sources. Meanwhile, the government schools are there for the purpose of creating cannon fodder, with its flag worship every morning and the forced admission of military recruiters under No Child Left Behind for as early as third grade. And when they do grab a hold of an effective pedagogy like Montessori, they pervert it by adding standardized testing and segregating by ages (e.g. two-year age groups rather than the three-year age groups prescribed by Montessori).
By eliminating public education, and by reducing the morass of regulations for running a private school, the free market could decide how important math education really is, rather than hearing hot air about it from public officials and CEOs, or by listening to earnest mathematicians such as Paul Lockhart, the author of this white paper, attempt to influence curriculum, presumably in government schools. The century-long battle between phonetics and "whole word" in the area of language (and the resulting reading levels no matter what is done) should be evidence enough of the futility of this approach (to use an anlogy, which Lockhart seems to love).
Comment removed (Score:3, Insightful)
Re:Cue the other subjects (Score:5, Insightful)
Even worse is the move away from competitiveness in many areas. I was a teacher for a while, and much of my teacher training was tainted by what was mislabeled "child-centered education" - basically don't do anything that might hurt the feelings of the most sensitive child you could imagine. Don't use a red pen to mark their work because that's an angry color; don't correct their spelling because that stifles their creativity; don't hold academic competitions because the kids who don't win (don't dare call them losers!) will be upset.
This trend continued despite the fact that high schools started graduating functionally illiterate and innumerate kids, even though they had passed the courses that should have given them reasonable skills in those subjects. Colleges and universities expended their gradual entry programs (basically high school subjects aimed at those who came from a disadvantaged background) until first-year studies were assumed to be nothing more than a high school refresher.
I left teaching mainly because the schools where I taught were basically big-kid daycare centers where there was very little learning to interfere with the political agendas of the administration and the school boards, but not before I subversively gave a few students the motivation to question what they were taught and learn on their own.
Re:I Sympathize With Him But Too Idyllic (Score:5, Insightful)
To be honest, I thoroughly disagree with you, because I DID HAVE just such a teacher. She wasn't some kind of superwoman either, she was just very competent at math (no advanced degrees, but good enough to teach basic calculus, algebra, and geometry in a way that made pretty much all the students at my school respect her). More importantly, she was passionate about giving students a fundamental understanding of the subject matter. She didn't want to just cross her T's and dot her I's and be done with it, she wanted us to learn what it was all about. She was a hard teacher, but she was almost remarkable in that nearly the entire student body had a great deal of respect for her.
I think the author's whole POINT was that it's claims like yours--that this is some kind of unreasonable expectation--that are entirely the problem with the situation we have. The simple fact is, it is not unreasonable. My personal experience has shown me that there ARE such teachers out there; mine as well as others I've known.
My own personal take is that our society simply doesn't give educators the respect they deserve. There's very little motivation for the kind of intelligent, competent, passionate people to go into to lower tiers of the world of education. We pay them peanuts and there's not nearly the kind of appreciation and respect out there for them to want to do those jobs. I happened to go to a private Catholic school, where neither of those things are true, and let me tell you the difference was obvious.
Re:Cue the other subjects (Score:4, Insightful)
What studies I've seen show approximately no difference between children who have been in day care and children with a stay-at-home parent. (Okay, there's some detail differences early on, but they fade).
The important thing is the parents' attitude. Young children will emulate their parents, and will try to please them. If the parents make it clear that education will please them, and put enough time and effort into monitoring it to make that perfectly clear, and to be able to tell the difference between learning things and getting good grades, the children will respond appropriately.
A parent who wants to encourage education, and isn't totally swamped with other things that he or she is basically incapable of parenting, can find a way to do so.
Re:The way math is structured is disconnected from (Score:3, Insightful)
What your holding as a genius way to do things is no different then Roman numerals. It gets extremely unwieldily for anything other then simple addition and subtraction or basic counting, and they aren't any less arbitrary in their symbolism then Arabic numerals are.
Re:I Sympathize With Him But Too Idyllic (Score:4, Insightful)
We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science. It's just the reality of academia right now.
Of course it is, because we have these ridiculous stigmas:
Art is passionate, frivolous, and beautiful.
Math is boring, uninspiring, and useful.
What?! There is no such thing as frivolous beauty; no utility is uninspiring and cold. Lockhart, I fear, misses this point. I understand the frustration Lockhart feels at the 'math = boring' stigma, but countering that 'math = art' is just as damning in our obsessed-with-mutual-exclusion society.
Beauty and utility have long been a happy couple. The false rumors of their divorce is, I think, the root of Lockhart's (and my) frustration.
Re:I Sympathize With Him But Too Idyllic (Score:3, Insightful)
The only way this guy would get the class he wants is to only teach elective courses that aren't pre-reqs for anything. That's the only way to make sure that your students actually care about the subject and aren't taking the class just because they were forced to. In public education this does not exist until sometimes very very late in a child's development (when it's already too late).
Re:I Sympathize With Him But Too Idyllic (Score:3, Insightful)
It's not necessary to put a perfect math teacher in every classroom. Elementary school teachers are perfectly capable of teaching a math curriculum that presents kids with mathematical concepts in game form as Lockhart mentions. Later in their school careers the kids who show interest and aptitude for math could be taught algebra etc, and the rest could stick with the mechanics of arithmetic that will enable them to deal with checkbooks and mortgages. I think our problem today is that we use a one-size-fits-all approach that evolved from the "new math" of the 1960s, which was aimed at teaching kids mathematical concepts instead of practical arithmetic. It was based on the theory that students would see the beauty and wonder of math, and as a result the mechanics would come naturally. That didn't happen, but rather than scrap the whole idea the education system kept the subject matter and devolved the teaching approach. There's a lot of window dressing but basically it's the same kind of rote instruction as before. I think the author's lament is that the system has been trying to teach the beauty of mathematics like a metal shop class.
Re:I Sympathize With Him But Too Idyllic (Score:3, Insightful)
In history, a lot of very prominent mathematicians of their day and age made their living privately teaching high school kids. In modern times, mathematics isn't seen as an important an asset to have to spend that kind of money even if one has it.
I don't understand why education is seen the way it is in the US. What does the teacher have to do with the quality of education? Does anyone think their teacher helped them become a good programmer. NO. Why do people think their math teachers will make them good mathematicians?
Anyway, I challenge people to name 10 prominent American mathematicians - please non-mathematicians only and let's take Nash as given. Name the last American mathematician to be featured on a postage stamp. Do the same for musician and see how long that takes.
My point is that the US doesn't really have a mathematics appreciating society. It reflects in the education as well. And, don't blame the teachers or the administrators for it.
Re:Cue the other subjects (Score:5, Insightful)
If everyone was smart, who would work at mcdonalds?
Robots obviously.
Re:The way math is structured is disconnected from (Score:3, Insightful)
"Dude, now you're approaching xenophobia. Have you looked at the state of mathematics in American universities? A conspicuous amount of highly original researchers are the product of foreign educational systems. They aren't doomed to being tech support monkeys like you insinuate."
I don't know how the heck you got that out of my statement. I'm not saying these people are not smart, I'm not saying they are not mathematical prodigies, but they have all learned math in a particular way, many mathematicians don't even realize it because their mind is *naturally suited* to the symbolic form in which the were taught.
Drilling kids with a structure of math when they have no idea how to relate it to their own natural knowledge limits their ability to understand what 'math' is. Most people have never really looked into what mathematics is, where it comes from, how it is derived. I've got books I and articles I've slogged through doing my own research in my spare time and I've realized how disconnected and arbitrary how math is structured in our society really is, and I'm not discounting these peoples contributions to society.
I'm telling you math is much more rich then what most people have even begun to think about*, yes even the PHD's.
I'm talking about how mathematics is *structured* how it is represented.
I remember taking "gifted" tests in school that structured mathematical principles using colored shapes/empty shapes for patterns and principles.
Kids need a way to *connect* what they see as meaningless symbols and see they are *derived* from observations in the world, mathematics *began* as a way for someone to take their observations and format them in a systematic way, but there are many ways to do this and the way something is presented matters A LOT.
I wish I could find the article at about how someone built a physical model as a metaphor of mathematical principles that explained the principles better then the equations and graphics they had made.
Either way there are better ways to communicate mathematical principles and ideas then has been traditionally been taught in societies institutions because I have spent a heck of a lot of time researching this on my own time. As expected on slashdot I would meet a lot of resistance for people who are without my lifetime of experiences that I have yet to congeal into a work of origina lresearch.
A teachers take (Score:5, Insightful)
Would our culture demand effort from our students instead of recognizing talent we'd be much further along.
I'm not suggesting that talent should go un-nurtured but, at least from an educators point of view, the effort of the students should be the focus of rewards.
Re:The way math is structured is disconnected from (Score:3, Insightful)
A lot of math reads like extremely bad Perl programs too, with tons of functionality on every line and no documentation except for a giant paragraph at the top written by someone who is apparently from Mars.
On the other hand, a lot of math is just pattern recognition. Realizing when you need to use one transform over another is a fundamental part of mathematics. Maybe the language simplifies this task somehow? I'm not sure. It always seemed to obscure it more than anything else to me.
Comment removed (Score:3, Insightful)
Re:Eh. (Score:3, Insightful)
90% of the student population isn't interested in math because it's taught in the way and by the people he talks about in his text.
*insert snide comment about reading comprehension here*
There are _lots_ of people (Score:3, Insightful)
... with the ability, knowledge and inclination. The real problem is that they can all make twice or more money by doing some other line of work. This is a matter of paying what is necessary to compete with the other possibilities open to mathematically able, knowledgeable and inclined people.
Re:School Choice is part of the answer (Score:4, Insightful)
1) Yes NCLB is an excuse to close down public schools - it was designed as such, and they intentionally fabricated a study [exposed as a fraud 2 years later] to get congressional support
2) Defunding them further with vouchers (most of which would be going to religious indoctrination centers that masquarade as schools) is not a solution
3) "Failing schools based on geopgrahy" is a problem with two things
a) How we fund schools [how about pool money state wide and dole out as needed instead of tying funding to their service areas land values.. that kidn of funding arraignment was obviously designed to serve only the rich neighbors]
b) home lives in disadvantaged areas are more often than not are harmful to getting an education.
The NEA would CORRECTLY resist #2. They would support repleaing NCLB and getting all schools funded better.
Vouchers are not a solution, they're just a furtherance of stripping funding from public schools so that they fail.
Re:Several Proxies (Score:3, Insightful)
Like most natural human languages (those spoken by beings who are trying to communicate with one another and who exhibit the power of judgment), English allows some variation in what elements of sentences go where. No competent English-speaker who hasn't remained retarded in their sexual development at the anal-retentive stage, or developed a weird fetish by the daily practice of putting parentheses around symbolic expressions to coerce mechanical systems into evaluating them in the preferred order, could ever actually misconstrue this sentence as you are doing or pretend to be doing.
It's ironic that in a comment on a story about the joy of pattern-making and pattern-recognition, you should reveal the ugliness of pattern-enforcement. Don't, for the love of humanity, be a lexer (of any languages but those that need it), and don't go around insisting others think like machines.
Mathematician, Taught Public HS for 5 Years (Score:3, Insightful)
Though I don't need the rhetoric, this hits it on the head, in every aspect.
I'd like to try teaching math like English -- Math 1, Math 2, Math 3, Math 4, with curriculum determined in part by such apparently meaningless factors as what might be useful in other classes or what's happening, you know, outside of my room.
The textbook comments are particularly right on -- step 1, burn them. If teachers complain that they won't know what to teach, fire them on the spot.
Geometry is also a lousy place for proof. Teach deduction all the time, in every topic -- and in classrooms other than math. "Here's a bunch of fake stuff you don't know anything about that's hard to draw. Now let's think really abstractly about how we're thinking about it!" And induction doesn't get taught at all.
The practical deal-killer, the one that drove me out of the profession, is that the barrel full of math teachers is so close to empty that you're pretty much scraping bottom from day 1. This kind of instruction -- and this kind of critique -- can only originate with someone who likes math, and is sort of good at it. You'd be amazed (or maybe you wouldn't) at how few public high school math teachers this describes.
America has gotten the math teaching instruction it asked for when it decided to prop up bad teachers with lousy but easy-to-use texts, and to boot it got the benefit of not having to pay very well for people willing to go through these motions. (It's not about money, but really, it's a little bit about money. I doubled my salary when I left last year.) It's a big, huge problem, and since you're going to have to convince parents that it needs the kind of dramatic overhaul this (great) article describes, and since parents were largely victimized by the existing system, I'm pretty sure it's a losing battle.
Re:It starts with the textbooks. . . (Score:3, Insightful)
Wow, you didn't read the paper very closely if you think he could produce a textbook (or a series) to implement what he's advocating.
Re:Cue the other subjects (Score:3, Insightful)
I would point out that the vast majority of senior McDonald's executives started out in a restaurant.
The ratio of McDonald's executives to Mcdonald's grill / fry / sandwich / cashier persons is pretty daunting. Ultimately only a handful can rise to executive level. Even if everyone wanted to and was capable of the job their isn't room for everyone to advance.
Re:Cue the other subjects (Score:5, Insightful)
What's wrong with smart people working in the service industries?
That's somewhat of a rhetorical question, but it really isn't a great thing that we have a defacto class system based on keeping some people ignorant and poor while others enjoy luxury. We assume that working in a restaurant should be a job of lesser human beings who aren't deserving of respect, and we've ensured that those jobs don't pay a livable wage.
We complain about foreigners stealing our jobs, and we complain that poor people are so filled with vice that they don't pull themselves up by the bootstraps. Meanwhile, we make sure our economy is filled with jobs that can't provide what we consider an acceptable quality of life, and we close off routes for upward mobility wherever we can.
And if smart people did work at McDonalds, their intelligence and education still wouldn't be a complete waste. They'd still probably be better citizens, run the restaurant better, and maybe get my order right every once in a while. And who knows, maybe one of them would someday revolutionize the food service industry with innovative new ideas.
Re:Cue the other subjects (Score:1, Insightful)
Re:Cue the other subjects (Score:3, Insightful)
However, I think it's unfair to specifically single out these groups without including what seems to me to be a "lax" attitude by parents (including college educated parents) in middle-class homes where the kid's great-grandparents (or earlier) lived in the US (having immigrated or having been born in the US). In the public middle-class schools these kids go to, parents complain that poor Jason just doesn't have enough time after school for all his activities and his life is so stressful so the schools should cut back on expectations (including the amount of homework). Or, when their sweet Heather is called out at school for behavior problems, her parents raise a ruckus about how the teacher picks on poor Heather (when I was a kid [get off my lawn] it was assumed it was me who had the problem, not the teacher -- unless a lot of parents were complaining bitterly about one particular teacher).
Of course, all this has given us public school teachers who are willing to accept this lax attitude and have low achievement expectations -- which results in a vicious cycle.
From a practical standpoint, the primary source of effective practicing engineers and scientists is going to be middle class households with educated parents -- unfortunately, many of these families are/have raised soft kids who feel entitled to get whatever they want just because "I want it" and don't expect to "work" for it.
At this point, I fear the US's only hope is the legal immigrants from India and China (in particular, due to their numbers) whose parents actually believe that their childrens' main "job" is getting a good education and don't mind that the kids sometimes feel some stress about it. This is not a terrible thing except that as the US builds up more and more deadwood (all of whom get to vote, but most of whom will pay few taxes due to their limited income producing potential) we cross the tipping point where 5% are paying the other 95% to exist - and the 95% keep trying to get more from the 5% until it all collapses when a few of the 5% say "screw it, I'm not going to work this hard to give most of my earnings to someone else. Don't oppose generous issuance of H1Bs to well educated individuals - we need them to help keep Medicare (and the whole government bubble) propped up for a few more years - we need to keep this Ponzi scheme afloat...
Re:Cue the other subjects (Score:1, Insightful)
I decided to have a look at your "proof." In "The Deliberate Dumbing Down of America", the author begins with two commonly held "beliefs" (his word, not mine):
"1.) If a child can read, write and compute at a reasonably proficient level, he will be able to do just about anything he wishes, enabling him to control his destiny to the extent that God allows (remaining free);
2.) Providing such basic educational proficiencies is not and should not be an expensive proposition."
He then immediately draws the conclusion that since "basic" education is inexpensive:
"...it becomes obvious that it is only a radical agenda, the purpose of which is to change values and attitudes (brainwash), that is the costly agenda. In other words, brainwashing by our schools and universities is what is bankrupting our nation and our children's minds."
Yeah, that's certainly the unsupported conclusion I'd draw. It certainly explains why my kid's minds are "bankrupt."
Re:Cue the other subjects (Score:3, Insightful)
There are certainly some good teachers that stick it out and I don't blame anyone for bailing out of an untenable situation, but society has got to recognize that education is important, equality should be about opportunity not outcome, working hard is an important component to success, and teachers should be accountable (and not "entitled" to their job just because they have seniority).
Oh, and and parents have to realize that just because they were clever (or careless) enough to figure out how to spawn, it doesn't mean their children are perfect angels entitled to whatever they want without hard work.
Re:Wrong tool for the job (Score:3, Insightful)
While I appreciate where you're going with your statement: "the way the discoverer came to understand a principle is often more important to grasp than the principle itself", the hope that this will be clear by reading an original work is just too much to ask for. Science historians labor for years to try to grasp some of those original thought processes. I personally find it much more fruitful to read these histories or a good modern textbook with a historical bent (An imaginary tale and Dr. Euler's fabulous formula - while not textbooks - are excellent examples of this species) to obtain some understanding of how the scientist actually thought of doing this. It just doesn't seem like a good use of one's time to wade through obsolete jargon and obscure (and nearly always annoying) notation just for that one spark of inspiring genius, which can be found readily in modern treatments because modern authors usually worship these ancient masters and provide these little gems at no extra cost
Early notation is almost always ridiculous complicated (when you look at it in hindsight). Take the idea of vector notation that people use as a matter of course in nursery school math. It is remarkably elegant - especially the ideas of dot and cross products and the determinant form for the latter. Look at any old textbook on the subject and you'll get arcane and obfuscatory animals like dyads and triads. Tensor notation (relatively recent) revolutionized the way this subject (and it is used almost everywhere in physics, engineering, hell - even computer graphics, so it is VERY important as a practical matter).
Brilliant (often crazy) people give birth to a new subject - one feels only awe when one considers these people. Wiser people then consolidate the subject over the next N years until it hold together beautifully. Even wiser people then continue to find deeper connections between this new subject and others that have lain around for a while.
In fact, in physics, the only book from the horse's mouth (so to say) that I actually found halfway understandable was Dirac's treatment of Quantum Mechanics. Even so, more modern books (Sakurai for grads or Griffiths for undergrads) is entirely more clear because by then any redundancies and clumsy notations been polished away, things feel right because they are consistent notationally with the rest of physics. I cannot over-emphasize the importance of consistent, clean and meaningful notation in trying to convey scientific knowledge successfully. The Humanities can be wishy washy in this regard but science can never afford the loss the clarity that ensues.
Another example: for a graduate level introduction to General Relativity, one might try to read Einstein's original paper - historically significant no doubt. A better way would be to read the fearsome Landau for field theories (not bad at all but not easy) or Wald (1984) - even better and getting more modern in terms of things we know. Or one might do the wise thing and go straight for Sean Carroll (2003!) for what might the MOST lucid treatment of GR ever written. I have great respect for a man who spends time clarifying (and thereby making laughably simple) the ferocious tensor notation of GR. Indeed, it is so clear, that I wished it had come out before I graduated with my B.S. (coincidentally in 2003
Do you see a pattern here? I do no
Re:It starts with the textbooks. . . (Score:1, Insightful)
Re:Eh. (Score:3, Insightful)
You overlooked the absolute core of his argument: a lot of high school students think they don't like math because they've been presented with a pale shadow of math for the previous eight years. Of course a high school student couldn't handle what he's describing; all of their previous schooling has emphasized rote memorization, blind pattern matching, and robotic application of rules. He thinks we need to rethink things all the way back to first grade.
By odd coincidence, I had an english literature teacher in high school who taught english the same way math is frequently taught. You read the book, and during class he lectured on the details of the story, the author's background, and the context of the world in which the story was written. While this might sound interesting, it was presented as a serious facts. Indeed, a few days before a test, he helpfully gave a study session that amounted to listing 100 or so facts from the book and his lectures. You memorized them, then regurgitated 20 or so back on the multiple choice test. It was mindless. It was admittedly very easy, at least if you could memorize a list of 100 or so facts, but it did crap all for my appreciation for literature in the english language. (At the time I liked his class. I found it trivially easy. But looking back on it in hindsight, especially after reading that essay, what a massive waste of time. What a terrible teacher.)
In english class in high school you can ask students to read a work, then write an essay on the themes. In the process they will have to learn to actually pay attention to what they're reading, to consider it on a level beyond a simple telling of events. Maybe the student will hate reading, writing, or both, but the overwhelming majority can manage to write that essay. The original author argues that the same model can work for mathematics and that the idea that it will be too hard for many students is a false one created a system that already fails.
Re:You can convince me (Score:3, Insightful)
Part of his argument is that by focusing on "math as tool" via "math as rote memorization", you fail even at that. Math at higher levels becomes cryptic symbols that you manipulate according to cryptic rules to make your teacher happy. And a few years out of school you promptly forget the whole thing. If they forget most of it, and for the overwhelming majority it never hurts them to have forgotten it, what was the point in having "taught" it in the first place? He argues that it's such a waste of time that we might simply drop some math courses entirely and we would be better off. (Indeed, I suspect that if you replace your average American's high school senior math courses with Spanish that society on the whole would benefit. They're more likely to make use of the Spanish.)
The author believes that his proposal will lead to more students discovering that they actually like math, and more students as a whole actually retaining what they learned. While they might learn less, they'll actually retain more in the long run, and be better armed to figure out things for themselves.