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A Mathematician's Lament — an Indictment of US Math Education
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."
The problems with K-12 education go WAY BEYOND mathematics.
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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.
My work here is dung.
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.
A slashdotter who didn't build his own computer is like a Jedi who didn't build his own lightsaber.
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
Lost at C:>. Found at C.
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.
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.
The United States is being outclassed in math and science education by a host of other nations. Those nations, for the most part, teach the subject in an exceedingly traditional format. Asia, for example, is still really keen on rote learning. The failure of American pupils is probably not due to the way the subject is taught, but rather because they don't feel the pressure to excel like students in other cultures.
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).
Welcome to the Panopticon. Used to be a prison, now it's your home.
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.
A slashdotter who didn't build his own computer is like a Jedi who didn't build his own lightsaber.
Troll? Fucking mods don't know humour when they see it.
Next time link to a video of someone getting a baseball in the nuts, they'll love that..
Trolling is a art,
This man is a beautiful dreamer. I don't think his rather Platonic vision of the perfect math class will ever be acheivable. But there are a bunch of half steps that I think would really help math and address his fundamental point that math, as it's currently taught, is boring as all heck and does nothing for the vast majority of us who don't use calculus or even algebra in our day-to-day lives. I mean really, the last time I did anything more than basic algebra was tutoring others! And while learning math so that you can help someone elses' kids study for a test is a fine goal, I'm not sure it's really worth the thousands of hours I spent taking math!
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.) 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.
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?
But then I realized the cable was blue, so I only gave it one star. I hate blue.
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).
I am a teacher, albeit not a a math teacher but teaching in general has a lot of problems in the U.S. The largest problem that I see in America is that we have a system of education that is largely based on talent. We recognize it, reward it, and care for it like a price flower. Effort on the other hand is culturally unappreciated and that cultural attitude is reflected in education. The talented students have the opportunity to shine, and they always have.
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.
load "$",8,1
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.
If you cannot keep politics out of your moderation remove yourself from the Mod Lottery.. NOW!