# A Mathematician's Lament — an Indictment of US Math Education

#### ScuttleMonkey posted more than 4 years ago | from the beating-the-joy-out-of-education dept.

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."*

## Can't count (5, Funny)

## Anonymous Coward | more than 4 years ago | (#28392757)

second!

## Re:Can't count (1)

## nicolas.kassis (875270) | more than 4 years ago | (#28392775)

## Re:Can't count (1)

## AliasMarlowe (1042386) | more than 4 years ago | (#28392873)

one, two, few, some, many, too many.

At least, that's the level of many high school leavers in the U.S. these days. Counting badly on the fingers of one hand because they don't want to put down the GameBoy/iPhone or whatever they're jerking in the other hand.

## Re:Can't count (1)

## nicolas.kassis (875270) | more than 4 years ago | (#28393421)

## Several Proxies (5, Informative)

## eldavojohn (898314) | more than 4 years ago | (#28392769)

From what I can tell, they all look to be the same length and size and hopefully are not older revisions of this paper.

## Re:Several Proxies (5, Funny)

## Red Flayer (890720) | more than 4 years ago | (#28393011)

For example (FTS):

And just how, pray tell, are we supposed to read his essay with every atom of your being?

I mean sure, I could read his essay with every atom of

mybeing, but wouldn't it violate some mathematical and physical principles for me to read it with the submitter's being?## Re:Several Proxies (3, Insightful)

## grub (11606) | more than 4 years ago | (#28393245)

Next time link to a video of someone getting a baseball in the nuts, they'll love that..

## Re:Several Proxies (1)

## louiswins (1017272) | more than 4 years ago | (#28393499)

Get it?

## Re:Several Proxies (0, Troll)

## Gerzel (240421) | more than 4 years ago | (#28393249)

2 + 2 = Jesus and that is all they need to know!

## Re:Several Proxies (2, Funny)

## LordKazan (558383) | more than 4 years ago | (#28393343)

And Pi = 3. So says Jaysus!

## Zeroth Post. (0, Offtopic)

## mosel-saar-ruwer (732341) | more than 4 years ago | (#28392771)

Pwned.

## Slashdotted (3, Funny)

## PPH (736903) | more than 4 years ago | (#28392881)

## Cue the other subjects (4, Insightful)

## b0r1s (170449) | more than 4 years ago | (#28392889)

The problems with K-12 education go WAY BEYOND mathematics.

## Re:Cue the other subjects (5, Funny)

## SomeJoel (1061138) | more than 4 years ago | (#28392901)

## Re:Cue the other subjects (4, Insightful)

## LordKazan (558383) | more than 4 years ago | (#28393083)

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.

## Re:Cue the other subjects (4, Insightful)

## bluefoxlucid (723572) | more than 4 years ago | (#28393237)

## Re:Cue the other subjects (3, Insightful)

## grub (11606) | more than 4 years ago | (#28393341)

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:Cue the other subjects (1)

## superwiz (655733) | more than 4 years ago | (#28393279)

## Re:Cue the other subjects (1)

## LordKazan (558383) | more than 4 years ago | (#28393375)

december 7th, 1941

what's your point?

## Re:Cue the other subjects (2, Interesting)

## b0r1s (170449) | more than 4 years ago | (#28393347)

Personally, I put the blame less on fundamentalists and more on decreasing importance of education in the home.

There are dozens of examples (single mothers with multiple jobs and multiple kids who just don't have time to parent, illegal immigrants raising kids that accept no-skill jobs as manual labor as sufficient for a lifetime instead of working to get an education and work in a skilled field), but the basic problem is that kids don't believe that they need a real education to live.

## Re:Cue the other subjects (0)

## Anonymous Coward | more than 4 years ago | (#28393349)

Really? Fundamentalists? The kind of people that home school their kids? They're to blame? Not teacher's unions? Not parents who treat school like a babysitter? Not the kids who graduate high school unable to read?

## Re:Cue the other subjects (1, Interesting)

## LordKazan (558383) | more than 4 years ago | (#28393505)

Read The Fundamentals of Extremism:

The Christian Right in AmericaThey've staged a long and protracted anti-education war in government for 3 decades.

http://www.amazon.com/Fundamentals-Extremism-Christian-Right-America/dp/0972549609/ref=sr_1_1?ie=UTF8&s=books&qid=1245437556&sr=8-1 [amazon.com]

## Re:Cue the other subjects (3, Interesting)

## mh1997 (1065630) | more than 4 years ago | (#28393491)

American education was designed to fail. Read the book (it's free online) The Underground History of American Education by John Taylor Gatto. He is a former New York State and New York City Teacher of the Year

http://www.johntaylorgatto.com/underground/

## Re:Cue the other subjects (0)

## Anonymous Coward | more than 4 years ago | (#28393123)

Queue.

## Re:Cue the other subjects (4, Informative)

## PitaBred (632671) | more than 4 years ago | (#28393191)

## Re:Cue the other subjects (0)

## Anonymous Coward | more than 4 years ago | (#28393377)

Fail.

## Re:Cue the other subjects (4, Insightful)

## Em Emalb (452530) | more than 4 years ago | (#28393137)

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.

## Re:Cue the other subjects (0)

## Anonymous Coward | more than 4 years ago | (#28393143)

I think one of the problems is a subject that doesn't exist - logic. Something so basic and we don't teach it at all.

## Re:Cue the other subjects (1, Informative)

## bluefoxlucid (723572) | more than 4 years ago | (#28393247)

## tl;dr (1)

## Enuratique (993250) | more than 4 years ago | (#28392895)

## Re:tl;dr (4, Interesting)

## Fallingcow (213461) | more than 4 years ago | (#28393039)

Bingo, and that's one of the big problems with trying to do anything about the issues the paper raises: there are only so many people with the 1) ability, 2) knowledge, and 3) inclination, to do the kind of

realmathematics he's talking about.We'd have to re-vamp our teacher training along the lines of what's talked about in the paper to try to increase the number of people who could do it, and

hopeLockhart's right about this being an art with universal appeal so that enough of the teacher candidates "get" it. Even if elementary schools began using dedicated math teachers (some already do, but many don't) we'd still need a shitload of people trained in this "math as an art/math as play" style, and we currently have approximately zero in elementary education.## It starts with the textbooks. . . (0)

## Anonymous Coward | more than 4 years ago | (#28393441)

You start by having someone like the gentleman who wrote that paper create a new textbook and teachers' manual to go along with it (or, really, a 'series' of textbooks that go through the different grades) that implements the different way of teaching mathematics which he is espousing. It then dies in state and local education department when there is resistance from comittees on doing things differently than they've been done before, and anyhow there is no funding for new textbooks anyhow.

. . . But if you can manage to get some school districts to attempt the material, you basically have the teachers go through a math 're-education' using the textbook and teachers' manual, then they just teach from the book (of course, there needs to be *some* creativity on the part of the teacher, in adding new examples or explanations that the textbook author might not have thought of, but is necessary to help students who aren't 'getting' the examples and explanations in the book). But, if the teachers themselves have read through the book and the manual(and hopefully there is good supplemental discussion in the teachers' manual about *how* to teach the material), they should be prepared to teach the new method themselves.

## Re:tl;dr (1)

## CRCulver (715279) | more than 4 years ago | (#28393055)

My high school algebra teacher was female, but had come to high school teaching after spending much of her time in university research rounds. Her qualifications were impeccable. That didn't make my classmates anymore successful with their studies than the average. I'm inclined to think it's a problem of unmotivated students in all fields of education in general.

## Re:tl;dr (2, Insightful)

## fuzzyfuzzyfungus (1223518) | more than 4 years ago | (#28393447)

## Re:tl;dr (1)

## superwiz (655733) | more than 4 years ago | (#28393353)

## Re:tl;dr (1)

## Enuratique (993250) | more than 4 years ago | (#28393439)

## I Sympathize With Him But Too Idyllic (4, Insightful)

## eldavojohn (898314) | more than 4 years ago | (#28392903)

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 mathThe 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

andlive/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.

## Re:I Sympathize With Him But Too Idyllic (4, Insightful)

## conspirator57 (1123519) | more than 4 years ago | (#28393037)

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:I Sympathize With Him But Too Idyllic (3, Interesting)

## langelgjm (860756) | more than 4 years ago | (#28393307)

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.

Isn't his point that we don't really know if that's true, since math isn't taught in a way to inspire passion? That if more people were able to glimpse some of the beauty and creativity in it, there might be more interest in it?

Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?

I agree we can't expect every teacher to be awe-inspiring; even getting (and retaining) enough marginally competent teachers is a challenge. However, you needn't be a university-level mathematics professor to know some of what he's suggested. For example, public school teachers are supposed to have Master's degrees, right? Now, isn't there something funny about the fact that teachers will go and get their BS in the subject they will teach, but get their Master's degree in "education"? Cue the "Philosophy of science is about as useful to scientists as ornithology is to birds" quotes. I'd think that teachers might be better served by a decent master's degree in their field of teaching, rather than "education". That would allow them the opportunity to study the history and philosophy of their subject, get a grasp of recent developments (maybe not in all subjects, but they could at least be able to pick up journals), etc. The really good ones could even get published (I just got my Master's degree, and was able to get a paper published, so yes, it's possible).

## Re:I Sympathize With Him But Too Idyllic (0)

## Anonymous Coward | more than 4 years ago | (#28393461)

If they had masters degrees in their subject areas, they wouldn't ever want to bother with the bullshit of being a teacher.

## it's really bad (4, Insightful)

## Lord Ender (156273) | more than 4 years ago | (#28392911)

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.

## Re:it's really bad (1)

## LordKazan (558383) | more than 4 years ago | (#28393105)

I'm excellent with logic and I had a terrible time with proofs. Both in HS geometry and in Discrete Math and Theory of Computing in my CS degree. Good proofs are a form of artistry as far as I'm concerned. They certainly can do a lot better job teaching how to do them - but some people will always be better at it.

## Re:it's really bad (4, Insightful)

## Lord Ender (156273) | more than 4 years ago | (#28393167)

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:it's really bad (1)

## LordKazan (558383) | more than 4 years ago | (#28393327)

You're right when you say Bureaucrats.. No honest educational professional would be behind many of the debates (evolution baiting anyone?) we see all over the US.

The only thing that should be done nationally is a standardized curriculum : IE All schools [public and private] in the US must teach atleast THIS to give a HS diploma. Just to make things equitable. In reality a HS diploma from my state, from the public schools in Cedar Rapids and Des Moines are worth A LOT more than an HS diploma from... say mississippi.. but they're treated the same. Same thing with public education in my home town and say.. the religious school that's science textbook had this for evolution:

"Evolution

There is absolutely no evidence that this ever has happened."

that was it's entire entry.

We need standardization, but not rote memorization like NCLB has forced many schools to implement. I graduated from high school in 2002. I had been taking standardized tests for years* and my teachers were great and not "just teaching the test" as became common after NCLB.

* always scored top notch.. was Iowa Test of Basic Skills (ITBS) prior to HS and Iowa Test of Education Development (ITED) in HS. Always scored top... one of my friends filled in the dots in an artistic pattern.. still scored higher than some of the educational FAILdrones in our class who tried.. was pathetic.

================

If we start treating education as what it is, an investment in the future national security and economic strength of our country, and spending on it accordingly we might get somewhere.

We're failing to recruit valuable teachers these days due to 3 decades of attacks on our schools by the Christian Supremacist movement and conservatives as a whole. (Read

The Fundamentals of Extremismsometime) - almost all the great teachers I had in HS went early retirement the year after I graduated because of budget cuts## Re:it's really bad (1)

## gbarules2999 (1440265) | more than 4 years ago | (#28393127)

## Re:it's really bad (0)

## Anonymous Coward | more than 4 years ago | (#28393289)

What are you talking about? Middle school geometry (that's what it is whether it's taught in high school or not) has really simply proofs where each line is the result of the application of a single proof rule. You don't need axiomatic or natural logic or type theory or any of that stuff. Even Euclid got by with a few axioms and a few (unnecessary) definitions.

## Re:it's really bad (1)

## Gat0r30y (957941) | more than 4 years ago | (#28393329)

While we are on the subject - the whole public school system is no longer really teaching kids anything of value. Its basically an expensive babysitting service. What exactly is a high school graduate qualified for anymore?

## Re:it's really bad (1)

## LordKazan (558383) | more than 4 years ago | (#28393423)

that depends on the state. if you're not in the top 10 states.. you're screwed these days. Iowa sat top 5 for a LONG time fortunately. One of our biggest exports is educated young people. Hell if it wasn't for the economy causing hiring freezes at a lot of software shops I would have been one of those exported educated young people to!

## Re:it's really bad (1)

## NewbieProgrammerMan (558327) | more than 4 years ago | (#28393339)

So I shouldn't have enjoyed all those proofs in geometry and trig, then? Dammit, why doesn't anybody tell me these things--here I was growing up without knowing there's only one proper order in which to learn things!

## Re:it's really bad (1)

## delphi125 (544730) | more than 4 years ago | (#28393445)

The problem with proofs has nothing to do with logic.

It is necessary to be able to understand proofs, but duplicating them under exam conditions means you have to memorize them by rote.

At a certain point (for me it was the Cambridge maths tripos part IB) you are going to get exposed to maths you have to do but don't fully understand.

People who can memorise the proofs but only understand them partially do better than people than those who understand the material better, but prefer to "solve a problem" and struggle to memorize a proof verbatim.

## The way math is structured is disconnected from... (4, Interesting)

## blahplusplus (757119) | more than 4 years ago | (#28392921)

... interesting things kids want to do.

Lets face it a minority of people will like math, but matehmaticians have done a lot to make mathematics overly complicated.

I struggled with the symbolic format math was presented in highschool because it was so disconnected from the world, only as I got older did I realize how arbitrary and how that was only one way to present mathematics. To really teach math one must learn how to observe first before one even gets into symbolic computation, math at it's most basic is about observing relationships, patterns of : Size, ratio, proportion, etc. It's really a language invented to systematize structure and relationships of the real world, therefore how math is represented and structured and is taught matters a hell of a lot.

I've learned over the years that many mathematical systems are totally arbitrary are are more obtuse then they need to be, math comes from the simplest observations. Math has built up a lot of cruft and wasteful jargon disconnecting math from the world.

For instance I had no idea for a long time that the way math is structured could be restructured when I was young and it was one group of peoples perspective on mathematical principles, I came across debates and alernative systems like:

http://www.symmetryperfect.com/ [symmetryperfect.com]

And it showed me how arbitrary mathematical systems and their structures really are and they are built to suit particular kinds of minds or cultures.

For instance the ancient mayans used shapes for numbers, instead of 1, 2, 3

See here:

http://en.wikipedia.org/wiki/Maya_numerals [wikipedia.org]

Math is a very rich subject which unfortunately has a lot of cultish like people who think themselves the gatekeepers of mathematics.

I've thought about writing a book in my spare time about how badly mathematicians and the academia has blinded themselves to simplifying mathematics by focusing too much on symbolic jargon and not teaching children how 'mathematical' relationships are related to our simplest observations of the world: Size, shape, form, color, motion, etc.

## Re:The way math is structured is disconnected from (5, Informative)

## DriedClexler (814907) | more than 4 years ago | (#28393065)

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:The way math is structured is disconnected from (1)

## blahplusplus (757119) | more than 4 years ago | (#28393457)

Yes they are but notice how

3 hides the fact that its actualyl THREE 1's

(1) (1) (1)

of couse all systems use shorthand to compress teh relationships but when we say 3, we mean *three distinct shapes/objects/things*

Our characters we use for numbers *hide* those relationships.

## Re:The way math is structured is disconnected from (4, Insightful)

## CRCulver (715279) | more than 4 years ago | (#28393115)

## Re:The way math is structured is disconnected from (1)

## blahplusplus (757119) | more than 4 years ago | (#28393369)

"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."

Performance is unrelated to the overly jargonistic complexity, just because asia and india are harsh and drill their kids to perform does not mean they have any clue how to derive creatively go beyond what they are learning. They may make good workers but that doesn't mean anything.

One gains a fuller understanding of math when you realize how to start from the beginning and learn how to observe, if you look at the progress of mathematics over the centuries - systems of symbols and other systems were created to systematize a problem and break it down, most people didn't have to sit down and come up with calculus or algebra themselves, but you can teach kids how to observe and derive things themselves and not feel ashamed to get creative and "go outside" traditional symbolic jargon for leaps forward in creatively seeing underlying relationships between things beyond symbolic computation.

One can be a good performing mathematician and still be clueless about the deeper relationships and observational skills required to become very versed in what math is, outside of what one is taught.

Math has an enormous amount of dogmatism attached to it. Performance in mathematics is only one aspect, we should ask - besides performance, what about understanding? I mean everything I've learned about mathematics I had to teach myself, so I could see through the bullshit of the establishment. I learned I was a visual mathematician, that I understand math through more natural mode of thought: pictures and geometry.

Math is really the language of form and structure, and all structure is necessarily geometric in some way, even relationships (structures of information).

## Re:The way math is structured is disconnected from (1)

## CRCulver (715279) | more than 4 years ago | (#28393451)

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.

## Re:The way math is structured is disconnected from (1)

## maraist (68387) | more than 4 years ago | (#28393535)

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.Huh? Getting into college isn't an extremely pressing/taxing/competitive ordeal?

I'll tell you why US students are degrading in test-worthy performance: Grade-inflation forced down the throats of schools by bitchy parents who can't believe their kid got a C when in prior years they'd gotten an A (most likely due to grade-inflation having to slowly work it's way up and through college). This does a tremendous disservice to the children, as they are less and less prepared for each successive year, until the overwhelming feeling completely puts them off of any subject that has prerequisites (like math/science).

## Re:The way math is structured is disconnected from (1)

## mario_grgic (515333) | more than 4 years ago | (#28393397)

You are not truly a mathematician until you learn to abstract. Symbols are ultimate abstractions. Yes, you can invent your own symbols, but you will still have symbols.

Think about how children learn to count. They first count concrete objects, one finger, two fingers, ... one apple, two apples, etc. and then we abstract. Remove the object being counted and just have one, two. This is where the big abstraction happens. We arrive to the concept of oneness, without thinking about 1 something. Now add symbols for those abstractions 1, 2 and now you can do some neat things with symbols that translate into concrete objects when applied. This is the essence of math.

Yes, symbolism introduced is standardized so that we can talk to each other and exchange ideas. Otherwise, it would take a lot of time for you to explain all your symbols to me before we could have any meaningful conversation.

## OP's feelings about the article (1)

## grepya (67436) | more than 4 years ago | (#28392929)

I don't know Scott.... I'm getting mixed messages from you about the article. Why don't you open up and tell us what you really think ;-)

## True story .... (5, Insightful)

## gstoddart (321705) | more than 4 years ago | (#28392947)

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

## Re:True story .... (1)

## retchdog (1319261) | more than 4 years ago | (#28393063)

And years later, you would learn it's never really 95% anyway (nominal vs. actual level; all models are wrong; &c.).

But what a ghastly example. It made me cringe.

## Re:True story .... (1)

## gstoddart (321705) | more than 4 years ago | (#28393221)

Which was well outside of the scope of that class anyway.

Truly, it was ghastly. Especially since it was a course on logic and reasoning.

Cheers

## Re:True story .... (1)

## Lord Ender (156273) | more than 4 years ago | (#28393199)

No, that's just indicative of lazy teachers. Since most humans are lazy and all teachers are human, this is to be expected.

## Re:True story .... (1)

## gstoddart (321705) | more than 4 years ago | (#28393257)

Which, if one is decrying the state of education, is a valid concern.

If the teachers are doing it by rote, how the hell can the kids be expected to grasp the underlying concept?

Cheers

## Re:True story .... (1)

## Neil Blender (555885) | more than 4 years ago | (#28393443)

"No, that's just indicative of lazy teachers. Since most humans are lazy and all teachers are human, this is to be expected."

In college, I found it's more likely that profs refuse to admit they are wrong. I got dinged more than once for typos/errors in books that the professor wrote for the class.

## Re:True story .... (2, Informative)

## Gunnut1124 (961311) | more than 4 years ago | (#28393413)

If that's indicative of how math is taught nowadays, we're all hosed.

It is. We are.

## Could be worse... (1, Interesting)

## Anonymous Coward | more than 4 years ago | (#28392957)

## Eh. (4, Interesting)

## gbarules2999 (1440265) | more than 4 years ago | (#28392961)

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.

## Re:Eh. (0)

## Anonymous Coward | more than 4 years ago | (#28393215)

I think the major point is that most students never have a base of reason when dealing with math. To them it's just arbitrary rules that they apply to some arbitrary numbers so they get an A. They never learn that those rules are arbitrary and are not right most of the time....

for example, many first year students in engineering have a tough time grasping the concept of tolerance and significant digits.... and these are engineering students, they are already supposed to be good at math. The fact they don't understand such a simple concept out of high school is frightening...

## Re:Eh. (2, Informative)

## AnotherBlackHat (265897) | more than 4 years ago | (#28393427)

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.

## It's a problem (1)

## SEWilco (27983) | more than 4 years ago | (#28392969)

Solve for education.

## Hmm (4, Funny)

## Quiet_Desperation (858215) | more than 4 years ago | (#28392981)

I implore you to read his essay with every atom of my being.

Well, OK, seeing as I can use *your* atoms.

## US K-12 MATH = Real world fail. (1, Interesting)

## Anonymous Coward | more than 4 years ago | (#28392991)

Just the other day, I was watching "Who wants to be a Millionare?" And a 24 year long high school teacher didn't know what the sign for factorial means. Choices where along the lines of : ! & %

## Re:US K-12 MATH = Real world fail. (0)

## Anonymous Coward | more than 4 years ago | (#28393153)

When I was in the sixth grade (1980), my teacher didn't know that '/' could be used for division when he asked the class "what can you use '/' for?"

He told me I was wrong.

## Re:US K-12 MATH = Real world fail. (1)

## DragonWriter (970822) | more than 4 years ago | (#28393233)

<pedantic>

Well, from those choices, I would know that "!" was probably intended, but that's as much skill at dealing with improperly-posed questions as anything else.

In fact, though, none of the options are correct as you have related the question: what the sign for factorial means is "factorial", just as a stop sign (or "sign for stop") means "stop", not "red octagon with a white border".

</pedantic>

## Re:US K-12 MATH = Real world fail. (1)

## Kratisto (1080113) | more than 4 years ago | (#28393335)

I'm not sure which is more concerning: That anyone still watches "Who Wants To Be A Millionaire," or that anyone is still surprised by the abject stupidity therein.

## Re:US K-12 MATH = Real world fail. (0)

## Anonymous Coward | more than 4 years ago | (#28393507)

And you don't seem to know what the word means means.

The symbol for factorial

is!.! (the symbol for factorial)

meansthe product of the series of integers all integers from 1 to the integer which precedes the factorial symbol.See the difference?

## Oh give it a rest (5, Insightful)

## eln (21727) | more than 4 years ago | (#28392993)

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.

## An allegedly true story from a professor (4, Interesting)

## thirty-seven (568076) | more than 4 years ago | (#28393023)

While I was in university, a computer science professor in the faculty of mathematics told me (and the rest of the class) a cute and funny story about what happens "when the children of math professors get together". He and a colleague, who each had a young daughter at that time, were walking together in a park with their daughters. The children were old enough to have picked up some math-related words and phrases from their fathers, but young enough to have no idea what they really meant - six or seven years old, maybe? The daughters went off to play and their fathers overheard them arguing about who had seen the most flowers in the park.

My professor's daughter said, "I saw five flowers!"

"And I saw... six!", the other girl replied.

Not to be outdone, my professor's daughter said, "I saw a million flowers."

"Oh yeah? I saw infinity flowers."

This, according to my professor, caused his daughter to pause - she had never heard of "infinity" before. How could she top "infinity flowers", especially since she didn't know what it meant?

But after thinking for a few seconds, she said, "Well, I saw

allthe flowers."## Re:An allegedly true story from a professor (1)

## superwiz (655733) | more than 4 years ago | (#28393433)

## US School System compared to Europes School System (5, Informative)

## 0x000000 (841725) | more than 4 years ago | (#28393035)

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:US School System compared to Europes School Sys (0)

## GodfatherofSoul (174979) | more than 4 years ago | (#28393209)

While I like our system, I think there are two things that need to happen in the US.

## Re:US School System compared to Europes School Sys (3, Insightful)

## Lord Ender (156273) | more than 4 years ago | (#28393241)

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:US School System compared to Europes School Sys (2, Interesting)

## jimbobborg (128330) | more than 4 years ago | (#28393449)

I saw the issue the OP stated in all of the K-12 schools I went to. As my father was in the military, I got to go to 3 elementary schools, 1 middle school, and 2 high schools. Some teachers were able to handle students at different reading/math levels in elementary school, but once I hit middle/high school, everything except math was lowest common denominator. In Seventh grade, the English class was using the reader I used in Fifth grade. And people in the class were having a hard time with it! The only way I could get away from the morons was to get into an AP class. Of course, I couldn't get into the AP English classes as my grades were too low in Eighth grade (should have actually done my homework.) Math was something I was good at. I had excellent Math teachers in HS. Sadly, I went to college. By my second quarter, I had enough of the stupid rote memorization of proofs that had to be regurgitated on exams to just stop attending classes. Feh.

## Re:US School System compared to Europes School Sys (0)

## Anonymous Coward | more than 4 years ago | (#28393517)

Most US schools have different courses based on skill level.Um, no they don't, apart from a

verylimited portion of Honors/AP courses. The rest are one-size-fits-all, based on some sort of misguided egalitarianism.## Re:US School System compared to Europes School Sys (1)

## Quiet_Desperation (858215) | more than 4 years ago | (#28393475)

Not sure where you went to school, but in my high school, you took the class most appropriate to your abilities at the time. Some were taking basic math and algebra in 10th grade while I was in a precalculus class. In 12th grade I was in an early morning advanced calculus class taught by a professor from the local university.

There is no "math class" at that level anymore, at least in my experience. Even middle school was like that because I got my advanced algebra there.

As for the essay linked by the original article. it smacks of the "whole language" approach that swept through schools here in California in the 1980s and 1990s, much to its detriment. I actually went into the article expecting to agree with Mr. Mathematician, but wound up thinking the guy is a loon (after slogging through *TWO* overwrought analogies). I get what he wants, but you don't toss out the basic foundations of functional mathematics to accomplish it.

## Re:US School System compared to Europes School Sys (1)

## Fallingcow (213461) | more than 4 years ago | (#28393495)

The big buzz word/trendy strategy in elementary-level teaching right now is "differentiated instruction". What it means is teaching a single concept at several levels of difficulty simultaneously. It's sort of like ability grouping into different classes like you talk about, but all in one classroom and with one teacher (and maybe a TA or Para or some such).

It's actually pretty good when it's done right, but as far as I can tell most elementary school teachers are

awfulat coming up with effective differentiated lesson plans. Many just think it's impossible and refuse to even try. I expect it to go away in a few years, just like most of the other trendy teaching ideas since, well,foreverago. Maybe we'll move toward having separate ability-grouped classes after it fails.## Re:US School System compared to Europes School Sys (1)

## PeanutButterBreath (1224570) | more than 4 years ago | (#28393503)

US schools have Advanced Placement classes. Oh yeah, and there is no reason motivated students can't move at their own pace outside of the classroom (or inside).

All you are calling for is a system that offers more than one sized spoon with which to feed students. That's just a better version of a fundamentally flawed educational philosophy. Or rather, it stretches a fine philosophy beyond its logical limit and makes it flawed. A chef can get by just fine with a US HS level understanding of math, for example. More math won't make better chefs (the opposite, potentially).

If a person's excuse for having less education than they wanted (or than Europenas might have) is that the US school system only caters to the lowest common denominator, they are lazy, not deprived.

## Meanwhile, the English teachers lament... (1)

## scalpod (666558) | more than 4 years ago | (#28393149)

## You can convince me (4, Insightful)

## idontgno (624372) | more than 4 years ago | (#28393159)

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 Bachreally 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).

## As an old codger.... (1)

## John Hasler (414242) | more than 4 years ago | (#28393185)

...I know I'm supposed to say "Things ain't like they used to be!" but the fact is, they never were. K12 in the fifties and sixties tried hard to convince me that I was to hate math and science and treated me as wierdo when I didn't. Instead I learned to despise classroom education, which did me incalculable harm at university.

Basically, public education sucks.

## Re:As an old codger.... (1)

## TheRaven64 (641858) | more than 4 years ago | (#28393511)

It certainly isn't how it used to be on this side of the pond. You used to take an exam at 11 here, and go to either a grammar school or a comprehensive depending on your result. Within these, it you would typically have different sets for each subject, so the best students were in one class and the worst in the other (quite often the same child would be in the top set for some and the bottom for others).

In the '80s, this system was dismantled because it was 'elitist'. The result is that you now have the complete ability range of children in the same class. The teacher has to try pitch the lessons at a level where they are applicable to every student. I was lucky in that my parents sent me to a public[1] school which still did this; you passed an entrance exam to get in and then were divided into sets based on ability for most subjects. Different sets were taught in different ways, and at different speeds. I hated the subjects which weren't split in this way; you were always in with a bunch of people who got everything faster than you so you had to struggle to keep up, or with a group of people who were so slow you were bored (or both). Even in the classes with different ability sets, you got this to a certain degree, but not to anything like the same level.

[1] Note to Americans: Historically, in Britain, there were private schools that were run by individuals or companies to make a profit, and public schools which were run as charities (often Church-financed, sometimes funded by donations from industrialists). The government-funded schools were introduced a few hundred years later, and are referred to as state schools.

## There's lots to disagree with... (1)

## twistedcubic (577194) | more than 4 years ago | (#28393195)

Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever.I guess he's exaggerating, since he must be aware of the deep connection between algebra and geometry which is realized via manipulating equations. And this provides lots of approaches for a good teacher. I dunno, he just comes off as a garden-variety teacher with strong opinions.

## There are 10 kinds of people......... (-1, Redundant)

## i_want_you_to_throw_ (559379) | more than 4 years ago | (#28393229)

## Vulcans are doing it right (1)

## jrowlingson (1003641) | more than 4 years ago | (#28393253)

## bfrist ps0t (-1, Offtopic)

## Anonymous Coward | more than 4 years ago | (#28393255)

## Two mathematicians (4, Funny)

## Conspiracy_Of_Doves (236787) | more than 4 years ago | (#28393275)

Two mathematics professors are having lunch at a restaurant. The first mathematician keeps complaining about how ignorant the typical American is and how he's suprised that the average person in this country has enough mathematical prowess to balance a checkbook.

The second mathematician says, "Don't you think you're being a little harsh? The average person surely has more mathematical ability than you give them credit for."

The first mathematician responds, "Absolutely not! I'm sure if you asked the first person you met on the street to solve a basic algebra problem, they would have no idea where to start."

The second mathematician says, "Okay, I'll make a bet with you. At the end of the meal, I'll ask our waitress to solve a calculus problem. If she can solve it, you pay for lunch. If she can't, I'll pay."

"Thanks in advance for lunch!" the first mathematician says confidently.

Later, while the first mathematician is in the bathroom, the second mathematician flags the waitress down and says, "Listen, when you bring us our check I'm going to ask you a math question. I want you to answer, âone-half x-squared.' Can you remember that? If you do, I'll leave an extra big tip." He encourages her to write it down phonetically and practice it so that it seems natural.

At the end of the meal, after the waitress puts the bill on the table, the second mathematician says, "Oh, could you answer a little question for me? What's the integral of x with respect to x?"

The waitress looks unsure at first, but says, "One-half x-squared."

With a grin, the second mathematician slides the bill over to the first mathematician.

As the waitress is walking away, she turns back and says over her shoulder "plus a constant!"

## Half Steps (3, Insightful)

## sampson7 (536545) | more than 4 years ago | (#28393305)

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.

## Wrong tool for the job (1)

## tyrione (134248) | more than 4 years ago | (#28393389)

Stop hiring Education Majors to teach The Hard Sciences. Unless you include Historical Curriculum of famous and infamous Scientists into your early days of learning the Hard Sciences will forever be a mystery.

If you want a kid to know Euclidean Plane Geometry you better make ``The Elements Books I-XIII'', by Euclid part of the curriculum early on and gradually bring into view the history of its making followed by the actually application.

The same goes for Physics with Newton, Robert Boyle, Euler, etc.

Hell, I'm just getting all the backlog history of these giants and I'm a M.E. It would have made my days far more enriching to know how they came up with this crap outside of the Calculus derived explanations. I love Mathematics and it's endless Engineering Applications [mainly because I could always visualize their application--something innate and not taught] but reading the greats memoirs and more makes it come together.

Instead of just History over political events we need History over Mathematics, Physics, Chemistry, EE, ME, CE, etc.

You don't suddenly become educated in Paleontology without first knowing it's foundation, heavily grounded in History. Hell even Fine Arts requires a massive background in the history of the fields pioneers.

## Teachers Unions (1)

## NotWithABang (1570431) | more than 4 years ago | (#28393479)

I'm sure there's many factors contributing to our declining educational systems, but I don't think anyone can deny that attempting to standardize teaching and "level the playing field" as it were may not be as great of an idea as it sounds in theory. For many, math can be a hard subject. All arguments about relative difficulties and complexities aside, maths and sciences are at least not as accessible as, say, literature, history, or art. So it would stand to reason, that with less people gaining a firm and passionate grasp on a subject, there would be less available who are qualified to not only teach it, but teach it

well.Now, with teacher's unions gaining the same benefits for all teachers, where a history teacher and a calculus teacher of the same level of skill and experience receive the same compensation for their troubles, how much motivation does the truly talented mathmetician have to teach in highschool when various industries will pay him ridiculously more to work for them instead? How many history teachers would get offered $100K plus by the private sector?

So with supply and demand being what they are and all teachers NOT being created equal, why are they being paid the same? This only results in lesser qualified and lesser motivated math and science teachers in highschool resulting in less motivated and less educated students who have less chance of going into post-secondary math and science. Less post-secondary math and science students means a smaller number of talented mathmeticians and scientists graduating. This means a smaller number of potential future highschool teachers who are talented and educated enough to guide and motivate students in those fields. The cycle repeats.

I can't see the current educational crisis improving at all if these unions continue to insist that a history major has the same value as a good mathematician. I'm pretty sure we would have never made it to the moon if all we did was research the details of the war of 1812.