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Fifty Years of Math

My globe-toodling has at least given me an appreciation for the fact that fast food in an airport (and there isn't any other kind) is an order of magnitude higher than the price of fast food anywhere else. And I noticed something else about fast food -- or it's purveyors, anyway.

Last week I purchased a burger at the local Chew-'n'-Choke for $1.58. The counter girl took my $2 while I dug a bit for some coinage, then pulled 8 cents from my pocket and gave it to her. She stood there, holding the nickel and 3 pennies, while looking at the screen on her register. I sensed her discomfort and tried to tell her to just give me two quarters, but she hailed the manager for help. While he tried to explain the transaction to her, she stood there and cried.

My purpose inrelating this vignette?

Because of the evolution in teaching math since the 1950s. Of course, none of the Denizennes will be able to relate to the *earlier* years, say, those prior to 1997...

*cherubic smile* *batting eyelashes*

1. Teaching Math In 1950s

A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?

2. Teaching Math In 1960s

A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?

3. Teaching Math In 1970s

A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?

4. Teaching Math In 1980s

A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.

5. Teaching Math In 1990s

A logger cuts down a beautiful old-growth hardwood forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes?
Remember, there are no wrong answers, and if you feel like crying, it's okay.

6. Teaching Math In 2007

Un hachero vende una carretada de maderapara $100. El costo de la producciones es $80. Cuanto dinero ha hecho?

Heh. I *dare* the NEA to tell me I'm exaggerating...


[Update: Greetings to visitors from Instapundit. If you've the inclination to hang around, we've got civil-military affairs here and here this week, and some more funny stuff in tips for bosses of military planners and Ballad of the Powerpoint Ranger, and a little bit about "Why do people like to shoot?" Since you're here, feel free to knock about! -the Armorer]

53 Comments

Dam right you're exaggerating, Chief! When did a logger ever make *that* kinda profit?!
 
I bet this is the way it is with some school systems. I do not know if they are all like this but the math skills do seem to be lacking. I have seen most movie theaters make certain everything is charged to the nearest Quarter. Tax is included in the item cost. It could very well be that is done to solve the issue you had at the Restraunt.
 
Oh great! Now the NEA is neither teaching proper Arithmetic nor Spanish. That poor attempt of Castilian is atrocious.
 
Related trivia: Waffle House still uses the old fashioned cash registers that don't figure the change. They use being able to make change the old fashioned way as an aptitude test for employment. Which could indicate that a workforce that is predominantly red-neck has superior math skills to the rest of the service industry employees.
 
I've had loads of fun showing other students at my flight school that you really can do an accurate weight and balance using the E-6B (flight computer) as a slide rule... Hee, hee...
 
I used to amaze and baffle my fellow officers demonstrating the old army slide rule (which I have two of, still). And then showing them the site sticks were essentially just slide rules.
 
Neffi -- there's *lots* of profit in exotic wood. Just think how much cheaper your bug-smasher would be if it weren't made of balsa...
 
there's *lots* of profit in exotic wood *walks away, biting tongue, shaking head*
 
Heh, Sad to relate, but for a couple months my wife worked at a local McDonalds in between jobs. She does pretty well with math, but she was shocked her first day there. Rather than put numbers on the cash registers, they have symbols of the various products, and the teller just punches the buttons relating to what you order. The machine automatically figures the math for you. What gets my wife, though, is how I can figure totals, including taxes, in my head while shopping. She can't do that. On a related note, I lit into my younget's 4th-grade teacher last conference. They no longer teach multiplication tables by rote. I asked her how she could justify it, and she quoted the party line about some kids not being able to memorize as well as others, etc. The school didn't want to injure self-esteem. When my youngest finishes this year, we're going to be home schooling from now on. Respects,
 
'Just think how much cheaper your bug-smasher would be if it weren't made of balsa...' That's 6061 T6 aluminum to *you*, Bubba... and if you ever make it out to these here parts I'll strap you in the back seat and show you how to chase coyotes... and don't look up when we go under the wires. Beer and BBQ to follow... yow! If'n we make it back.
 
Probably right on about the pitiful education in the public schools. But your math is off. Production costs may be $80 but you forgot to add the costs for: OSHA compliance officer EEOC compliance officer EPA compliance officer DOT compliance officer Human Resources manager Extra costs for a driver with a CDL to run across town. "Extra" cost for that tank of diesel. Higher taxes, insurance, permit fees, ad infinitum. Bottom line is that the $100 load of lumber costs about $125. Your poor sucker's out of business with his first shipment. Unless, of course, he lays off all of his employees, buys a load of lumber drop shipped from China for $50, and has the customer pick it up at the terminal. Then the math problem is simpler. "If the customer pays cash, does the logger have to tell the IRS?"
 
Dang! When I was in school, in the fifties and sixties, we learned about commutative, associative, and other properties of arithmetic, and the number line, and real and rational numbers, and cetera. We learned in 7th grade, taught by a crabby old smart woman, how to change from decimal to octal to binary and back and forth any which way. (She always corrected us when we called the course "math"; she told us we were learning arithmetic and that math would come later) We were taught how to make change in ELEMENTARY school. Third grade, mayb
 
p.s. Besides, what's so hard about making change? Let's say the bill comes to $12.58 and the customer hands me $20.00. I think, ok, two cents makes sixty, a dime makes seventy, a nickel makes seventy-five, and a quarter makes $13.00, and seven makes twenty. I think modern technology makes it too easy to be dumb.
 
And just think CW4, who will be designing those fun collections of parts moving in formation? Just better hope myself and other don't punch in numbers wrong for the finite element code! Of course the 5 foot blade can take 10 feet of deflection, Mr Computer tells me so! I thank a nice lady (and double PHD) from Pakistan who decided that teaching Calc in an american school was her calling in life. Set me up pretty well for these here classes.
 
Guys, I just have to be contrary (of course) That was funny, but.... My 9th grade daughter is no math wiz, but she is doing math that I was never taught to do. She uses graphic calculators, and she is doing algebra using shortcuts and tools that I'd never seen before. Moreover, she is doing similar kinds of math in both her biology class (genetics) and her math class, which is cool because it shows how the stuff is applied--AND she is in the class for people who need extra help!!! Look, I know there are folks at McDs who can't make change without a machine to tell them how, but the schools (at least in mid-Texas) are teaching real math and the students are being tested in it. Also, even though the Spanish bit was funny, the kids here are NOT taking the tests in Spanish unless that's the language they speak best. Yeah, yeah, I know, our 'sovereignty' demands they should be taking the test in English, the only language of our land, blah, blah, blah... What do I care what language they are speaking if they are doing the math properly, eh? As for my kid... Well, she didn't do so well on the state test last year, so she goes to tutoring 3 times a week before school, and she is in a class where the teacher gets to spend more time with her. Is this universally true? No, and I know it, but I also know that the 5-6,000 kids in high school in this school district (and it's not a 'rich' one either) are all being taught the same stuff, and they are being held to the state standard. And yeah, we could argue the point about standards, and value of same, etc., but what I know, what I see with my own eyes, is that my daughter is getting a far better education than I did, and I finished HS in 73. She is doing more, her classes are more connected, there are more counselers, I can look up her grades on line, and so on. All in all, I think the current crop of kids are being offered a much better public school education than most people realize (at least in some places). Now whether the kids and parents put effort into themselves and take advantage of what they are being offered, well, that's another story.
 
ooooohhhhhhh Neffi's gonna strap Bill into his backseat....??? must be present for that, so please give me enough warning to arrange transportation. *grin*
 
HI SANGER!!!!!!!!!!!!!!!! How's it goin', stranger? Re. your daughter: My son has been taught "traditional" math so far, including this year. But, next year, in 6th grade, he'll start using a calculator for most things, and he'll no longer have spelling tests. Their reasoning? Because in the real world, people use calculators and they use spell-check on computers. But... they're not having computer classes or typing, because funding has been cut. I am determined to make sure my kids are not hunt-n-peckers, so I'll have to teach them my mad typing skilz at home.
 
Calculators? CALCULATORS? I remember my Algebra II teacher in High School, Mrs. Taber, slapping me down (verbally) for daring to draw a slide rule in her class. It was log tables in the back of the book, and linear interpolation done with pencil and paper, dammit!
 
P.s. And yes, I did walk to and from school, at age 7 or so, and it wasn't uphill either way, and there was no snow, it being Southern FL, and there was no barbed wire around my elementary school, and I and my parents were perfectly OK with all of that.
 
GeoSTI: And just think CW4, who will be designing those fun collections of parts moving in formation?

The same people doing it now -- H1Bs from Asia. Hired at 50¢ on the dollar. Or Asian immigrants -- the bulk of the people sticking it out in engineering schools today.

Meanwhile, our native-born mathphobes are graduating with degrees in pre-Columbian Art Appreciation and $100,000 loan balances, and they're shocked, shocked to find that employers are not beckoning them, and casting rose petals in their path.

Understand numeric concepts and you will always be able to make yourself useful. I never understood why one can graduate college without a single statistics class. If that were a requirement, we'd hear much less nonsense use of factoids based on mean averages, for one thing.

 
It's the same here in Doity Joisey except the little counter "Chicklets" don't cry, they get hostile. What-the-hell.
 
You'd think that if any region would be likely to go all touchy-feely and self-esteemy on math skills and the like it would be mine in suburban New Jersey. But they are as serious as rain about this type of thing in our district. The kids are expected to know their tables before entering 3rd grade. The middle schoolers get 2+ hours of homework per night. It's all about college prep here and it is just ridiculously competitive. The administrators tell the parents that there isn't a school in the NE actively seeking more students from North Jersey and you must compete against your own region for spots. I feel bad for the little goomers. I never had to work anywhere near that hard in school.
 
Being somewhat younger (not quite 30 now) I will have to disagree a little bit with the bemoaning of math skills. I was counting in binary in fourth grade (it was actually being taught in my class, so we all were) and we were learning all the geometric and trigonometric concepts through high school. We used graphing calculators, sure, but we also had to be able to graph by hand, and we had all previously been able to do most functions without the aid of a calculator. Except logarithms and the like, but seriously, before calculators to do logarithms for you everybody had tables anyway, right? In addition, my senior year of high school the math class was calculus, although just single-variable. First semester differential, second semester integral, although I graduated before the second semester. Now, my public school might have been an aberration, and I'll be damned sure my son is able to learn math at least as fast as I was able, but I think it's a bit of a mistake to say that math isn't being taught in schools. On the other hand, my mother mentioned to me the other day that one of my younger sister's teachers claimed in a PTA meeting there wasn't any need to teach long division anymore since all the kids would have calculators anyway....
 
When Thurber wrote "The Figgerin' of Aunt Wilma," it was funny. Except we now know it wasn't funny; it was prophetic.
 
My wife and I agreed that we still think public school is important, as crazy and wrongheaded as it can be at times. But we also agreed that we would not rely on it for our kid's education. Ours learn math and science at my feet, mainly because of my enthusiasm for the subjects, and we divide other duties. I have opinions about what schools ought to be teaching, but what the kids actually learn is more important to me.
 
I had an similar experience at a restaurant a while back where I gave the cashier a $10 bill and she accidentally entered into the cash register that I had given her a $5 bill. She realized she had made a mistake, but had no clue how to fix it. She asked her coworkers for help and they had no clue and none of them had a calculator. After a few minutes they gave up trying and I ended up with a dollar extra in change. Also, I heard one of the bank managers at my local branch say the reason an not enough people with the math skills to do the job.
but I think it's a bit of a mistake to say that math isn't being taught in schools.
Math is being taught, but students are often not learning it. My high school offered calculus as well, but only 5-10% of the students actually took calculus before they graduated.
 
AW1 Tim... ...she quoted the party line about some kids not being able to memorize as well as others, etc. The school didn't want to injure self-esteem. 10th grade, '63, English teacher required us to memorize the 'helping verbs'. I did not succeed and could not recite next day in class. She told me, in language I understood, that I would know them next day. Next day, my recitation was flawless as it is today.
 
What I observe is a huge disparity between schools, and maybe even between classes within a particular high school. I know many kids at church who are in public schools who are clearly doing challenging work in math and other subjects. OTOH, students at the local community college tell me that almost half the students coming into the college go into developmental math, developmental reading and writing because they are NOT prepared for college work. Furthermore, the developmental math classes aren't just helping students master algebra, they are working on basic addition and multiplication. Why is there such disparity between students in the same community? I'm sure some of it can be attributed to parental involvement, and to socioeconomic conditions, but I think part of it is the trend away from teaching elementary kids the basics. When schools teach the basics, all the kids get the foundation to build on. When the basics, like multiplication tables, are glossed over or pushed aside to make time for more "interesting and challenging" work, a lot of kids get left behind. The kids who are slightly ahead developmentally will be fine, and the kids whose parents make sure they learn the basics will be okay, and they probably benefit from the opportunity to play around with interesting problems and applications. The problem is that about half the class is left without the tools needed to understand the work they are doing or to move on to more advanced material. By the time the kids reach high school, the gap is huge, and while some kids are doing great things, others are just marking time to get a diploma. I went to private school and did lots of interesting stuff with math in grade school. We are homeschooling our kids, and I make a real effort to go beyond "drill and kill", but all the fun stuff is in addition to, not instead of covering the basics.
 
Back in the mid-90's I worked at a craft store. Applicants had to take a one-page arithmetic test that consisted largely of problems like "clothespins are 5 for $1, how much do 60 clothespins cost?" The vast majority of our workers were older women. Most of our younger applicants couldn't pass the test, including two memorable high school students who were enrolled in a class called "calculus" who couldn't pass it despite cheating off each other. And that doesn't include the number who didn't even bother applying once they found out there was a math test involved. Monkeys can be trained to punch buttons on a graphing calculator, especially if you call it "calculus" and tell them it will prepare them for college. I can't begin to number the remedial algebra students I've taught and failed who had taken high school "calculus" and "trigonometry". So SangerM, your daughter's "math" class may include stuff you've never learned before, but that just means that she's not even learning the basic stuff you learned. Instead she's being trained to be a calculator monkey. Trust me, I've seen her type in my college classes. They end up in my office not understanding how to deal with rational expressions because they've never done fractions without a calculator. They either learn some real math real quick, or they flunk out of college. Because in the REAL real world, we have to do arithmetic on the fly. I took my kids out of school because they weren't teaching them enough math. True, all our kids won't be engineers. But if we don't at least attempt to teach them math like they're going to be engineers, we cut them off from the possibility altogether.
 
Hi! Terrifically funny post! However I do think AW1 Tim and Sanger have hit on one of the issues. Calculators are introduced very early today which results in two things 1. The younger kids don't learn their math facts (thus the problems with making change) 2. The older kids are doing more advanced math sooner. However I still wonder if they are just hitting the function key on the calculator or are they really learning the math? Now I sent my kids to an elementary charter school where the math facts were drilled into them. Unfortunately the school's scores on the state required end of grade test weren't great for younger kids because that test doesn't test math facts but tests the kids ability to use a calculator. Arggh! Now my kids go to a different charter middle school and many of their classmates came from our local public school system. The teachers greatest complaint -- most kids don't know their math facts! But also to add a little balance to the funny post -- here is a problem from my 6th graders math homework last night (paraphrased as I'm doing this from memory): Tom bought 45 pencils which was as many as he could buy with the $20. he had. How much change did he get back? And I'll almost guarantee you that a question like this shows up on his math test too.
 
Public schools is fo po fokes like me. If'n you's can rilly giv yo kids a ril edumcash'n, you's gots to do it.
 
Public schools is fo po fokes like me. If'n you's can rilly giv yo kids a ril edumcash'n, you's gots to do it.
 
Three kids in college, all did very well in high school (honors and AP courses) and are doing well in college, too. Their math classes are much more advanced (as some commenters have noted), and that is great. And the best use of their time is not spending hours and hours memorizing multiplication tables like we did; that would limit the time spent on more advanced topics. However, the pendulum has swung too far the other direction. There should be more time spent on basic arithmetic, because that will be a huge time saver and money saver in their day-to-day lives.
 
I had exactly that experience in a Kentucky Fried Chicken last fall. There was no manager to help out and the kid was so confused, I left with about a dollar less than I should have gotten. The alternative was to hold up the line while I tried to explain. I tried for a minute and gave up.
 
I went to the hardware store to purchase three or four small items. At the checkout, the clerk miscalculated the sum, shorting herself. I warned her about it, so she recalculated, getting a second wrong answer. I warned her again, so she tried a third time, getting a third wrong charge. I couldn't wait any longer, so I just accepted the third wrong charge. This was all despite the fact that she had a calculator available. Oh well.
 
Not everyone teaches just the touchy feely stuff. I teach science in a public high school. We do math and lots of it. Volumes, density, wavelengths, Flux, Energy, size distance ratios, graphing, analysis, etc. I had a young man tell me today that he didn't think he really needed to know how to solve a simple algebraic formula as he was going into the Air Force and therefore didn't need to do the math. Hmmmm..... I think there is a sergeant waiting for him out there somewhere. By the way, take a minute to think about the type of student that may be working that counter job at McDonald's. They may not necessarily be the best student. The really good students often find better jobs; jobs that are higher paying and more closely related to their interests. In addition the brighter and more motivated workers often find themselves promoted to positions other than the counter.
 
"Kevin R.C. 'Hognose' O'Brien And just think CW4, who will be designing those fun collections of parts moving in formation? The same people doing it now -- H1Bs from Asia. Hired at 50¢ on the dollar. Or Asian immigrants -- the bulk of the people sticking it out in engineering schools today. " Ahem. I'm sitting here at my desk in Lockheed building 158, and there's not an H1B in sight, and few enough Asian faces for that matter. Don't assume that the Computer Science courses are indicative of the general population of engineers.
 
I got a super discount at a taco bell once because the kids couldn't figure out the change and ended up giving me back way more than they should have. I decided to keep the cash. Food was bad , service was terrible and yet I came away feeling good about the whole thing.
 
Not everyone teaches just the touchy feely stuff. I teach science in a public high school. We do math and lots of it. Volumes, density, wavelengths, Flux, Energy, size distance ratios, graphing, analysis, etc. I used to teach all that stuff in my 9th grade classes, but don't any more. Why? It's not on the test. And too many of them can't do it anyway, for the exact reasons discussed here: they do not learn the basics in elementary school and cannot solve problems. It's gonna suck when they're adults.
 
It's odd that the experience you're claiming to have recently was posted by another blogger almost two years ago. The two stories are almost identical. Care to explain? I'm guessing you finally got your flux capacitor working and went back and posted that comment in '06. If that's the case, I'll give you a good price for your "Mr. Fusion."
 
Grandaddy - I'll answer for Bill... it was a joke. Bill likes to personalize jokes, like any good stand-up comedian does in his act. And everything goes 'round and 'round and 'round on the Internet. And if there is an implication of plagiarism of *that* particular blogger... he doesn't even show up as the first entry in this Google search of the joke's text. The Virginia Department of Education does... And a lot of people resonated to it when they found it this time, for the first time or no, because there is a perceived kernel of truth in it. Which, of course, is the essence of a good joke.
 
I feel a sudden hunger. I have to listen to Frank Zappa's 'Flakes.'
 
Has anyone noticed the difference between arithmetic and mathematics? Physics envy has fooled us into teaching math in place of philosophy as the highest mental exercise. The ass-hat who sold the restauranteur his automatic change-calculating inventory-verifying invoice generator (replacing the register), convinced him that he'd no longer have to pay the long dollar to get employees who had change-making skills. His programmer was highly math-enabled. Pre-columbian art appreciation is now taught on a calculus model. You end up with very pretty graphs (with the area under them in color!), and counter clerks who are told they don't have to make change. We have a shortage of arithmetic, but a psychotic abundance of "math."
 
I don't mind it being in Spanish if that means it actually returns to teaching MATH. The 1950s version is Spanish is still preferable to the 1990s liberal [elided] version.
 
Um, GK, here at Argghhh! we frown on language like that, however honestly felt, and otherwise valid the point. Which is why I edited the comment. We're odd that way, 'round here. It doesn't add to the discussion, it usually deflects it to something less useful.
 
When schools teach the basics, all the kids get the foundation to build on. When the basics, like multiplication tables, are glossed over or pushed aside to make time for more "interesting and challenging" work, a lot of kids get left behind.[snip] By the time the kids reach high school, the gap is huge, and while some kids are doing great things, others are just marking time to get a diploma.
I think this about says it. One issue with teaching advanced anything is whether everyone really can meet those guideleins. On the other hand, people need more math and science. The fastest growing job category IS technology and that requires some skill sets that have been highly specialized In fact, someone mentioned the HB1 visas for this country. You know that the highest number of HB1s are given to techie foreigners?
 
John & Bill, I wasn't suggesting plagiarism -- just pointing out the lack of a link. And I tried to keep it lighthearted.
 
Well, like I provided with the Google search... which link of hundreds should I choose? Your point would be taken, if Bill had taken it from Polipundit. But I suspect Bill's had that in his kitbag for some time now!
 
I went to the hardware store to purchase three or four small items. At the checkout, the clerk miscalculated the sum, shorting herself. I warned her about it, so she recalculated, getting a second wrong answer. I warned her again, so she tried a third time, getting a third wrong charge. I couldn't wait any longer, so I just accepted the third wrong charge. This was all despite the fact that she had a calculator available. Oh well.
Have you considered the possibility that you miscalculated?
 
CharterMom @9:32am, I do not understand what is wrong with the problem you wrote "Tom bought 45 pencils which was as many as he could buy with the $20. he had. How much change did he get back? " It seems like a practical problem that requires a touch of Algebra to solve. Two dimes.
 
It is a funny Joke, but I went to a non magnet Public High School in the south in the early eighties and a large percentage of the students there took calculus. So I don’t want to hear about how much better older folk’s math knowledge and education was unless they were calculating the volumes of solids of revolution. I will listen to complaints about my English education, Tess of the D’Urbervilles and My Antonia, what a waste of time.
 
It's a nice story but if you check Snopes, it's also an old, old one. Bad form, donovan. Here's a new, true story that makes the same point. I was helping my grandson in 1st grade with his arithmetic homework. They were learning addition and substraction THIS way: Take the numbers 2, 6, and 8 Put them in their proper slots: __ + __ = __ __ - __ = __ or __ + __ = __ This is not a joke, it's from a good elementary school in suburban Houston, Texas. Fortunately, I taught my kids real arithmetic, and will do the same for their kids. It gives them such an advantage over their peers that one admitted to feeling a little guilty about the 'unfairness' of him knowing how to get the right answer, or recognize the wrong answer, so much more quickly than anybody around him. But he quickly figured out that he had nothing to be ashamed of, and has become quite adept at exploiting the situation in everything from poker to life insurance to splitting tabs at parties. That's the ultimate in justice -- the innumerate PAY for their ignorance. The downside is, they blame George Bush. Jim O world's tallest retired rocket scientist
 
I remember seeing an "educator" talking about how computers will do all the hard stuff so the students' little minds can soar -- no mastery of arithmetic required. My first thought was: How will they recognize the correct answer? Because the computer told them so? Or because they understand it to be the correct answer? GIGO.