Teaching Math Through the Decades...

Einhander Sn0m4n · Post by **Einhander Sn0m4n** » 2005-07-31 02:25am

Teaching Math through the decades*

Last week a I purchased a burger for $1.58. I handed the cashier $2.00
and started digging for some change. I pulled out 8 cents and gave it
to her. She stood there with $2 and 8 cents. She looked bewildered,
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 burst into tears. The incident got
me thinking about how our kids were learning math in school (or not).

Teaching Math In 1950: A logger sells a truckload of lumber for $100.
His cost of production is 4/5ths of the price. What is his profit?

Teaching Math In 1960: A logger sells a truckload of lumber for $100.
His cost of production is 4/5ths of the price, or $80. What is his
profit?

Teaching Math In 1970: A logger exchanges a set "L" of lumber for a set
of "M" of money. The cardinality of set "M" is 100. Each element is
worth one dollar. Make 100 dots representing the elements of the set
"M." The set "C," the cost of product ion, contains 20 fewer points
than set "M."
Represent the set "C" as a subset of set "M." Answer this question:
What is the cardinality of the set "P" of profits?

Teaching Math In 1980: 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.

Teaching Math In 1990: By cutting down beautiful forest trees, the
logger makes $20. What do you think of this way of making a living?
Topic for class participation after answering the question: How did the
forest birds and squirrels feel as the logger cut down the trees.
(There are no wrong answers)

Teaching Math In 2000: A logger sells a truckload of lumber for $100.
His cost of production is $120. How does Arthur Anderson determine that
his profit margin is $60?

Teaching Math in 2005: El hachero vende un camion carga por $100. La
cuesta de production es ...

*(Found this on the web in a number of locations. I didn't write it.)

Found at http://www.varmintal.com/aengr.htm

Crown · Post by **Crown** » 2005-07-31 06:14am

Okay ... huh?

Lord Zentei · Post by **Lord Zentei** » 2005-07-31 06:37am

And true. Unfortunately.

Crown: it's an attack on the decline of Math teaching in America.

Post by **Mr Bean** » 2005-07-31 06:40am

All hail the allmighty calcuator!
Speaking of which this is not new, its old, REALY old. I first got it in a chain email letter about ten years ago.

Son of the Suns · Post by **Son of the Suns** » 2005-07-31 07:30am

Mr Bean wrote:All hail the allmighty calcuator!
Speaking of which this is not new, its old, REALY old. I first got it in a chain email letter about ten years ago.

They must have added the stuff about Aurther Anderson and the spanish.

Incidently, I went to a private school where we were not allowed to use calculators in math. We had to do everything by hand. As a result, I was way ahead of everyone else in college as far as my algebra and trig abilities go, however, when I got into the higher levels of math I found it difficult to keep up when the instructor said, "Ok now that you've seen how to set it up, just plug the numbers into your calculator." I really wasn't that proficient with a caluculator, but I understood how the problems were worked and whether or not the answer I got was reasonable far better than the majority of my classmates. I also noticed that students that had always used a calculator to do their algebra more often had the attitude that they were "not smart enough to learn math."

Zadius · Post by **Zadius** » 2005-07-31 07:41am

The 1970's example is apparently a reference to "New Math".

Enforcer Talen · Post by **Enforcer Talen** » 2005-07-31 05:13pm

Course, as a cashier, I would just take the money, plug it into the cash register, and itll tell me what change to give back.

Zero · Post by **Zero** » 2005-07-31 05:17pm

Calculators do kind of make developement of abilities in math kind of.. erm.. shitty. Lucky for me, I'm so disorganized that I keep losing my calculators, and often paper and pencil/pen, as well, so usually I gotta try and work shit out in me head. I have a feeling this isn't going to go well in calc. next year... wish me luck..

Post by **Surlethe** » 2005-07-31 05:20pm

Son of the Suns wrote:Incidently, I went to a private school where we were not allowed to use calculators in math. We had to do everything by hand. As a result, I was way ahead of everyone else in college as far as my algebra and trig abilities go, however, when I got into the higher levels of math I found it difficult to keep up when the instructor said, "Ok now that you've seen how to set it up, just plug the numbers into your calculator." I really wasn't that proficient with a caluculator, but I understood how the problems were worked and whether or not the answer I got was reasonable far better than the majority of my classmates. I also noticed that students that had always used a calculator to do their algebra more often had the attitude that they were "not smart enough to learn math."

I had that experience just this past year in Calc.; the instructor would show us the setup, then tell us to do it on the calculator. I always preferred doing math by hand, and using the calculator for number crunching (i.e., 20556/1052, stuff like that).

As for the OP: I've seen that before, and always thought it's pretty damn funny.

Frank Hipper · Post by **Frank Hipper** » 2005-07-31 05:39pm

Zadius wrote:The 1970's example is apparently a reference to "New Math".

Indeedely, I recognised it by having experience with the shit!

I can most certainly vouch for the bit in Wikipedia stressing teachers having problems with it, and, IIRC, we only had to suffer through it briefly with no one learning a damned thing about it.

Zadius · Post by **Zadius** » 2005-07-31 06:33pm

In high school, we had no restrictions on using calculators. I was very good at doing symbolic manipulation in algebra, and later in calculus for differentiating and integrating, but I would always reach for my calculator for numeric computations. I got so dependant on the calculator that I would reach for it even for simple things that I could easily have done in my head.

This was all fine until I had to take a test and calculators were prohibited. I found out to my horror that I had forgotten how to do long division!

Jarl Sven · Post by **Jarl Sven** » 2005-07-31 06:40pm

Zadius wrote:The 1970's example is apparently a reference to "New Math".

yeah I remember that stuff
the text books were ...interesting

although, looking back on it, it wasn't all that bad

clearly a cut above rote memorization

and yes, I've been the cranky old guy making the burger girl cry by giving her $2.08

sketerpot · Post by **sketerpot** » 2005-07-31 10:03pm

Zadius wrote:This was all fine until I had to take a test and calculators were prohibited. I found out to my horror that I had forgotten how to do long division!

Hee hee! That happened to me once. After a bit of semi-panic, I fell back on my good knowledge of algebra and invented my own algorithms for doing arithmetic on the spot. It worked decently (and fast!), and I got my usual grades on the test. This has happened to me a disconcerting number of times, actually.

Plushie · Post by **Plushie** » 2005-07-31 10:28pm

Zadius wrote: This was all fine until I had to take a test and calculators were prohibited. I found out to my horror that I had forgotten how to do long division!

Long division's useless, anyway >_>

No, seriously, for some odd reason, I can work out how to divide the traditional way in my head. I know long division is more useful for that, but I forgot how to do it by the afternoon after they taught it to us years ago.

Alyeska · Post by **Alyeska** » 2005-07-31 11:55pm

I've forgotten how to do long division a LONG time ago. I started using calculators and worked Albegbra since the 6th grade. I could do the algebra, but when it came to doing the simple math I always used a calculator.

DrkHelmet · Post by **DrkHelmet** » 2005-08-01 12:04am

That is nothing new under the sun. I've had it happen to me several... thousand times. I usually have to tell them what the change is.

I once had a Wal-Mart cashier who was willing to accept my $1,000,000 bill and go back to the office to get enough cash to change it.

The stupid are everywhere. Be afraid.

Brother-Captain Gaius · Post by **Brother-Captain Gaius** » 2005-08-01 12:08am

Wow. I thought I was alone in forgetting (multi-digit divisor) long division.

TimothyC · Post by **TimothyC** » 2005-08-01 12:39am

Plushie wrote:Long division's useless, anyway >_>

Ah, My guess is you haven't taken a Calculus class in a while

. Without it I would have been sunk on last weeks DiffyQ quiz.

Durandal · Post by **Durandal** » 2005-08-01 12:59am

The fun thing about having been in a physics curriculum for two years is that you learn to approximate on the fly really well. For example, if I'm driving back to school, I'm probably doing about 85 mph. If I see a sign that says "Bloomington 65 miles", I think, "Well 65 over 85 is a little more than 6 over 8, which is 3 over 4. So I've got about 45 or 50 minutes left."

People always look at me funny when I crunch numbers in my head. It's such a rare skill nowadays, especially on college campuses. That's why good professors design tests with nice, even numbers. If you have to use a calculator for those kinds of calculations, you're penalized with time by not being able to run the simple stuff in your head.

Captain tycho · Post by **Captain tycho** » 2005-08-01 01:15am

I do basic rote math so much I don't even bother using a calculator sometimes, even for larger problems. It's simply faster that way.

SpacedTeddyBear · Post by **SpacedTeddyBear** » 2005-08-01 01:45am

People always look at me funny when I crunch numbers in my head. It's such a rare skill nowadays, especially on college campuses. That's why good professors design tests with nice, even numbers. If you have to use a calculator for those kinds of calculations, you're penalized with time by not being able to run the simple stuff in your head.

I noticed that as well. After calculus and diffeqs, basic number crunching and approximating with good accuracy takes a few seconds. On one occasion, me and my friends were playing paintball one day, and they were trying to figure minimum number of shots you should get from your compressed air tank. The general rule is if it's a tank pressurized at 4500 psi, you multiply 15 with the volume of the tank ( in cubic inches). I don't know where this "rule" came from, it just is. The tank that they had was a 68ci/4.5kpsi. So I jumped in after about about 10 seconds and said " It's 1020 shots". They looked at me funny, and after a little bickering, one pulled out his cell phone/calculator. Sure enough, it was 1020.

Plushie · Post by **Plushie** » 2005-08-01 02:22am

MariusRoi wrote:
Plushie wrote:Long division's useless, anyway >_>
Ah, My guess is you haven't taken a Calculus class in a while . Without it I would have been sunk on last weeks DiffyQ quiz.

I, *ahem*, kind of ignored calc. Well, not so much ignored as ran on auto-pilot. My concious mind slept while the rest differentiated. I couldn't for the life of me tell you anything about it (well, anything of importance) but I can still do the math itself.

Dooey Jo · Post by **Dooey Jo** » 2005-08-01 05:47am

I didn't know long division for a very long time. I think we did it for a week or so in fifth grade, but I could never get the hang of it. That thing was the most illogical thing ever! Or so I thought back then anyway. But if you want to solve some more complex differential equations, long division is your friend. Just put the polynoms in, instead of the numbers, and it's so easy it isn't even funny.

Zadius · Post by **Zadius** » 2005-08-01 07:57am

Durandal wrote:People always look at me funny when I crunch numbers in my head.

I've had that experience as well. Back in algebra class I was always looking for short-cut methods to find the answers faster. I figured out that the x-value for a parabola's vertex was always -b/2a. I started amazing people with my 'superhuman' mental vertex finding ability.

sketerpot · Post by **sketerpot** » 2005-08-01 09:53am

SpacedTeddyBear wrote:I noticed that as well. After calculus and diffeqs, basic number crunching and approximating with good accuracy takes a few seconds. On one occasion, me and my friends were playing paintball one day, and they were trying to figure minimum number of shots you should get from your compressed air tank. The general rule is if it's a tank pressurized at 4500 psi, you multiply 15 with the volume of the tank ( in cubic inches). I don't know where this "rule" came from, it just is. The tank that they had was a 68ci/4.5kpsi. So I jumped in after about about 10 seconds and said " It's 1020 shots". They looked at me funny, and after a little bickering, one pulled out his cell phone/calculator. Sure enough, it was 1020.

Well sure, to calculate 15n you just need to calculate 10n+5n, and those can be calculated easily. To multiply by 10, just add a zero. To multiply by 5, divide by 2 and add a zero. Then you just need to find 340+680, which is equivalent to 900+120, which is 1020.

That was fun!

Zadius wrote:Back in algebra class I was always looking for short-cut methods to find the answers faster. I figured out that the x-value for a parabola's vertex was always -b/2a. I started amazing people with my 'superhuman' mental vertex finding ability.

You figured that out without looking it up in the book or using calculus? Most impressive.