04032015, 05:12 PM



Location: Tucson, AZ
1,527 posts, read 1,671,792 times
Reputation: 3753


My son brought his homework home last night and there are some very simple percentage questions.
What is 40% of 200. Six is 20% of a number. You get the idea...
So he looks at it and says "Dad, can you look at this?" He has 4 pages of notes on how to do simple percentages. Why 4 pages? Because he has to set it up algebraically.
is/of=x/100 so x= you get the idea.
Why do we do this? At first I said okay it's some sort of mental math thing, but after looking at the numbers it would behoove you to have a calculator.
I am an engineer and have always hated what colleges and schools consider applied mathematics. I got into an argument with a professor one day when we were doing ideal gas law conversions because he always loves these long complicated formulas with the units. I said to him "It's plug and chug, there is no need for all this algebra." So he says to me okay, what if your units are different? I said, "I would make sure they all worked out before I started (in this case it was pascals and atmospheres.) Plus, you must have a conversion factor anyway during the problem so why not get all of that out of the way before you start?" Then the professor said. "This is the way they want us to teach it, they want to drill the concepts into your head."
This to me is the problem with math education in this country. We don't teach the easy way first. We have specific rigid operations that we attempt to force a practical application into.
My son did not understand .075 is 7.5% he did not understand that 155% would be 1.55. And I believe this was not taught to him. I get what it's doing but why the long unnecessary baby steps toward something so simple? Give them a large problem to work on, just one. Not 35 not 25 of the same problem with different numbers just one complex multistage problem.
A couple of weeks we were talking about the dangers of tailgating reaction time and distance traveled at 80 vs 65. And a smart guy I know says yeah you travel like 200 more feet between braking at 80 and braking at 60. I said well I agree with the sentiment but the math is wrong." he said no at 80 your traveling like 200 feet a second. I said I think it's more like 120 ft/sec. Then he mumbles some numbers and starts jotting down a algebraic formula and then looks at it confused, erases it and then tries again. I pull out my phone and type and say at the same time 5280x80/60/60= and 117.33 comes up. I said yeah its 117 ft per second at 80mph and he says, no because you did not account for the seconds..... I said "What?, no I'm pretty positive that is correct" At this time he is thoroughly confused. So he goes to the internet and looks it up and I'm right and he says "oh that's what I missed the 3600 secs in the formula" and then shows me a half page of numbers divided and multiplied with cancellations and 3600 sec for 1 hour. I tell you that because it think it's a symptom of a bigger problem in society. When it comes to simple math people are not good at it because what they teach in school is so disjointed from the real world. "Practical applications" most often are not. We are taught from an early to be mathematicians first and problem solvers second.
My point is this: We should teach our kids the easiest way to figure out problems. We are teaching them rigid and overly complicated ways to solve simple problems with specific formulas. The thing that makes me laugh is every newsletter I get from the school repeats the same tag line over and over.
"Education for Creative thinking and life long learning."
Kids don't enjoy or like math because we teach the long way of solving a simple problem. In my opinion every kids has enough knowledge to solve any PRACTICAL problem by 7th grade.
I don't know about anyone else* (*math teachers, we get it, you love math and dream at night about disproving E=mc^2) but could you solve a random CALC II problem 5 years out from the class? I couldn't. I'm still employed regardless of the fact I don't remember anything from CALC II so it's obviously not that important.
Why do we continue to shove algebra and other more complicated stuff dow kids throats and just continue to pass kids though the system when they won't be able to tell you what 7.5% of 200 is when they are 24? The fact that people pay for tip calculator app and that it has over 3 million downloads blows my friggen mind.

04032015, 05:26 PM



Location: Heart of Dixie
11,491 posts, read 8,578,041 times
Reputation: 25567


It's part of the mental development process.
In my work I use highlevel math on a regular basis. If I had been restricted by someone who decided I didn't need any more math than what I had learned by the seventh grade, I'd probably be cutting lawns, flipping burgers, or washing dishes.

04032015, 07:46 PM



14,794 posts, read 15,266,341 times
Reputation: 14324


Quote:
Originally Posted by AndyAMG
My son brought his homework home last night and there are some very simple percentage questions.
What is 40% of 200. Six is 20% of a number. You get the idea...
So he looks at it and says "Dad, can you look at this?" He has 4 pages of notes on how to do simple percentages. Why 4 pages? Because he has to set it up algebraically.
is/of=x/100 so x= you get the idea.
Why do we do this? At first I said okay it's some sort of mental math thing, but after looking at the numbers it would behoove you to have a calculator.
<snip>
My son did not understand .075 is 7.5% he did not understand that 155% would be 1.55. And I believe this was not taught to him. I get what it's doing but why the long unnecessary baby steps toward something so simple? Give them a large problem to work on, just one. Not 35 not 25 of the same problem with different numbers just one complex multistage problem.
<snip>
My point is this: We should teach our kids the easiest way to figure out problems. We are teaching them rigid and overly complicated ways to solve simple problems with specific formulas. The thing that makes me laugh is every newsletter I get from the school repeats the same tag line over and over.
"Education for Creative thinking and life long learning."
Kids don't enjoy or like math because we teach the long way of solving a simple problem. In my opinion every kids has enough knowledge to solve any PRACTICAL problem by 7th grade.
I don't know about anyone else* (*math teachers, we get it, you love math and dream at night about disproving E=mc^2) but could you solve a random CALC II problem 5 years out from the class? I couldn't. I'm still employed regardless of the fact I don't remember anything from CALC II so it's obviously not that important.
Why do we continue to shove algebra and other more complicated stuff dow kids throats and just continue to pass kids though the system when they won't be able to tell you what 7.5% of 200 is when they are 24? The fact that people pay for tip calculator app and that it has over 3 million downloads blows my friggen mind.

First, is/of = x/100 is a bad mnemonic. The way to look at this is part/whole = %/100. Percentages are just ratios with 100 as the whole. There are 3 types of percent problems that you may need to figure out and all can be done as ratios. You should NOT need a calculator to do these. This method works for each of the three types of percent problems.
Ratios are not a *long way* to solve percent problems. They begin with the definition of percentage. Per Cent just means per 100. If you understand percent, then ratios make a lot of sense.
What number is 75% of 4?  this becomes x (part)/ 4(whole) = 75/100, so 100x = 75*4 or 100 x = 300, so x = 3
3 is what percent of 4?  this becomes 3 (part)/ 4 (whole) = x (percent) /100 so 3/4 = x/100 or 4x = 300
so x = 75%
75% of what number is 3?  this becomes 75/100 = x (part)/ 3(whole) so 100x = 3(75) or 100x = 225, so x = 2.25
You can check of course by multiplying if you know how to do that.
At some point, the class should certainly be teaching how to change a decimal to a percent and vice versa, but it isn't the best way to understand percents.
Btw, if they understand the ratio, they can easily figure out what 7.5% of 200 is using this method.
7.5/100 = x/200 or 75/1000 = x/200 so you get 1000x = 75*200 or 1000x = 15000 or x = 15. It's no more difficult than multiplying 200*.075

04032015, 08:11 PM

Status:
"RIP Roxy and April"
(set 6 days ago)


Location: The New England part of Ohio
16,256 posts, read 19,511,901 times
Reputation: 37599


Quote:
Originally Posted by AndyAMG
My son brought his homework home last night and there are some very simple percentage questions.
What is 40% of 200. Six is 20% of a number. You get the idea...
So he looks at it and says "Dad, can you look at this?" He has 4 pages of notes on how to do simple percentages. Why 4 pages? Because he has to set it up algebraically.
is/of=x/100 so x= you get the idea.
Why do we do this? At first I said okay it's some sort of mental math thing, but after looking at the numbers it would behoove you to have a calculator.
I am an engineer and have always hated what colleges and schools consider applied mathematics. I got into an argument with a professor one day when we were doing ideal gas law conversions because he always loves these long complicated formulas with the units. I said to him "It's plug and chug, there is no need for all this algebra." So he says to me okay, what if your units are different? I said, "I would make sure they all worked out before I started (in this case it was pascals and atmospheres.) Plus, you must have a conversion factor anyway during the problem so why not get all of that out of the way before you start?" Then the professor said. "This is the way they want us to teach it, they want to drill the concepts into your head."
This to me is the problem with math education in this country. We don't teach the easy way first. We have specific rigid operations that we attempt to force a practical application into.
My son did not understand .075 is 7.5% he did not understand that 155% would be 1.55. And I believe this was not taught to him. I get what it's doing but why the long unnecessary baby steps toward something so simple? Give them a large problem to work on, just one. Not 35 not 25 of the same problem with different numbers just one complex multistage problem.
A couple of weeks we were talking about the dangers of tailgating reaction time and distance traveled at 80 vs 65. And a smart guy I know says yeah you travel like 200 more feet between braking at 80 and braking at 60. I said well I agree with the sentiment but the math is wrong." he said no at 80 your traveling like 200 feet a second. I said I think it's more like 120 ft/sec. Then he mumbles some numbers and starts jotting down a algebraic formula and then looks at it confused, erases it and then tries again. I pull out my phone and type and say at the same time 5280x80/60/60= and 117.33 comes up. I said yeah its 117 ft per second at 80mph and he says, no because you did not account for the seconds..... I said "What?, no I'm pretty positive that is correct" At this time he is thoroughly confused. So he goes to the internet and looks it up and I'm right and he says "oh that's what I missed the 3600 secs in the formula" and then shows me a half page of numbers divided and multiplied with cancellations and 3600 sec for 1 hour. I tell you that because it think it's a symptom of a bigger problem in society. When it comes to simple math people are not good at it because what they teach in school is so disjointed from the real world. "Practical applications" most often are not. We are taught from an early to be mathematicians first and problem solvers second.
My point is this: We should teach our kids the easiest way to figure out problems. We are teaching them rigid and overly complicated ways to solve simple problems with specific formulas. The thing that makes me laugh is every newsletter I get from the school repeats the same tag line over and over.
"Education for Creative thinking and life long learning."
Kids don't enjoy or like math because we teach the long way of solving a simple problem. In my opinion every kids has enough knowledge to solve any PRACTICAL problem by 7th grade.
I don't know about anyone else* (*math teachers, we get it, you love math and dream at night about disproving E=mc^2) but could you solve a random CALC II problem 5 years out from the class? I couldn't. I'm still employed regardless of the fact I don't remember anything from CALC II so it's obviously not that important.
Why do we continue to shove algebra and other more complicated stuff down kids throats and just continue to pass kids though the system when they won't be able to tell you what 7.5% of 200 is when they are 24? The fact that people pay for tip calculator app and that it has over 3 million downloads blows my friggen mind.

I agree with you 1000x over.

04032015, 09:14 PM



4,288 posts, read 2,034,129 times
Reputation: 10393


I don't see where the "algebra" was in your problem. That just arithmetic, not algebra. The reason is people need to learn how to think. Yes, you can plug in the numbers to a smart phone, but that's not the point. The point is exercising and learning how to use the brain to set up a problem, whether it's math or science, or just figuring out how to assemble a swing set. There's a good line in the Imitation Game where Benedict Cumberbach (as Turing) is explaining the point of a test is not whether the prospective code breakers could solve the puzzle, but rather their thought process in how the approach an "unsolvable" problem.

04032015, 09:27 PM



Location: Philaburbia
29,868 posts, read 53,244,264 times
Reputation: 49085


The "why" is just as important as the "how".

04032015, 10:13 PM



3,212 posts, read 4,938,439 times
Reputation: 2268


I see both sides to the "argument," but I generally do agree that a stronger emphasis needs to be placed on problemsolving. Math is more than just the manipulation of numbers, though I would disagree that this should be downplayed.

04042015, 12:10 AM



Location: SF Bay Area
14,331 posts, read 18,034,806 times
Reputation: 18436


Algebra is extremely important
A deeper understanding is gained by the longstanding method and I wholeheartedly support it. Teaching the "easy way" is the shallow approach to a magnificent subject. The subject commands a deeper understanding, and as one poster said, it's part of the mental development process.
Kids have problems with it for a variety of reasons such as 1) don't have the aptitude to understand math; 2) don't like the personality of the teacher which taints their enthusiasm to even try; 3) too lazy and impatient; 4) ADD or some other complication; 5) discouraging parents; 6) problems at home.
The way algebra has been taught has worked very well for me and my wife, and our kids. I disagree.

04042015, 12:33 AM



Location: Montana
1,682 posts, read 1,333,152 times
Reputation: 5498


Algebra teaches logic as much as it teaches math. I haven't used algebra since I was a kid, but the logical thinking is used daily  although my wife would disagree with that last statement!

04042015, 05:00 AM



997 posts, read 687,907 times
Reputation: 1455


Because it helps to separate brainless from those who do have brain, and divide the latter into those who can and those who whine. Those who can do things, those why whine do politics, and brainless flip burgers. I'm a real Socrates, huh?

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