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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."
second!
From what I can tell, they all look to be the same length and size and hopefully are not older revisions of this paper.
My work here is dung.
Yeah, but I lost count.
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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.
I myself have gone through the US school system starting at grade 7 (lived in Switzerland and The Netherlands before then), I am currently in uni for a software engineering degree. While I have read only part of the article (the blog post) I wanted to post my experience compared to that of my cousin who went through school in The Netherlands.
Math at the schools I went to was catered to the lowest common denominator, the slowest person in the class, the person who would just not get it got the most attention and the rest of the class was stuck at that level until that person tagged along and finally got moving. Whereas in Europe and other places they place those students in various levels of math dependent on their skill level so that those that don't need the extra time are able to get to the higher level maths faster. This creates a gap between the math that is considered required at age 18 in the US and The Netherlands. My cousin was going for a degree in hotel management and food preparation (chef). He at the age of 18 had a better understanding of math, and had more knowledge of high level math (Linear Algebra, Calculus and others) than I did when I graduated High School, and the classes he were in were considered the slower less demanding classes since it was not as much of a requirement for the degree he was going to be pursuing.
This is the same with a lot of the classes though, history, english, and science classes. Especially for English, you don't get to think for yourself anymore, you have to follow exactly what the teacher told you. If the teacher says this is important for this reason, and you attempt to argue it differently in a paper you fail, everyone coming out of high school has been passed through a cookie cutter, there is no innovation left, there is no real thinking for oneself anymore.
It is sad, and the state the US educational system is currently in will not allow it to compete in the global market, it will not allow it to be innovate and provide new ideas, but what it will provide is people who are like sheep and are more than willing to follow the crowd and just do it because everyone does. These people will be easy to govern and control since they won't ask questions and least of all will they rebel and fight for their beliefs. In other words, the US education system as it currently stands is making zombies.
cat
For instance the ancient mayans used shapes for numbers, instead of 1, 2, 3
Psst! The numerals "1", "2", and "3" are shapes too!
F***in' indocentrists...
Information theory is life. The rest is just the KL divergence.
If everyone was smart, who would work at mcdonalds?
Smart people. Wouldn't that be awesome?
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.
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And you get around the economic obstacles by subverting the system: Crowdsource the textbook to a group of interested mathematicians. Publish it online for free, with printed copies available for a price far below what a crooked textbook publisher would charge. Add value by posting demonstrations by mathematicians, math historians, and math professors on YouTube, linked to the relevant chapter of this comprehensive, global mathematics resource.
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But who would eat there?
Feature, not a bug.
Linux, you magnificent bastard, I read the fucking manual!
If everyone was smart, who would work at mcdonalds?
Robots obviously.
Mada mada dane.
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.