Editore"s Note
Tilting at Windmills

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February 17, 2006
By: Kevin Drum

THE ALGEBRA HATERS CLUB....Just for the record, I think that a lot of people are missing the point of Richard Cohen's anti-algebra screed in today's Washington Post. To be sure, I'll grant that this sentence about algebra's value is beyond idiotic:

It has its uses, I suppose, and I think it should be available for people who want to take it.

Gee, thanks, Richard! That's mighty open-minded of you! But setting this silliness aside, Cohen's serious point isn't really whether algebra is useful or not, it's whether it should be required to graduate from high school. That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout? I don't really have an opinion about this, but it's a serious question.

On the other hand, Cohen says he can't do percentages either, and if that's the case then maybe he should go back to high school. At the very least, he should be as ashamed of this as he apparently is of his nameless high school friend who didn't know where the Sahara Desert was. I'd venture to guess that calculating percentages is a whole lot more useful in modern adult life than knowing the location of the world's great deserts.

Kevin Drum 12:16 PM Permalink | Trackbacks | Comments (250)

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Comments

Inadvertently Cohen is making a good point about the lack of recognition and rewards given to people who do the heavy lifting that produces real goods and services in the country. The only recourse that these people have is to make a shitload of money like Gates or the Google founders. Otherwise these nerds do their own thing, living in dark cubicles of corporate America that pays much more to 6 feet blonde male MBAs whose main skills involve populating pre-programmed spreadsheets than to the people who actually design planes and computers and cars and software programs.

On another note, Washington Post should fire Richard Cohen for betraying so much ignorance about what 'reasoning' is.

Posted by: lib on February 17, 2006 at 12:19 PM | PERMALINK

As far as I know, you can take algebra in high school and fail it, but still graduate as long as your other grades/tests compensate for such a failure. So Cohen really doesn't have a point, unless he thinks algrebra should not be a required subject in school.

Posted by: David W. on February 17, 2006 at 12:21 PM | PERMALINK

setting this silliness aside, Cohen's serious point isn't really whether algebra is useful or not, it's whether it should be required to graduate from high school. That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout?

That may be his point, Kevin, but it's cloaked in so much silliness -- I'd say so many layers of disgustingly anti-intellectual bullshit -- as to be completely obscured.

A screed like Cohen's doesn't deserve consideration of its "serious point." If he wanted to discuss a serious point, he could have written a serious column. "Algebra is useless" isn't it.

Posted by: Gregory on February 17, 2006 at 12:22 PM | PERMALINK

That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout?

Is this a serious question? The U.S. continues to fall behind the rest of the world in terms of education, and you want to know if the answer is to dumb down our schools even more?

If I had my way, calculus, physics, chemistry, and biology would all be requirements for a high school diploma. Would that lead to fewer people with high-school diplomas? Yes. But that's life.

Posted by: Doctor Gonzo on February 17, 2006 at 12:23 PM | PERMALINK

, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout

A GED is an option.

What on earth do we award high school diplomas these days for, anyway? Turning 18?

Posted by: Constantine on February 17, 2006 at 12:23 PM | PERMALINK
Gee, thanks, Richard! That's mighty open-minded of you! But setting this silliness aside, Cohen's serious point isn't really whether algebra is useful or not, it's whether it should be required to graduate from high school. That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout?

If High School graduation is to mean anything, there must be standards. Ultimately, yeah, anywhere you draw the line, lots of people are going to argue about "well, shouldn't you make the standard one quantum more demanding?" or "shouldn't you make it one quantum less demanding?", and any of those requests, individually, is going to seem not unreasonable.

But you've got to ask, what is the value of the change?

And, frankly, algebra is largely basic problem solving. If you can handle elementary school word problems, you can probably handle algebra just fine if taught properly; if people aren't learning it, there is a problem in teaching (not necessarily a problem with the teachers -- it could be a problem with the way the schools are run which prevents the teachers from having a manageable environment to work with.)

Seems better to fix the problem than just to accept the failure.

Posted by: cmdicely on February 17, 2006 at 12:23 PM | PERMALINK

I do think that basic algebra should be required to graduate, since almost any individual should be able to pass a basic algebra class, if even on a second pass. Start them in freshman year, and let them keep trying all four years if necessary. I'd accept the alternative of passing a "logic" class, one focused on real-world critical thinking and basic rhetoric. Of course, this "logic" class, one focused on critical thinking and basic rhetoric, should be required foremost, in a free country led by voting citizens.

Posted by: Jimm on February 17, 2006 at 12:25 PM | PERMALINK

Argh.

Math isn't just for engineers. Reporters--good ones, anyway--can't report simple facts about important stories without a basic level of mathematic literacy.

Remember the 2000 debates? George Bush stood on the stage and told some whoppers about his budget plans. Gore called him out on them. But were our big shot reporters able to sort it all out?

Ted Koppel, for one, admitted openly that all those numbers were just incomprehensible. So the media turned instead to reporting on earth tones and doggie pills.

Bah.

Posted by: Quaker in a Basement on February 17, 2006 at 12:26 PM | PERMALINK

Lets see.......Bush is 100% ASSFACE! I know that's right!

Posted by: R.L. on February 17, 2006 at 12:26 PM | PERMALINK

if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout? I don't really have an opinion about this, but it's a serious question.

Close to a quarter of the population -- presumably including nearly all students unable to fathom algebra -- doesn't finish high school now. Why? That's the serious question.

Posted by: penalcolony on February 17, 2006 at 12:26 PM | PERMALINK

Part of the reason people are "completely unable to fathom algebra" is because of this attitude- that it has no application to real life. There are many ways of teaching it that make it much more accessible. But when people like Cohen propagate such an ignorant view, it makes it acceptable to throw up your hands and say, "I just don't get math!" You can see that in his statement about not knowing how to do percentages- it's something some people are, if not proud of, at least willing to admit. How many people would be willing to tell others, "I just don't get that reading thing! But it doesn't matter, I only watch TV, so I don't need it!"

Posted by: SP on February 17, 2006 at 12:26 PM | PERMALINK

My take on the Cohen article, even though it's unsaid, is that the guy is just upset that education has dared to move into the future.

Botney for crying out loud. Botney. My biology teacher gave us an introduction into it. It was a day. Then he, to be honest who was a great mind for biology, said that it was a waste of bloody time. Memorizing scientific names...for what purpose? To make us look smart?

Cohen wants a population that looks and sounds smart...but is dumb as a box of rocks. Much like himself!

Posted by: Karmakin on February 17, 2006 at 12:29 PM | PERMALINK

This is what happens when you tie the ability to live a decent life with being smart. It really illustrates the fundamental problem with meritocracies.

Richard aruges one fair point--that not everyone is a brilliant generalist, and your specialists shouldn't be screwed out of success because they aren't generalists. But really, he's just hairsplitting how you define "better" in a meritocracy.

Kevin takes on a different issue--the importance of not being a "high school dropout." If you're a dropout, you can't get a decent job doing anything--driving a bus, answering a phone in an office, whatever.

This is tied to a bigger issue--one's inability to do algebra shouldn't be a barrier to living a decent life. Similarly, one's inability to do math or do ANY mental exercise exceptionally well (or even in the top 30th percentile) shouldn't consign you to shit jobs and a lousy life.

Dumb people aren't less deserving of a decent life and good stuff than smart people are. The irredemable problem with a true meritocracy is that it says they are.

Posted by: theorajones on February 17, 2006 at 12:30 PM | PERMALINK

I don't know why they don't have a required course in logic instead of Algebra and Geometry in high school. It does not need to be symbolic logic, but any high school student who does not understand modus ponens and other basic principles of logic inside out should not be allowed to graduate. Then the likes of Richard Cohen will have no grounds to complain.

Come to think of it, in such a scenario they would not even be able to graduate to be in a position to write idiotic columns in national newspapers.

Posted by: nut on February 17, 2006 at 12:30 PM | PERMALINK

I can't say I'm surprised by Cohen's admission about percentages. In my travels around the world, I've come to realize that the level of education for many Americans approaches Third-World level. I've noticed that there is a palpable lack of respect for education in many parts of our country. Maybe that's why conservatives' slander of "pointy-head liberals" has been so effective for them.

Posted by: Taobhan on February 17, 2006 at 12:31 PM | PERMALINK

Sure, I think his substantive point about requiring students to pass algebra to graduate high school is fine. However, he took the opportunity to claim intellectual superiority for the literati he imagines himself a part of.

There's more than a bit of "nerd-bashing" going on there, complete with idiotic stereotypes (nerds can't write, nerds can't locate deserts, etc.) I'm sure it was mostly tongue in cheek, but I for one won't take a ribbing from someone ("Barbie") who is the very definition of a pseudo-intellectual.

Posted by: Will on February 17, 2006 at 12:31 PM | PERMALINK

I guess it depends on one's position in life. I can see where knowing the location of the world's deserts might be pretty important in some job descriptions.

Posted by: Tony Shifflett on February 17, 2006 at 12:33 PM | PERMALINK

Most importantly, one should be able to calculate the yearly desertification rate, as a percentage of current desert size.

Posted by: K on February 17, 2006 at 12:34 PM | PERMALINK

Requiring basic logic would not be an improvement for the type of student Cohen is talking about. The fact is that if you can't understand basic algebra then you aren't likely to do much better understanding the sort of logical puzzles that are part of any logic class. The truth is that on a conceptual level, which is really the root of the problem that students are having, basic math and basic logic are really the same thing.

Posted by: brent on February 17, 2006 at 12:40 PM | PERMALINK

I volunteer as a classroom tutor in Algebra 1 in a local middle school, as well as in a 4th grade math class. I have watched many, many kids struggle with Algebra. In my experience, almost anyone can master first year Algebra if they are willing to pay attention, follow directions and learn to solve problems in a step-by-step fashion, and this includes many special ed kids. One the other hand, someone who blows off the class isn't going to get it. It is my suspicion that Algebra is now required on the exit exam and by most California school districts as a proxy for determining who has the brains and self-control (and believe me, this is very hard for 8th and 9th graders) to pay attention long enough to master basic Algebra, because that is probably a very good predictor of who can cope with college and with a decent job.

As for Algebra's actual worth, obviously it is necessary for setting up and solving problems in science classes. It is great for solving certain kinds of puzzles and everyday problems that otherwise require sometimes tedious guess-and-check strategies. But that's only if you understand it. Like most people, I forgot Algebra and thus never used it for 35 years. Only when I became proficient again because of tutoring did I realize how helpful it could be. For example, the ratio method with cross-multiplication is the easiest way to solve percentage problems other than the "what is 10% of $20?" type.

Cohen is probably like students I have seen who develop a resistence and simply cannot understand it because they refuse to open their minds enough to do so. On the other hand, Algebra concepts are now bewing introduced in the 4th grade in California, and three years ago I taught two 4th graders most of first year Algebra, including factoring of quadratic equations, because they were eager to learn it.

Posted by: Mimikatz on February 17, 2006 at 12:41 PM | PERMALINK

Well, of course he's never used something at which he's incompetent. But, for instance, not being able to pass my driver's license test doesn't allow me to conclude that driving is useless.

Posted by: thump on February 17, 2006 at 12:42 PM | PERMALINK

Look, I certainly think that knowing math, and pushing students to master as much math as they can, is a very good thing.

I also think there's a correlation between mathematical ability and the general ability to analyze things. But it is a highly imperfect correlation. There really ARE people who are impressively good at reasoning in other areas who are simply wretched at math. Likewise, there are a goodly number of idiot savants in engineering and science who are utterly hopeless when it comes to moral or political reasoning -- just listen to them!

Why pretend to ourselves that the ability to do math well is essential to success in our society? Why pretend that mathematical ability is somehow perfectly correlated with other kinds of abilities? Why not instead recognize that, sometimes, just as with musical ability, a person is born "tone deaf" to certain concepts? Are such people to be treated as inconsequential in our society, despite impressive gifts elsewhere?

In the end, we have to organize our society so that the gifts people do possess are placed in positions where those gifts are important. Everything else is destructive, self-congratulatory prejudice.

Posted by: frankly0 on February 17, 2006 at 12:43 PM | PERMALINK

Math isn't just for engineers. Reporters--good ones, anyway--can't report simple facts about important stories without a basic level of mathematic literacy.

The importance of this can't be underestimated. All those journalists who avoided any sort of math or science because they planned on becoming writers, like Cohen, have an inability to understand even the most basic principles of the topics they write about.

Algebra isn't particularly useful on an everyday basis, but it is a foundation for understanding almost anything else requiring math and statistics - e.g. science, healthcare, economics.

Posted by: tinfoil on February 17, 2006 at 12:43 PM | PERMALINK

Anybody who thinks algebra is useless has never doubled a recipe, figured out how much four tires cost, decided how much sod to buy for that bare spot in the backyard, or worked out how much to save each month for the property tax bill due in July...

Geez.

Posted by: cmac on February 17, 2006 at 12:43 PM | PERMALINK

I'm just glad to see that Richard was able to find a job. I'm sure it was challenging. Algebra, siance, even Botney, are all weighted heavily in favor of the smart kids. (sheeesh)

Theora - I gotta differ. While I believe dumb people should be afforded every opportunity to attempt to attain a decent life, they are by their abilities and merits, less deserving than smart people.

(that's what my smart friends tell ME, anyhow)

Posted by: wishIwuz2 on February 17, 2006 at 12:45 PM | PERMALINK

Karmakin,

What, in the name of God, is "botney"? Were you talking about botany? (And if you were, what's so damn useless about understanding plants?)

Posted by: waterfowl on February 17, 2006 at 12:45 PM | PERMALINK

One can't learn basic statistics without knowing basic algebra. But I guess one can become a news reporter on a national scale without understanding basic statistics? Sufficient for he said/she said stenography I suppose.

Cranky

Posted by: Cranky Observer on February 17, 2006 at 12:45 PM | PERMALINK

brent:

But basic logic can be taught by using examples from every day life that appear to be much less contrived than Algebra or Geometry problems.

Moreover, no one can seriously dispute the necessity of logic as a requirement for graduation from high school. Not even Richard Cohen.

The only problem will be that with a population that understands logic, Republicans can never be in power again. But not from my point of view.

Posted by: nut on February 17, 2006 at 12:45 PM | PERMALINK

if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout

If you find yourself completely unable to master anatomy, should you be condemned to spend the rest of your life as a medical school dropout?

Posted by: Stefan on February 17, 2006 at 12:46 PM | PERMALINK

As a professional geographer, I'm appalled by the thought of someone who doesn't know where the Sahara is...but overall Kevin's right that understanding basic math concepts is more important in everyday life.
The thing about algebra that many people don't get is that you use it even if you don't realize you're using it. Sure, you might not be physically writing down things like "y = 5 + (x/6.5)^2" on a regular basis, but internally you're using it for things like basic economic decisions involving multiple variables (or at least you should be).

Posted by: drs on February 17, 2006 at 12:46 PM | PERMALINK

When our students fail... just lower the bar!

This is soooooo pathetic.

Let's see... hmm... should I learn BASIC math or should I learn BASIC geography? I know for certain that I can't learn both (even in the most simple and fundamental way)... so I must chose?

Again... this is soooooo pathetic.

I fear for the future of this country... and, by extension, the entire world.

Posted by: Mitch on February 17, 2006 at 12:47 PM | PERMALINK

Asserting that "Most of math can now be done by a computer or a calculator" is true, but if you can't parse a word problem into an equation, no calculator will help you.

There are plenty of people who make it through life functionally illiterate. Do they get to assert that reading doesn't matter and shouldn't be required to graduate HS? Removing it means that a lot of people who could do it, but find it difficult will just skip it. Many of them would have found it makes them better citizens and enriches their lives.

At the end of the day, I'd go with what the competition is doing (India, Korea, China) to set educational standards, not a happily ignorant columnist.

Posted by: Tentakles on February 17, 2006 at 12:47 PM | PERMALINK

I call BULLSHIT on all you algebra advocates, and I can PROVE it.

TBROSZ is a fucking rocket scientist. His math skills are probably better than 99% of the people that read this blog.

Yet, his slavish devotion to all things Bush and Republican demonstrate convincingly that his logic, reasoning and critical thinking skills are about the same as a bag of rocks.

Posted by: SteveK on February 17, 2006 at 12:48 PM | PERMALINK
Reporters--good ones, anyway--can't report simple facts about important stories without a basic level of mathematic literacy.

Unfortunately, in the real world, we're stuck with reporters (on TV) whose primary skills are looking good (however their target audience visually cues on "trustworthy) and having a nice speaking voice, and (in print, and writing the copy for the TV "reporters") whose skills are the ability to take a press release, the responses from relevant interest groups, and fit them into a canned "neutral" format that avoids any attempt to determine the truth beyond "who said what".

Its not just mathematical literacy than the press lacks, but real competence in any of the fields they cover.

Posted by: cmdicely on February 17, 2006 at 12:48 PM | PERMALINK

I'd accept the alternative of passing a "logic" class, one focused on real-world critical thinking and basic rhetoric. Of course, this "logic" class, one focused on critical thinking and basic rhetoric, should be required foremost, in a free country led by voting citizens.

I agree, and I also think that algebra is useful because it at least is an introduction to setting up equations and models for reasoning. I never liked algebra-- was mediocre in high school and only managed to get an A in college, by the skin of my teeth, because I was better at basic arithmetic than the TA was, which kept me engaged-- but it does teach one to think in ways that presumably help in real-life problem solving, even if quadratic equations aren't part of the process. I use geometry (and percentages) far more in everyday life than I've ever used algebra, but that doesn't mean that I don't use hypothetical factors, etc., when dealing with complicated situations... and algebra is really where most of us learn those methods in an orderly fashion.

I understand that algebra is being introduced much earlier than it was whan I was kid, and that's probably a good thing. Except for word problems, it was completely unknown to me & my peers until eighth grade at the earliest, and I don't think that's really a good age to start applying abstract concepts.

Posted by: latts on February 17, 2006 at 12:49 PM | PERMALINK

The object of high school, or college for that matter, is not simply to shove information into your head, it's to develop the skills required to learn something and think about it. When you're out in real life, you're going to need to learn things that are going to be difficult to learn. New things they don't teach in school, if you're going anywhere at all in life.

There's a difference between not being able to pass algebra, and not wanting to do the work to pass algebra. I hit a wall with calculus in high school, myself, but managed to pass it. Summer school reared its ugly head.

After you get out of school, you retain and learn what you need to know, and some of the rest goes by the wayside. I can locate the Sahara Desert, among many other things, but if you put an unlabeled political map of Africa on the table and told me to label every last country, I wouldn't be able to do it. That just doesn't come up that much in my work, and as with most people nowadays, the data is there when I need it.

Algebra, like science, teaches people how to think, even if they don't remember the formulas or the Periodic Table of Elements later on. Data you can look up. Analyzing it and drawing conclusions is the hard part.

"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house."

- "Notebooks of Lazarus Long," by Robert A. Heinlein

Posted by: tbrosz on February 17, 2006 at 12:53 PM | PERMALINK

Well, since we require people to do their taxes, they should be able to handle basic mathematics. Or will the computers do that for them as well?

Figuring out what your 401(k) is doing, balancing your checkbook, understanding the costs of things like doing some sort of work on the house (taking measurements, etc.)......basic algebra, that is, simple problem-solving, are necessary. Yes, you should be able to do the basics.

Geometry is basic logic -- taking an abstract set of facts and making conclusions. It's not overhard, and it's very valuable.

Calculus, the language of higher mathematics, is not *necessary* but it's desirable to get an introduction to it.

To the good points above about reporters not being able to follow the math in a Presidential campaign -- being lazy -- all the more argument in a democracy to require that voters know *something* so they're not so easily bamboozled by charming rogues. And might even vote for the egghead sometime.

We have a brutish, celebrity culture, that celebrates force and rudeness rather, and disdains thought and introspection. Donald Trump should be a pariah but for some reason he's feted (while I think he's fetid).

Posted by: zmulls on February 17, 2006 at 12:53 PM | PERMALINK

"I'd venture to guess that calculating percentages is a whole lot more useful in modern adult life than knowing the location of the world's great deserts."

And geography gets dissed again. Sorry, Kevin - I understand your point; from a day-to-day practical matter, algebra likely is more useful than knowing the location of the world's greatest deserts (although given that the Sahara desert is the largest in the world, not knowing that it's located in northern Africa indicates an appaling lack of even the most rudimentary of basic geographic knowledge).

But, then again, much could be said about a lot of other things. Like history, politcs, literature, music, etc.

Posted by: eponymous on February 17, 2006 at 12:53 PM | PERMALINK

"Setting this silliness aside, Cohen's serious point isn't really whether algebra is useful or not, it's whether it should be required to graduate from high school. That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout?"

Kevin, does this ambiguity extend to other courses or is it just the typical liberal arts majors disdain for math & science? Would you substitute history or English composition for algebra in the above quote?

Doesn't there have to be some specific standard for what constitutes a high school education? Humanities, math, science, the arts...all are necessary to a well-rounded education.

Posted by: orogeny on February 17, 2006 at 12:54 PM | PERMALINK

Dear SteveK,

I am glad I was eating clam chowder instead of drinking something when I read your post. The chowder makes a bigger mess, but it doesn't travel nearly as far when laughed out of my mouth, and managed to avoid the monitor.

Posted by: Arr-squared on February 17, 2006 at 12:56 PM | PERMALINK

People often do wonder what the point of many of the classes they took in school was. Undoubtedly, the practical application of many subjects seems unclear. And then, as life takes unexpected turns, many subjects turn out to have suprising relevance in ways both highly significant and trivial. Perhaps one becomes an investment banker, and suddenly needs to have a command of all manner of historic, geographic, etc facts. Or perhaps some other unexpected career opportunity presents itself that requires a sound grounding in the fundamentals of subjects that seemded exosteric when one was young. Or perhaps one just begins to actually take pleasure in delving into science or whatever as a hobby. In any case, education should be about opening doors to future opportunities and unexpected avenues for personal fulfillment...

Posted by: Aidan on February 17, 2006 at 12:57 PM | PERMALINK

If you find yourself completely unable to master reading, should you be condemned to spend the rest of your life as a high school dropout?

If you find yourself completely unable to master writing, should you be condemned to spend the rest of your life as a high school dropout?

If you find yourself completely unable to master spelling, should you be condemned to spend the rest of your life as a high school dropout?

If you find yourself completely unable to master arithmetic, should you be condemned to spend the rest of your life as a high school dropout?

OF COURSE YOU SHOULD. You shouldn't get a high school diploma just for showing up. Everyone, and I mean everyone that I knew in high school who had problems learning math didn't pay attention or work at it. Now I happened to like math and hate English classes, but I still had to read, interpret and express my thoughts in those classes. Should I have been allowed to graduate without taking English?

I think our educational system is becoming sub third world, mostly because I hear parents saying stupid things like this (oh, I can't do math) all the time. My experience is that it is not the schools failing our children, but their parents.

Posted by: HankP on February 17, 2006 at 12:59 PM | PERMALINK

I think Cohen has just admitted that he has never paid taxes, tipped a waiter, compared mortgages or healthcare plans. If you're wealthy enough to hire an accountant, I doubt you need any math skills at all.

Posted by: brent on February 17, 2006 at 1:02 PM | PERMALINK

Richard Cohen is right. You can be a President without knowing Algebra.

Posted by: lib on February 17, 2006 at 1:02 PM | PERMALINK

"Algebra, like science, teaches people how to think, even if they don't remember the formulas or the Periodic Table of Elements later on. Data you can look up. Analyzing it and drawing conclusions is the hard part."

Many Americans don't want to think. That's no problem - there are plenty of thinking kids taking algebra, geometry, biology, physics in India and China who will be happy to hire you to work for them at Wendys!

Posted by: CParis on February 17, 2006 at 1:03 PM | PERMALINK

I'd actually be okay if they taught a sort of 'everyday algebra' class for those not going into the sciences, that included how to apply it in statistics, economics, cooking, home finances, and other everyday logic/word problems.

Same with Geometry. And even languages (wouldn't it be usefull if everyone could at least exchange a few words of Spanish, Arabic and Chinese?)

Basically where they would teach just enough to get by as a member of society. I think we'd all be better off.

Posted by: tinfoil on February 17, 2006 at 1:03 PM | PERMALINK

I will interject with a short essay I wrote a few years ago, on what happens when people don't know basic algebra.

Summary: math-ignorant salesmen almost drove a company to bankruptcy because they couldn't do simple calculations even with a calculator.

Posted by: charlie don't surf on February 17, 2006 at 1:04 PM | PERMALINK

Algebra is nothing more than practicing logic using numbers. The fact that Mr. Cohen does not care for algebra should not suprise anyone.

Posted by: Charles on February 17, 2006 at 1:06 PM | PERMALINK

If algebra isn't required for high school graduation, what would one require to graduate? In fact, we can add geometry in there too.

Algebra geometry aren't some high forms of mathematics, they are a level one needs to get through life reasonably well and they develop basic critical thinking skills.

There are different forms of algebra education available to those who are not good at it or having learning disabilities in most schools.

We require students to have a base knowledge to get a degree, algebra and geometry are as basic as it gets at the high school level.

Posted by: ArchPundit on February 17, 2006 at 1:09 PM | PERMALINK

Boy, would I love to be a contractor and get hired to remodel Cohen's house. With all sorts of complicated tile work and molding and whatnot, stuff with per-unit costs. I could pad the bill six ways to Sunday, and he -- not understanding algebra and having never, ever used it once since high school -- would never know the difference.

Posted by: Phil on February 17, 2006 at 1:09 PM | PERMALINK

C'mon, people! The real motivating force behind Cohen's article is a sub rosa Freedom Fries-style purge of Arabic-rooted words and technologies from the public sphere!

Posted by: The Confidence Man on February 17, 2006 at 1:10 PM | PERMALINK

Kevin,

Actually, in CA, the more serious question is whether you should be "condemned to spend the rest of your life as a high school dropout" if you can't read or write English. See Arturo Gonzlez's piece in today's San Francisco Chronicle, [tried to link it, but evidently the URL was too long; go to www.sfgate.com/chronicle and you can find it] and ponder the case of Liliana Valenzuela, who has a 3.84 GPA and ranks 12th in a class of 413 students, despite not being able to read or write well enough to pass the test (which demands tenth-grade language skills) despite several attempts. There is no way this kid could have that GPA and that class rank unless someone has repeatedly given her at worst B's in English, despite her not actually mastering the material.

This is, quite simply, cruel. This girl, if graduated, is probably going to go to college and find that she can't cope with the material because she just plain doesn't know how to read well enough. And all along she's been assured that she's reading just fine.

Gonzlez, by the way, is a lawyer involved in a suit to require CA to supply diplomas to all high school students who have passed all the required classes. Though why that's not also discriminatory I don't know. Just because you flunk history, you're condemned to spend the rest of your life as a high-school dropout? That's harsh.

Posted by: waterfowl on February 17, 2006 at 1:11 PM | PERMALINK

That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout?

Absolutely.

That some people disagree is testament to the amount of entitlement young people feel nowadays. My wife for one encounters this daily in the college classes she teaches, where students apparently expect a good grade just because they showed up for class. College students, thinking that they've accomplished something just through perfect attendance! Don't get me wrong, showing up is great, but that's just the first step. The second step is actually using your goddamn brain.

We're growing a nation of fucking Barbie dolls. "Math is hard!"

Posted by: Irony Man on February 17, 2006 at 1:11 PM | PERMALINK

True story - I was riding the subway in Washington DC a few years ago when two young men boarded the train. They looked to be in their mid twenties. One of them said to the other "Hey, is Wahington DC in the District of Columbia or in the state of Maryland?" The other one answered, "It's not in either one. It's in Virginia." I looked at the one who answered and he looked at me. I'm sure my expression, without any words, communicated that he was a horses ass. He then said to his friend, "I'm sorry, it's not in Virginia, it's in West Virginia." WE WERE IN WASHINGTON DC! The very next day a group of young construction workers (they were wearing hard hats) were talking about a land surveyor who was working at their job site. One said this about the surveyor, "Before this job he was working for the federal government out on the West Coast, or wherever the Appalachian Mountains are." Another one of them corrected him and said, The Appalachian Mountains are not on the West Coast, they're in Virginia and West Virginia and North Carolina." "OK," said the other one, "The midwest."

Couple that story with the fact that Richard Cohen "can't do percentages" - i.e. he doesn't know how much a 15% tip will cost him at the restaurant - and we have a scary society. I'm not really looking forward to the future.

Posted by: Lamonte on February 17, 2006 at 1:14 PM | PERMALINK

I guess it depends on one's position in life. I can see where knowing the location of the world's deserts might be pretty important in some job descriptions.

Knowing where the Sahara is, is trivia. Knowing how to use a map/encyclopedia/CIA World Factbook to find the Sahara when you need to is a far more useful skill. Do you know where the Gibson desert is? The Thar? The Atacama? The Kyzyl-Kum?

I'd actually be okay if they taught a sort of 'everyday algebra' class for those not going into the sciences, that included how to apply it in statistics, economics, cooking, home finances, and other everyday logic/word problems.

Huh? It's not like the rules of algebra change depending on the problem domain. That's kind of the point. Was your high school algebra instructor unable to give you word problems from everyday contexts for some reason?

Posted by: Hamilton Lovecraft on February 17, 2006 at 1:14 PM | PERMALINK

Now that all the news you need is on TV and talk radio, and the GPS in your car eliminates the need to read road signs, why should we insist that you have to be able to read in order to graduate from high school? Why don't we just hand a diploma to everyone who manages to get to 18? Or 16? Or 12?

Actually, I'm perfectly fine with that, as long as employers and college admissions officers know what a high school diploma really means, and both require employees and students to have somehow acquired actual knowledge of words, math, science, history and yes, geography since they're obviously not going to learn them in high school.

Posted by: yellowdog on February 17, 2006 at 1:18 PM | PERMALINK
That some people disagree is testament to the amount of entitlement young people feel nowadays.

I think its at least as much a testament to the degree of entitlement that many parents feel today.

Posted by: cmdicely on February 17, 2006 at 1:20 PM | PERMALINK

The point of Kevin's post is that there are a huge number of California kids who are in danger of being high school dropouts because they can't pass a TEST in algebra.

The subtext of that is that if you don't have a high school diploma, you are pretty much relegated to the underclass for the rest of your life. I think that's clearly a bad thing for everyone, not just the kids.

As to the assertion that it's just lack of hard work that makes it impossible for some kids to get algebra, that's bullshit. I'm on the other side of that. Algebra and Trig were easy for me when I was 10 or so, but I know some extremely bright and creative and functional and hard-working people who just don't have the brain for that kind of symbolic, abstracted thinking. It just ain't there, and trying to beat it into them with a stick (that is going to whack the rest of society in the butt, too) won't put it there.

Saying that you must be able to pass an algebra test (again, something entirely different than being able to use it) to avoid being relegated to the underclass for the rest of your life seems just a bit arbitrary.

I would suggest the following alternative. If these kids can't pass the test, require that they attend a class in algebra or logical reasoning or something similar, and that to pass the test, they have to have been at every class, and turned in every assignment with at least some attempt at completing it. That would indicate the ability to behave responsibly and at least try to do the required work. That tells me more about the person than their ability to learn algebra.

And I think it teaches them more about what it takes to be successful: show up and do the best you can. That actually works.

Posted by: Charles on February 17, 2006 at 1:22 PM | PERMALINK

Richard Cohen just admitted he's an idiot - and we take his argument seriously?

A high school diploma is supposed to prove basic comptency in reading, 'riting and 'rithmetic. Algerbra is basic 'rithmetic. If you don't know it, you're missing one of the 3 "R's" and shouldn't have a diploma.

Richard Cohen himself is a great example of a great yapper who clearly hasn't learned basic logic. How many times does he leap from one unproven fact to another? How many times has written about elections and polls - and clearluy didn't have a clue about the numbers? Now we know why.

It's actually funny in a certain way. People feel perfectly comfortable saying " I don't know math." or "math is too hard, etc." In what other area are people so happy to trumpet their own ignorance or laziness?

Basic math is needed to understand basic concepts and logic. You don't know it, you don't understand basic concepts.

Posted by: Samuel Knight on February 17, 2006 at 1:22 PM | PERMALINK

Maybe, just maybe, kids need different skills today than they did when Cohen went to high school.

Posted by: dk on February 17, 2006 at 1:22 PM | PERMALINK

You don't need math these days. When the customer says they want a hamburger and coke, you press the key with a picture of a hamburger, then press the key with a picture of coke. The total price and the change are calculated. The hard part is learning to say "You want fries with that?"
What we ought to do in our schools is teach the controversy. Polls show that less than 30 percent of the population believes that only algebraic functions should be taught, whereas two-thirds of Americans believe that transcendental functions should be taught also--let the students decide!

Posted by: mark on February 17, 2006 at 1:23 PM | PERMALINK

You know, no Ancient Greek, not Aristotle or Plato or Socrates, knew a single thing about algebra, because, well, it hadn't been invented yet. And the geometry was nothing more than Euclid -- pretty much at most what is covered in HS geometry.

Were they one and all bad at reasoning?

Posted by: frankly0 on February 17, 2006 at 1:24 PM | PERMALINK

Lamonte,

A commenter on another blog reported a few days ago that a high school student he was tutoring was unable to "compute" 2% of 100 without using a calculator. What can you say?

As for tips, I always use 1/6 rather than 15%, not that it makes much difference. I think early on one of my parents must have told me that was the rule, and it stuck.

Posted by: waterfowl on February 17, 2006 at 1:24 PM | PERMALINK

As for tips, I always use 1/6 rather than 15%, not that it makes much difference. I think early on one of my parents must have told me that was the rule, and it stuck.

You should tip 20%.

It improves calculations and human relations.

Posted by: frankly0 on February 17, 2006 at 1:27 PM | PERMALINK

Only three percent of what we learn in school is useful. Education is for educators, and its purpose is pre-employment screening on behalf of the education/human-resource complex.

Posted by: Myron on February 17, 2006 at 1:29 PM | PERMALINK
The subtext of that is that if you don't have a high school diploma, you are pretty much relegated to the underclass for the rest of your life.

Inasmuch as that is true, that is the problem, not the specific requirements of the high school diploma. So trying to fix it by weakening the high school diploma until it is meaningless is not the solution -- if you are going to do that to solve the problem, you might as well not have high school diplomas at all.

Posted by: cmdicely on February 17, 2006 at 1:30 PM | PERMALINK

Somehow I actually made it all the way through calculus in high school, and even tested out of one required math class in college. So I guess I did retain something from it, even though I was totally confused most of the time.

Anyway, I don't know that algebra should be required, basic arithmetic is much more useful for most of us in the real world. Maybe I do use what I learned in algebra and calculus, a way of thinking or whatever, and I just don't know it.

The thing that bothers me much more was being required to take math and science courses in college, which cost me a lot of money, and had nothing to do with my major. It wasn't until my junior year that I was finally taking all courses in subjects that I actually wanted to study.

Posted by: Ringo on February 17, 2006 at 1:32 PM | PERMALINK

The California Exit Exam is just eighth grade level pre-algebra. Arturo Gonzalez is still suing the state on behalf of those who can't pass.

Posted by: SF on February 17, 2006 at 1:33 PM | PERMALINK

No one who makes the statement that 'the Laffer curve is real, though no one knows its shape or how many peaks it has' should be allowed to graduate second grade.

Posted by: lib on February 17, 2006 at 1:33 PM | PERMALINK

Samuel Knight:

A high school diploma is supposed to prove basic comptency in reading, 'riting and 'rithmetic. Algerbra is basic 'rithmetic. If you don't know it, you're missing one of the 3 "R's" and shouldn't have a diploma.

That's really easy to say for someone who has a diploma and was blessed with the ability to think abstractly about mathematical constructs.

"Hey, if you can't think like I can, look forward to unemployment and disability for the rest of your life. What do I care? At least my standards for your understanding will be upheld."

Crap. This is much more important than that. A hgih school diploma is a critical piece of paper without which it is pretty much impossible to function in today's world.

And if someone can't pass a test in Algebra despite multiple attempts, then their brain just ain't gonna get it. And I don't think that says their lives should just be discarded.

We need an alternative other than "Fuck off and die." And I don't think we should dumb things down, but we gotta find another way to help these kids learn, because that's the point isn't it?

I guess the other point is survival of the fittest, but I don't think abstract mathematical thinking ability is an aboslute marker for fitness.

And these kids just aren't going to go away into the bush and die. This isn't like not being able to hunt antelope. They are going to hang around, many of them jobless, discouraged, and angry. That's a good thing?

Posted by: Charles Richardson on February 17, 2006 at 1:33 PM | PERMALINK

frankly0,

Were [the ancient Greeks] one and all bad at reasoning?

[snark] Of course they were, the same way they mysteriously forgot the principal battles of WWII.[/snark] No one is asking high school students to invent algebra, any more than they're asking them to write Shakespeare.

Posted by: waterfowl on February 17, 2006 at 1:34 PM | PERMALINK

Before we can decide on whether or not a competency in algebra should be required to graduate high school, we should decide on what it means to society to be a high school graduate. Why do we, as a society, invest in public education? What return do we want for that investment? Is a compentency in algebra a requisite return on our investment?

Posted by: dvg4048 on February 17, 2006 at 1:34 PM | PERMALINK

Algebra?...math?...history major!!!!!

Posted by: TJM on February 17, 2006 at 1:35 PM | PERMALINK

For goodness sake, are we becoming a nation of weenies? Yes, math is hard for some. Chemistry is hard for others. Latin almost drove me to the edge. However, the process of recognizing the fear, overcoming the frustration, doing what it takes to get to the aHA moment and learning how to hang in there are invaluable life lessons.

These prepare us to face the other really tough times coming in our lives, both intellectual and emotional. So suck it up and enjoy the challenge.

At 66 I'm taking Spanish. I'm the least talented and experienced in the class....hard on my ego as a retired professor but great fun to have a new challenge and getting closer to the aHA moment!

Posted by: Rain on February 17, 2006 at 1:36 PM | PERMALINK

More idiocy from the egalitarianism-uber-alles crowd.

That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout?

If passing algebra is required to graduate?

Yes.

What does "high school dropout" mean? It means that you did not graduate from high school. That you did not pass enough classes to do so. If Algebra is required to graduate, and you can't hack it, then you don't graduate.

If we simply wave a hand and graduate everyone, then a high school diploma means nothing. Literally nothing. Everyone gets one. The having of one is meaningless.

The purpose of any degree is not to make the holder of the degree feel good. It is to indicate that the holder of the degree has, legitimately, accomplished a certain series of tasks and can reasonably be inferred to have a certain set of skills.

I'm sorry if that makes those who do not have those skills feel badly, but the bottom line is they do not have those skills, and that's what the damn diploma means.

Should algebra be required to graduate from high school?

Absolutely. That, however, is a matter of opinion.

Posted by: S Ra on February 17, 2006 at 1:36 PM | PERMALINK

So Cohen and Barbie are the same person?

Posted by: craigie on February 17, 2006 at 1:36 PM | PERMALINK

No one is asking high school students to invent algebra, any more than they're asking them to write Shakespeare.

But they ARE demanding that people master something the ignorance of which, demonstrably, had NO effect on the reasoning abilities of some of the greatest philosophers of all time.

Posted by: frankly0 on February 17, 2006 at 1:37 PM | PERMALINK

Did it ever occur to you that columnists write stupid shit merely because: They have a deadline, a column due, and no better ideas of what to write?

Just like some bloggers, some of the time.

Posted by: Libby Sosume on February 17, 2006 at 1:37 PM | PERMALINK

Myron,

Only three percent of what we learn in school is useful.

Don't tell that to Richard Cohen; he can't do percentages.

(Just getting in the lame-but too-obvious joke before anyone else does.)

Posted by: waterfowl on February 17, 2006 at 1:38 PM | PERMALINK
Anyway, I don't know that algebra should be required, basic arithmetic is much more useful for most of us in the real world.

Even granting, arguendo, that this is true, it is irrelevant unless you assume that the alternatives are "learn basic arithmetic" or "learn algebra".

Posted by: cmdicely on February 17, 2006 at 1:39 PM | PERMALINK

Gee, thanks, Richard! That's mighty open-minded of you! But setting this silliness aside, Cohen's serious point isn't really whether algebra is useful or not, it's whether it should be required to graduate from high school. That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout? I don't really have an opinion about this, but it's a serious question.

You're a moron Drum.

Absolutely, let's graduate people who will go to college or into life with a world of possibilities cut off for them, possibilities they will never know exist, because Drum thinks there's a legion of people who just can't possibly learn algebra.

Let's move them along, let's "graduate" them. The GOP needs fresh blood.

Posted by: Lettuce on February 17, 2006 at 1:42 PM | PERMALINK
But they ARE demanding that people master something the ignorance of which, demonstrably, had NO effect on the reasoning abilities of some of the greatest philosophers of all time.

You are abusing the word "demonstrably". Or are you claiming that you can prove, somehow, that Aristotle, Socrates, Plato, et al. would not have been even better when it came to reasoning had they been exposed to algebra?

Posted by: cmdicely on February 17, 2006 at 1:43 PM | PERMALINK

cmdnicely:

Inasmuch as that is true, that is the problem, not the specific requirements of the high school diploma. So trying to fix it by weakening the high school diploma until it is meaningless is not the solution -- if you are going to do that to solve the problem, you might as well not have high school diplomas at all.

Agreed. I'm not suggesting we weaken it. I'm suggesting we take individual differences into account and be more flexible in the requirements, and be more realistic about what it takes to function, and more aware of the consequences of discarding the lives of a lot of kids.

That takes an intelligent approach to the problem, not just arbitrary standards that may or may not be functionally correct, but are easy to test for.

As another commetor pointed out, high school is just pre-screening. If that's the case, let's teach showing up and working and sincerely trying tolearn, and make that a requirement. The trouble is that's not easily testable, and it's all about testing. It's the German factory model.

Again, some peoples' brains just don't do abstract symbolic thining very well. But they do other stuff just fine. My wife is a briliant and accomplihsed composer and musician, and has a electronic music setup of computers and gear that looks like something out of Star Wars but she still has trouble computing percentages for tipping.

Peoples' brains are different and unique. They don't always meet our standards. They are still worth something. It may not be simple to determine and nurture that worth, but it benefits all of us to do so.

Posted by: Charles Richardson on February 17, 2006 at 1:44 PM | PERMALINK
And if someone can't pass a test in Algebra despite multiple attempts, then their brain just ain't gonna get it.

Strange, my mother couldn't despite multiple tests in high school. She got through it quite well -- not without lots of work and frustration, but still with good grades and understanding -- when she went to the community college in here 40's.

And I've known many other people that couldn't get through algebra despite multiple attempts until they found the right class, right tutor, or otherwise right learning environment.

I doubt there are very many people who are unable to learn algebra. There are lots of people whose abilities aren't being taught to.

The solution is not for society to accept that we are failing to teach those people.

Posted by: cmdicely on February 17, 2006 at 1:48 PM | PERMALINK

"knowing the location of the world's great deserts"

Well, I had no problem with algebra, and I know where to find Baked Alaska.

Posted by: stupid git on February 17, 2006 at 1:49 PM | PERMALINK

Or are you claiming that you can prove, somehow, that Aristotle, Socrates, Plato, et al. would not have been even better when it came to reasoning had they been exposed to algebra?

How about finding me a contemporary philosopher more capable than Aristotle, Plato, or Socrates? Failing that, don't you think my point is pretty well made?

Posted by: frankly0 on February 17, 2006 at 1:50 PM | PERMALINK
Agreed. I'm not suggesting we weaken it. I'm suggesting we take individual differences into account and be more flexible in the requirements, and be more realistic about what it takes to function, and more aware of the consequences of discarding the lives of a lot of kids.

No, see, this is where I disagree.

Setting the standards for a high school diploma ought to have nothing to do with "discarding the lives of a lot of kids".

If it does, there is something fundamentally wrong with the way the diploma is treated that cannot be corrected, at all, by changing what the requirements are for the diploma, whether by weakening them or "making them more flexible" or anything else, because the problem isn't with the standards at all.

Posted by: cmdicely on February 17, 2006 at 1:50 PM | PERMALINK

One of the great virtues of studying algebra, and math in general, is that bullshitting is completely meaningless. You either got the right answer or you didn't. Emotionally, you must be prepared to accept failure, because it's going to be in your face.

This is why lots of people don't like it. It reminds them of their failure, failure that is unambiguous. That's pretty uncomfortable.

Posted by: Doctor Jay on February 17, 2006 at 1:51 PM | PERMALINK

This is like my nephew paying H&R Block $75 so he can get his $1000 refund now rather than in a few weeks. It never occured to him that he just paid them 7.5% of his refund to get it early.

He basically paid H&R Block 90%+ annualized interest on that $1000 he borrowed from them.

You see this over and over with the poor and uneducated at rent-a-centers and the like. We DON'T need a dumber America so that smart, unethical types can take advantage of them.

Posted by: tripoley on February 17, 2006 at 1:52 PM | PERMALINK

The president's budget is published...and met with a collective yawn. Deeply troubling, as what gets funded and what doesn't affects people far more than, say, same-sex unions. Not surprising, however, given the general level of mathematical illiteracy in the nation.

I can't believe someone who thinks average citizens should be involved in informing public policy can even suggest that algebra (and math in general) is unimportant.

Posted by: moderleft on February 17, 2006 at 1:52 PM | PERMALINK

frankly0,

But they ARE demanding that people master something the ignorance of which, demonstrably, had NO effect on the reasoning abilities of some of the greatest philosophers of all time.

I wouldn't quite say that; I imagine that a Euclid who did know algebra would have done even greater things than he in fact did. More tools are not always an advantage, but most of the time they are. And algebra is a powerful tool.

Yes, some commenters have been laying stress on the ability of algebra to improve "reasoning skills" and the like. I don't see it like that, exactly. I think there are certain things important to know, and among them are human accomplishments. I think people should know algebra in the same way that they should know Shakespeare and know the great cathedrals and know the great works of art and music and science and engineering. All this is our legacy. Humanity made it individual human beings made it and every person has to understand how precious it is.

And they need to know the worst, too what we and others have done, what we and others have left undone. Would you countenance an exit exam about world history with that focus?

Posted by: waterfowl on February 17, 2006 at 1:53 PM | PERMALINK

My wife is a briliant and accomplihsed composer and musician, and has a electronic music setup of computers and gear that looks like something out of Star Wars but she still has trouble computing percentages for tipping.

That's actually interesting, because apparently musical & mathematical abilities are closely related in how the brain works. Then again, percentages are just arithmetic, not higher mathematics, and I've known quite a few people (similar to the college algebra TA I mentioned above) who actually had a good understanding of higher mathematical concepts, but difficulties with basic arithmetic made subjects like calculus unappealing or impossible. I guess that situation would be like undertaking musical composition or performance without the ability to read music, in that it might be possible to excel without the basic tools, but it would take additional talent and enthusiasm to overcome that lack.

Posted by: latts on February 17, 2006 at 1:54 PM | PERMALINK

cmdnicely:

I agree. The problem is not with the standards. It's with the whole system. Or i'm probalby missing your point, so enlighten me by expanding on what you said.

But we can some drowning kids here, almost literally. While we chat, their boats are sinking. And it's a big group, mainly already in the poorer schools and nighborhoods. What do we do now?

I am not for lowering standards, if anything I'm for raising them. But this particular standard is so arbitrary, and such a hot button for all the technocrats and engineering types out there...and like I said, algebra is easy for me, always was.


Posted by: Charles Richardson on February 17, 2006 at 1:58 PM | PERMALINK
How about finding me a contemporary philosopher more capable than Aristotle, Plato, or Socrates?

"More capable" is hardly objectively definable. Newton and Galileo -- who you will note were exposed to algebra -- were quite a bit better at reasoning about physical phenomena than Aristotle. I'd take Rawls over any of them when it comes to moral reasoning. I'd take any of a number of political philosophers of the last several centuries, most of whom had probably encountered algebra, over any of them where it comes to reasoning about human societies (and not just ones I agree with) -- from Hobbes to Locke to Marx to...

Now, of course, given that all of them lived in a world influenced by Aristotle, Plato, and Socrates, its impossible to isolate the effect to compare them, and, anyway, any such comparison is inherently subjective. Which, of course, further undermines your claim that the earlier ones were "demonstrably" unaffected by absence of exposure to algebra.

OTOH, assuming you were exposed to algebra, I think your whole line of argument here demonstrates that exposure to algebra is certainly no guarantee of even minimal reasoning skills outside of its bounds.

Posted by: cmdicely on February 17, 2006 at 2:01 PM | PERMALINK

Maybe I'm crazy, but I've always thought that minimal proficiency at basic mathematics (algebra, geometry and trig for high school, calculus for college) should be an absolute requirement for graduation. People that can't handle these are either too stupid or too lazy to deserve to graduate.

And I'm throwing down the BS card on Cohen's "I knew this girl that aced math but couldn't locate the Sahara desert" crap. My general experience has been that people that are good at math are usually pretty good at the other subjects as well; the same cannot be said about people that are good in English or history or whatever. Seriously, I bet I know 50 "I love Shakespeare, but I can't solve a binomial equation" people for every single "I think I'll use the shell method to integrate, but I'm not quite sure what a complete sentence is."

(And, by the way, I was a triple major in college, with two of the degrees in theoretical mathematics and American history. The other was management science, and I'm current a lawyer.)

Posted by: Joe on February 17, 2006 at 2:02 PM | PERMALINK

Algebra is Arabic. The DoHS is gonna outlaw it.

Posted by: W on February 17, 2006 at 2:02 PM | PERMALINK

Some things that girls have used Algebra to do "in real life":

Sail around the world.

Build the coolest houses, ever.

Help to find a cure for Cohen's brain damage.

Make a shitload of money.

Just sayin'

Posted by: Brautigan on February 17, 2006 at 2:02 PM | PERMALINK

latts:

I guess that situation would be like undertaking musical composition or performance without the ability to read music, in that it might be possible to excel without the basic tools, but it would take additional talent and enthusiasm to overcome that lack.

Something like that. My wife has been composing since she was 8. And she's a great sound engineer, and was doing electronic music with the first syntehsizers. But basic math eludes her. And she went to one of the best private schools in Manhattan, and was a hard worker.

In many, cases, it ain't effort.

Posted by: Charles Richardson on February 17, 2006 at 2:02 PM | PERMALINK

waterfowl,

Mostly I agree with your latest post.

I DO think that students today absolutely should be put under a good deal of pressure to master algebra and other kinds of basic math. The thing that I DO find rather repulsive in Cohen's column is his clear contempt for math, and attitude which I find simply arrogant and dismissive in the extreme. The one thing that a mathematically impaired person requires above all else is a sense of humility, and of their own limits -- just as the many idiot savants who find ready places in our engineering and scientific enterprises should with real humility know what they don't know about many other areas of human knowledge.

Yet, while students should be pushed to master what mathematics they can, there most definitely exist people who have a complete blind spot to mathematics, but who are brilliant at many other things. It would be tragic if such people could not make their way in our society.

Posted by: frankly0 on February 17, 2006 at 2:03 PM | PERMALINK

OTOH, assuming you were exposed to algebra, I think your whole line of argument here demonstrates that exposure to algebra is certainly no guarantee of even minimal reasoning skills outside of its bounds.

What kind of childish cheapshot is this?

Posted by: frankly0 on February 17, 2006 at 2:07 PM | PERMALINK

frankly0: many idiot savants who find ready places in our engineering and scientific enterprises

Hey, who you calling a savant?

Posted by: alex on February 17, 2006 at 2:09 PM | PERMALINK

I've noticed how much fun it is to judge others for not being as smart and quick to learn as I am... until I notice others much smarter and quicker than I judging me.

Then, not so much fun.

--
HRlaughed

Posted by: HRlaughed on February 17, 2006 at 2:09 PM | PERMALINK
Maybe I'm crazy, but I've always thought that minimal proficiency at basic mathematics (algebra, geometry and trig for high school, calculus for college) should be an absolute requirement for graduation. People that can't handle these are either too stupid or too lazy to deserve to graduate.

I just can't live my life with that attitude. Maybe you can. But it really doesn't help anyone, as far as I can tell.

If, as someone suggests, we're just trying to move people through, and make some attempt at screening, then fine, you miss, you lose.

But from a purely utilitarian point of view (though I'm probably misstating that), it doesn't help society as a whole to have a lot more high school dropouts. It just doesn't. Well, that's not true, more unemployment does help the corporations to keep wages down.

Posted by: Charles Richardson on February 17, 2006 at 2:10 PM | PERMALINK
But we can some drowning kids here, almost literally. While we chat, their boats are sinking. And it's a big group, mainly already in the poorer schools and nighborhoods. What do we do now?

We can do what to some drowning kids?

Look, first, I can't accept (though for the sake of argument I've granted it previously) the premise that lack of a diploma is a virtual death sentence. I've known people without diplomas that have gotten decent jobs based on demonstrated relevant skills. Sometimes, they've had trouble keeping them because of, e.g., drug or behavior problems that were part of what kept them from getting the diploma in the first place. Sometimes, especially when they didn't have those kinds of problems, they've succeeded quite well in them.

So I don't accept the premise that if we don't start handing out diplomas, we are generally condemning people permanently even if nothing changes. Further, to the extent that diplomas are treated as too important, the solution is to change how they are treated. No, that's not easy, but its the only solution that addresses the problem.

I am not for lowering standards, if anything I'm for raising them. But this particular standard is so arbitrary, and such a hot button for all the technocrats and engineering types out there...

Its no more arbitrary than any other standard. Frankly, aside from basic language proficiency, (and "how to deal with boneheads in authority", which isn't really a formal part of the curriculum) I don't think there is anything taught typically at the high school level that I've made as much use of as algebra in non-technical aspects of my life (like, say, planning household finances, dealing with the kitchen, etc.)


Posted by: cmdicely on February 17, 2006 at 2:14 PM | PERMALINK
What kind of childish cheapshot is this?

I wasn't aware there were whole categories of different kinds of childish cheapshots; if I were going to categorize it I'd call it "gratuitous application of the subject matter of the debate to frame a closing insult to the opponent."

But I suppose that was probably meant as a rhetorical question.

Posted by: cmdicely on February 17, 2006 at 2:17 PM | PERMALINK

Woah ... the hostility directed at Cohen in this thread is really remarkable.

Lemme say first that I identify strongly with his position. I had the "fortune" to go to an alternative HS in the 70s that didn't force me to take any math (or any subject at all, truthfully) and provided me with a HS diploma, anyway. So when I went back to college, elementary algebra kicked my ass eight ways to Sunday -- although I finally passed it.

I completely agree with Cohen that mathematical reasoning is divorced from most other (and much more useful) kinds. Nothing about English, History, Sociology (I was using a calc for stats) gave me much of a hard time. My verbal reasoning skills have stood me in good stead.

Mathmatical reasoning, though, can be kludged intuitively. I can figure out simple algebraic word problems by reducing them to equations, have no trouble with percentages, can double recipes, do taxes etc. -- because these are real-world skills that I practice almost daily. Nothing is *systematized* about it, though. If I sat down and *thought about it* I could probably pull out the logic it's based on, but I don't. And a quadratic equation would be absolutely Greek to me. Cohen has a point.

What's also odd is that a major hobby of mine is music composition, something which is heavily immersed in mathematical concepts -- and also flat-out numerological ones that I fixate on for no other reason than that I tell myself they have aesthetic value. I love extremely odd and changing time signatures and simultaneous tempo ratios, and take great joy in reducing them, expanding them, relating them to each other. And all of this from a decidedly innumerate mind, as public HS math testing would demonstrate..

Should someone like this be deprived of a decent life because of the way math is taught in public HS? I don't think that would be either equitable *or* meritocratic. Mathematical reasoning does not necessarily equate to the ability to absorb a corpus of abstract concepts.

Bob

Posted by: rmck1 on February 17, 2006 at 2:18 PM | PERMALINK


But from a purely utilitarian point of view (though I'm probably misstating that), it doesn't help society as a whole to have a lot more high school dropouts.

The problem lies more, I think, in having more people without the skills that high school is supposed to teach, not in having more people that happen to lack a high school diploma. The solution is teaching better.

Posted by: cmdicely on February 17, 2006 at 2:19 PM | PERMALINK

OK long time reader first time blah blah...

"As for tips, I always use 1/6 rather than 15%, not that it makes much difference. I think early on one of my parents must have told me that was the rule, and it stuck."

This is wildly OT but it's important that people understand this. You need to tip at least 15% at every meal. Waiters actually pay all or part of the salaries for the bussers, hosts/greeters, bartenders, and pretty much anyone who isn't a cook or prep guy. And they are paid $2.13 an hour in most states. On paydays, I always owe money to the restaurant I work for -- usually just $45.00 every two weeks for my health insurance with the check taken for taxes, but frequently my salary doesn't meet the minimum in taxes removed and I owe my company cash. Think about this please the next time you are considering 10%.

Posted by: Tom in Texas on February 17, 2006 at 2:21 PM | PERMALINK
Should someone like this be deprived of a decent life because of the way math is taught in public HS?

Having a high school diploma is neither a guarantee of nor a requirement for a "decent life".

Posted by: cmdicely on February 17, 2006 at 2:22 PM | PERMALINK

Also tip on wine if you dine in higher end restaurants. Your server does.

Posted by: Tom in Texas on February 17, 2006 at 2:23 PM | PERMALINK

"'As for tips, I always use 1/6 rather than 15%, not that it makes much difference. I think early on one of my parents must have told me that was the rule, and it stuck.'

You should tip 20%.

It improves calculations and human relations."

And service. If you're a 'regular' at a restaurant, you can bet the servers know just how much you tip.

As for algebra vs. logic, Don had it right. Algebra IS logic. If you can't fathom algebra but think you can fathom logic, either you had a lousy algebra teacher, you have a phobia about numbers, or you're wrong about your logic skills.

I love logic and logic problems and I loved basic algebra. A couple of times recently, having to figure out some complicated financial projections and I found myself with paper and pen figuring was the value of "x" was. It was fun and I was proud to have pulled it off.

But when math gets beyond logic, into "imaginary numbers" and the square root of minus one, I get lost.

Finally, I think the faith in calculators is SO misplaced. If you don't know how to solve a problem, the calculator will do you no good. Yes, it can do calculations, but it can't tell you the route to the solution, the steps in which the calculations need to be made. Sure, we no longer need to know how to figure a square root (I knew once) but it can't tell us WHEN to use a square root.

Posted by: Cal Gal on February 17, 2006 at 2:25 PM | PERMALINK

Really, why should algebra be required to graduate from high school? We already confer degrees on the illiterate.

Posted by: Yancey Ward on February 17, 2006 at 2:28 PM | PERMALINK

"But it really doesn't help anyone, as far as I can tell.

If, as someone suggests, we're just trying to move people through, and make some attempt at screening, then fine, you miss, you lose."

I'm not advocating mandatory mathematics education because the subject matter will necessarily be used later in life, nor am I advocating it as a screening mechanism. I'm advocating it because absent such a substantial penalty, many students will give up trying to learn it altogether, and that sets a horrible precedent for the rest of their lives.

The thing is, for virtually everybody on the face of the planet, there is some level of mathematics at which you are forced to think about things in a manner that is different from which you are accustomed, and the subject becomes very, very hard (for me, it was group theory). At that point, you have one of two options. You can either struggle with it and do your best--you probably won't thrive or impress anybody, but you should be able to scrape out a pass. Or you can throw your hands up and say "math is hard, I don't want to do it." This latter approach is easy. It's also the height of intellectual laziness. You are no shit saying "thinking this hard makes my brain hurt and I just don't want to have to do it." That is a lesson that is bad enough for a college kid taking differential equations; for a high school student trying the solve x^2+2x+1=0, it is utterly disgraceful.

Posted by: Joe on February 17, 2006 at 2:31 PM | PERMALINK

Really, I think nearly everything that was covered in my high school could have, and should have, been covered in the first four or five grades of elementary school.

If we simply move the curriculum south like that, and build from there in grades 6 through 12, it would improve life immeasurably.

Posted by: cld on February 17, 2006 at 2:32 PM | PERMALINK

No one who says "graduate high school" should be allowed to graduate from high school.

Posted by: Bob Munck on February 17, 2006 at 2:34 PM | PERMALINK

Someone wrote that in their high school all the history teachers were gym teachers or athletic coaches.

Is that really standard everywhere? In my high school all the math teachers were gym teachers, which probably does explain why I never learned a thing from them. They kept trying to inspire 'competition'.


(Whereas all the history teachers I had had political ambitions. . .)

Posted by: cld on February 17, 2006 at 2:36 PM | PERMALINK

cmdicely:

Having a high school diploma is neither a guarantee of nor a requirement for a "decent life".

Makes it a hell of a lot easier, though, if we're talking about earning a decent living, not morality.

Posted by: tbrosz on February 17, 2006 at 2:36 PM | PERMALINK
Makes it a hell of a lot easier, though, if we're talking about earning a decent living, not morality.

Sure, but how much of that is having the piece of paper, and how much is having the minimal skill level necessary to get the piece of paper? Because the argument that the algebra standard condemns people implicitly argues that having the piece of paper itself is a critical piece, even where the skills necessary to meet the existing standards are not relevant.

I don't think that any substantial evidence or reasoning to support that rather non-obvious position has been offered.

Posted by: cmdicely on February 17, 2006 at 2:42 PM | PERMALINK

It's actually funny in a certain way. People feel perfectly comfortable saying " I don't know math." or "math is too hard, etc." In what other area are people so happy to trumpet their own ignorance or laziness?

Spelling. People, especially math people, who can't spell are likely to be proud of that fact -- because they don't waste time with unimportant details or something.

Posted by: DonBoy on February 17, 2006 at 2:49 PM | PERMALINK

Cal Gal:

Well, I have to disagree with you on several points. First, math is *always* logical; what happens with higher math is that the logic becomes too fine-grained to be intuitively graspable for non-mathmatically inclined people. My point is that most of the concepts that come into play with arithmetic and basic algebra are simply intuitive logic, and some of the people who have trouble with it are actually having trouble with the syntax of mathematics, not the underlying logic.

Nothing about verbal reasoning gives me any trouble at all. I've never read a "difficult" novel that made my head hurt -- and I've made a specialty of reading the "difficult fiction" that was au courant in the 60s and 70s. I can spot logical fallacies from 300 yards -- remembering what Aristotle named them's a different story sometimes :)

And yet I absolutely sucked at Elementary Algebra, and my basic math skills are shaky on the fly (which is probably why I had such trouble on the tests -- make one mistake in a series of calculations and you're screwed from that moment on).

It may have to do more with the way that the mind copes with *precision*. I'm not a very precise thinker -- but I'm a very synoptic and context-aware one. I do believe these are two entirely different skill sets.

Bob

Posted by: rmck1 on February 17, 2006 at 2:49 PM | PERMALINK

A big leap forward will come when big bucks for education research are put into the hands of our brightest, can-do people.

Posted by: ferd on February 17, 2006 at 2:49 PM | PERMALINK

"know where the Sahara Desert is" should be "know where the Sahara is". Sahara Desert is redundant (and shows lamentable ignorance).

Posted by: LeisureGuy on February 17, 2006 at 2:50 PM | PERMALINK

It's actually funny in a certain way. People feel perfectly comfortable saying " I don't know math." or "math is too hard, etc." In what other area are people so happy to trumpet their own ignorance or laziness?

I've certainly met my share of engineers who seem equally proud of their inability to write.

Posted by: frankly0 on February 17, 2006 at 2:51 PM | PERMALINK

frankly0: I've certainly met my share of engineers who seem equally proud of their inability to write.

Or read. We're very proud of our comprehensive illiteracy.

Posted by: alex on February 17, 2006 at 2:55 PM | PERMALINK

We're very proud of our comprehensive illiteracy.

See? I told you.

Posted by: frankly0 on February 17, 2006 at 2:56 PM | PERMALINK

I concur with Doctor Gonzo, supra.

And, cmdicely, you can do better, surely. Graduating with a HS diploma is a proxy for a bunch of things that we as a society ought to value, encourage, reward - the ability to work hard and defer gratification - as well as the rudimentary knowledge that an educated citizen ought to have. And how do you know what skills will be relevant 30 years from know? That's one reason we should expect young people to have a well rounded education in a variety of disciplines, including those that may be difficult for them (algreba for some, foreign languages for others). That's the least we owe them.

Posted by: DBL on February 17, 2006 at 2:57 PM | PERMALINK

should be "know where the Sahara is"

I know!

2535 Las Vegas Blvd South, Las Vegas, NV

Thank you very much.

Posted by: Ray on February 17, 2006 at 2:58 PM | PERMALINK

Posters way back when said:
"'As for tips, I always use 1/6 rather than 15%, not that it makes much difference. I think early on one of my parents must have told me that was the rule, and it stuck.'

You should tip 20%.

Actually, you should tip at least 175%.

Remember, most of the servants are paying the restaurateur for the privilege of employment; for them to be able to pay their taxes, they'll need at least half again the cost of the food. Most restaurants will allow the servants to take food home for their mandatory children, but it's still considered more Christian to give them a little extra to tithe with. And can be reported as such on your Christian Behavior form.

Do remember, though, ever since Bush VI enacted the maximum wage laws, that giving too much is considered liberal; so stick to 175% (in WeMeanItThisTime Dollars) and be safe.

Posted by: S Ra, in the year 2050 on February 17, 2006 at 2:59 PM | PERMALINK

One last point: Mathematics opens doors. Calculus opens more doors than algebra, but even basic algebra will give students far more opportunities in life, even if they don't want to pursue those opportunities, than giving up on math in middle school. How could we not insist that kids at least have those opportunities?

Posted by: DBL on February 17, 2006 at 3:00 PM | PERMALINK
"know where the Sahara Desert is" should be "know where the Sahara is". Sahara Desert is redundant (and shows lamentable ignorance).

Or, rather, "Sahara Desert" is redundant.

Posted by: cmdicely on February 17, 2006 at 3:00 PM | PERMALINK

Let's see, I've been out of junior high and high school for over 30 years ago. I practice law, understand how to dissect arguments and rhetoric and yet for some reason I've had no reason to actually use the algebra I was taught back then. Absolutely none. It's not that I shy away from statistics and economic analysis. Part of what I do involves evaluating economic arguments and principals and economimc analysis. But still the actual grunt work of algebra, don't use it, don't have to.

Now was learning algebra completely worthless? Nope, it was kind of fun going through the process if i recall, but at the same time, I think all of this bs about how important a skill algebra is as a skill for the average person is overblown hogwash.

I'd say that more important than algebra was a course I took back in my undergraduate skill re: experimental design. Now that was valueable. Learning how people screw up the design of their experiments, studies and how to draw unwarranted conclusions from data, for most people who need to become informed rational decision makers on issues of public policy, I'd take that over algebra any day.

Rigel

Posted by: rigel on February 17, 2006 at 3:02 PM | PERMALINK

I'm perfectly happy to trumpet my ignorance of math because math is of only minimal importance in my life. Math is a tool, important only for those who need it in order to achieve their chosen goals.
It is absolutely unfair to make an unnecessary skill a requirement for a diploma.
Yes I am being defensive here. Thank goodness I graduated from high school before all this crap was imposed. I have three university degrees, make about 60 grand a year and the only math I do is quick estimating of purchases and calculator-assisted checkbook management ( and I never balance my checkbook. I just keep a running total.) That's it. No other math. Algebra is not a necessary skill for citizenship, nor is it necessary for a multiplicity of occupations and avocations, nor is it essential for ordinary daily funtioning. It is totally unfair to require it for high school graduation and totally mistaken to see it as an essential life skill.

Posted by: lily on February 17, 2006 at 3:05 PM | PERMALINK

frankly0: You know, no Ancient Greek, not Aristotle or Plato or Socrates, knew a single thing about algebra, because, well, it hadn't been invented yet. And the geometry was nothing more than Euclid

Buts we duz knows numbas.

Sukratees: 469 BC 399 BC
Plaatooz: 427 BC 347 BC
aRistotel: 384 BC 322 BC
UkLid: 325 BC 265 BC

And Ize nows Uklid not doo muchly afores hes wuz 3.

Posted by: alex on February 17, 2006 at 3:11 PM | PERMALINK

"If you find yourself completely unable to master anatomy, should you be condemned to spend the rest of your life as a medical school dropout?

Posted by: Stefan"

No, you become an internist.

Just kidding.

Actually not.

Posted by: Mike K on February 17, 2006 at 3:11 PM | PERMALINK

Piffle. And worse than piffle. The LA Times article to which Cohen refers clearly shows the girl didn't even attend the algebra class most of the time. She simply failed to show up. Is this the type of effort that should be rewarded with a diploma of any sort? The nonsense meme that she tried to do it but was somehow intellectually incapable and should therefore be excused is plainly silly and controverted by the facts. She did not go to the class so what do we base the excuse of "algebra learning disability" on?

High school diplomas, especially in certain parts of our country, are circling the drain of worthlessness now. Should we make them more worthless by excusing students from requirements that they haven't even made a valid attempt to complete?

Posted by: solar on February 17, 2006 at 3:13 PM | PERMALINK

Incidentally for people to lazy to do math, 20% is the easiest number to figure out. Just move the decimal to the right and double it. Takes 2 seconds. Don't even need a calculator.

Posted by: Tom in Texas on February 17, 2006 at 3:18 PM | PERMALINK

And in 20 years we can dispense with simple addition, subtraction, multiplication, and division.

Oh, wait, we have already done that.

Posted by: Yancey Ward on February 17, 2006 at 3:21 PM | PERMALINK

"It is absolutely unfair to make an unnecessary skill a requirement for a diploma."

I'd love to go to that high school, were the only mandatory subjects are reading, basic arithmetic and consumer economics.

Seriously. There are certain educational standards that you should be able to meet in order to call yourself a high school (or college, or grad school) graduate. Having a passing familiarity with Shakespeare is one of them. Knowing basic facts about the Revolutionary War is another. Being able to apply basic math skills (and note that I said "math" and not "arithmetic") is yet another. Not because you will use these in the future. But rather, because it is important for society at large to know that you are capable of applying yourself and achieving these basic standards when you hold yourself out as an educated person.

Do people that proudly trumpet their own ignorance in math really not understand that they are saying, in no uncertain words, "thinking that way makes my brain hurt, and I'd rather just not even try to do something that have THAT happen"? This is a liberal blog. Do you not understand that you sound EXACTLY like the "ignorant" red state conservatives dealing with gays, or minorities, or any number of things that they don't like? "I'm just not used to it, I don't understand it, so I don't think that I or anybody else should have to deal with it if we don't want to."

Posted by: Joe on February 17, 2006 at 3:25 PM | PERMALINK

Fact. If you can't do basic algebra you are mathematically illiterate. If you are mathematically illiterate, you will make horrible financial decisions. Not only that, but because you do not understand things like interest rates and budget numbers and statistics, you will be unable to make informed decisions about whom and what to vote for, thus allowing politicans to get away with making horrible financial decisions.

Does anybody wonder why most of our populace is over their head in debt to credit card companies, why we as a country have a negative savings rate and a monstrous national debt, and why Social Security and Medicare are heading towards insolvency? It because we have a population that is largely mathematically illiterate and who has elected politicians who are largely mathematically illiterate.

Take all the members of Congress, all the members of the 50 state legislatures, the President, the Vice-President, and the heads of all the cabinet agencies, and I bet less than 50% of them could pass a 10th grade level math test.

The simple truth is that we are a mathematically illiterate nation, where people who do know math routinely take advantage of those who don't.

Posted by: MattW on February 17, 2006 at 3:25 PM | PERMALINK

Writing is the highest form of reasoning

May be the single stupidest thing I have ever read. His "proof" just shows how little this idiot understands about logic. My wife, a technical writer, was left rolling on the floor laughing after reading that.

Now, all you folks exclaiming about how you never use algebra and thus it shouldn't be required I must point out that I, an engineer, never use history, foreign languages, fine arts, social studies or phys ed in my job. Should we shitcan them from highscool too and just give a diploma out for showing up for 6 years?

This ain't the 20th century any more. If your kids don't learn algebra in this day and age they can look forward to a job bagging groceries (until the robots replace them) or writing for the Washington Times (until AIs replace them) and that's about it.

Posted by: Sarcastro on February 17, 2006 at 3:26 PM | PERMALINK

As I've been thinking about this it occurs to me that while I like to say I didn't learn a shred of algebra in high school, there may well be a wide variety of daily problems that I solve, altogether unconsciously, using some of the mental disciplines I internalized whether I knew it or not.

Using x and y as mental place-fillers, for instance.

I don't think the point of learning is to 'learn how to think'. It's more like acquiring conversation.

Posted by: cld on February 17, 2006 at 3:27 PM | PERMALINK

The worst part of Cohen's article is that his claims of higher reasoning skills and the ability to write coherently are proven false by his own writing. He states: "Writing is the highest form of reasoning. This is a fact. Algebra is not [a fact? or the highest form of reasoning?]. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence." I could prove the opposite with the equally absurd "look at all the people in my high school who were whizzes in history but couldn't understand simple mathematical relationships." Neither proves anything, except that Cohen's writing, at least, is not the highest form of reasoning.

And while Cohen may be able to put a decent sentence together, he has a harder time with a paragraph. He started one ("Look, Gabriela, I am not anti-algebra") addressing a single person. Two sentences later ("There of those of you, and Gabriella you are one"), he is addressing more than one person. The change in number is confusing at first, and awkward thereafter, since "you" can be either singular or plural. Then, in what appears to be a sentence of parallel construction, he switched from "you" to "us," although he appears to be talking about the same group of people.

I'm not sure how this made it to print; his editor must have been a fine art major.

Posted by: me on February 17, 2006 at 3:29 PM | PERMALINK

Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence. I can cite Shelly, whose last name will not be mentioned, who aced algebra but when called to the board in geography class, located the Sahara Desert right where the Gobi usually is. She was off by a whole continent.

Wow.

I'd like you all to read that one again.

Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence. I can cite Shelly, whose last name will not be mentioned, who aced algebra but when called to the board in geography class, located the Sahara Desert right where the Gobi usually is. She was off by a whole continent.

Let's break this down, shall we?

Writing is the highest form of reasoning - interesting how it's his profession and it's the highest form. Cohen states this is a fact, as if a factual assertion can be made about something that is so transparently a subjective judgement.

The fact that some people are good at math and poor and writing demonstrates that they are disparate skills, not the superiority of one over the other. Cohen apparently was a typing whiz, and yet can't do simple percentages; this doesn't demonstrate superiority, merely difference.

He also cites one instance of a person called to the board who got a fact incorrect - specifically, the location of the Sahara, by pointing to one of world's other great deserts. This is clearly a problem; U.S. students need more grounding in geography, but it hardly points to an error in reasoning. Not knowing where the Sahara was, but knowing is was a desert and presumably knowing it was not in the U.S., pointed to a big desert elsewhere. A reasonably logical choice, even if it was factually incorrect.

Interestingly, that kind of factual recall is something that computers are far better at than they are at mathematical reasoning. While computers can handle arithmatic more powerfully than humans can, try asking a computer about that boys mowing lawns question - unless you have the skills to formulate the question, they can't find the answer. On the other hand, the question "Where is the Sahara?" is easy to formulate, and Google will find the answer for you in its first hit.

Posted by: Fides on February 17, 2006 at 3:32 PM | PERMALINK

I really liked Cohen's statement about how calculators and computers can do most ordinary math for you, and that this fact obviates the need to require algebra study. So, by extension, when speech recognition software becomes sophisticated enough, I assume we can finally dispense with learning reading and writing.

Posted by: Yancey Ward on February 17, 2006 at 3:50 PM | PERMALINK

alex,

Good to see how well you spel, of course.

But Euclid pretty much just summarized the state of geometric knowledge at the time -- no one claimed he invented much of anything.

The Pythagoreans had already come up with their eponymous theorem by Socrates' time, and in fact had hit upon the devastating discovery of irrational numbers, to which Plato alludes in some of his writings, and which Aristotle describes explicitly with example. Pythagoras himself lived 569-475 BC, earlier than even Socrates.

But, if there's more in Euclid than even Socrates and Plato or Aristotle knew of, that only goes to prove my point afortiori, which was that the Greeks did a bang up job doing analytical thinking in the face of profound ignorance of all but the most basic of mathematics.

Posted by: frankly0 on February 17, 2006 at 3:54 PM | PERMALINK

It is absolutely unfair to make an unnecessary skill a requirement for a diploma.

I had to take a number of non-math courses, which I have found to have been of limited utility during my long life. I guess we should not have any standards for a diploma. Let's raise mediocrity as the new standard for excellence to which all can be above average.

Posted by: Alf on February 17, 2006 at 3:54 PM | PERMALINK

The underlying basis for understanding algebra, as opposed to being able to rotely apply certain well-practiced basic algebraic functions to specific classes of recognized problems, is the ability to understand abstract reasoning.

We know from research by Piaget and others that the most people develop abstract reasoning skills somewhere between 11 and adulthood, with a median age (IIRC) of 14 or 15 years old. Obviously some high school seniors will not develop abstract reasoning skills. In fact, research has shown that only about 35% of high school graduates in industrialized countries have fully developed abstract reasoning abilities.

Given the role that the high school diploma plays as a door opener for jobs and higher education, should students whose minds have not developed to the point where they can succeed at algebra be punished by withholding the degree? I don't know. I tend to think that requiring algebra is reasonable, but then I begin wondering about the minimal "reading, writing and arithmetic" skill set that a high school diploma should signify.

To what extent should a high school diploma be used to signal educational achievement in higher level subjects? Should it instead indicate that the holder has achieved a level of basic education that indicates he or she is likely to be able to successfully complete further training and/or education? Would requiring employers and admissions officers to use the diploma in conjunction with other indicators such as interviews and tests to clarify a graduate's suitability for their jobs or programs be too onerous?

A concrete example may illustrate the question. My wife tutors a senior girl who is taking Algebra I for the third time. The girl has A's and B's in all of her other subjects through high school. She wants to be a fashion or interior designer and has already had some of her work shown at shows.

This girl can estimate and order the right quantities of fabric for her designs. She helps keep the books for her mothers business. She shops on her own, manages her own checking and credit card accounts, books her own trips to fashion shows and competitions, etc. She has been accepted to a nationally recognized design program at a major university, provided she graduates from high school. That program does not require algebra.

Should she be denied a diploma, and thus admission to the college and program best suited for her, because this school district has decided that all of its students must pass algebra?

Perhaps we should offer different types of diplomas, say HSDA for Arts, HSDS for Science and maybe even HSDV for Vocational.

Posted by: Paul E. Tickle on February 17, 2006 at 4:00 PM | PERMALINK

frankly0: But Euclid pretty much just summarized the state of geometric knowledge at the time -- no one claimed he invented much of anything.

Euclid's big accomplishment was axiomatic development, rather than relying on ad hoc proofs.

Posted by: alex on February 17, 2006 at 4:00 PM | PERMALINK

alex,

According to wikipedia,

Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework. In addition to providing some missing proofs, Euclid's text also includes sections on number theory and three-dimensional geometry. In particular, Euclid's proof of the infinitude of prime numbers is in Book IX, Proposition 20.

Now I'm guessing that a good many of the proofs were derived from the work of earlier mathematicians, even with respect to the explict assumptions they made. I don't know whether Euclid really simplified the axioms and or the number of them, but the wikipedia entry at least is consistent with a great deal of this work being done by others.

Maybe Euclid is really like a popular mathematical textbook writer, whose work becomes the standard for the subject, and little else.

Posted by: frankly0 on February 17, 2006 at 4:13 PM | PERMALINK

cmdicely,

The argument was that Plato, Artistotle and Socrates achieved quite a lot without algebra, not that they wouldn't have achieved more with it.

The 'demonstrability' of algebra not being available to them is standard history, though a determined, math-minded scholar could probably demonstrate that a lot of fundamental algebraic ideas must have been known to the Greeks of that era.

Posted by: cld on February 17, 2006 at 4:15 PM | PERMALINK

Paul E. Tickle:

Very provocative story.

Summarizes my thinking exactly. Learning the *syntax* of algebra is not the same thing as being able to reason accurately with numbers, as your wife's student seems to demonstrate.

The syntax of algegra busted my ass -- though I eventually passed the final requirement.

The logic of algebra is with me daily -- though I wouldn't know what-all to call it if I had to formalize what I was doing.

Bob

Posted by: rmck1 on February 17, 2006 at 4:16 PM | PERMALINK

frankly0,

But, if there's more in Euclid than even Socrates and Plato or Aristotle knew of, that only goes to prove my point afortiori, which was that the Greeks did a bang up job doing analytical thinking in the face of profound ignorance of all but the most basic of mathematics.

And I suppose anyone who couldn't discover, independently, the existence of irrational numbers is therefore "profoundly ignorant of all but the most basic of mathematics"? Is there something wrong with building knowledge on knowledge?

I love the ancient proof of the irrationality of root-2, though. So compact, so simple.

Posted by: waterfowl on February 17, 2006 at 4:17 PM | PERMALINK

It is absolutely unfair to make an unnecessary skill a requirement for a diploma.

The skills actually necessary for humans are pretty much acquired naturally with or without school and if you don't have them, pretty much by definition, you end up dead fairly expeditiously. We don't give diplomas for the ability to breathe, eat, and excrete -- you either do them or you die, further recognition is superfluous.

Utility (and, in the given that it is a public context, social rather than personal utility, though they often overlap), not necessity, has got to be the basis of any public education standards.

Certainly, the social utility of basic mathematical proficiency might be subject to debate, and that would be a good debate. But necessity is either the wrong standard, or so vague of a term as to make meaningful discussion difficult.

Posted by: cmdicely on February 17, 2006 at 4:18 PM | PERMALINK

In Texas, where I went to high school, you have to pass a standardized test to graduate. We had the same argument then, "If you can't pass it should you be condemed to a future as a drop-out?" The answer is yes! The algebra you are required to pass is very basic, the kind of thing that gets you through the line at the grocery store. Our kids can't figure out 20% of 100, but they can certainly go to war just fine!

Posted by: Clair on February 17, 2006 at 4:21 PM | PERMALINK

And I suppose anyone who couldn't discover, independently, the existence of irrational numbers is therefore "profoundly ignorant of all but the most basic of mathematics"?

My point is simple: the Greeks, even the very best of them, knew FAR LESS mathematics than the typical HS grad today. They didn't know algebra. They didn't know trigonometry. They didn't know analytical geometry. And they sure as hell had no clue about any calculus.

And they did fine, thank you.

Posted by: frankly0 on February 17, 2006 at 4:22 PM | PERMALINK
The argument was that Plato, Artistotle and Socrates achieved quite a lot without algebra, not that they wouldn't have achieved more with it.

Wrong.

The argument was that they wouldn't have achieved more with it. Specifically, it was that "...ignorance of [algebra], demonstrably, had NO effect on the reasoning abilities of some of the greatest philosophers of all time." Which means first that they wouldn't have reasoned better with it (because if they would have, the ignorance had some negative effect, making the claim false), and second that it can be proved that they would not have (because if it can't be proved, it is not demonstrable, making the claim false.)

Posted by: cmdicely on February 17, 2006 at 4:22 PM | PERMALINK

cmdicely,

Still waiting for an example from you of a contemporary philosopher with superior analytical abilities to Socrates, Plato, or Aristotle.

Time to put up or shut up.

Posted by: frankly0 on February 17, 2006 at 4:25 PM | PERMALINK
Incidentally for people to lazy to do math, 20% is the easiest number to figure out. Just move the decimal to the right and double it.

Well, no, you have clearly just demonstrated that 10% is easier to figure out. :P

Posted by: cmdicely on February 17, 2006 at 4:26 PM | PERMALINK

The arrogance (a) multiplied by the innumeracy and idiocy (i) of the fourth estate (4e, with e being very small due to media consolidation) equals democracy (D) divided by zero. And you know dividing by zero is impossible.

Posted by: pk on February 17, 2006 at 4:28 PM | PERMALINK

frankly0: Maybe Euclid is really like a popular mathematical textbook writer, whose work becomes the standard for the subject, and little else.

While I don't claim to be an expert on the history of math, Wikipedia does jive with my Euclidean claim. From http://en.wikipedia.org/wiki/Euclid%27s_Elements

The Elements is one of the oldest extant axiomatic deductive treatments of geometry, and has proved instrumental in the development of logic and modern science.

Posted by: alex on February 17, 2006 at 4:32 PM | PERMALINK
Still waiting for an example from you of a contemporary philosopher with superior analytical abilities to Socrates, Plato, or Aristotle.

Why? That would only be necessary if I made the claim that there were current people with demonstrably better analytical skills. As I don't even think such a statement is a demonstrable claim of fact, rather than a purely subjective statement of preference, its unlikely that I would make such a statment.

You, on the other hand, made the claim that they were demonstrably not inhibited by not having exposure to algebra. Asking other people to provide evidence which (even if the request was coherent) would neither prove nor disprove your original claim is pointless. You claimed it was demonstrable that lack of access to algebra had no effect. So, demonstrate it.

Time to put up or shut up.Indeed it is. So, do so. All I've claimed is that you have not shown that what you claim is demonstrably true is, in fact, demonstrably true. Indeed, I don't even see how one conceptually could demonstrate it, but I'm willing to be suprised by your genius.
Posted by: cmdicely on February 17, 2006 at 4:33 PM | PERMALINK

Writing is the highest form of reasoning. This is a fact.

Isn't writing a way to explain your reasoning, not reasoning itself?

Posted by: dave m on February 17, 2006 at 4:35 PM | PERMALINK

cmdicely: Well, no, you have clearly just demonstrated that 10% is easier to figure out.

Actually 0% is the easiest, but it'll get you a lot of dirty looks.

Posted by: alex on February 17, 2006 at 4:36 PM | PERMALINK

That is, if you find yourself completely unable to fathom algebra, should you be condemned to spend the rest of your life as a high school dropout? I don't really have an opinion about this, but it's a serious question.

Actually it's an inarticulate and misleading question, Kevin, but I know now we need to cut you slack in this area.

Basic algebra is fucking easy. If you can't do basic math, it's a problem for the rest of us who are looking to hire and/or work with someone who can.

End. Of. Story.

Posted by: Distiller on February 17, 2006 at 4:37 PM | PERMALINK

Who says they were ignorant of algebra - of the infantile sort that idiot Americans learn?

Posted by: cdj on February 17, 2006 at 4:38 PM | PERMALINK

cmdicely,

=erk*, inarguably, and I was reading almost as fast as frankly0 was typing.

I thought the original intent was self-evident, but he'd probably reword it if given the chance.

Posted by: cld on February 17, 2006 at 4:40 PM | PERMALINK

Contemp philosophers with analytical abilities superior to the big ol greeks? Sheesh - hard to find any withOUT superior abilities...

Is Dummett dead? McDowell, Brandom, Belnap (dead?)...

What an odd challenge...

Posted by: cdj on February 17, 2006 at 4:41 PM | PERMALINK

frankly0 has the most bizarre idea of the state of greek mathematics i've ever seen.

Didn't have trig? (of the infantile sort that high schoolers "learn") LOLOL

The egyptians had trig for crap's sake...

Posted by: cdj on February 17, 2006 at 4:44 PM | PERMALINK

If either of my kids gets a high school diploma without knowing algebra, they'd better not be expecting to be going to college, because we're not helping them and they're clearly too lazy to work out the terms of a loan. (They're tots, but I already know they're not stupid.)

For cripes sake, are there any standards *at all*? No wonder my husband ran screaming from teaching college students math.

Posted by: Magenta on February 17, 2006 at 4:49 PM | PERMALINK
Isn't writing a way to explain your reasoning, not reasoning itself?

There is a certain reasoning involved in reducing an idea to writing in a way which clearly communicates it to another person, though the idea that it could be stated as a fact whether this is the highest form of reasoning or not, either involves a rather unique use of "highest form of reasoning" that requires some definition, or reveals an fundamental confusion regarding the nature of issues of fact versus issues of pure subjective opinion.

Posted by: cmdicely on February 17, 2006 at 4:50 PM | PERMALINK

A lot of the arguement on this thread regarding Philosophers being able to reason without it misses the point entirely.

First off, a lot of those same philosophers built the tools that led to algebra - it took a lot of thinking to get there.

Second, a big part of the point of mathematical advances is to find ways to systematize and simplify complex tasks. Algebra is a much simpler approach to solving many of the kinds of problems first solved by the Greek philosophers.

Third, the point of teaching algebra is not to necessarily build great Philosophers, and no one has claimed that algebra is the highest form of reasoning (unlike Cohen, who explicity claims that writing is.) It is an excellent way of teaching good reasoning/logical skills while giving the students powerful mathematical tools for solving many everyday problems, from figuring out how much paint you should buy to understanding the basics of income taxes. Questions that you want your housepainter and your voters to understand.

Posted by: Fides on February 17, 2006 at 4:51 PM | PERMALINK

Seems better to fix the problem than just to accept the failure. Posted by: cmdicely on February 17, 2006 at 12:23 PM

I whole-heartedly agree. We should be focusing on how to teach algebra, geography, biology, chemistry, etc. so that more students graduate with a good understanding.

Right now testing is more akin to a trial-by-fire right than a tool to measure the effectiveness of the teaching regimen and the student's efforts.

Posted by: Dr. Morpheus on February 17, 2006 at 4:52 PM | PERMALINK

Dr. Morpheus -

How to teach math et al? Start with teachers who have bonafide MATH degrees, and not education "degrees".

Posted by: cdj on February 17, 2006 at 4:57 PM | PERMALINK
Right now testing is more akin to a trial-by-fire right than a tool to measure the effectiveness of the teaching regimen and the student's efforts.

Right. We test students to see if they should advance, we test schools to see if they are "failing". But we don't spend nearly as much effort tracking different teaching regimens and testing in a way which lets us evaluate them against each other so that we can improve processes. Which is, of course, the kind of testing we need.

Our testing is all too much about reward and punishment, at every level, and not enough about process evaluation and improvement. Which, I suppose, reflects many of the adversarial rather than cooperative elements of our society.

Posted by: cmdicely on February 17, 2006 at 4:59 PM | PERMALINK

Shame on you Kevin Drum!!

You fail to see that Cohen's screed is not a plea for help from the math challenged, but an argument for no-nothingness, stupidity, ignorance. You want more than we already have? Go ahead.

Shame on you Kevin Drum!!

Posted by: CSTAR on February 17, 2006 at 5:00 PM | PERMALINK

But the best teachers in the world won't make up for lying, cheating, stupid, apathetic, uncurious students.

They come from the bulk of America, naturally - which is populated with lying, cheating, stupid, apathetic, uncurious parents.

The people are the lion's share of the problem. Folks of late seem hell-bent on a "process" solution. The best process in the world will turn out crap when implemented with crappy people.

I suggest we need to focus on the people involved with the process, more than the process itself. People (Americans) simply don't care much about honesty, hard work, dililgence, thinking, and so on. No process in the world can succeed with that kinda people.

Posted by: cdj on February 17, 2006 at 5:01 PM | PERMALINK

Is anyone surprised? People that can't do percentages or work with numbers are much more easily misled. Do you think the "masses" that parrot the lying liars talking points have the ability to think critically about the crap that was given to them?

Posted by: anonymous on February 17, 2006 at 5:02 PM | PERMALINK
How to teach math et al? Start with teachers who have bonafide MATH degrees, and not education "degrees".

I don't think it is necessarily the case that a math degree is more relevant to teaching math than an education degree. You obviously need to have a proficiency in math which extends beyond the immediate subject matter to include an appreciation of its applications and what the students need to succeed in further classes, but for teaching, e.g., algebra or geometry that probably doesn't require much knowledge of mathematics beyond Calculus, and certainly doesn't require a bachelor's degree in math.

OTOH, it does require considerable understanding of how to teach, which you can get a degree in math without learning at all, but can't, or at least shouldn't, be able to get an "education" degree without knowing something about.

I don't think most people who fail to learn math because it is taught poorly do so because the teacher doesn't know math well enough; I suspect many do because the teacher doesn't teach well enough, or the school doesn't have the right resources or environment to teach it properly.

Posted by: cmdicely on February 17, 2006 at 5:04 PM | PERMALINK

The egyptians had trig for crap's sake...

From wikipedia:

The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 BC), who tabulated the lengths of circle arcs (angle A times radius r) with the lengths of the subtending chords (2r sin(A/2)). Later, Ptolemy (2nd century) expanded upon this work in his Almagest, deriving addition/subtraction formulas for the equivalent of sin(A + B) and cos(A + B). Ptolemy also derived the equivalent of the half-angle formula sin2(A/2) = (1 − cos(A))/2, allowing him to create tables with any desired accuracy. Neither the tables of Hipparchus nor of Ptolemy have survived to the present day.

180-125 BC came a little bit after Socrates, Plato and Aristotle, smartass.

Posted by: frankly0 on February 17, 2006 at 5:05 PM | PERMALINK

Writing is the highest form of reasoning. This is a fact. Algebra is not.

If by Algebra you mean the manipulation of symbols by the rules for manipulating them, I agree. You can buy a symbolic manipulation package that will absolutely crank on algebra problems. I am sure there are savants in Algebra who are otherwise considered mentally handicapped.

But if you mean the process of converting an amorphous problem to something with structure, that can then have rules applied to it to get an aswer, then I don't think they are so different.

The nice thing about Algebra is that it offers an independent truth. Right or wrong. The nice thing about writing is it doesn't.

I teach at the college level, and I basically teach 3 things, no matter the course. Skills & drills (solving basic problems rapidly and efficiently), puzzle solving, and problem solving. The difference between the last two are pauzzles have nice single solutions, and problems don't. They can have many solutions or none. Guess which of the three we use most in life? I'd say (1) and (3).

I submit it is possible to teach people to solve problems amenable to Algebra without teaching Algebra. Drill them on the problems enough, and they will internalize the solution approach. That's what they need to know.

Posted by: Red State Mike on February 17, 2006 at 5:06 PM | PERMALINK

cmdicely wrote:

"Because the argument that the algebra standard condemns people implicitly argues that having the piece of paper itself is a critical piece, even where the skills necessary to meet the existing standards are not relevant."

"The piece of paper itself" can be a major difference. The US military (until recently) tried to avoid recruiting non-High School Diploma Graduates (HSDG). Research showed that completing high school was the single best predictor identifying potential recruits likely to successfully complete their basic training and their enlistment contract. HDSGs had proven their abililty to "stick it out," so to speak. The bias in favor of HSDG's was such that HSDGs who scored significantly lower on the enlistment test than non-grads (and GED holders) were preferred over non-grads/GEDs.

A number of civilian companies, especially DoD contractors or other companies that invest a lot of money to recruit and train employees, have adopted the same logic based on their own experience or the military's research. They even apply it to positions that do not require lots of training. My current and previous employers do not accept non-grads for any position, including security guard, shipping/receiving clerks or administrative assistants unless they have a GED AND two or more years of continuous employment in positions of increasing responsibility.

Wonder if there is a study somewhere comparing economic outcomes for grads and non-grads after adjusting for differences in academic background other than "the piece of paper itself."

Posted by: Paul E. Tickle on February 17, 2006 at 5:06 PM | PERMALINK

Tom in Texas, 100% is the easiest.:~)

However, accepting that 20% is, then shouldn't you move the decimal point to the left?

Posted by: Yancey Ward on February 17, 2006 at 5:07 PM | PERMALINK

However, accepting that 20% is, then shouldn't you move the decimal point to the left?

I want to wait on Tom's table.

Posted by: frankly0 on February 17, 2006 at 5:10 PM | PERMALINK

Waterfowl,

I also remember that proof, if it is the same one you wrote about. I think I first came across it in a Schaum's Outline book my father had when I was about 13 or 14. Beautiful little proof. I still remember my delight in the last step when, for the root to be rational, 1 must equal 2

Posted by: Yancey Ward on February 17, 2006 at 5:12 PM | PERMALINK

frankly0 -

So much the worse for the wikipedia.

Posted by: cdj on February 17, 2006 at 5:14 PM | PERMALINK
"The piece of paper itself" can be a major difference. The US military (until recently) tried to avoid recruiting non-High School Diploma Graduates (HSDG). Research showed that completing high school was the single best predictor identifying potential recruits likely to successfully complete their basic training and their enlistment contract.

Right, but changing the standard would, of course, invalidate that research and make it likely that the Army would switch to a different criteria that approximated the predictive power of the diploma under the old standard. Unless, of course, one assumes that math requirements were not a component of the predictive power of the diploma.

If one invokes the existence of criteria based on the empirical predictive power of the diploma to say that the diploma itself, rather than the present standards, are important, one bears the burden of at least presenting some reason to believe that the proposed change to the standard would not change that observed empirical relationship such that people with the new, easier to attain diplomas would lack the opportunities opened by the old, more rigorous diplomans, because the diploma would no longer have the same implications for success.


Posted by: cmdicely on February 17, 2006 at 5:15 PM | PERMALINK

Damn it, franlky0, I wish I had thought of that one!

LMAO!

Posted by: Yancey Ward on February 17, 2006 at 5:15 PM | PERMALINK

Contemp philosophers with analytical abilities superior to the big ol greeks? Sheesh - hard to find any withOUT superior abilities...

This is just bizarre. If you can't step back from what we happen to know nowadays, and acknowledge that, say, the creator of logic and biology, Aristotle, probably had a greater analytic gift than Dummett, etc., I just don't know what to say.

What the hell did, say, Dummett ever contribute to the larger knowledge of mankind, that might begin to match Aristotle's accomplishments?

Or do you think that a high schooler who has mastered algebra is already the superior thinker to Aristotle by that fact alone?

Posted by: frankly0 on February 17, 2006 at 5:19 PM | PERMALINK

In this thread I have encountered many posts where the author boldly exhorts how important algebra is to basic daily fuctions only to see that the writer uses as an example a basic math operation and not algebra.

Just an obsevation.

Posted by: Keith G on February 17, 2006 at 5:23 PM | PERMALINK

LOL -

Frege is the creator of logic. What Aristotle et al did in that area was drivel - any fool coulda come up with the square of opposition.

Biology? LOL. Zoology would be a better term for what Aristotle did.

I noticed you didn't mention his groundbreaking, lasting work in physics. Animism was SUCH genius, after all...

Bout the only thing worthwhile in Ari were things like the Nico Ethics and the like...

It's a bit like comparing the best athletes of yesteryonderyear with the best of today. Sure Mr. Marathon was great for his day, but he wouldn't make even a top 10000 list by today's standards.

Posted by: cdj on February 17, 2006 at 5:25 PM | PERMALINK

Posted by: Paul E. Tickle on February 17, 2006 at 4:00 PM

Agreed. Thank you for taking this out of the abstract and applying it to the situation of a real person. The fashion design student who is required to take Algebra is akin to engineering student who must write an essay on "Finnegan's Wake" in order to be awarded a degree.

Posted by: dannyinla on February 17, 2006 at 5:25 PM | PERMALINK

A nation whose voting citizens were competent at algebra - competent at elementary-school arithmetic, in fact - would never have elected Reagan or GWB after hearing their preposterous fiscal proposals. The citizens of such a country would have reacted to that rubbish the way Professor Krugman did in 2000 - with astonishment at first, graduating into a sense of outrage, that these people must think we're all idiots who can't add.

But if that had happened, then Mr. Cohen would not have gotten his huge, repeated, upper-income tax cuts. Therefore, algebra is very, very bad.

Posted by: W. Kiernan on February 17, 2006 at 5:26 PM | PERMALINK

It seems to me that the greatest value in algebra is the pure logic it contains. So give people the option...either algebra or logic. Better yet, teach them together! Who knows, people may even start liking the subject.

Posted by: Brian Lewis on February 17, 2006 at 5:26 PM | PERMALINK

"The Egyptians had trig..."
They, like the Mesopotamians, had bags of mathematical tricks, algorithms that let them calculate what thye needed to. Given the dimensions of a proposed stone pyramid and a formula for the volume of a pyramid, you can calculate how much stone you will need to build it. But you cannot prove that your formula for the volume of a pyramid follows from the assumptions of your geometry if you don't have a science of geometry. West of the Indus (I don't know about Indian or E. Asian mathematical traditions), the Greeks invented the formal science of mathematics. With it they could not only solve the practical problems of the two millennia preceding but do proofs as well.
As for KD's question, I ask: should you graduate high school if you can't write passable English sentences and paragraphs?

Posted by: Dabodius on February 17, 2006 at 5:26 PM | PERMALINK
If you can't step back from what we happen to know nowadays, and acknowledge that, say, the creator of logic and biology, Aristotle, probably had a greater analytic gift than Dummett, etc., I just don't know what to say.

I dunno. Maybe you could actually propose an objective definition of the degree of someone's "analytic gift" since you seem to think that this is a nondebatable, objective, definable quantity.

Or maybe you can just berate everyone whose subjective assessment differs from the one you have offered as supposedly objectively correct without one iota of support. Its your choice which approach to take.

What the hell did, say, Dummett ever contribute to the larger knowledge of mankind, that might begin to match Aristotle's accomplishments?

Its a lot easier, I'd say, to contribute something fundamental and broadly applicable when there is a smaller store of existing knowledge.

This isn't, to me, a sign of necessarily superior analytical ability (though, at least when it comes to abstract reasoning, I'd say Aristotle was no slouch there), but simply a difference of context.

Or do you think that a high schooler who has mastered algebra is already the superior thinker to Aristotle by that fact alone?

I think that the phrase "superior thinker" is almost completely meaningless without further explication of what it is intended to mean in a particular context.

Posted by: cmdicely on February 17, 2006 at 5:26 PM | PERMALINK

frankly0 -

But more on point - American kids today don't even "know" as much as Aristotle. (Quotes in place because the bulk of what Ari "knew" is simply false.)

But it's wonderful how happy people are to advocate less knowledge for our kids.

I can hear gw now - "The problem with America is that people know too much".

Less knowledge! LESS KNOWLEDGE!

A truly Nietzchean turn (losers-are-winners-ism).

Posted by: cdj on February 17, 2006 at 5:29 PM | PERMALINK

What Aristotle et al did in that area was drivel - any fool coulda come up with the square of opposition.

How funny, then, that even a thinker as late in the game and as sophisticated as Kant would say that Aristotle had said the last word on logic. And of course, even within logic, it is understood that Aristotle pretty much DID have the final word within the narrow field of unary predicates and quantifiers.

Really, if you think that Aristotle was surpassed in his abilities by just about any and all contemporary thinkers, why argue with you?

Posted by: frankly0 on February 17, 2006 at 5:32 PM | PERMALINK

Well, CDJ, there are the things that Americans know, and the things that American don't know, and the things that American knows the don't know. But there are also the things that Americans don't know that they don't know.

Posted by: dannyinla on February 17, 2006 at 5:33 PM | PERMALINK

Dabodious -

Ah yes - those great invalid proofs of Euclid... With gaps you could drive a truck through...

What's of far more interest than the sandstone-foundation Euclid put maths on is the manner in which he tied the various fields together. In particular, then manner in which algebra n number theory were cast as geometric problems.

Posted by: cdj on February 17, 2006 at 5:37 PM | PERMALINK

The tendency of people to trivialize the accomplishments of the past is pretty astonishing.

Look, there's a REASON it took mankind close to forever to discover such things as the concept of logic, of algebra, of zero, of trigonometry, of biology, etc., etc., even though every one of those disciplines is better understood by most high schoolers than it was by the inventors -- namely, those concepts, as trivial as they may seem, are VERY HARD TO INVENT.

The inventors of those concepts, insofar as they are known, deserve great recognition, precisely because they were NONINTUITIVE ideas, as demonstrated by the very length of time it took mankind to come around to them.

Posted by: frankly0 on February 17, 2006 at 5:41 PM | PERMALINK

frankly0 -

Yup - it IS to Kant's discredit that he thought such. It made his job of reconciling Newton with God much harder. Not that the project woulda been successful anyway, but still - don't need to make an impossible task fucking-impossible...

OTOH, it's not like he was a Frege or anything...

LOL

Posted by: cdj on February 17, 2006 at 5:42 PM | PERMALINK

More on the value of Algebra: again, if ypu don't know HOW to use it, you won't realize you CAN use it to solve a problem quickly.

The textbook used in our (CA) school district has lots of examples such as how to calculate which cell phone plan, rental car plan, amusement park plan etc is better, the one with the high initial cost but low per minute, mile or ride charge or the one with the low initial cost or higher per unit charge, and how to find the cross-over point where one plan is superior. Lots of problems on profit margins and discounts. Inetrest rates etc. Most of it is real-world oriented, once one has the basic skills to solve the problem. Cohen probably just has someone else do it all for him, or spends more than he has to because he can.

I agree the real problem with the schools is kids passing for just showing up but not mastering the skills, then getting to a state college and having to take a year or more of remedial work, as is happening in California.

Posted by: Mimikatz on February 17, 2006 at 5:43 PM | PERMALINK
How funny, then, that even a thinker as late in the game and as sophisticated as Kant would say that Aristotle had said the last word on logic.

Not really "funny"; its hardly surprising that, if a field is (as cdj seemed to characterize the parts of logic addressed by Aristotle) fairly simple, that the earliest description of it would be fairly complete.

Really, if you think that Aristotle was surpassed in his abilities by just about any and all contemporary thinkers, why argue with you?

Really, if you think its an objective fact that Aristotle was superior to all contemporary thinkers, why not provide an objective definition against which your claim can be evaluated?

Posted by: cmdicely on February 17, 2006 at 5:43 PM | PERMALINK

frankly0 -

The biggest reason for the historical retardation of people is that the church locked in the idiocy of aristotle/ptolemy VERY early.

Posted by: cdj on February 17, 2006 at 5:47 PM | PERMALINK

dannyinla -

LOL

Posted by: cdj on February 17, 2006 at 5:48 PM | PERMALINK
Look, there's a REASON it took mankind close to forever to discover such things as the concept of logic, of algebra, of zero, of trigonometry, of biology, etc., etc., even though every one of those disciplines is better understood by most high schoolers than it was by the inventors -- namely, those concepts, as trivial as they may seem, are VERY HARD TO INVENT.

Rather, I'd say inventing them may be hard or easy (that's pretty hard to evaluate), but it requires people with both permanent recording of thoughts and plenty of free time not spent taking care of the necessities of survival. They require the development of a leisure class that can survive while devoting much of their time to non-immediate concerns.

Developing basic logic may not be nearly as hard as developing the agricultural and social infrastructure that allows someone the luxury of developing logic.

The inventors of those concepts, insofar as they are known, deserve great recognition, precisely because they were NONINTUITIVE ideas, as demonstrated by the very length of time it took mankind to come around to them.

Aristotle gets plenty of recognition. But you have some supposedly demonstrable facts that you ought to be demonstrating about now, don't you?

Posted by: cmdicely on February 17, 2006 at 5:49 PM | PERMALINK

Yup - it IS to Kant's discredit that he thought such.

As usual, you're just missing the point.

The point is that even over 2,000 years after Aristotle came up with his logic, he was still considered the final word. THE LIMITATIONS OF HIS LOGIC WERE OBVIOUS TO NO ONE. Indeed, they didn't become obvious until Frege himself realized that they could NOT generally apply to mathematical reasoning, which inherently involved relational predicates.

Frege's contribution was indeed major; but he had the benefit of over 2,000 years of further mathematical and cultural development.

Posted by: frankly0 on February 17, 2006 at 5:50 PM | PERMALINK
As usual, you're just missing the point.

The point is that even over 2,000 years after Aristotle came up with his logic, he was still considered the final word. THE LIMITATIONS OF HIS LOGIC WERE OBVIOUS TO NO ONE.

Which, of course, demonstrates that the later developments that Aristotle did not do were probably pretty difficult, which doesn't really say anything about Aristotle's abilities, since he didn't do them.

It also doesn't say anything about the difficulty of the parts of logic that Aristotle did develop.

Posted by: cmdicely on February 17, 2006 at 5:53 PM | PERMALINK

frankly0 -

Asked and answered: church make people stoopid.

And Frege didn't contribute, he invented.

I do agree with you on one thing tho - in a backhanded way - it IS easier to figure shit out when you have 2k years of well-developed idiocy to compare.

With that much silliness, it's almost hard to NOT get it right. Being a mathematician helps too, i spose... LOL

Rather like Churchill's paradigmatic American: can be counted on to do the right thing, after every other avenue has been explored.

Posted by: cdj on February 17, 2006 at 5:54 PM | PERMALINK

And to all of you who think that Algebra and math in general are important for kids to learn, I invite you to volunteer in your local schools to actually help kids learn math skills. Middle school kids are hard, but elementary kids are a treat, and ypu might actually do some good.

Posted by: Mimikatz on February 17, 2006 at 5:55 PM | PERMALINK

I've read Cohen's article a couple of times now, and no, that was not his point. It was not a serious discussion of whether algebra is a necessary and legitimate requirement for a high school diploma.

It was a tirade against algebra. Nothing more. It was a guy who can't calculate percentages, whose best course in HS was typing, insisting that the stuff he isn't smart enough to do is unimportant.

If you want to make it a serious discussion, though, I'll say yes: basic algebra ought to be a requirement for graduation, as should being able to read and write. A diploma shouldn't be an award for surviving to age 18, but should be an indication that one has at least a few basic skills.

Posted by: PZ Myers on February 17, 2006 at 5:55 PM | PERMALINK

And the limitations of Ari logic were patently obvious to a mathematician - even of yore. That's why proofs, such as they were, were not done in syllogistic form.

Duh.

That's why for Kant logic was analytic, while mathematics was synthetic.

Duh.

The limitations of Ari logic were patently obvious.

Similarly were the limitations of geometry-a-la-Euclid patently obvious. Thus the bigtime critic (forget his name - referred to for comparison in the Heath volume). Thus Saccerri. Thus....

Posted by: cdj on February 17, 2006 at 6:00 PM | PERMALINK

Which, of course, demonstrates that the later developments that Aristotle did not do were probably pretty difficult, which doesn't really say anything about Aristotle's abilities, since he didn't do them.

Look, Aristotle's logic was considered one of the great achievements of human intellect by virtually all serious thinkers for literally thousands of years. Mastering the Organon was regarded as an enterprise only the most disciplined of students and scholars would undertake. That Kant, for example, thought it was the last word is certainly a testament to the perfection of Aristotle's treatment, from Kant's point of view. And indeed, as I said, Aristotle's logic is essentially complete, within its limited realm, even as subsumed under Frege's far more powerful apparatus and logic.

Now, I guess this doesn't much convince you of anything, because, of course, Aristotlean logic has been supplanted by logics far more elaborate and capable. But if there can be a case in which only in hindsight does something seem trivial and obvious, I should think this would have to be it.

Posted by: frankly0 on February 17, 2006 at 6:07 PM | PERMALINK

I quit high school on my 16th birthday, the age the law then allowed, so I've had to live the last 59 years as a high school dropout. Oh, the shame of it all!

What a waste of time high school was. Bells and balls and brawls in the halls. One of the smartest things I ever did was skip over all that adolescent crap. Of course I later graduated with honors from the University of Michigan, but that's another story.

Algebra? Never needed it, except for once when I wanted to know the heighth of a Douglas fir before cutting it down, for fear of laying it on my neighbor's summer cottage. I did what an old Greek did when measuring the heighth of a pyramid: measured the tree's shadow and my own. Since I knew I was six feet tall, then the tree....

Was that Algebra?

Posted by: buddy66 on February 17, 2006 at 6:07 PM | PERMALINK

cmdicely wrote:
"... such that people with the new, easier to attain diplomas would lack the opportunities opened by the old, more rigorous diplomans, because the diploma would no longer have the same implications for success."

The studies were based on nationwide data, thus including recruits from districts that had fairly rigorous requirements as well as those from districts less demanding. The studies controlled for differences in courses (by title and description) and grade point average. Thus the decision to value "the paper" in and of itself.

You might be hard pressed to find more many school districts making their diplomas easier to get. According to articles in the general press and the journals of the math and science teachers' organizations and information on the US and state-level Departments of Education, math course requirements are going up all across the country, at least as much as teacher availability allows. Science course requirements are moving up less quickly.

The above does not even take into account the number of states imposing statewide minimum core competency testing for graduation. Back when the recruiting studies were done, only a few states had any sort of statewide graduation test requirments. Of the dozens of districts in the state where I directed recruiting, all had requirements for one or two years of math, but only a handful specified algebra as a requirement. A friend is a high school principal in that state now and reports that he knows of no district in the entire state not requiring or about to require algebra for graduation.

In my wife's district, long regarded as one of the best in the nation, the geometry requirement kicks in next year. The state graduation tests will include a geometry component. Now, being the district it is, the current goal is to have all "average" students take Algebra I in 8th grade and Geometry in 9th. "Above average" students (the overwhelming majority since the children in this district are, like those in Keilor's "Lake Wobegon, all above average) are to do Alg I in 7th grade and Geometry in 8th. Given the requirement for two (talking about three) years of high school math classes, this means most students will end up finishing with at least pre-Calc. My wife, a math major with a MA in education, has been asked to go back and refresh her multivariate calc and linear algebra skills as her school (and several others) plans to introduce AP Multivariate next year and AP Linear Algebra the year after.

Not sure what the plans are for dealing with the fact that most students are not cognitively readly to understand algegra in the 7th grade. Guess as long as they can "plug'n chug" standard problems into standard formulae they'll be ok.

More than half way into the school year and in my wife's AP Calc classes more than half of the mistakes on quizzes and test are still algebra mistakes. Can't see that getting any better soon.

Posted by: Paul E. Tickle on February 17, 2006 at 6:10 PM | PERMALINK

frankly0 -

Wow.

"Essentially complete"? Asinine. Kant, along with every mathematician from Ari on understood the inadequacy of Ari logic.

Ari invented a playtoy. Frege invented logic.

Back on topic tho - it would be a dramatic improvement in Americans if they knew as much "math" and "logic" as Ari/Euclid knew. A DRAMATIC improvement.

I'd even be willing to trade an idiotic belief in "rock-nature" for just that lil bit of math/logic knowledge... LOL

Posted by: cdj on February 17, 2006 at 6:13 PM | PERMALINK
Look, Aristotle's logic was considered one of the great achievements of human intellect by virtually all serious thinkers for literally thousands of years.

Granting, arguendo, that that is true, so what?

Even if that is true and, further, even if it were an objective fact that Artistotle's logic was one of the -- or even the one -- greatest acheivement of human intellect ever, it wouldn't prove your point that Aristotle, Plato, and Socrates weren't disadvantaged by lack of exposure to algebra and, from which incomplete handful of special cases we are supposed to draw the conclusion that algebra isn't really a desirable core component of modern high school education.

Now, I guess this doesn't much convince you of anything, because, of course, Aristotlean logic has been supplanted by logics far more elaborate and capable.

It doesn't convince me of anything relevant to the debate here, not for the reason you suggest, but instead because it is completely irrelevant to the propositions which it has been offered to support.

Posted by: cmdicely on February 17, 2006 at 6:15 PM | PERMALINK

And the limitations of Ari logic were patently obvious to a mathematician - even of yore. That's why proofs, such as they were, were not done in syllogistic form. Duh.

Why, then didn't these mathematicians make this very point, that they needed a new logic for mathematics? Why did it await Frege for this to happen?

Here's the reality: even in EUCLID'S axiomatic proofs, which, surely, employ logic, NO ONE UNDERSTOOD that there was a distinct logic that should be developed to handle those inferences.

It remained for Frege to have precisely that insight. THAT was his greatest achievement, to develop a RELATIONAL predicate calculus that COULD express the truths of mathematics; the logic could only be built on that relational formalism.

Pretending that all kinds of mathematicians realized the limitations of logic before Frege is pure ignorance of the history. Show me a quote from a mathematician before Frege that demonstrates this supposed realization. The only thing I can think of was Liebniz's idea that someone should develop a formalism in which you can settle moral and philosophical disputes just by "calculation", and that was so woolly and undeveloped as to be essentially meaningless.

Posted by: frankly0 on February 17, 2006 at 6:16 PM | PERMALINK
Not sure what the plans are for dealing with the fact that most students are not cognitively readly to understand algegra in the 7th grade.

Maybe this assumption is not a fact.

Posted by: cmdicely on February 17, 2006 at 6:18 PM | PERMALINK

franky0 -

And you seem to think it means something that "people genuflected to Ari for 2k years". You keep mentioning it - and I've already answered it.

The church locked it in. The church retarded the West. Much to Copernicus' consternation, and Galieo's woe. Newton was lucky, since he was already going to hell - lol. And Hume was just plain smart - to bad he's unanimously massively non-understood...

Also too bad that you have apparently read none of the works you refer to.

Posted by: cdj on February 17, 2006 at 6:19 PM | PERMALINK
The church locked it in. The church retarded the West.

While certainly there are areas where this is the case, you'd expect other parts of the world, not under the thumb of the Church, with access to Classical learning, to have flowered in logic if this was the explanation.

Rather, I think the a better explanation is that the developments after Aristotle were non-obvious and challenging.

Posted by: cmdicely on February 17, 2006 at 6:22 PM | PERMALINK

cdj,

Do you even understand the difference between unary predicates and relational predicates, and the enormous differences that difference implies?

If not, maybe it's time to shut up?

Posted by: frankly0 on February 17, 2006 at 6:24 PM | PERMALINK

frankly0 -

Sigh. Philosophy and history are there to be read to any who are interested... There MUST be a semi-complete university within 10 miles of you....

Everyone knowledgable of the two realized perfectly well that Euclid could not be cast syllogistically.

It's asinine that you say otherwise.

The demonstration that mathematicians recognized the inadequacy of Ari is in their practice: even with all their blemishes, what passed for mathematical proofs were NOT cast in Ari form. Ever. Really - they weren't. Go look. Seriously.

The demonstration that Kant recognized the inadequacy of Ari logic is in the fact that math was synthetic for him, while logic was analytic

The demonstration that Newton recognized the inadequacy of everything Ari was the Principia.

Sheesh. Go read.

Posted by: cdj on February 17, 2006 at 6:25 PM | PERMALINK

cmdicely -

Not necessarily. While I agree that THAT explanation doesn't suffice for other parts of the world, that doesn't mean it doesn't suffice for the part of the world under discussion....

Lotta pronouns there... hope that made sense... lol

Posted by: cdj on February 17, 2006 at 6:26 PM | PERMALINK

frankly0 -

re: predicates with different numbers of args

You talkin to urself again?

Well lessee here... the theory of one is decidable, the other not... Is that what you were after?

Posted by: cdj on February 17, 2006 at 6:28 PM | PERMALINK

"Or are you claiming that you can prove, somehow, that Aristotle, Socrates, Plato, et al. would not have been even better when it came to reasoning had they been exposed to algebra?"

Um, Plato studied under Pythagoras for a while - wanna bet he could do simple algebra?

Posted by: Arr-squared on February 17, 2006 at 6:29 PM | PERMALINK

cmdicely,

If the acceptance of Aristotle as one of the great thinkers for over two thousand years does not in any way impress you as good evidence that he had remarkable analytical abilities, what can I say? Remember: this is two thousand years of highest accolades from the top thinkers mankind has had to offer (unless you think they're idiots too, or that I have to establish THEIR credentials). Even those who had problems with his assertions most basically had a problem with the fools who simply took literally everything the "Master" had to say, rather than with what Aristotle came up with given his own historical context.

I've reduced you to the absurd, and you're happy to be there. Really, my work is done.

Posted by: frankly0 on February 17, 2006 at 6:33 PM | PERMALINK

Arr-squared -

Of COURSE he could - at the idiotic level of the American high school at least.

It's only non-readers who think differently...

Posted by: cdj on February 17, 2006 at 6:33 PM | PERMALINK

cdj,

How about the idea that Aristotle's theory of logic WAS complete, for unary predicates.

Is that hard to understand?

Posted by: frankly0 on February 17, 2006 at 6:34 PM | PERMALINK

Everyone knowledgable of the two realized perfectly well that Euclid could not be cast syllogistically.

Then why didn't they come up with an adequate logic FOR TWO THOUSAND YEARS??

The point is, they DIDN'T explicitly realize the need for such a logic.

If you think otherwise, come up with a quote, one single quote, from a mathematician, indicating that, gee, we need a better logic than Aristotle's.

ONE QUOTE.

Posted by: frankly0 on February 17, 2006 at 6:37 PM | PERMALINK
If the acceptance of Aristotle as one of the great thinkers for over two thousand years does not in any way impress you as good evidence that he had remarkable analytical abilities, what can I say?

I am willing to grant that Aristotle, Plato, and Socrates had "remarkable" analytical abilities, without reference to the popularity of their works.

Of course, since that doesn't prove the contention that you made -- that Aristotle (along with Socrates and Plato) was demonstrably unhindered by lack of access to algebra -- or the further contention that was apparently offered in support of -- that algebra is, therefore, not a desirable core component of the high school curriculum -- I think that you've failed in your argument.

Really, my work is done.

Well, if your work was merely to make the relatively uncontroversial point that Aristotle was a pretty smart guy, sure, but that's a far weaker position, and irrelevant to the fundamental debate here, than your original offering.

Posted by: cmdicely on February 17, 2006 at 6:41 PM | PERMALINK

Um, Plato studied under Pythagoras for a while - wanna bet he could do simple algebra?

I was, for the sake of argument, accepting frankly0's premise about absence of exposure to algebra since there were enough other holes in the argument that semantic quibbling over where to draw the line with "algebra" wasn't the most productive line of attack.

Posted by: cmdicely on February 17, 2006 at 6:45 PM | PERMALINK

franky0 -

Why didn't they? Duh. Because "logic" to them meant "something completely useless" - namely Ari logic. They wanted to do math, so they just barrelled on ahead.

Duh.

Except in exceptional circumstances, one doesn't need FORMAL logic to do math. But using only Ari logic will simply prevent math from being done.

What is this infatile fascination you have with quotes? The practice of mathematicians makes it perfectly clear.

Make you a deal: I'll get you that quote, if you cast a single "proof" from the Elements in syllogistic form.

(Hint: It's an unfair deal. Only one of them actually CAN be done.)

Posted by: cdj on February 17, 2006 at 6:47 PM | PERMALINK

cmdicely,

Look, if Aristotle is one of the great thinkers in history, which I think would be contradicted only by people who have some crazy axe to grind, and Aristotle had no exposure to anything but the most elementary of mathematics, I think it should be pretty obvious that general analytical abilities can be developed almost entirely independently of exposure to mathematics. Maybe Aristotle would have gained some further ability had he done more math, or tonal music, or done video games, or whatever.

But being one of the smartest people ever to live is smart enough to make my underlying point. I'm not hanging anything important on whatever minor improvement in talent Aristotle might or might not have enjoyed had he actually been able to solve the quadratic equation. And I can't imagine what you could be hanging on this possibility either.

Posted by: frankly0 on February 17, 2006 at 6:51 PM | PERMALINK

cdj,

Make you a deal: I'll get you that quote, if you cast a single "proof" from the Elements in syllogistic form.

Now you're just completely confused and incoherent.

I can't even begin to imagine what makes you think I was saying that such a proof might be forthcoming, especially when I was arguing throughout that it most definitely was not possible -- you can't even EXPRESS the axioms of Euclid's geometry with unary predicates.

Posted by: frankly0 on February 17, 2006 at 6:56 PM | PERMALINK

Well Euclid could solve quadratics...

Posted by: cdj on February 17, 2006 at 6:59 PM | PERMALINK

frankly0 -

I claimed that ari "logic" was inadequate for mathematics, and that every mathematician from ari on acknowledged this at least in practice by eschewing ari "logic" in all serious mathematics. Kant acknowledged this by classifying "logic" and "math" differently. Newton recognized this just by thinking.

You took issue with this - for reasons known only to to you.

Posted by: cdj on February 17, 2006 at 7:10 PM | PERMALINK
Look, if Aristotle is one of the great thinkers in history, which I think would be contradicted only by people who have some crazy axe to grind, and Aristotle had no exposure to anything but the most elementary of mathematics, I think it should be pretty obvious that general analytical abilities can be developed almost entirely independently of exposure to mathematics.

So? Certainly, this is possible. This in no way contradicts the idea that mathematics in general and algebra in particular are particularly valuable in this regard, even if it is possible to develope analytical skill without exposure to them, and therefore that it is a desirable component of a core curriculum for the purpose of fostering analytical development.

But being one of the smartest people ever to live is smart enough to make my underlying point.

No, one (or even 3) people being among the "smartest" people ever, even if true, does not make the case for your original claim, or the case against algebra in the core curriculum.

I'm not hanging anything important on whatever minor improvement in talent Aristotle might or might not have enjoyed had he actually been able to solve the quadratic equation. And I can't imagine what you could be hanging on this possibility either.

Hey, you are the one who claimed they were demonstrably unhindered by lack of access to algebra, so its your burden to carry, unless you wish to withdraw the claim.

I'm just saying that you have not demonstrated what you claim is demonstrable and, further, that even if it were demonstrated that those three exceptional individuals were not hindered,
it wouldn't make the case against algebra in the core curriculum.

I'm not hanging anything on the possibility you refer to, except that the fact that you have not demonstrated the absence of that possibility indicates that what you previously claimed to be demonstrably true is not demonstrably true. But, even if it were, it doesn't mean anything to the broader debate.

Essentially, you are arguing seems to be, implicitly:

P1. Aristotle (Socrates/Plato) is a person.
P2. Aristotle (Socrates/Plato) was not disadvantaged in development of his analytic ability by not being exposed to algebra.
C. Therefore, no person is disadvantaged in development of analytic ability by not being exposed to algebra.

I'm saying that P2 is not, as you have claimed explicitly, demonstrably true and, furthermore, the logic is invalid, anyway.

Posted by: cmdicely on February 17, 2006 at 7:18 PM | PERMALINK

Most American high schools use Carnagie Units [i.e. credits in required and non-required courses] which must be earned in order to earn a diploma. A typical state requirement is that students earn 40 or more credits [two semesters per year---six classes per semester]. Students must earn a passing grade in each required class. Credits are not averaged out, although total GPA--grade point averages--are averaged. Algebra is the first year of the high school math curriculum, which also includes geometry, trigonometry [or pre-calculus], and calculus. For non-engineering and non-science students, the value of learning algebra is in learning logical, abstract thinking . Obviously, students who cannot think logically and critically also struggle with such tasks as understanding history and government, writing a persuasive essay, and understanding literary works. In Indiana, the 10th grade Graduation Qualifying Exam requires that students write some variation of a persuasive essay [the common 1-3-1: introduction, three main points, conclusion essay], a difficult task if one cannot think logically and clearly. Students who don't understand algebra also have difficulty in the required science classes, which include biology, and in the more advanced classes of chemistry and physics. Having taught high school for 28 years, my belief is that students "rise to expectation." What students are capable of doing is different from what they want to do. Our huge dropout rate is a function of "want," as in "I don't want to work that hard and you can't make me." Raising educational standards in the US means "upping" the requirements and demanding that high school students learn the basic concepts of Western knowledge. Those concepts include the core subjects of composition, literature, speech, history, government, geography, biology, mathmatics, chemistry, physics, and others, as well as music and art. In my experience of working with rural and small town students, every student of normal intelligence can---and should---learn the core curriculum [the old college-prep curriculum]. Democracy requires well-educated voters and citizens who can think critically and logically.

Posted by: applecrisp on February 17, 2006 at 9:42 PM | PERMALINK

My childrens' grade school uses the Investigations method for teaching math. I am completely sold. It emphasizes teaching concepts before math facts. Most importantly, it teaches children concrete principles of learning. Richard Cohen completely misses the point by dismissing mathematics as impractical and un-useful in day-to-day life. The rational tools are widely applicable to any problem-solving situation. I heard a principal from Belleview, Washington discuss his school's success with the program and he was inspiring. I'll never do justice to his comments, but the thrust was that mathematics is a wonderful vehicle for teaching empirical thought. As a member of the reality-based community, I applaud a teaching system founded in fact and rational thinking. To lazy, pseudo-intellectuals like Cohen, I quote the Poorman, "chew me."

Posted by: pollyanna on February 17, 2006 at 10:48 PM | PERMALINK

Sorry, moonbats, but Cohen's column was right on the money. Check out my blog scrutator.net for a free-ranging discussion of the issues contained therein.

Posted by: Leonidas on February 17, 2006 at 11:40 PM | PERMALINK

I guess I made my point. I went through advanced math in high school with a 3.0 grade point average, and my father has a masters in math and neither one of us can spell at all. My daughter can spell well and pull a 2 inch hose, and a 4 inch hose ( don't ask me what is the diffence other then one is twice as large as the first one.) I do get that she uses math a lot more than she thinks she is,The direction of the hose, how much water,how much air she has left in the bdu. But that is not anything she learned in high school math. I will be honest, she dose not get math at all. She is not even able to double a recipe, but the guy whose life she saved pulling him out of a burning car I am sure he dosen't care if she knows how to double a reciept. I guess what I am trying to say here is it seems to me on this page everyone thinks that you need a four year college degree to be a active member of society. I have 4 children. The oldest is the only one with a white coller job(and the biggest pain in the butt of the group). The next oldest is back home after 5 years in the army. Yes if anyone wants to know what 2 years of Afganisan and Irac was like from Parents view point I will be happy to vent. The other two are twins, one who works for Pg&E (for people in Calif he reads you meater( hate hiim if you want, I do every month), and our daughter the firefighter. Not one of them needed algerbar to go on to what they do for a livining. May not be a college degree, but people you all need (not the PG&E guy). No we don't get a discount.

Posted by: caren on February 18, 2006 at 12:38 AM | PERMALINK
And if someone can't pass a test in Algebra despite multiple attempts, then their brain just ain't gonna get it. And I don't think that says their lives should just be discarded.

No one says their lives should be discarded. We will always need people to scrape gum off sidewalks, clean toilets, and say "Do you want fries with that?"

Harsh? Yes. But there's no law or anything out there that makes a highschool diploma a prerequisite for rewarding jobs. Businesses set their standards based on what they need.

If diplomas become irrelevant businesses will use other criteria or start making people take entry tests.

In today's economy the marginal production of an additional manual worker is much lower than the marginal production of an additional knowlege worker. Therefore people who do not have the ability to be knowlege workers will do poorly no matter how many degrees they have.

Posted by: Michael Friedman on February 18, 2006 at 1:55 AM | PERMALINK

It has its uses, I suppose, and I think it should be available for people who want to take it.

Meanwhile, we're trying to figure out ways to import more scientists and engineers from foreign countries... Coincidence?

Posted by: E. Nonee Moose on February 18, 2006 at 7:14 AM | PERMALINK

E. Nonee Moose: Meanwhile, we're trying to figure out ways to import more scientists and engineers from foreign countries... Coincidence?

"Import more scientists and engineers" is a way to manipulate the market to reduce salaries. Engineers have an unemployment rate higher than average, let alone the average for the college educated. Fewer than half the people with Ph.D.'s in science, math, etc. have jobs that require that level of education.

Look at the facts, not tbe hype and propaganda.

Posted by: alex on February 18, 2006 at 12:42 PM | PERMALINK

I can't tell you how pleased I am with the consensus of this comments section. You guys (and Kevin) make Lynn Cheney sound like Tommy Chong in your rigid, up-tight defense of standards. Maybe there is hope for America yet.

Posted by: wks on February 18, 2006 at 1:44 PM | PERMALINK

Can we allow people with such low intelligence to be in charge of nuclear weapons?

George Bush is.

Posted by: MarkH on February 19, 2006 at 11:08 AM | PERMALINK

Dumb people aren't less deserving of a decent life and good stuff than smart people are.
Posted by: theorajones on February 17, 2006 at 12:30 PM |

Oh. My. God. This nonsense is EXACTLY what the righties always accuse us of, and I've always said they were straw-manning it. And yet, here it is, in all its glory. I wonder how many more liberals, when pushed, will admit they actually believe this obscenity?
This, at its heart, may be the real problem with Dem politics today -- even more than being "soft" on national security, even more than being "messageless," even more than having the corporate media totally against us, and lying and cheating for the Repukes.
It is entirely possible that there are too damn many Dem's that still believe this -- and want to spend MY hard-earned money, and Jane and Joe Six-Pack's -- to just GIVE stupid and lazy people the middle-class life that they can't and won't earn on their own.
A social safety net to cover the very basics of existence, so that people won't starve, or die on the streets? Sure. All over that.
Tax us at MUCH higher rates than today, if it ensures equal opportunities -- at the highest possible levels -- for everyone? Absolutely. Bring it on.
But giving to people who are too stupid or too lazy to earn it on their own entitlements that let them live at the same level of extravagance as only the very rich in any earlier century -- and paying them out of MY pocket? Fuck that. And I'm WAY more liberal than 99.9% of red-staters.
Until Dems lose these most extreme of redistributionists such as this, we will keep losing -- and we will deserve to. How DARE you tell me I should work harder to pay for someone who won't? It's enough to send me back to the Ayn Rand shelves -- as a believer.

Posted by: smartalek on February 20, 2006 at 3:12 PM | PERMALINK

Incidentally for people to lazy to do math, 20% is the easiest number to figure out. Just move the decimal to the right and double it. Takes 2 seconds. Don't even need a calculator.
Posted by: Tom in Texas on February 17, 2006 at 3:18 PM |

Tom of course meant to write, "for people too lazy" to do the math," and "move the decimal one place to the LEFT and then double [the number]" -- because the "it," as written, refers to the decimal point, and you're not doubling the decimal point, you're doubling the number.
Or perhaps he's writing in Hebrew or Arabic? (Then again, I read neither; do they also write numerals from right to left, or no?)
Yes, I am a teacher. Don't try this at home without supervision.

Posted by: smartalek on February 20, 2006 at 3:29 PM | PERMALINK




 

 

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