quote:You will never need to know algebra. I have never once used it and never once even rued that I could not use it. You will never need to know -- never mind want to know -- how many boys it will take to mow a lawn if one of them quits halfway and two more show up later -- or something like that. Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note -- or reason even a little bit.
This man is insane.
Posted by Teshi (Member # 5024) on :
*facepalm*
Posted by erosomniac (Member # 6834) on :
He's failing to recognize that many forms and applications of mathematics require as much creativity and artistic talent as composition does.
He's also failing to recognize the hundreds of daily applications of algebra.
Posted by SC Carver (Member # 8173) on :
This guy would be one of the cashiers who looks at you funny when you give them $21.15 for a $16.15 total.
quote: The L.A. school district now requires all students to pass a year of algebra and a year of geometry in order to graduate. This is something new for Los Angeles
South Carolina is supposed to be 48th in education but I thought this was requirement 15 years ago when I was in school.
Posted by Juxtapose (Member # 8837) on :
And how is this quotee defining, "reason?" AI is improving constantly. It's really only a matter of time before programs CAN do things that require "creativity."
And denying the engineering often necessary in creative pursuites is ludicrous. I don't know how many art pieces I've been working on in which I've needed geometry and algebra to produce the results that I was looking for. For example, if I were to enter a submission for a public artwork, it would be expected that I could present a bird's-eye and elevation plan, and that both of these would be fairly accurate in terms of scale and proportion.
Posted by Tante Shvester (Member # 8202) on :
*suspicious* Irami wrote that, neh?
Posted by lem (Member # 6914) on :
quote: Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers. 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.
You can't argue that kind of proof! Debate closed. Richard Cohen wins.
Posted by mr_porteiro_head (Member # 4644) on :
quote:I can do my basic arithmetic all right (although not percentages)
If you can't do percentages, you can't do basic math.
Posted by Mr.Funny (Member # 4467) on :
quote: 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.
You've got to love how he first makes a claim that writing is the highest form of reasoning and then immediately follows it with a sentence that is not grammatically correct.
Posted by MandyM (Member # 8375) on :
If you can't do algebra, you shouldn't graduate from high school. Here in Texas kids have to pass the TAKS test in English, math, science and history. The English is pretty hard too since the questions over the reading passages are short-answer as well as multiple choice and there is a writing prompt related to the readings.
Posted by HollowEarth (Member # 2586) on :
I guess I think you probably shouldn't have been able to pass your earlier math classes if you failed algebra 7 times.
Posted by Soara (Member # 6729) on :
"This is a fact" is not grammatically correct?
Posted by Celaeno (Member # 8562) on :
quote: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.
Straw man, anyone? I like how he claims that writing is the highest form of reasoning but backs that up by not giving an argument to prove it. Instead he provides an argument to attack a completely different statement: algebra is not the highest form of reasoning. Even if his algebra conclusion were correct, he still hasn't proved his initial statement. That's no proof at all.
edited for clarity Posted by Evie3217 (Member # 5426) on :
quote:Originally posted by Soara: "This is a fact" is not grammatically correct?
I don't think that's the sentence they were talking about. This sentence however:
quote: 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.
is not a grammatically correct sentence.
And personally, I was pretty good at math, and I can still write a coherent sentence. This guy is a kook.
Posted by Celaeno (Member # 8562) on :
Me too, Evie. Math and English were my stronger subjects in high school.
Posted by Synesthesia (Member # 4774) on :
I hate algebra. It makes my head hurt It makes me miserable The site of it depresses me and I have not used it once, ever! I so strongly dislike and despise math! But, I have discalclia (sp) or something because i can barely do simple math... I could write a novel... or even a short story or think of some odd random idea for a novel or short story, I can remember details from a book I read ages ago or historical facts or various Japanese words like kuroshi but I simply cannot add 3424234 + 34234 in my head or figure out x + y = z or whatever... Don't know why that is.
Posted by Eldrad (Member # 8578) on :
I saw this article earlier today, too, and it infuriated me, not least because I'm majoring in mathematics. How are we supposed to improve the quality of our education system if we make it easier for people to graduate? That seems more like quantity over quality to me.
Also, how can he rightfully say that writing is the highest form of reasoning if the extent of his exposure to mathematics is geometry? Sure, algebra and geometry are two fundamental branches, but the courses taught in high school, and thus those which he would have taken, are relatively mindless number crunching in comparison to higher math. That said, while math doesn't teach a person reasoning (it's more of an innate trait anyway), it most definitely refines it, as do other classes which require critical thinking, like writing or history courses as examples.
And I'd still say math is as high a form of reasoning as you can get, but that's the major in me taking hold, I think. Posted by TomDavidson (Member # 124) on :
Actually, that sentence -- while not actually logically sound -- is in fact grammatical. It breaks down as follows:
The proof is all the people.
The long "who" bit at the end is just flimsily attached to "people."
Posted by HollowEarth (Member # 2586) on :
quote:How are we supposed to improve the quality of our education system if we make it easier for people to graduate? That seems more like quantity over quality to me.
Keep in mind that failing math doesn't mean that you are unfit for basically any job that will pay you enough to live on. Which is what the lack of a HS diploma pretty much means.
Posted by mr_porteiro_head (Member # 4644) on :
Does anybody actually care or check if their employees have high school diplomas anymore?
Posted by Kasie H (Member # 2120) on :
This, ladies and germs, was one of those days that Richard Cohen really didn't have any column ideas whatsoever, so he decided to write about what he hated in high school.
He gets a slap on the wrist for the grammatical error, but it seems to me his tongue was already poking into his cheek just a little.
Posted by AvidReader (Member # 6007) on :
Um, I almost majored in math, and I agree with this guy. Intro to Number Theory was the greatest course I ever took, but I never use more than multiplication as a bank teller.
I believe some people's brains are not wired for algebra or other higher maths. My mom is very intelligent. However, she had to take algebra three times and still only passed by the skin of her teeth. She writes poetry and teaches SEDs. Algebra only comes up if one of her students makes it that far.
My baby sister made it through algebra but not trig. She joined the Air Force and does some kind of emergency training for the pilots. Algebra not required.
What does requiring algebra actually accomplish? It has the potential to help some students realize they like math, true. However, it also has the potential to keep our artists and authors from graduating. If they don't pass, they can't get in to college where advanced training could improve their craft and help them earn a living.
I think most people know if they prefer math or english. I don't think there's a large market of untapped engineers waiting for someone to show them the light of mathematics. I really don't think that the reward outweighs the risk here.
Posted by Tatiana (Member # 6776) on :
AvidReader, engineers are pretty important in the process of creating all the thousands of products you use every day without knowing how they work. Someone needs to know. I had such lousy math education in school that had I not had a totally independent source of math learning, I would never have realized I wanted to be an engineer, and never have bothered to take it in college and find out how much I loved it.
My father was a math major, and he, along with stuff I read for fun like Martin Gardner's Mathematical Games columns in Scientific American magazine, are the main reason I found out I like math. I also was lucky enough to get two teachers in grades 1-12 that were pretty decent math teachers. They were sort of out of the ordinary.
I really think if we want to have any engineers and scientists at all, we need to have better math teaching in grades 1-12 instead of worse.
[ February 20, 2006, 08:53 PM: Message edited by: Tatiana ]
Posted by Joldo (Member # 6991) on :
You know, I think this proves a point. So often I read a column, I read an article, a column or article that uses statistical math or some science work, and me, I check it, I find errors. (And that last sentence was calculated to give a heart attack to punctuation Nazis. It's called vernacular. Live with it, you. Faugh) And these I find, they're big errors, things that disprove or soften the point.
Hm. Someone need a math course?
Posted by Avatar300 (Member # 5108) on :
That's funny, my arm just went numb.
Posted by EarlNMeyer-Flask (Member # 1546) on :
Computers can write postmodern essays, so they can write columns.
Everyone does algebra everyday, all the time- whether they realize it or not. Realizing how it's done just leads you to be better at it. I don't understand how he doesn't get that.
Posted by 0range7Penguin (Member # 7337) on :
I was both good at/enjoyed algebra. What I can't do is Geometry. It made me want to commit mass murder or suicide. Grrr...
And I did use algebra in physics. I loved physics class and all physics is just applied algebra.
Posted by rivka (Member # 4859) on :
Actually, most physics is applied calculus. Which is precisely why Newton invented calculus.
Posted by Irami Osei-Frimpong (Member # 2229) on :
I didn't write the article, but I am sympathetic with the sentiment.
quote:He's failing to recognize that many forms and applications of mathematics require as much creativity and artistic talent as composition does.
So what. Juggling and video games take as much hand eye coordination as surgery. Nobody, outside of EA and maybe the Flying Karamazov brothers are seeking to push mandatory juggling requirement.
If we are speaking about cultivating creativity, for the sake of creativity, I think that we ought we out to advocate verbal manipulation. At least words are tied to thoughts, I'm not sure what numbers are tied to.
quote:He's also failing to recognize the hundreds of daily applications of algebra.
With your rigorous math education, I imagine that you can see the logical fallacy your argument.
quote:AvidReader, engineers are pretty important in the process of creating all the thousands of products you use every day without knowing how they work. Someone needs to know.
This is something I agree with. Someone needs to know. I also think that someone should know how the mail works, set theory, the expanding universe, and the difference between a triple loop and a Salchow. I'm glad someone knows, but I'm not going to say that everybody needs to know, and I'm not going to say that everyone ought to know. Building cooler, more efficient gadgets isn't the most important priority in life or education, and I don't think that such knowledge is universally necessary, and I'm good at math-- much better at math than an I've ever been at anything regarding writing-- I just don't think that it's as important as we propose. What math is, and this is no small issue, is teachable. I actually think that math's objectivity, universality, and teachablility explain why a rigorous math curriculum is so durably entrenched in public education. You can teach it, you can test it, and so in a pinch, we've elevated its importance over other subjects that are harder to adjudicate.
[ February 21, 2006, 02:51 AM: Message edited by: Irami Osei-Frimpong ]
Posted by erosomniac (Member # 6834) on :
quote:Does anybody actually care or check if their employees have high school diplomas anymore?
Go to www.craigslist.org and check the job listings. Look at how many specify high school diploma or GED required.
Not everyone actually checks, but two (of seven) of the places that've interviewed me recently asked not only for college transcripts (for the courses I completed), but for a highschool transcript as well.
Posted by erosomniac (Member # 6834) on :
quote:So what. Juggling and video games take as much hand eye coordination as surgery. If we are speaking about cultivating creativity, for the sake of creativity, I think that we ought to push verbal for manipulation.
As soon as juggling and video games take the same amount of education as surgery, make sure you go out and look for a job as a surgeon, citing your extensive juggling and video game playing experience as your qualifications.
quote:With your rigorous math education, I imagine that you can see the logical fallacy your argument.
What rigorous math education? I passed algebra, aced geometry and then nearly failed trig. I dropped out of pre-calculus (too difficult) and have no experience with collegiate-level mathematics. With your rigorous liberal arts education, however, I imagine that you can see the error in your sentence. Posted by Jon Boy (Member # 4284) on :
quote:Originally posted by Evie3217: I don't think that's the sentence they were talking about. This sentence however:
quote: 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.
is not a grammatically correct sentence.
And personally, I was pretty good at math, and I can still write a coherent sentence. This guy is a kook.
As Tom already said, it's perfectly grammatically correct, and it's even coherent to boot.
The guy is a kook, though. Knowing where the Sahara is has nothing to do with the ability to reason.
Posted by Jon Boy (Member # 4284) on :
quote:Originally posted by Joldo: You know, I think this proves a point. So often I read a column, I read an article, a column or article that uses statistical math or some science work, and me, I check it, I find errors. (And that last sentence was calculated to give a heart attack to punctuation Nazis. It's called vernacular. Live with it, you. Faugh)
That's not vernacular. That's just gibberish. The problem isn't even with the punctuation, but with the syntax.
Posted by cheiros do ender (Member # 8849) on :
quote:This man is insane.
No, these men are insane. Posted by clod (Member # 9084) on :
*poof*
and so it goes.
Posted by Tresopax (Member # 1063) on :
quote:Writing is the highest form of reasoning. This is a fact. Algebra is not.
I guess we can get rid of symbolic logic then....
...of course then we'd have to get rid of all the computers that are constructed around that system of logic. And without computers, who would we get to do our math for us?
Posted by Joldo (Member # 6991) on :
quote:Originally posted by Jon Boy:
quote:Originally posted by Joldo: You know, I think this proves a point. So often I read a column, I read an article, a column or article that uses statistical math or some science work, and me, I check it, I find errors. (And that last sentence was calculated to give a heart attack to punctuation Nazis. It's called vernacular. Live with it, you. Faugh)
That's not vernacular. That's just gibberish. The problem isn't even with the punctuation, but with the syntax.
Vernacular, Jon Boy, is a device in writing by which one bypasses the conventions of standardized grammar or punctuation or spelling in order to preserve a particular quality of speech, usually regional. This is how a lot of the people from around here, how we talk. The problems include: comma splice, weird subject-verb use, and run-ons. All of these I deliberately used as a reflection of the tempo and rhythm of speech.
Posted by El JT de Spang (Member # 7742) on :
quote:I simply cannot figure out x + y = z
There's not a mathemetician in history who can resolve that expression, so don't feel bad.
quote:Actually, most physics is applied calculus. Which is precisely why Newton invented calculus.
Very true. Of course, calculus totally encompasses algebra so saying physics is applied algebra isn't totally off base.
Posted by Ela (Member # 1365) on :
quote:Originally posted by erosomniac: He's also failing to recognize the hundreds of daily applications of algebra.
Bingo!
Posted by edgardu (Member # 242) on :
quote: Look, Gabriela, I am not anti-algebra. It has its uses, I suppose, and I think it should be available for people who want to take it. Maybe students should even be compelled to take it, but it should not be a requirement for graduation.
He's not saying algebra is useless. He's saying algebra is not necessary in order to be successful in life.
Posted by Xavier (Member # 405) on :
You have a group of 12 people, and you need to split them into three groups.
3x = 12 x = 4
Algebra!
You have 12 people, only seven can fit in your van, how many do you need to tell to get a ride with someone else?
12 - x = 7 x = 5
Algebra!
Its simple algebra, but people do it every day and don't realize they are doing it.
Now, do I think that you should need to be able to do formalized algebra to get a basic high school diploma? No, but I don't want to give my whole spiel as to my reasons why.
Posted by Irregardless (Member # 8529) on :
Richard Cohen is an idiot, but he is correct that the vast majority of people will never need to use algebra.
Posted by Jon Boy (Member # 4284) on :
quote:Originally posted by Joldo: Vernacular, Jon Boy, is a device in writing by which one bypasses the conventions of standardized grammar or punctuation or spelling in order to preserve a particular quality of speech, usually regional. This is how a lot of the people from around here, how we talk. The problems include: comma splice, weird subject-verb use, and run-ons. All of these I deliberately used as a reflection of the tempo and rhythm of speech.
"Vernacular" is not a writing device. You also don't need to tell me what the problems in that sentence are; they're all pretty clear (except for the fact that there were actually no subject-verb agreement problems). The one thing that's not clear, though, is what point you were trying to make.
Posted by rivka (Member # 4859) on :
quote:Originally posted by El JT de Spang: Of course, calculus totally encompasses algebra so saying physics is applied algebra isn't totally off base.
True enough. Posted by Xavier (Member # 405) on :
I don't know, Jon Boy, this part seemed to fit both what Joldo said and what he described:
quote:1 a : using a language or dialect native to a region or country rather than a literary, cultured, or foreign language b : of, relating to, or being a nonstandard language or dialect of a place, region, or country
From your link.
Posted by Avin (Member # 7751) on :
I was a Discrete Math major, still am an avid math lover, and I found the article to be on target in some respects and completely inane in others.
What I agree with is the sentiment is that not everyone should need to know Algebra. This is because there are legitimate occupations which would not directly benefit from it, and what benefit can be derived (such as any improved reasoning) could be derived in other ways. However, what high schooler knows what they are going to do for the rest of their lives? In many ways, a poor grasp of Algebra may hinder them several years down the road when they find themselves interested in something completely different from what they were interested in while a high schooler. Or it may not at all, and like the author of this article will consider it wasted time. Well that's tough. If our schools aim at providing the minimum requirements for what everyone will need in life and make all other things optional, we will be churning out students who have a poor appreciation for the various disciplines of knowledge. I took many courses in school, both in public school and college, that I today have no "obvious" use for. I was in my high school orchestra, which in fact was optional past the first year, yet I don't consider that time wasted. My hands have received no benefit that I can think of from having learned the mechanics of playing a violin, and what I learned of music theory or appreciation from that period I could have easily covered directly by other means. For a slightly more relevent analogy, I despised art lessons in elementary school and anything that required artistic thought in classes beyond that, and I don't see what benefit I have derived from those lessons or projects (although I can't brashly claim that I must have "never used" those skills), but I don't crusade against art classes because I recognize that it is something I have experienced that I would not desire to un-experience. However, once the schools decide to require a subject that is deemed important, it is their responsibility to make sure that it is taught accurately and engagingly, in such a way as to not alienate students. I find that more often than not with math, teachers will teach the rote formulas or theorems without teaching the actual reasoning involved. This is admittedly harder to do than for any other subject, because the memorization or experimentation approach can work pretty well in most other academic fields (memorization for things such as history, vocabulary, rules of grammar, scientific definitions, and experimentation for scientific theories, reading comprehension or writing).
Xavier well covered the argument that the author does not use algebra; in reality the author does use it without knowing it in answering the sort of simple questions Xavier posed.
The argument that REALLY irked me, however, was the author's take on why "writing" was a higher form of reasoning than "algebra". The argument that follows that assertion I find to be one of the most horrible examples of reasoning I have seen, which weakens his argument considerably.
Certainly, good persuasive writing will *use* reasoning, and certainly someone can learn good reasoning skills by a study of good rhetoric, but that does not demonstrate any relative worth in terms of reasoning between writing and mathematics. The author's use of the word "reasoning" in fact seems to betray his misunderstanding of what it actually is; a perfect logician who was the master of reason could fail to locate the Sahara desert if he did not ever possess the knowledge of its existence, and not knowing this fact does not denigrate his reasoning abilities one whit. The author seems to define reasoning in terms of literary ability and then express astonishment that people who were more mathematically minded demonstrated less "reasoning" by his definition. This is a circular argument if there ever was one! By that same logic, I could make the opposing case that Mathematics is the highest form of logic, and use this very writer as the "proof" of my statement because by his own admission he is poor at Mathematics.
Posted by Irami Osei-Frimpong (Member # 2229) on :
quote:quote: -------------------------------------------------------------------------------- Originally posted by erosomniac: He's also failing to recognize the hundreds of daily applications of algebra. --------------------------------------------------------------------------------
Bingo!
I still think that if the main argument for Algebra is that Algebra is ever practical, then we are in a bad way, but Algebra is not ever practical. The only way I'm going to be convinced that algebra is appropriate, for all of the time spent teaching it, is to learn that math influences, in a positive manner, ones general mental acquity. My problem with the general push for math and science education is that keeping up and being competitive with the Chinese and Indians isn't a compelling. I don't care that we are blank out of blank of industrial nations with respect to math and science scores.
Our main problems with public education concern character, and I think the push for math and science is distracting. (And yes, I'd be curious to see the scores of all of these politicians clamoring about math and science education if they were to take an algebra test now. And yet, they are perfectly competent in their capacities as American royalty.)
My second problem is that I think math and science dull certain other faculties, namely, an appreciation of the non-fungible things in this world. This is a deep problem, and I don't have a clear thesis adequate the severity of this issue, but I do believe that the virtues of science and math, universality and demonstrability, lead one to expect every other worhty pursuit to be universally understood and publically demonstrable. People ask for proof in geometry, leading to proof in legal situations, then eventually to proof of love and God. Math solutions are perfect for numbers, then widgets, then we start applying them to people's lives, with the same rigidity, and the unaccounted for patterns are lumped off as outliers.
I think the muscular influence of math and science on other, more important, facets of moral thinking is unbecoming. Maybe my issue isn't that I think people are using too little math and science, I think people are using too much, as a substitute for the more fragile exercise of thinking and caring.
[ February 21, 2006, 02:17 PM: Message edited by: Irami Osei-Frimpong ]
Posted by Dagonee (Member # 5818) on :
quote:The only way I'm going to be convinced that algebra is appropriate, for all of the time spent teaching it, is to learn that math influence, in a positive manner, ones general mental acquity.
OK, here goes: There is a type of thinking taught that is taught in math, symbolic logic, and software development (including data modeling) that is not generally taught elsewhere. I don't know the jargon-name for it, but it involves pattern recognition, abstraction, and substitution.
Many different fields use it, including most sciences, law, social sciences, and even literature. Many people are capable of learning it during the course of learning those fields, but it is generally not taught as a separate kind of thinking. Post-algebra math, symbolic logic, and software development all teach it explicitly. Of these, algebra requires the least amount of prerequisite knowledge to learn and has the most daily applicability. To me, this makes it the best candidate of the three for a highschool requirement.
Why is this type of thinking so important? Because it allows examining the specific to deduce the general in a testable and repeatable way. It also allows manipulation of the pattern in the abstract in order to see if additional knowledge can be gained from what we already know.
The basic concept of abstraction and substitution is critical to this kind of thinking. Too many people do it without realizing what they are doing, and it seriously hinders their ability to understand a situation.
In my current field of study, law, many engineers, programmers, and mathematicians do better than they expected, because this type of thinking is critical to truly understanding the law. Moreover, it can be applied to the law without thinking of the law as something subject to total quantification and proof.
What it allows you to do is identify the specific questions that need to be answered in order to maximize ones ability to think and care about the situation at hand.
Posted by King of Men (Member # 6684) on :
That is very well put, Dag; I was trying to articulate this precise thought just the other day, and didn't do well at it.
Posted by rivka (Member # 4859) on :
Indeed.
Chemistry (especially general chemistry classes) also does this. And while I don't think chemistry should be required, I certainly encourage many students who will never become scientists to take it.
Posted by El JT de Spang (Member # 7742) on :
The discussion that my classmates and I had over our last year of college was that, of all the things we'd learned, the actual engineering was the least important thing. Critical thinking, problem solving, and research skills are all much more valuable than specific applications of complicated principles. Which is good because two years later I've forgotten nearly every formula, but I've retained the ability to go find them, relearn them, and apply them if necessary.
Posted by Irami Osei-Frimpong (Member # 2229) on :
quote:Many different fields use it, including most sciences, law, social sciences, and even literature. Many people are capable of learning it during the course of learning those fields, but it is generally not taught as a separate kind of thinking. Post-algebra math, symbolic logic, and software development all teach it explicitly. Of these, algebra requires the least amount of prerequisite knowledge to learn and has the most daily applicability. To me, this makes it the best candidate of the three for a highschool requirement.
That's fine reason to require algebra as part of education.
quote:Which is good because two years later I've forgotten nearly every formula, but I've retained the ability to go find them, relearn them, and apply them if necessary.
My problem is in the application, as in, this species of critical thinking and problem solving is overprescribed or often misprescribed. Teaching Algebra won't help people think about when to use Algebra in the same way that teaching people how to build a bomb won't help people think about when to use the bomb.
The fact that the standards of mathematical reasoning hold sway in so many of the public fields Dagonee mentions is a danger, not a excuse to teach mathematical reasoning.
quote:The basic concept of abstraction and substitution is critical to this kind of thinking.
Dag, both substitution and abstraction demand that the variables be interchangble. And, rivka, chemistry, of all the sciences, teaches this understanding. (As an aside, in one of Karen Armstrong's books, I'm pretty sure it was Muhammad but she goes over the same territory in most of her books, she says that monotheism was a natural biproduct of science and atomism, that is, if everything is made out of the same thing, then it only makes sense that there is one God of that thing.)
On a metaphysical level, I think that we've gone too far with this substituting and abstracting, and supposing the fungibility of the beings in the world.
[ March 02, 2007, 11:06 PM: Message edited by: Irami Osei-Frimpong ]
Posted by King of Men (Member # 6684) on :
quote:Teaching Algebra won't help people think about when to use Algebra in the same way that teaching people how to build a bomb won't help people think about when to use the bomb.
Talk about your strained analogies! 'When to use algebra' is not a moral question; it is a purely technical question. It is applicable to some situations and not to others, but you can't know which ones without knowing what its strengths and weaknesses are, which requires you to know the subject.
Posted by Dagonee (Member # 5818) on :
quote:The fact that the standards of mathematical reasoning hold sway in so many of the public fields Dagonee mentions is danger, not a excuse to teach mathematical reasoning.
I think you've missed my point if you think mathematical reasoning holds sway in the areas I mentioned (exlcuding certain hard sciences I alluded to). It doesn't hold sway. There is a type of thinking, not specific to mathematics, that mathematics is particularly good at teaching.
quote:Dag, both substitution and abstraction demand that the variables be interchangble.
No, they don't require that they be interchangeable, although much of algebra does. That's why it's so strong. What it requires is an understanding of what the attributes are that have an effect.
The best type of thinking is neither exlcusively systematic nor exclusively intuitive/creative. It is both. And math is particularly good at teaching the systematic.
The most important subjects absolutely require both to reach anything more than a trivial conclusion.
Posted by Irami Osei-Frimpong (Member # 2229) on :
quote:'When to use algebra' is not a moral question; it is a purely technical question.
In law, economics, or the behavioral sciences, it becomes a moral question.
quote:The most important subjects absolutely require both to reach anything more than a trivial conclusion.
I'm not sure that's true. I'm pretty sure that final judgment about any of the important subjects is solely a matter of ones perception/intuition, and not a calculus or analysis of different variables. I'm pretty sure that's what free will is, unless we aim to dethrone freedom and put math in its place.
Systems and analysis and proofs may have their work done in the background in construing the final object of ones judgement, but the judgment itself is not a matter of calculating. In the important issues, its a matter of character.
The close argument is this, in what way is the study of Algebra appropriate to the education of a person, as he/she is a person. And as the primary role of public education is to cultivate humanity, not produce tradesman or worker bees, how does Algebra serve this aim. I think Dagonee hit on some points.
[ February 21, 2006, 04:26 PM: Message edited by: Irami Osei-Frimpong ]
Posted by TomDavidson (Member # 124) on :
quote:I'm pretty sure that final judgment about any of the important subjects is solely a matter of ones perception/intuition, and not a calculus or analysis of different variables
I believe one's perception and intution ARE merely a calculus and analysis of different variables. Posted by Dagonee (Member # 5818) on :
quote:I'm not sure that's true. I'm pretty sure that final judgment about any of the important subjects is solely a matter of ones perception/intuition, and not a calculus or analysis of different variables.
I really think I haven't communicated my point to you adequately. I have not said algebra should be taught because it is useful in moral questions. I have said that algebra should be taught because it teaches a kind of reasoning that is used both in Algebra and in moral thinking.
Unsystematic moral thinking is dangerous. So is moral thinking not informed by intuition and perception.
If you think I'm talking about anything such as plugging one thing into a standard formula to arrive at a moral decision, please let me know and I'll try to clarify further. This is a topic of enormous interest to me, but I don't have time to fully explain right now.
quote:I believe one's perception and intution ARE merely a calculus and analysis of different variables.
Let me note I utterly disagree with this. While it's certainly a topic worthy of discussion, please don't think I am advocating this statement either as a premise or a conclusion of my thoughts on systematic thinking.
Posted by Bokonon (Member # 480) on :
You all (including the author of the op-ed) should just read The Phantom Tollbooth. Mr. Juster has it all figured out.
-Bok
Posted by Joldo (Member # 6991) on :
Jon Boy: Wasn't trying to make a point. Wrote my post like that, read it, thought a bit. Realized it could be used as evidence of Math Skills = Bad English Decided to explain. That's pretty much it.
Posted by Tatiana (Member # 6776) on :
quote: Building cooler, more efficient gadgets isn't the most important priority in life or education, and I don't think that such knowledge is universally necessary...
Irami, it's not about gadgets, it's about life and death. Without electricity, clean water to drink, heating of some kind, food delivery systems that stock grocery stores, and all the many factories that process your food and drink, the clothes you wear, the roads the trucks drive on to bring food to the shelves, gasoline to run those trucks, spare parts to maintain them, and on and on and on, you would not be able to survive. Maybe 1 person in 10,000 would. Technology is how the human species lives in a harsh world. People who understand technology are necessary to keep us all alive.
I'm reading about the Chernobyl disaster now, in great detail. In case anyone is too young to remember, it happened in 1986 and it is the worst nuclear disaster the world has ever known, barring possibly the atomic bombs dropped on Hiroshima and Nagasaki. (By some measures Chernobyl was worse, producing far higher radioactivity in some places, though with much less loss of life.) Reading all this data about what led up to the disaster, and the aftermath, the major cause I see is ignorance of bosses. They probably said to themselves "my techical people know about all those details so I don't have to", and yet, because of their criminal ignorance, they gave the wrong orders again and again, causing the disaster to begin with, making it worse after the fact by ordering the wrong actions, and then causing needless deaths afterwards from continuing to do the exact wrong thing. There's no substitute for having people who understand what they are doing at the highest levels.
But you know what? I see again and again people who are non-technical (usually bosses) who have this idea that technology works because they ordered it to. They have no clue of the actual behavior of the physical universe. They think we can legislate unlimited fuel efficiency, or that the wind holds enough power to run our cities, to name just two nonsensical statements I've heard. They think that all this stuff just happens by itself. They are blissfully ignorant of what it takes to make things actually work so that they can live in the way they take for granted. They think technology is a matter of cool gadgetry, and have totally forgotten that their lives depend on it every day, that it is how they survive in the world.
If we further dumb down the science and math curriculum in grades 1-12, I only see this problem getting much worse. And it's a Really Bad Idea. On a par with the idea that Razim Ilgamovich Davletbayev had that the test on Unit 4 of the Chernobyl reactor on April 26th, 1986 must continue, despite the insistance of the operator, Leonid Toptunov, (who understood what they were doing) that the reactor be shut down immediately. Let us hope that we don't all have to pay the inevitable price of such ignorance, death.
[ February 21, 2006, 08:25 PM: Message edited by: Tatiana ]
Posted by theamazeeaz (Member # 6970) on :
The whole article reminds me of a conversation my grandmother had with an denist regarding my uncle and braces about 45 years ago. He said it was only worth it if my uncle was on T.V. Guess what my uncle does for a living? My grandma's mad she listened to that man.
It also reminds me of what the principal of my high school told a friend who complained to him about scheduling conflicts and taking AP and honors classes. He said that my friend shouldn't worry because you only needed to pass gym and English. Yeah....
Posted by The Rabbit (Member # 671) on :
quote:My second problem is that I think math and science dull certain other faculties, namely, an appreciation of the non-fungible things in this world. This is a deep problem, and I don't have a clear thesis adequate the severity of this issue, but I do believe that the virtues of science and math, universality and demonstrability, lead one to expect every other worhty pursuit to be universally understood and publically demonstrable. People ask for proof in geometry, leading to proof in legal situations, then eventually to proof of love and God. Math solutions are perfect for numbers, then widgets, then we start applying them to people's lives, with the same rigidity, and the unaccounted for patterns are lumped off as outliers.
Your absolutely right. I used to be highly creative. I used to believe in God, love music, adore reading fiction, muse over painting and revel in love. But now that I've spent most of my adult life first studying and then teaching engineering and higher math -- all those faculties are dulled. I've become a mindless, heartless automoton.
Not!
Science and math are not the only valuable skills. People can lead rich and happy lives and never learn algebra. But the same can be said of history, art, literature, music, and any other field of study. But the idea that learning science and math dulls your sensitivity is utter horse s__t. Perhaps the biggest and most serious misconception of science and math is that problems in these fields always have a single right answer. Nothing could be further from the truth. In science, nothing is ever black and white. Science is, at its base, a method for making judgements in the presence of irreducible uncertainty.
Math does teach important reasoning skills, but even more important than that -- it is a basic foundational skill for many many disciplines. There are very few professions that are closed to you if you can't remember who won the war of 1812 or quote Shakespeare, there are hundreds of fields which will be totally inaccessable to you can't do basic algebra. A basic education should give people a plethora of options for their future and to do that, algebra needs to be a core subject.
Posted by Orincoro (Member # 8854) on :
quote:Originally posted by SC Carver: This guy would be one of the cashiers who looks at you funny when you give them $21.15 for a $16.15 total.
I have yet in my life to have a cashier not look at me with a mix of confusion, awe and vacancy when I hand them 3.17 for a tab of 2.67
ITS 50 CENTS PEOPLE!! ROUND NUMBERS!!!!! On the other hand I have worked as a cashier in years past, and had often to deal with people's foolish miscalculations, or their reaching into my tip jar for spare change, sometimes as much as 50 cents. So I suppose there are bad feelings on both sides.
Posted by Irami Osei-Frimpong (Member # 2229) on :
quote:They think we can legislate unlimited fuel efficiency, or that the wind holds enough power to run our cities, to name just two nonsensical statements I've heard.
For the record, I think that both these statements are true. Time will tell.
quote:But the idea that learning science and math dulls your sensitivity is utter horse s__t.
We'll disagree about this, but the idea that everything in the world is subject to publically demostrable laws, or even Laws, which rule the workings of the world and are not contingent upon circumstance is the root of kinds of evil. (It's ironic how money- often considered the root of all kinds of evil- and integers are both fungible. I think that their evil is linked to their lack of essence. It's like those to things are all quantity, no quality.)
Valuing laws and proofs is fine with numbers, and even physics, but then you get people trying to "prove" guilt or innocence in a court room, we get these pre-nup agreements-- which I view as the triumph of law over thought --because instead of thinking about marriage, you posit rules governing the allocation of goods, trying to engineer a marriage. Lastly, you have a waste of a thousand years of the greatest minds in the western world trying to "Prove" the existence of God. And yes, any God that has to be proved, isn't much of a God in my esteem.
There are three demands of science I have a problem with: The demand for certainty, the demand for security, and the demand for a constancy outside of contingent circumstances, none of the three belong to any important matters, i.e., human relations, but all three are demands which hold enormous sway in science and engineering. In short, I think that the perogatives and priorities of science and math have run roughshod over too much of our culture. Now, I blame the Romans. Or I can blame Hobbes. Or I can blame Liebniz. I can blame any so-called "political scientist," as well as any logical or legal positivist. The principles of building conflated with thinking and being resulting in great engineering feats and horrible, dehumanizing ontology, human relations and philosophy. The culmination of this muddle is an amoral affluent slum which includes the proliferation of all of these behavioral sciences, the degradation of the humanities, and the appearance of the atom bomb.
I'm not saying that society is going to collapse, implode, or explode under the sway of science. We are better engineers than that. I think that biological life will continue, but the spirit of humanity, all of the muses, will all decay for want of thinking and the love of calculating.
There is a great quote that's sitting in my storage locker in Ca. It's something about not confusing size with granduer and how the great question is, "What are we to do with all of these things."
[ February 24, 2006, 11:37 AM: Message edited by: Irami Osei-Frimpong ]
Posted by Tante Shvester (Member # 8202) on :
I'm a nursing supervisor, and part of my job is interviewing and competency testing applicant nurses. Part of that competency testing is medication dosage calculation. I would not feel at all safe hiring a nurse who could not independently calculate a correct dosage. And I tell any applicants that they shouldn't feel safe practicing nursing if they can't independently calculate a correct dose.
If they are willing to learn and demonstrate their competency to me, I'll hire them. If they argue that it is not important, not their role, or something that they've never been good at or had to do before, well, they can apply elsewhere.
How do you go about calculating a correct medication dosage? Simple algebra.
Posted by twinky (Member # 693) on :
quote:My second problem is that I think math and science dull certain other faculties, namely, an appreciation of the non-fungible things in this world.
This is complete bunk. Studying math and science gives you a greater appreciation for the numinous nature of the universe. There will always be things that can't be understood.
quote:We'll disagree about this, but the idea that everything in the world is subject to publically demostrable laws, or even Laws, which rule the workings of the world and are not contingent upon circumstance is the root of kinds of evil.
What the heck does this have to do with studying science and math? This idea is not part of science, math, or the teaching thereof.
quote:Originally posted by Irami Osei-Frimpong:
quote:They think we can legislate unlimited fuel efficiency, or that the wind holds enough power to run our cities, to name just two nonsensical statements I've heard.
For the record, I think that both these statements are true. Time will tell.
For someone so uninterested in and disdainful of math and science, you're putting an awful lot of trust in the ingenuity of people who are interested in math and science. It's precisely this sort of attitude that fosters the Western culture of sloth, the "oh, the engineers will solve all of our problems, I don't need to conserve engery" rubbish.
Posted by SenojRetep (Member # 8614) on :
I had several thoughts on reading the article and the subsequent messages:
1) I had to do a literary analysis of The Great Gatsby in 10th grade. The Algebra I learned has proved imminently more useful to me. And beyond being useful, it has opened up avenues of edification and illumination of which I never would have dreamed.
2) I think mathematical illiteracy (or innumeracy ) is responsible for the crushing amount of consumer debt in many people's lives. Money is important, and managing your money well without algebra is impossible.
3) I know more mathematicians, engineers and scientists who can speak sensibly about world events or 18th century English literature than I do historians and writers who can speak intelligently about set theory or quantum physics.
4) Integers (and numbers in general) are not fungible. They can be used to represent amounts of fungible things, but they are not, of themselves, interchangable, since they are unitary abstractions (i.e. there's nothing to interchange them with).
So, what is the purpose of public education? Specifically, what should be required? Tools that are likely to be useful to the student? Or is there a core truth or set of truths that must be conveyed about the world in which we live? What education is necessary for creating good citizens, and can therefore be justified by law? My short list: ethics, civics, linguistics, rhetoric, science. Not math (although it's inherent in the science), and not literature, although those were/are my favorite subjects. Huh. That surprises me.
Posted by twinky (Member # 693) on :
I agree very strongly with your point (2).
Posted by Irregardless (Member # 8529) on :
Irami, your display of stubborn ignorance on this thread makes you singularly unqualified to comment on matters of science education.
Posted by Irami Osei-Frimpong (Member # 2229) on :
quote:For someone so uninterested in and disdainful of math and science, you're putting an awful lot of trust in the ingenuity of people who are interested in math and science.
The biggest problems with wind power are storage and stability. Overlapping power grids does well to mitigate the problem of stability, as to storage, yep, I'm assuming we can build a better mouse trap. In this random life it happened that a few years ago, I found myself studying the slings and arrows of wind power for research on a short story. In addition, if I remember correctly, The Rabbit worked extensively on wind power research, and maybe if she weighs in the subject we can get a more informed answer to the viability of wind power. I happen to disagree with Tatiana, and unless this one of those rare instances of unanimity within the scientific world, I'm sticking to my dissent.
[ February 22, 2006, 03:51 PM: Message edited by: Irami Osei-Frimpong ]
Posted by The Rabbit (Member # 671) on :
quote:the idea that everything in the world is subject to publically demostrable laws, or even Laws, which rule the workings of the world and are not contingent upon circumstance is the root of kinds of evil.
This idea is not a tenet of either science or math but rather the result of a very simplistic misunderstand of math and science. In fact, Gödel (a famous 19th century mathematician, constructed an elegant proof that all logical systems are incomplete. Anyone who truly understands mathematical reasoning or the scientific method understands that they are very powerful systems for understanding a limited number of problems and that they can not be applied to all things. That is why your original statement is utter nonsense. All it proves is that you have a very naive understanding of math and science.
Posted by Boothby171 (Member # 807) on :
Maybe we should have a national "Day without Math", perhaps even a "Day without Engineering."
You would not be allowed to use math or take advantage of things created with math, or engineering for an entire day. Every time you did, you'd have to put a dollar in to your favorite engineering society (or mine, if you don't have one).
So, what do you think? Good idea?
We could also have a "Day without Evolution" for all our die-hard creationist/fundamentalist friends. You would not be allowed to use any biologicals that were developed to fight against organisms that had recently evolved. No antibiotics, for instance.
Any other contributions?
Posted by Dagonee (Member # 5818) on :
Yeah - a national day without the right to life, liberty, and the pursuit of happiness that we were endowed with by the Creator. Posted by Lyrhawn (Member # 7039) on :
I'm alright with basic algebra being a required subject, but I think anything beyond it isn't necessary. I was forced to take three years, so, algebra, that was fine, geometry, unnecessary but also fine, and Trig, which I will never use in my life to come as a history teacher. I would have been better served taking something else.
As far as science goes, biology should be required, but not chemistry, or at least, not a full year of it. I wasted a year taking chem, which was the only class in high school I failed. And they would've either tried to stick me in "Descriptive Chem" which is for the slow kids, or jump me into Physics, if I hadn't demanded they put me in AP Biology instead. Rather than waste another year of that, I got straight A's in AP Bio. Sometimes, kids know what they need more than adults do. Not always, maybe not even often, but sometimes.
I think everyone should be forced to take at least one year of every subject, because without it being forced on them, they might not realize how much they like it. But once they know what it's all about, why should they be forced to take three of four years of a subject they honestly will never use?
Some kids just like math, good for them, give them all the math they want. But for the kids who don't, give them what they need to get by in life, and then let them take something else that will help them in their future.
Posted by twinky (Member # 693) on :
quote:Originally posted by Irami Osei-Frimpong:
quote:For someone so uninterested in and disdainful of math and science, you're putting an awful lot of trust in the ingenuity of people who are interested in math and science.
The biggest problems with wind power are storage and stability. Overlapping power grids does well to mitigate the problem of stability, as to storage, yep, I'm assuming we can build a better mouse trap. In this random life it happened that a few years ago, I found myself studying the slings and arrows of wind power for research on a short story. In addition, if I remember correctly, The Rabbit worked extensively on wind power research, and maybe if she weighs in the subject we can get a more informed answer to the viability of wind power. I happen to disagree with Titiana, and unless this one of those rare instances of unanimity within the scientific world, I'm sticking to my dissent.
While I certainly think that wind power is going to be an important component of any potential solution to the energy problem, I think Tatiana's statement, essentially "it can't power our cities," is entirely valid. It certainly can't power the greedy and inefficient cities that are the present hallmark of the industrialized world. It is not the panacea that will solve the energy problem all on its own -- indeed, I don't think that any one resource or technology is up to that task in the same way that fossil fuels manage it now.
It's easy to wave your hands and say "Oh, someone else will solve it," and go back to spouting off about how we don't need to learn how to add, subtract, multiply, or divide in school, but really, "build a better mousetrap" is awfully dismissive of the mountains of human effort that go into providing you with the lifestyle you enjoy as a resident of an industrialized nation.
There's an interesting book on this subject, by the way, called The Ingenuity Gap. The core thesis is that the problems we collectively face are growing in complexity faster than we are collectively growing in, well, ingenuity.
quote:I think all of these lay latent in the metaphysics of science.
I don't think that's true at all. Rabbit's post in particular is apt.
Posted by Stasia (Member # 9122) on :
I think that algebra and geometry are worthwhile subjects in highschool. Math at this level helps students be prepared for college, forces their minds to think in a logical fashion, keeps future career options open (even if they don't go on to college), and really does teach usable skills.
I know that some people just aren't naturally good at math. However, I think that a lot of the kids failing algebra aren't really trying. The vast majority of people could pass algebra and geometry in high school if they tried their best, given the glacial pace of most high school math courses coupled with the fact that most high school teachers give at least equal weight to homework as tests (plus give extra credit, plus help after school).
When I failed algebra the first time I took it, it was because I wasn't doing my homework. I was copying off of other people and trying to cram the night before tests. Quite honestly, up until that point, I had never had a class that required any significant effort on my part to learn and/or pass. Algebra was different. It wasn't obvious. It wasn't easy. And *I* had to be the one to put in the time studying.
Whenever my teacher questioned me, I lied and said I was trying my best but I just didn't get it. Whenever my parents peeked into my room, I had the book open. I refused the neighbor's offers of tutoring (she was a math major at the Univeristy). I was just lazy and did not want do my homework. I kept telling myself and anybody who would listen that algebra was too hard and that my teacher was an unfair meanie.
By the next year, I was a little more mature and had figured out that I did want to go to college and I did want to pass algebra, even if that meant spending time on the dreaded homework.
Posted by Boothby171 (Member # 807) on :
How ya doin', Dag?!
--Steve
Posted by Dagonee (Member # 5818) on :
Boothby!
Posted by HollowEarth (Member # 2586) on :
Large numbers of those that fail high school math classes are because they never had a good enough grasp of the arithmetic that came first. Its not enough to just do the homework for the algebra class, you have to have actually learned all that stuff from the classes years before.
As far as the statements on high school sciences, you're largely missing the point. Science in high school isn't mainly about teaching the you the science. Thats a nice benefit and certainly a secondary goal. The real point to it is to teach a way of thinking and some problem solving--giving you the skills to learn these subjects as well as other things.
Posted by Tatiana (Member # 6776) on :
Unlimited fuel efficiency equals perpetual motion equals a lack of understanding of the basic laws of physics. Irami, you are smarter than this! I know you aren't an ignoramus. You can learn anything at all you put your mind to. Don't let math and science scare you into thinking you can't do it.
The amount of energy that can be extracted from wind is limited to the amount of energy that the wind holds. Wind farms are huge and have many problems of efficiency (you can't put them anywhere that the wind doesn't blow almost all the time) and environmental impact. They just don't generate that much power. It's great for the applications that are suited to wind power, but it certainly cannot solve the world's energy problems.
twinky is correct that huge gains can be made in efficiency over what we currently practice, however, Californians aren't planning to turn off their air conditioners, to pick one illustration. Also, the whole world wants to raise themselves to the same standard of living that Californians now enjoy. Efficiency will take us a long way, but it won't solve everything. Efficiency is always a great idea because it's win-win. Not only it is great for the environment but it saves the consumer lots of money.
I want to make it clear that I'm highly in favor of using alternate methods, including conservation, wind, hydro, nuclear, etc. to decrease our use of fossil fuel. Fossil fuel is nasty stuff. It emits greenhouse gases, plus lots of other filth that fouls the earth in myriad ways.
The problem is, without some basic understanding of physics, and the ability to do the math, the electorate will vote for harebrained schemes, or for someone who lies and tells them there is an easy way out, instead of something that's reasonable and workable. We totally cannot afford in a democracy to promote even more innumeracy and lack of understanding of technology than we have now.
Posted by Irami Osei-Frimpong (Member # 2229) on :
quote:The real point to it is to teach a way of thinking and some problem solving--giving you the skills to learn these subjects as well as other things.
I agree. I'm also skeptical of that way of thinking.
Dr. Rabbit, my problem is this: I think that sentiments like the following one by Rakeesh, lifted from the Wal-mart thread, are evidence of the moral influence of science:
quote:People talk big about how unjustified it is for us to buy cheaper and thus harm standards of living abroad and sometimes even here in America...but I suspect that there isn't a single poster who deliberately buys the more expensive thing for humanistic reasons.
Now, I don't think this is true, but that's not the issue. I am disturbed with how casually he assumes that expense is the chief variable that governs a consumer's purchasing decisions. Somehow, in my mind, I tie this sentiment with the influence of science on this culture. I can probably draw a progression from science in the classroom, to the assumption that the consumer will always, and possibly even ought to always, choose the cheaper item, but the progression is a little fuzzy in my head, and I doubt that you all would believe me even if I do lay it out. But I think that that science is the cause, and the like assumptions about the moral behavior of others and even the impoverished morality of the agent is the effect.
quote:Unlimited fuel efficiency equals perpetual motion equals a lack of understanding of the basic laws of physics. Irami, you are smarter than this! I know you aren't an ignoramus. You can learn anything at all you put your mind to. Don't let math and science scare you into thinking you can't do it.
You got it, Tatiana, despite everything I've posted to the contrary, I'm scared of math and science. I have real fears, the academic ones include Greek and Hegel. If anything, I'm resentful of all of the math and science I do know. I also believe that we'll be able to build a machine that runs until the sun burns out, once started. I had a buddy with an old school metronome, one of the ones that are half pendulum, he made it run evenly without batteries buy using a smartly place magnet that supplied the pendulum with the lost work. Now I know that that's not perpetual motion, but its an elaborate system that mimics the effects of a perfectly efficient machine.
quote:We totally cannot afford in a democracy to promote even more innumeracy and lack of understanding of technology than we have now.
Sure we can.
quote:Yeah - a national day without the right to life, liberty, and the pursuit of happiness that we were endowed with by the Creator.
I think that prisoners are on that holiday for the duration of their sentence.
[ February 22, 2006, 08:03 PM: Message edited by: Irami Osei-Frimpong ]
Posted by Lyrhawn (Member # 7039) on :
quote:Originally posted by HollowEarth: Large numbers of those that fail high school math classes are because they never had a good enough grasp of the arithmetic that came first. Its not enough to just do the homework for the algebra class, you have to have actually learned all that stuff from the classes years before.
As far as the statements on high school sciences, you're largely missing the point. Science in high school isn't mainly about teaching the you the science. Thats a nice benefit and certainly a secondary goal. The real point to it is to teach a way of thinking and some problem solving--giving you the skills to learn these subjects as well as other things.
I'll buy that problem solving and the scientific method are valuable things to learn. But I learned those before I even got to high school. Once I hit high school, science became memorization, well, not entirely, but mostly. There's nothing in high school chemistry that will help me solve every day problems, or make me think about something a different way.
What grade level is being discussed here? I don't remember it being narrowed to a specific grade, or if this is just school in general.
And if science in high school is about anything other than "the science" then my high school teachers didn't know what they were doing, because that's all I got, and some of the time, not even that. Math, I buy it, science, nope.
Posted by Morbo (Member # 5309) on :
quote: Typing: Best class I ever took.
from Cohen's column
quote: It hardly matters. His favorite high-school class was freaking Typing.
From my brother's blog rant about that column, and Cohen in general.
Rabbit, Gödel was a 20th century mathematician.
Posted by Dan_raven (Member # 3383) on :
Irami you scare me.
Not your choice to avoid mathematics. That is your choice and since you dislike it so much, you have chosen well.
However, to suggest that the US should avoid teaching its children mathematics as a moral decision is setting us up for a great disaster. A country without math skills is a third rate country. No modern military can defend itself without these skills. No modern economy can flourish without these skills. No modern farm can grow enough food without these skills. No modern government can handle the needs of its people without these skills. With no army, no airforce, no money, no food, we become the plaything of those countries who's children know that if x+3=5 then x=2.
You base your arguments on two bad premises. 1) That learning is a closed-sum game. You imply that the brain has room for only so much reasoning--X-amount. There are two kinds of reasoning, Mathematical and Artistic, We'll call these M and A. M+A=X. The larger the value of M then the smaller must be the value of A.
I disagree, for X is not a constant. Increasing M does not diminish A, but increases X.
2) You assume that Amoral and Immoral are the same. Mathematics is an Amoral system. 2x+2x=4x no matter the morality of x. It could be good x or bad x or the son of Satan x, but that doesn't matter. Morality has no influence on the outcome of mathematics. You may argue that living an Amoral life is not living a Moral life, and that we should study Art and Literature to emphasize that morality. That is true. You may argue that time spent learning amoral mathematics is time spent away from learning the moral lessons found elsewhere. That is true. But the lessons that mathematics teach us in how to think are important in helping us dechipher the moral lessons we are given. Learning math does not teach us to be evil. It may not teach us to be good. It just teaches us to learn.
Posted by Eldrad (Member # 8578) on :
quote:Originally posted by Dan_raven: Irami you scare me.
Not your choice to avoid mathematics. That is your choice and since you dislike it so much, you have chosen well.
However, to suggest that the US should avoid teaching its children mathematics as a moral decision is setting us up for a great disaster. A country without math skills is a third rate country. No modern military can defend itself without these skills. No modern economy can flourish without these skills. No modern farm can grow enough food without these skills. No modern government can handle the needs of its people without these skills. With no army, no airforce, no money, no food, we become the plaything of those countries who's children know that if x+3=5 then x=2.
You base your arguments on two bad premises. 1) That learning is a closed-sum game. You imply that the brain has room for only so much reasoning--X-amount. There are two kinds of reasoning, Mathematical and Artistic, We'll call these M and A. M+A=X. The larger the value of M then the smaller must be the value of A.
I disagree, for X is not a constant. Increasing M does not diminish A, but increases X.
2) You assume that Amoral and Immoral are the same. Mathematics is an Amoral system. 2x+2x=4x no matter the morality of x. It could be good x or bad x or the son of Satan x, but that doesn't matter. Morality has no influence on the outcome of mathematics. You may argue that living an Amoral life is not living a Moral life, and that we should study Art and Literature to emphasize that morality. That is true. You may argue that time spent learning amoral mathematics is time spent away from learning the moral lessons found elsewhere. That is true. But the lessons that mathematics teach us in how to think are important in helping us dechipher the moral lessons we are given. Learning math does not teach us to be evil. It may not teach us to be good. It just teaches us to learn.
This is the best response the thread has produced yet. Marry me.
Posted by pepperuda (Member # 1573) on :
In appreciation of a tree. It's an idea I heard once that I've thought about often.
What I know allows me to appreciate different aspects of a tree.
If I know about biology, I can appreciate tree rings, the health of the tree, the growth, reproductive properties. I can appreciate it's place in the ecosystem and its prevention of erosion.
If I know about art, I can appreciate shade, symmetry, balance, form, and color.
If I know about mathematics, I can appreciate symmetry, number patterns, fractals, angles,curves, production, and growth.
Without knowing any of these things, I can still look at a tree and think it looks nice or it produces well. But, knowledge increases the ways in which I can appreciate the tree.
Knowing mathematics has never dulled my senses. It has only ever increased my capacity to learn, understand, and appreciate the world in which I live. Yes, I love to calculate. It's a game. I love to reduce fractions in my head. There are 11/30 of the school year left today. I like to figure out how fast I need to travel in order to get to my destination on time. And I do consider the morality and the feasibilty of traveling that speed. Mathematics isn't only numbers and calculations. There is logic and beauty, understanding and wisdom to be gleaned from its study.
Those who never learn mathematics effectively can not use it effectively. I calculated how much cement I would need for my odd shaped patio, how much grass seed to buy for my yard, how much sheetrock would be needed to build my family room, and how much interest I would make if I put the materials on a 1-year-interest-free card while I saved the money in a CD for a year. I didn't have to ask anyone or trust in the answers of someone who knew. I could do this for myself. There is a whole world of opportunity opened to someone who knows mathematics that is closed to those who do not know it or refuse to learn it.
What subjects should be required in high school? What will be most useful to students after graduation? Since no one knows the future, it's difficult to tell. Everyone is different. I believe that in America we try to give students a broad education that will give them the best opportunities to succeed in whatever field they fancy and also to enhance their everyday quality of living. Algebra seems to open doors and increase the quality of life of those who understand it.
Totally different question: Didn't those with the most mathematical and scientific responsibility for the Atomic bomb worry a great deal about the morality of using it?
Posted by The Rabbit (Member # 671) on :
quote:Now I am disturbed with how casually he assumes that expense is the chief variable that governs a consumer's purchasing decisions. Somehow, in my mind, I tie this sentiment with the influence of science on this culture.
I'm disturbed with how causually he draws this conclusion as well but think it is pure fallacy to tie this sentiment to the influence of science. I see it as precisely the opposite. People make such conclusions because they aren't properly trained in critical thinking skills. Science and math are basic critical thinking skills. Scientists are trained to view presumption like this with scepticism.
Posted by Dagonee (Member # 5818) on :
In a seminar today, we used algebraic symbols to clarify the differences between affirmative defenses and negative elements of criminal statutes and to map out the differences between voluntary intoxication and mental illness with respect to mental elements of crimes.
Using this symbolic representation, we managed to have a very in-depth discussion of some of the most intricate issues underlying substantive criminal laws. We used ethics, morality, justice, and legal precedent.
They symbolic representation made it possible to zero in on highly specific issues and to see how their resolution affected the whole. At the same time, we never lost sight of the whole or the moral issues implicated by these concepts.
Posted by The Rabbit (Member # 671) on :
quote:I'll buy that problem solving and the scientific method are valuable things to learn. But I learned those before I even got to high school. Once I hit high school, science became memorization, well, not entirely, but mostly. There's nothing in high school chemistry that will help me solve every day problems, or make me think about something a different way.
First Lyrhawn, I have never met anyone who had mastered problem solving and the scientific method by the time they obtained a BS degree in a scientific field, in fact most are barely competent in them when they receive Ph.Ds so you will excuse my scepticism when you say you had learned them before high school.
Second, learning what others have already done (i.e. all the memorizing facts) is the first step in the scientific process. You can't begin to form reasonable scientific hypotheses until you have a reasonable grasp of what others have already found.
Posted by rivka (Member # 4859) on :
Dags, that is awesome.
Posted by Lyrhawn (Member # 7039) on :
quote:Originally posted by The Rabbit:
quote:I'll buy that problem solving and the scientific method are valuable things to learn. But I learned those before I even got to high school. Once I hit high school, science became memorization, well, not entirely, but mostly. There's nothing in high school chemistry that will help me solve every day problems, or make me think about something a different way.
First Lyrhawn, I have never met anyone who had mastered problem solving and the scientific method by the time they obtained a BS degree in a scientific field, in fact most are barely competent in them when they receive Ph.Ds so you will excuse my scepticism when you say you had learned them before high school.
Second, learning what others have already done (i.e. all the memorizing facts) is the first step in the scientific process. You can't begin to form reasonable scientific hypotheses until you have a reasonable grasp of what others have already found.
I think we're talking about two different things, or just misunderstanding each other. The basic scientific method, that you form a theory, then a hypothesis, test it, test them in an experiment and then compare the data to answer your own hypothesis, that's the basic scientific method isn't it?
Second, you're talking about how to use science knowledge in the field of science, I'm talking about how you use science in every day life. The BASIC principles of problem solving and analytical thinking that you use later in life aren't the higher level stuff you're talking about, unless you're suggesting that everyone in the world without a BS is an incompetent idiot who can't solve problems or think critically, and I know that isn't what you're saying.
I agree, and I imagine anyone would agree that all that memorization would be invaluable if I were to lead a life of science, but all that crap I learned in chemistry, and the rote memorization, isn't going to help me balance my checkbooks, unless we stop using dollars and start paying for things with electrons.
Posted by Morbo (Member # 5309) on :
quote:Originally posted by pepperuda: Totally different question: Didn't those with the most mathematical and scientific responsibility for the Atomic bomb worry a great deal about the morality of using it?
Not only was there the morality of killing all those Japanese (the enemy, after all), some scientists had calculated that there was a chance that an atomic explosion could ignite the oxygen in the atmosphere, killing millions or maybe even everybody. The end of the world.
quote: They were not sure before they blew up the bomb that the whole atmosphere would not go critical. They were worried about this probability, so they redid their calculations and the probability remained the same. It was not extremely small. One technician was upset to hear Enrico Fermi taking side bets as the "gadget" [the first atom bomb] was hoisted to the tower, that New Mexico would be incinerated.
However much they worried, they built it and helped use it, in spite of the risk. Good thing the atmosphere didn't ignite, eh?
quote:the idea that everything in the world is subject to publically demostrable laws, or even Laws, which rule the workings of the world and are not contingent upon circumstance is the root of kinds of evil.
This idea is not a tenet of either science or math but rather the result of a very simplistic misunderstand of math and science. In fact, Gödel (a famous 19th century mathematician, constructed an elegant proof that all logical systems are incomplete. Anyone who truly understands mathematical reasoning or the scientific method understands that they are very powerful systems for understanding a limited number of problems and that they can not be applied to all things. That is why your original statement is utter nonsense. All it proves is that you have a very naive understanding of math and science.
Can you elaborate on your point? I don't necessarily understand the original statment, but its been my understanding that, for instance, particle physics can only provide predictions based on probability. If I hit a ball with another ball, the overwelming majority of the energy transfered will be pushing the hit-ball in the same direction as the flying ball, however I had thought that a very small bit would randomly move in a different direction (esentially quantum theory applied to everyday objects, except the effects are incalculably minute).
It has been my understanding too that we apply this principle to larger systems, and see that in truth, we cannot predict the results of complex interactions with any accuracy over long periods. So my question is: what about the day to day world is completely dependent of hard and fast physical laws which ARE completely predictable. Not a slight or a challenge, but I would like to know if we really see the world in such a "19th century" light, (to quote Orwell).
I find it interesting that the original quote espouses an idea which presents itself as iconoclastic and free-thinking, however it draws on the logic employed by Orwell's famous "engsoc," (breafly) the notion that real world events and circumstances can be as easily controlled by altering our perceptions of them, than by actually changing them, thus giving humanity reign on the laws of physics as we percieve them.
Posted by Irami Osei-Frimpong (Member # 2229) on :
quote:Didn't those with the most mathematical and scientific responsibility for the Atomic bomb worry a great deal about the morality of using it?
Hannah Arendt has my favorite answer to this question:
quote:For the sciences today have been forced to adopt a "language" of mathematical symbols which, though it was originally meant only as an abbreviation for spoken statements, now contains statements that in no way can be translated back into speech. The reason why it may be wise to distrust the political judgment of scientists qua scientitsts is not primarily their lack of "character"- that they did not refuse to develop atomic weapons- or their naivete- that they did not understand that once these weapons were developed they would be the last to be consulted about their use- but precisely the fact that they move in a world where speech has lost its power. And whatever men do or know or experience can make sense only to the extent that it can be spoken about. There may be truths beyond speech, and they may be of great relevance to man in the singular, that is, to man in so far as he is not a political being whatever else he may be. Men in plural, that is, men in so far as they live and move and act in this world, can experience meaningfulness only because they can talk with and make sense to each other and to themselves.
In short, the demands of science occur outside of the political sphere.
Posted by Tatiana (Member # 6776) on :
Mathematics makes sense to all of us, though, in a way that spoken words can't attain. Mathematics means the same thing to everyone, while political speech has as many interpretations as it does hearers. In other words, I think Hannah Arendt is all wet.
It honestly sounds to me as though she's saying "since I can't understand math and science, people shouldn't be allowed to pursue it." That's no more valid than me saying "since I can't play basketball, we must disband the NBA". The language of math and science is available to anyone who wants to learn it. It says not just things that people say, but also things that the universe says, or God says. If she is deeply distrustful of technology, then she can simply learn it. Make it her own. Gain mastery of it. There's nothing stopping her from doing that, and then she will understand this language.
It's as though an illiterate person wanted to ban writing.
Posted by Dagonee (Member # 5818) on :
To me, Hannah Arendt seems to be saying that because we've developed a language that can convey concepts that the vernacular can't, those concepts are suspect. Those concepts can be spoken about, and are to a great extent. Scientists are not in a world where speech has lost power, but rather in one where the power of speech has been increased.
Those statements using mathematical symbols are speech. And it's trivial to prove that the concepts expressed by those statements can be taught to someone who, at the time the teaching begins, only knows the vernacular.
Disguising the technical language of a field in words that also have meaning in the vernacular doesn't seem to help with clarity to me. It just means lay people think they understand things they really don't. Look at the trouble over the word "theory" in science and the vernacular, or "evidence" in law and the vernacular.
Posted by Orincoro (Member # 8854) on :
quote:Originally posted by Dagonee: Those concepts can be spoken about, and are to a great extent. Scientists are not in a world where speech has lost power, but rather in one where the power of speech has been increased.
why do people refuse to learn a language in which understanding can be conveyed? Its no different than, say, wanting to understand the history of the Roman empire as best you can; you would HAVE to learn Latin if you wanted to do that properly. Just because you have to learn another system to do it, doesn't mean that system is somehow suspect. How do we ever learn anything? We have to communicate inside the parameters of our languages, or extend them in specific and careful ways.
Posted by NotMe (Member # 10470) on :
I think Irami should try to spend a few days without any technology developed using algebra or any other branch of mathematics that is more advanced than arithmetic. Perhaps when he gets back from his Walden Pond he will be a bit more humble. He certainly should have a better appreciation for the good that can be accomplished with tools, be they physical or abstract.
Posted by HollowEarth (Member # 2586) on :
So you bumped a 2 year old thread just to jab at someone? That's class.
Posted by GodSpoken (Member # 9358) on :
Algebra not used? Bah! You use it every time you cut down a recipe or calculate how many invitations to send versus how much food to have at the party. I use it daily in my work, and I do not do rocket science.
Posted by Samprimary (Member # 8561) on :
quote: Juggling and video games take as much hand eye coordination as surgery.
Man, I'm in the wrong business then. I can beat Sonic 3 & Knuckles in under a half hour, think I should apply for organ surgery or start humble with appendectomies and stuff?
honestly though it's so nice to see Cohen mentioned again, even in an old thread. That guy's a little out there.
Posted by Omega M. (Member # 7924) on :
Can we at least agree that kids need to learn enough math to understand the probabilities and statistics that come up all the time in the news? Of course, this would include understanding what these numbers actually say, and, importantly, what they don't say, about issues. Still, I'm not sure you can do probability and statistics without some symbol manipulation of the type used in algebra.
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Debate closed. Richard Cohen wins.
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It's something about not confusing size with granduer and how the great question is, "What are we to do with all of these things."![[Wave]](graemlins/wave.gif)
Boothby!