47 percent of students passed the end-of-course assessment.
Hurray !!
Its hard to make that stuff feel relevant or interesting.
As a gamer I never feel that math is irrelevant or uninteresting.
*shrug*
As a gamer I never feel that math is irrelevant or uninteresting.
*shrug*
It stopped being both when i stopped getting numbers out of it. finding out that x was 6 was kinda cool, and you could plug it back into the beginning and see where it came from, but ending up with X-1/X just doesn't mean anything.
So the way something changes depending on another variable flatly doesn't mean anything? Really? Wow.
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It stopped being both when i stopped getting numbers out of it. finding out that x was 6 was kinda cool, and you could plug it back into the beginning and see where it came from, but ending up with X-1/X just doesn't mean anything.As a gamer I never feel that math is irrelevant or uninteresting.
*shrug*
If x=2 then 1/2, if x=3 then 2/3, if x=4 then 3/4. Your problem was x=1 then (1-0)/1=[0/1] and x=0 then (0-1)/0=[-1/0].
(x^(n-m))+{x^n}= everything.
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Uh, no. If x=2, x-1/x=1.5. If x=3 then x-1/x=2.6666..., 4 means 3.75, etc. X=1 gets you 1-1=0, and x=0 means it's undefined due to division by zero. If you plot it you will find it approaches negative infinity in x=0.
I hate math more so than Joss Whedon, Alton Brown and Mark Zuckerberg combined.
Congratulations to the students for mastering Algebra! While some may question it's usefulness, Algebra is required in a number of professional fields, and is requisite for most College degrees.
Edited to add: I hate Algebra!
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Uh, no. If x=2, x-1/x=1.5. If x=3 then x-1/x=2.6666..., 4 means 3.75, etc. X=1 gets you 1-1=0, and x=0 means it's undefined due to division by zero. If you plot it you will find it approaches negative infinity in x=0.
Now its just an argument over order of operations. I put everything left of the division above the line unless brackets define the order.
2-1=1 so its 1/2 or (x-1)/x...as opposed to x+(-1/x)...or worse still x*(-1/x).
Uh, no. If x=2, x-1/x=1.5. If x=3 then x-1/x=2.6666..., 4 means 3.75, etc. X=1 gets you 1-1=0, and x=0 means it's undefined due to division by zero. If you plot it you will find it approaches negative infinity in x=0.Now its just an argument over order of operations. I put everything left of the division above the line unless brackets define the order.
2-1=1 so its 1/2 or (x-1)/x...as opposed to x+(-1/x)...or worse still x*(-1/x).
The order of operations is quite clear. You need parentheses or a different division line to do it your way.
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The order of operations is quite clear. You need parentheses or a different division line to do it your way.Uh, no. If x=2, x-1/x=1.5. If x=3 then x-1/x=2.6666..., 4 means 3.75, etc. X=1 gets you 1-1=0, and x=0 means it's undefined due to division by zero. If you plot it you will find it approaches negative infinity in x=0.Now its just an argument over order of operations. I put everything left of the division above the line unless brackets define the order.
2-1=1 so its 1/2 or (x-1)/x...as opposed to x+(-1/x)...or worse still x*(-1/x).
But the order of priority is bracket, exponent, multiply, divide, addition, subtraction..
X-1/x is broken up in this order:
((x)-(1))/(x) where division separates subgroup a from subgroup b.
Then subtraction separates subgroup a(1) from subgroup a(2). This means x-1 takes place to determine above the line before the division by x occurs.
What you are suggesting is left to right order of operations.
The problem then becomes how computer software works: look-up tables as opposed to actual math.
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The order of operations is quite clear. You need parentheses or a different division line to do it your way.Uh, no. If x=2, x-1/x=1.5. If x=3 then x-1/x=2.6666..., 4 means 3.75, etc. X=1 gets you 1-1=0, and x=0 means it's undefined due to division by zero. If you plot it you will find it approaches negative infinity in x=0.Now its just an argument over order of operations. I put everything left of the division above the line unless brackets define the order.
2-1=1 so its 1/2 or (x-1)/x...as opposed to x+(-1/x)...or worse still x*(-1/x).
But the order of priority is bracket, exponent, multiply, divide, addition, subtraction..
X-1/x is broken up in this order:
((x)-(1))/(x) where division separates subgroup a from subgroup b.
Then subtraction separates subgroup a(1) from subgroup a(2). This means x-1 takes place to determine above the line before the division by x occurs.What you are suggesting is left to right order of operations.
But there are no brackets. You can't arbitrarily add brackets where every you want them to make it do what you want.
If the line was "((x)-(1))/(x)" or even "(x-1)/x)", then it does what you think. But it wasn't, it was just x-1/x. Since there are no brackets, divide has precedence over subraction and it comes out to be x-(1/x).
And you are wrong because everything above is divided by that which is below the divisor.
Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Because they're mostly a notion to save space on a slide ruler and to avoid having 8,0000 zeros written down somewhere, which... really isn't a problem anymore. *pat pats old sparky on his desk *
Because they're mostly a notion to save space on a slide ruler and to avoid having 8,0000 zeros written down somewhere, which... really isn't a problem anymore. *pat pats old sparky on his desk *Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Even with the advent of computer-aided tools for crunching data and storing numbers, logarithmic functions are incredibly useful for displaying graphical data with useful resolution. And then there are all the essential tasks that log functions are required for when manipulating data in reference to Euler's constant, or calculus functions where you divide by a variable.
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Even with the advent of computer-aided tools for crunching data and storing numbers, logarithmic functions are incredibly useful for displaying graphical data with useful resolution. And then there are all the essential tasks that log functions are required for when manipulating data in reference to Euler's constant, or calculus functions where you divide by a variable.
Or anything involving dynamic systems. If you plan to retire someday, for example, and want to see how how long your money will last. If you want to see how your mortgage payments will change if you can put an extra $100 into the account this month.
47 percent of students passed the end-of-course assessment.
Hurray !!
I think that's a bit of an unfair post; the article points out that the pass rate was for students who had already failed the assessment once, and were re-taking it after a remedial course. I don't want to tell you how many students I had to fail in algebra after their 4th or even 5th attempts.
The fact that the remedial course significantly raised the pass rate speaks well for the program, so I feel their celebration was warranted.
It even goes on to point out an 83% pass rate for the (admittedly small sample of) students who were taking the test for the first time, much higher than the state average. (Though of course standard deviations weren't provided, as always in such articles.)
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And this is from a man who resigned from teaching after being told he was required to pass 66 2/3% of his calculus students, no matter how poorly they performed, because the school had a reputation to maintain.
(I was very pleased that the school lost its math accreditation the year after I left -- spoke volumes for the system (eventually) working.)
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The mind boggles.
Stop embariasing the Australian educational system Dingo.
In what way? Im arguing that you can get any answer you want until brackets are used to define the actual order of operation.
X-1/X is little more than an opportunity to choose the mathematical equivalent of French over English.
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The mind boggles.
Stop embariasing the Australian educational system Dingo.
In what way? Im arguing that you can get any answer you want until brackets are used to define the actual order of operation.
X-1/X is little more than an opportunity to choose the mathematical equivalent of French over English.
I'm afraid this is incorrect.
PEMDAS is a generally-accepted international standard for order of operations.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Therefore X-1/X, having no parentheses, exponents, or multiplication, is always interpreted as X - (1/X).
If you prefer to interpret it differently, that is certainly your right, but it won't be right according to generally-accepted standards.
You neglected the negative operator.Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Whuh? An operator is not a term.
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Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
There was a great rain. For 40 days and 40 nights, the rain came down. And yet Noah and his ark of creatures survived, riding the waves until a dove returned with an olive branch, showing that land was near.
And they landed, and Noah send all the animals forth, saying, "Go forth and multiply!"
And the creatures went forth.
A few days later, Noah was laboring disassembling his ark to make a shelter for himself and his family. He saw two very sad little snakes. "What is wrong, little ones?" he asked.
"We can't multiply! We're adders," they squeaked.
And Noah pondered on this for 3 days and 3 nights.
And Noah returned to the wood pile where he had left them. Much to his amazement, the wood was aswarm with tiny little adders. Aghast, he blurted out, "I thought you couldn't multiply!"
The adders smiled and hissed, "We used logs."
Or anything involving dynamic systems. If you plan to retire someday, for example, and want to see how how long your money will last. If you want to see how your mortgage payments will change if you can put an extra $100 into the account this month.
Even with the advent of computer-aided tools for crunching data and storing numbers, logarithmic functions are incredibly useful for displaying graphical data with useful resolution. And then there are all the essential tasks that log functions are required for when manipulating data in reference to Euler's constant, or calculus functions where you divide by a variable.
Those are the sorts of things I'm talking about when I say "calculus functions where you divide by a variable." The formulae that govern the processes you discuss are integrations of some variation of (1/x)
Whuh? An operator is not a term.You neglected the negative operator.Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
He is saying that using standard conventions the expression can also be (rightly) read as X*(-1/X)
He is saying that using standard conventions the expression can also be (rightly) read as X*(-1/X)Whuh? An operator is not a term.You neglected the negative operator.Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Not in any text, paper, publication, or correspondence I have ever seen. If someone insisted that this was their convention, I would happily start an argument with them as to why reinterpreting long-accepted standards is a bad idea.
And I think this thread's derailment is a wonderful example of exactly why it's a bad idea. Redefine the standards and everything becomes unclear.
EDIT: In short, no mathematician, engineer, nor physicist I've ever met would write X - 1/X when they meant X(-1/X). Convention demands that without the parentheses, the - is treated as subtraction and not a negative sign.
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As a gamer I never feel that math is irrelevant or uninteresting.*shrug*
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Wow! What a coincidence you posted both those messages.
You know, when I was a child, I didn't fully understand logarithms either... until I got the DC Heroes Role Playing Game, First Edition, by Mayfair. I read the designer's notes and said "Oh!!! Now I get it!!! As Attribute Points increase linearly, linear units increase logarithmically! Logarithms are the inverse of exponentiation! (Well, assuming the same base, anyway.)"
I learned some neat stuff I never would have learned in school. Adding exponential units is like multiplying linear ones. Subtracting exponential units is like dividing linear ones. It's all so simple! And the game makes it fun!
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He is saying that using standard conventions the expression can also be (rightly) read as X*(-1/X)Whuh? An operator is not a term.You neglected the negative operator.Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Not in any text, paper, publication, or correspondence I have ever seen. If someone insisted that this was their convention, I would happily start an argument with them as to why reinterpreting long-accepted standards is a bad idea.
And I think this thread's derailment is a wonderful example of exactly why it's a bad idea. Redefine the standards and everything becomes unclear.
EDIT: In short, no mathematician, engineer, nor physicist I've ever met would write X - 1/X when they meant X(-1/X). Convention demands that without the parentheses, the - is treated as subtraction and not a negative sign.
And only a computer scientist would use Polish or Reverse Polish notation.
And only a very weird one these days.
My Hewlett Packard 11c says: die you casio watch.
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As a gamer I never feel that math is irrelevant or uninteresting.*shrug*Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.Wow! What a coincidence you posted both those messages.
You know, when I was a child, I didn't fully understand logarithms either... until I got the DC Heroes Role Playing Game, First Edition, by Mayfair. I read the designer's notes and said "Oh!!! Now I get it!!! As Attribute Points increase linearly, linear units increase logarithmically! Logarithms are the inverse of exponentiation! (Well, assuming the same base, anyway.)"
I learned some neat stuff I never would have learned in school. Adding exponential units is like multiplying linear ones. Subtracting exponential units is like dividing linear ones. It's all so simple! And the game makes it fun!
Wait, what? those are things you didn't learn in school? what were they even doing teaching you logarithms without explaining that they are the inverse of exponents? That's not all that different from trying to teach subtraction without mentioning that it's like addition in reverse.
Wait, what? those are things you didn't learn in school? what were they even doing teaching you logarithms without explaining that they are the inverse of exponents? That's not all that different from trying to teach subtraction without mentioning that it's like addition in reverse.
American school. Learn what to put down on the test, do so, get passing grade, clear brain for more room, move onto next subject.
I vaguely remember using inverse logs for pH in in freshmen chem, but that was with a calculator button. Can't say I've seen them since.
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Wait, what? those are things you didn't learn in school? what were they even doing teaching you logarithms without explaining that they are the inverse of exponents? That's not all that different from trying to teach subtraction without mentioning that it's like addition in reverse.
American school. Learn what to put down on the test, do so, get passing grade, clear brain for more room, move onto next subject.
I vaguely remember using inverse logs for pH in in freshmen chem, but that was with a calculator button. Can't say I've seen them since.
Much about your attitude towards math is much clearer to me now. If they teach you math as a bunch of meaningless symbols you punch into a calculator, it makes sense for you to think that math is about meaningless symbols.
He is saying that using standard conventions the expression can also be (rightly) read as X*(-1/X)Whuh? An operator is not a term.You neglected the negative operator.Correct. In the example provided there are two terms X and 1/X. not X-1 and X.
Regardless, the one thing I STILL don't really get in algebra is logarithms. Ugh. I don't know why, they throw my brain for a loop.
Not in any text, paper, publication, or correspondence I have ever seen. If someone insisted that this was their convention, I would happily start an argument with them as to why reinterpreting long-accepted standards is a bad idea.
And I think this thread's derailment is a wonderful example of exactly why it's a bad idea. Redefine the standards and everything becomes unclear.
EDIT: In short, no mathematician, engineer, nor physicist I've ever met would write X - 1/X when they meant X(-1/X). Convention demands that without the parentheses, the - is treated as subtraction and not a negative sign.
And only a computer scientist would use Polish or Reverse Polish notation.
And only a very weird one these days.
Hey, now! I still preciously cling to my 1983 HP 15C specifically because Reverse Polish lets me avoid all those pesky parentheses! Nyah!
...only a very weird one...
Oh, wait...
47 percent of students passed the end-of-course assessment.
Hurray !!
I think that's a bit of an unfair post; the article points out that the pass rate was for students who had already failed the assessment once, and were re-taking it after a remedial course. I don't want to tell you how many students I had to fail in algebra after their 4th or even 5th attempts.
The fact that the remedial course significantly raised the pass rate speaks well for the program, so I feel their celebration was warranted.
It even goes on to point out an 83% pass rate for the (admittedly small sample of) students who were taking the test for the first time, much higher than the state average. (Though of course standard deviations weren't provided, as always in such articles.)
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And this is from a man who resigned from teaching after being told he was required to pass 66 2/3% of his calculus students, no matter how poorly they performed, because the school had a reputation to maintain.(I was very pleased that the school lost its math accreditation the year after I left -- spoke volumes for the system (eventually) working.)
More proof of math's perfidy.
Much about your attitude towards math is much clearer to me now. If they teach you math as a bunch of meaningless symbols you punch into a calculator, it makes sense for you to think that math is about meaningless symbols.
Wait, what? those are things you didn't learn in school? what were they even doing teaching you logarithms without explaining that they are the inverse of exponents? That's not all that different from trying to teach subtraction without mentioning that it's like addition in reverse.
American school. Learn what to put down on the test, do so, get passing grade, clear brain for more room, move onto next subject.
I vaguely remember using inverse logs for pH in in freshmen chem, but that was with a calculator button. Can't say I've seen them since.
What BNW says is a reasonable approximation of the truth. At least in primary school (Kindergarten through 8th grade). I think they taught things an appropriate way in high school, but by then we already had it ingrained in our head the wrong way so it was double the work.
Common core is trying to correct this by teaching it right the first time, but then parents are freaking out like "why can't they just teach it to our kids the way WE learned it."
*flips table*
Much about your attitude towards math is much clearer to me now. If they teach you math as a bunch of meaningless symbols you punch into a calculator, it makes sense for you to think that math is about meaningless symbols.
Wait, what? those are things you didn't learn in school? what were they even doing teaching you logarithms without explaining that they are the inverse of exponents? That's not all that different from trying to teach subtraction without mentioning that it's like addition in reverse.
American school. Learn what to put down on the test, do so, get passing grade, clear brain for more room, move onto next subject.
I vaguely remember using inverse logs for pH in in freshmen chem, but that was with a calculator button. Can't say I've seen them since.
What BNW says is a reasonable approximation of the truth. At least in primary school (Kindergarten through 8th grade). I think they taught things an appropriate way in high school, but by then we already had it ingrained in our head the wrong way so it was double the work.
Common core is trying to correct this by teaching it right the first time, but then parents are freaking out like "why can't they just teach it to our kids the way WE learned it."
*flips table*
The quotes are getting huger and huger, but this is worth addressing. As a parent, my issue with common core isn't that it's "teaching it right" the first time, but that it's providing students with a veritable smorgasbord of options as to how to do a problem, then telling students, "Oh, none of these methods are wrong. Choose your favorite and do that one," but then forcing them to practice all the others.
So you have a bunch of students who learn that they can do multidigit multiplication six different ways, but they never practice any one way more than one or two nights, and they end up being completely lost as to how to do multiplication. And the constant re-examining and re-explanation of multi-digit multiplication makes it seem more like some arcane game a sadist made up than an actual method that should have an answer.
Watching students who've gone through common core is painful, because they mix methods with no understanding, get an answer that's completely off the wall, and have no idea why the answer is wrong. (My favorite was a woman who put 6*7 into her calculator, happily wrote the answer of 42,676 on her test, and then argued with me that it couldn't be wrong because it was the answer her calculator gave her.)
You may argue that this means that my school isn't "teaching right", but the school is in the top 10% in the state, and yet both of my kids suffered through this on multiple topics, and when I went to the tutoring center I found many others suffering the same fate.
I *DO* like common core's emphasis on understanding what you're doing and why you're doing it. When I tutor, I never let my student put pencil to paper until we've had a discussion of what we're trying to do, why, and how we might get where we're going. But I despise its emphasis on, "There are many ways to do every problem. Let's look at them ALL."
It's overwhelming the first time you're looking at a subject to be told, "Here's 6 different ways to do it."
Imagine picking up a Pathfinder rule book and having it list four different ways to figure out whether or not you hit an enemy, all equivalent, but all with a single example, and then saying, "Pick your favorite."
It would be a nightmare for a while until you gave up, picked one, and stuck with it.
And if in PFS you were then required to use one of the other methods on occasion, you'd just get peeved.
Hmmm. Let's apply some math to the math.
We've got a 33% in-county pass rate for remedials, without the program.
The program boosts that to 47%. So the net increase is 14% -- statistically-significant, but not thrilling, especially considering that these are kids who already failed once.
How much does this program cost? That key number is not disclosed, but I'd be interesting to see how many dollars per 1% increase -- not that you can put a price tag on education, but because you could compare what that money would have done for the top half of students (the ones who passed the first time) vs. what it does for the bottom half. (If that county is like the one where I taught high school, it spends $0 per year on advanced programs for the brightest kids, because No Child Left Behind takes precedence over needs of the students who are already getting at least Ds.) But, if spent, would that money have improved performance by 15% for the better-performing kids, instead of 14% By 20% By 90%? In other words, sometimes I wonder if it would be wise to devote some money to training the youth who will one day build the space shuttles, not just spend it all trying to teach algebra to the people who will one day collect their trash or mow their lawns.
@thejeff -- please note the following, from my post:
If that county is like the one where I taught high school, it spends $0 per year on advanced programs for the brightest kids.
sometimes I wonder if it would be wise to devote some money to training the youth who will one day...
No one is saying "write off the failures." What I am saying is, "Why do we devote 100% of the additional funding to the failures, and 0% to the 'passing' kids?"
Why not 50%/50%? Or, if spending on advanced kids brings less bang for the buck why not, 25%/75%? Or even 10%/90%?
Surely you can see that there are more ways to divide an amount other than "all" and "nothing."
@thejeff -- please note the following, from my post:
If that county is like the one where I taught high school, it spends $0 per year on advanced programs for the brightest kids.sometimes I wonder if it would be wise to devote some money to training the youth who will one day...No one is saying "write off the failures." What I am saying is, "Why do we devote 100% of the additional funding to the failures, and 0% to the 'passing' kids?"
Why not 50%/50%? Or, if spending on advanced kids brings less bang for the buck why not, 25%/75%? Or even 10%/90%?
Surely you can see that there are more ways to divide an amount other than "all" and "nothing."
It's a factor of Meta-governmental thrift. Every $1 spent on getting children (general) to point "x" in content mastery saves 10,000 dollars in public welfare expenditures over that child's life time.
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It's a factor of Meta-governmental thrift. Every $1 spent on getting children (general) to point "x" in content mastery saves 10,000 dollars in public welfare expenditures over that child's life time.
Assuming these numbers are accurate, we'd then need to quantify the effect of $1 spent on advanced opportunities in science, technology, medicine, and so on, and see how those pay off as well. Then we can compare. For example, if $1 remedial = $10,000 saved, but $1 advanced = $20,000 growth in economy, it would be hard to justify the whole dollar always going to the former. On the other hand, if $1 advanced = economy grows by $10, then the remedial spending is a slam-dunk winner.
I'm not saying either case is necessarily what we're facing; rather, I think we as a society have no idea, to be honest, because we haven't bothered to really look into it. I do feel that it's short-sighted to not even consider the options and go through the effort of making meaningful comparisons.
It's a factor of Meta-governmental thrift. Every $1 spent on getting children (general) to point "x" in content mastery saves 10,000 dollars in public welfare expenditures over that child's life time.Assuming these numbers are accurate, we'd then need to quantify the effect of $1 spent on advanced opportunities in science, technology, medicine, and so on, and see how those pay off as well. Then we can compare. For example, if $1 remedial = $10,000 saved, but $1 advanced = $20,000 growth in economy, it would be hard to justify the whole dollar always going to the former. On the other hand, if $1 advanced = economy grows by $10, then the remedial spending is a slam-dunk winner.
I'm not saying either case is necessarily what we're facing; rather, I think we as a society have no idea, to be honest, because we haven't bothered to really look into it. I do feel that it's short-sighted to not even consider the options and go through the effort of making meaningful comparisons.
The numbers are assuredly incorrect. I was drawing an example. The point was that the delta between what goes in and what gets saved is large.
As for dollars spent to support the gifted, I think one would be hard pressed to express it. Extreme intelligence (which I consider anything in the "near-genius" range and up, or IQ 150+) will find a way to obtain the education required to express that talent, and those are the people you are talking about with major STEM breakthroughs. Similarly supreme artistic talents will find the education needed to express their earth shattering artistic achievements.
So, the kids you are really talking about are those between IQ 120-149 who are smarter than "bright" but not approaching genius. Preparing these kids to fill the ranks of the STEM professions. The problem is all the programs which certify someone to fill the ranks in the STEM fields are turning applicants away already, creating more students prepared to apply and get rejected does not increase the economic impact of those kids. The system simply doesn't have the bandwidth. Those kids are still going to wind up filling the front line management jobs (either small business owners, office managers, or store managers) as they would have without the extra cash spent.
Now, if you want to argue that putting knowledge in the minds of those kids is good for society, from a cultural standpoint, I'm 100% behind that. Letting people live fulfilled lives through the love of learning is an admirable goal for a society to pursue as its rewards are self-evident and create a generally better society to live in (for the entire population, I will add, even those not directly benefitting will have their QOL improved by an increased number of those folks in the population), but let's not decide that it is a good idea for economic reasons because that is just false.
Extreme intelligence (which I consider anything in the "near-genius" range and up, or IQ 150+) will find a way to obtain the education required to express that talent...
This is the standard truism, but I'm not convinced it's correct. If we start with an IQ 150 kid and lump him in with the IQ 80 kids his whole life, and never do anything else for him, and we start with another IQ 150 kid and continue to accelerate his learning as fast as he can keep pace, in 10 years I do not believe they're going to end up at exactly the same point.
Which hitting method lets me target someone's jugular?
Extreme intelligence (which I consider anything in the "near-genius" range and up, or IQ 150+) will find a way to obtain the education required to express that talent...This is the standard truism, but I'm not convinced it's correct. If we start with an IQ 150 kid and lump him in with the IQ 80 kids his whole life, and never do anything else for him, and we start with another IQ 150 kid and continue to accelerate his learning as fast as he can keep pace, in 10 years I do not believe they're going to end up at exactly the same point.
Agreed, if you are talking about a system which doesn't have advanced classes then I agree that is an issue. I thought we were talking about money.
Let me be clear, you have 300+ kids in a 4AAAA high school class. You are going to have to split them up via some method. If your decision is to populate classes via raffle then you did a bad job, if instead, you split them up according to relative intelligence, subject mastery, and willingness to achieve then you have done a better job AND it doesn't cost any extra money.