posted
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.
Posts: 10645 | Registered: Jul 2004
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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.
Posts: 32919 | Registered: Mar 2003
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posted
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.
Posts: 5462 | Registered: Apr 2005
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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.
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.
Posts: 10645 | Registered: Jul 2004
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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.
Posts: 26071 | Registered: Oct 2003
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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.
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. Posts: 37449 | Registered: May 1999
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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.
Posts: 26071 | Registered: Oct 2003
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posted
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.
Posts: 1735 | Registered: Oct 2004
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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.
posted
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....
Posts: 1757 | Registered: Oct 2004
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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.
Posts: 12591 | Registered: Jan 2000
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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.
Posts: 9912 | Registered: Nov 2005
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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."
posted
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.
Posts: 10397 | Registered: Jun 2005
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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.
Posts: 10886 | Registered: Feb 2000
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posted
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.
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posted
Irami, your display of stubborn ignorance on this thread makes you singularly unqualified to comment on matters of science education.
Posts: 326 | Registered: Aug 2005
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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.
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.
Posts: 12591 | Registered: Jan 2000
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posted
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?
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posted
Yeah - a national day without the right to life, liberty, and the pursuit of happiness that we were endowed with by the Creator. Posts: 26071 | Registered: Oct 2003
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posted
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.
Posts: 21898 | Registered: Nov 2004
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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.
Posts: 10886 | Registered: Feb 2000
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posted
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.
Posts: 82 | Registered: Jan 2006
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posted
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.
Posts: 1621 | Registered: Oct 2001
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posted
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.
Posts: 6246 | Registered: Aug 2004
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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.
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.
Posts: 21898 | Registered: Nov 2004
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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.
Posts: 11895 | Registered: Apr 2002
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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.
Posts: 143 | Registered: Sep 2005
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posted
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?
Posts: 240 | Registered: Jan 2001
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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.
Posts: 12591 | Registered: Jan 2000
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posted
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.
Posts: 26071 | Registered: Oct 2003
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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.
Posts: 12591 | Registered: Jan 2000
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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.
Posts: 21898 | Registered: Nov 2004
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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.
Posts: 9912 | Registered: Nov 2005
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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.
Posts: 5600 | Registered: Jul 2001
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posted
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.
Posts: 6246 | Registered: Aug 2004
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posted
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.
Posts: 26071 | Registered: Oct 2003
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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.
Posts: 9912 | Registered: Nov 2005
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posted
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.
Posts: 145 | Registered: Apr 2007
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