I think you’re reading too specific a meaning into “logical thinking”. There’s a lot more to rationality than fits into any given predicate calculus. What I mean is the ability to follow (or, more importantly, to create) a coherent train of reasoning in general. It very much comes down to the sort of idea you advanced in your thesis on the other thread, I think.
How does using a limit statement to find the points where a tangent meets a circle and graphing it help me in daily life?
And easy is subjective. I cope better with algebra than with calc.
But all the examples here of algebra have been 9/10 grade level (at least where I am). Where do the extra years come in? Can we just stop teaching algebra once we get past those basic points?
And really, I’m not so stupid as to forget that a tangent meets a circle at only one point. :smack:
But it illustrates the point that you made–that you don’t “really” use the advanced equations. We can turn all these things into math.
Absolutely. But the only way you know this is because, as far as I can tell, you’re a reasonably well-schooled individual. Schooled to the point that you know what you got from it.
Your 13-year-old brother is still working under Daddy economics. This ends when you get to be 18.
You can tell him from me that I approve of his decision. We need a constant supply of submorons with no better skills who will make subsistence wages their entire lives so that they can say “want fries with that?” to people like me.
Not a big fan of the Church-Turing thesis, then? Where should a lay-person go to find out more about this C-T thesis? (apart from google)
The OP is obviously best answered by the testimony of the resident fireman. The following probably won’t work on a 13-year old, but what the heck. I work in a township that is dealing with growth. A segment of the population desparately wants to halt all growth, another segment wants “smart growth,” another wants to turn the place into a mini-Manhattan. Fact is, none of them have any idea whether their plan will make the world a better place. To even begin to decide that question, you need to know math—it is a sixth sense, so to speak. Starting on page 38 of this paper, you can see the sort of stuff that goes into trying to decide this sort of question. By contrast, the latest issue of Planning & Zoning News counts a “cost” of so-called sprawl as the loss of farm land—yet the author of the article makes no defense for the notion that welfare (i.e. human well-being) is increasing with farmland (it would be difficult to argue that there isn’t a surplus). These people are only able to assess the benefits of their chosen plans to the extent that they satisfy the Revealed Truths of their particular ideologies.
The point is that learning math is like learning to read. If you don’t know math, then you’re nothing more than a Guest on the Jerry Springer show of Life.
There are all sorts of ways to use algebra plus all the other advantages of knowing the discipline. But why in the hell do they just teach how to work algebra and not how it can be used? 
I don’t know. I think the amazing thing about math is that you can start from very very basic concepts (0, 1, addition, equality…) and a relatively small number of properties (a=a, a+0=a, 1a=a…) and work up to some amazing formulas. Just recently, I saw someone muttering to herself over a flashcard trying to remember that a[sub]n[/sub]=a[sub]1[/sub]+(n-1)d. “You know,” I said in what I intended to be a casual tone of voice, “it’s a lot easier if you derive it from the definition of an arithmetic sequence.” And I guess I scared her away. It’s as if we’re taught to hate the word “derive” or something. Not surprising either, given the problems in our textbook. Often, they’ll state the word problem, then give you the formula which reduces “Figure out when the ball will hit the ground.” to “Plug in 5 for x and 9 for y and solve for z.” Nobody will ever be excited by the fact that Descartes invented (or perhaps discovered) solutions to an infinite number of unsolvable quadratic equations, when he defined i=sqrt(-1) or by the fact that there is no highest prime number. Not if they keep teaching math the way they have been.
But I digress. In response to the OP, I’ve yet to see “the real world” so I can’t give firsthand advice. But my Geometry teacher last year said that math is like weight-lifting. Of course, you’ll never use it (unless you’re a weight-lifter, the equivalent of which would be this guy perhaps) but it will make your mind stronger for other events. On the other hand, I can almost hear the strength of my classmates’ minds decreasing every time they’re given another formula to memorize. Sigh.
I tell my son that the more he knows, the more options he has as an adult. He doesn’t find it totally satisfying, but enough so that he sticks with math.
Well, that’s it, then. We’re taught the formulas and to memorize them, we learn to recognize when to use them, we do well enough on the test, then we forget it.
And you get your ass handed to you again and agan by people who can actually think and you wonder what the hell happened.
Actually, I’m not, but for far more technical reasons. Church and Turing were early researchers in what is now called computer science. A discussion of the modern interpretation is found at MathWorld. The original idea was more overstated; basically that any two methods of evaluating any function were essentially performing equivalent steps.
Well, they should, to some extent. But to teach how algebra can be used in, say, firefighting, they’d have to teach about firefighting—about hoses and water pressure and all sorts of other specialized knowledge. Same thing with any other specialty it could be applied to.
Plus, what the typical math teacher is going to know most about is how algebra can be used in other, higher-level math (trigonometry, calculus, statistics, etc.); but that’s not going to be much help in motivating the students who dislike algebra.
oh, I don’t know. throw a “The King of France was a man; I was a man :. I was the King of France” at them for a giggle, and you might be surprised how many of them get interested, if for no other reason than to think up nonsense logic to throw their parents off.
Once upon a time I was loading boxes into a truck. Over one thousand boxes into a semi-trailer actually when the foreman said he only wanted the boxes to come back so far in the trailer.
Using A = H x W x L
Total number of boxes = Unknown Stack Height x Number of boxes that fit across the width of the trailer x Number of boxes from front of trailer to where foreman scratched his foot in the trailer dust.
So when the foreman came back later to check I knew exactyly how high to stack the boxes to reach where he wanted the load to end. When asked how I knew I told him it was a simple linear equation.
Some years ago, at a construction site they started filling a newly built swiming pool with a garden but nobody had the slightest idea of the time it would take. A few hours? days? weeks? not a clue. They did not dare leave the site with the hose running.
I measure the dimensions of the pool and calculated the capacity. I then took a bucket, measured its dimensions and calculated its capacity. I measured how long the bucket took to fill up and then calculated how long it would take for the pool to fill up. Now they knew they could safely leave the hose running all night and return the next day.
I have also calculated the height of the mast of a boat by triangulation and determined it could (barely) pass under a bridge.
I can’t begin to tell you the number of badly-constructed Excel formulas I’ve seen, many of which produced (incorrect) results upon which important decisions were made. I’m not even talking about typos and missing parentheses, but rather ones which demonstrate a fundamental lack of understanding of algebra and/or statistics. If you don’t understand how to put the numbers together, how can you know what they mean?
Of course, these errors are more than surpassed by the number of business docs I’ve seen with incomprehensibly bad grammar and punctuation, but that’s a subject for another thread.
I am very disappointed in this statement, true as it may be. For most students, the only reason they have to sit through algebra and calculus classes is so that they can learn to think analytically and problem solve. It’s really misfortunate that we can’t elevate both the levels of teaching (no offense!) and student learning so that algebra DOES become a lesson in critical thinking and not just pencil pushing.
I firmly believe that any activity that exercises the mind can only benefit you, if only in a small obscure way.
Okay here is a real world algebra problem:
http://www.1728.com/minmax3.htm
Granted it involves calculus, but a working knowledge of Agebra is <i>essential</i> in order to set up and solve the equations.
Actually, I think the answer to that one is “It doesn’t matter. Either way it’ll come in years late and way overbudget.” 