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."
Several Proxies (Score:5, Informative)
From what I can tell, they all look to be the same length and size and hopefully are not older revisions of this paper.
US School System compared to Europes School System (Score:5, Informative)
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.
Re:The way math is structured is disconnected from (Score:5, Informative)
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...
Re:Cue the other subjects (Score:5, Informative)
Re:Cue the other subjects (Score:2, Informative)
Re:True story .... (Score:2, Informative)
If that's indicative of how math is taught nowadays, we're all hosed.
It is. We are.
Re:Eh. (Score:3, Informative)
The whole idea behind his essay is that he liked playing with numbers and shapes as if it's an art, but he doesn't seem to realize most people don't share this love for math, like pretty much 90% of any student population. This is me speaking as a just-graduated senior: the things he suggests is beyond the ability of most math students in high school.
I think you missed the point.
His point IMO, is what we are teaching as "math" in school is totally useless and should be scrapped completely, because it's not even close to what math is.
We don't need to teach math to 100% of the students, just as we don't insist that 100% of the students can paint landscapes, or bake brownies.
Re:Cue the other subjects (Score:5, Informative)
Before you troll and bash "fundamentalists" with no proof you should read a few books on why education in the US is in the state we now see.
The Deliberate Dumbing Down of America [deliberate...ngdown.com] By Charlotte Iserbyt
An Underground History of Education [johntaylorgatto.com] by John Gatto
Or read the Dodd Report [scribd.com] to the Reece Committee which investigated Tax Free Foundations in the early 1950's.
Re:US School System compared to Europes School Sys (Score:2, Informative)
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.
Really? "Most US schools" have this? Maybe your school did, but my high school, which had over 1300 students in grades 10-12, most assuredly did not. Well, if your definition of "different" means "two", then mine did. My high school (that's "secondary school" for all you non-North Americans) offered one advanced level class in chemistry, math, English and Social Studies. Entry into those classes was restricted to the brighter students (I got in - lucky me). Then they had normal level classes in all those subjects that everyone else took. Granted, I graduated in the 1980s, but I don't know what the heck school you went to, but I tend to think that your experience is the atypical one here and not that of the guy who posted.
Re:Eh. (Score:3, Informative)
Is it the students who are incapable, or are they merely inexperienced?
Some people just don't get math, just like some people just don't get music or science or English. Around here, the math one is probably the largest.
You can ask any teacher. Some students just have a hard limit on their abilities. It's hard to manage these.
I'd also like to state that we have some pretty damn good teachers in our district, who approach math more like the essay stated. Lots of exploration and discovery. For a lot of students it just doesn't work, whether they're told outright (which the math teachers are inevitably forced to do on a one on one basis) or asked to discover the relationships themselves.
Re:Several Proxies (Score:3, Informative)
I understood what he was trying to say, but observed that there was potential for confusion based upon his word order.
Being that I'm a bit of a grammar nazi when I feel like it, and that it is Friday, and that we all need a quiet chuckle on Fridays, I decided to try my hand a crafting a somewhat amusing joke based upon the lack of clarity in the summary.
Does that make you feel better?
Re:I Sympathize With Him But Too Idyllic (Score:3, Informative)
Re:Several Proxies (Score:5, Informative)
Depends on what you mean by fundamentalists (Score:3, Informative)
and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education
Depends on what you mean by fundamentalists. Honestly, I have my doubts you can trace all our problems back to creationists and prudes. You'd have to get the market fundamentalists, the "one curriculum to bind them all" fundamentalists, the Fabians, the Rothschilds, the Rockafellers, and probably more in there to get a really good idea of why we've ended up so mixed up.
That said: I got a fantastic high school education. I learned quite a bit and could have gotten a lot more out of it if I'd had the inclination.
Speaking of hot mathematicians (Score:5, Informative)
http://www.danicamckellar.com/ [danicamckellar.com]
I can't believe Summer Glau is the chick geeks are hot after. Danica is Hot, has her name on a physic theorem, mathematician, and has written math books for girls.
Her acting career is full of geek as well.
Not to say either one of them is a geek, just that I scratch my head over why geeks prefer Summer.
Re:it's really bad (Score:3, Informative)
You might want to have a look through the articles on Wikipedia about logic [wikipedia.org], predicate-logic [wikipedia.org], and mathematical proofs [wikipedia.org].
Re:US School System compared to Europes School Sys (Score:3, Informative)
Saying knowledge comes from a schooling about as correct as saying milk comes from a store. When you understand in both cases it's just simple packaging and processing, you can start asking questions about what it is, why it is, and how you can get it on your own, and how to evaluate the quality of the sources you get it from.
Re:Several Proxies (Score:1, Informative)
Actually the bible contains 2 approximations for pi. Neither of them in the New Testament, though. The bible also clearly states in both cases that they're approximate, not exact.
One of them is indeed 3 (though Jesus never said that, it's in a piece about the architecture of the first temple, which, apparently had a round part). The other is a surprisingly accurate approximation for pi, and indeed a very useful one, since it is a fraction : 22/7. First 4 digits are correct (yes, I realise the fourth digit of 3.1428 is a two, not a one, however round(math.pi* 1000) = 3142, which means 4 correct digits)
The fraction is really useful because it can be used in building and quick calculations about adding a circular structure without complicating the matter to the point where you need a calculator to avoid mistakes. If you're good at calculating in your head, though, you might give 355/113 a try, which is a very, very good one. I've heard of a physics simulator that uses 22/7 and 355/113, because they allow it to avoid the need for floating point alltogether in a few special cases, which will still give a massive speedup on current processors.
Re:Several Proxies (Score:2, Informative)
Re:Cue the other subjects (Score:2, Informative)
What it REALLY comes down to, the REALLY important thing, is the motivation of the student. If the student wants to succeed, they will find the way to success (granted there are not too many institutional barriers to break through).
This is now a book (Score:3, Informative)