Drop everything and go immediately to YouTube to listen to this protracted conversation between a customer who has been quoted a price of .002 cents per kilobyte usage and two different reps who can't tell the difference between .002 cents and .002 dollars.
Here's Instructivist's take. Credit to Katie, a commenter on his blog, for finding the link.
More fun with decimals: the guy's got a blog and a t-shirt!
I'm going to have to get that t-shirt before Verizon makes it go away.
My favorite line thus far: "[.002 cents] is very much less than .002 dollars."
Second favorite:
"How do you write 1 cent?"
".01."
"How do you write 1/2 cent?"
"Ahhh that would be .005 I think...I don't know, I'm not a mathematician!"
Third favorite:
"It's obviously a difference of opinion."
"It's not opinion!"
+++++++
I wonder whether it would have helped if the customer had dropped the approach he was taking, which was correct but wasn't working, and started focusing repetitively - make that perseveratively - on units.
Over and over again the two customer service reps do the calculation on their calculators (.002 cents x 35,896 kilobytes), come up with an answer of 71.792, and then change the unit from cents to dollars.
If he'd pointed out that they'd just switched the unit, would that have helped?
What I assume is happening in this exchange is that the reps are reading decimal figures in terms of the everyday decimal figures they're used to seeing.
When they have a figure like ".002" they attach the unit "cents" because .002 is more similar to the way we write cents than to the way we write dollars.
Then when they suddenly have a figure like 71.792 they switch to dollars, because 71.792 more closely resembles the way we write dollars than the way we write cents.
That's my guess.
Apparently this customer was originally quoted a rate of .002 cents per kilobyte, which in fact was incorrect; the correct rate was .002 dollars.
The original reps must have looked at something like .002/kilobyte and read it as .002 cents.
I say we start teaching the entire Western World unit multipliers today.
Verizon Math, the t-shirt
I think your explanation is right on target.
ReplyDeleteThe conversation is interesting because it shows that using a calculator without real understanding of what one is doing (e.g. awareness of units) can lead one astray. There is a message there for the overreliance on calculators. That's why the use of calculators in the early grades is so harmful. NCTM may want to issue another Focal-Point type "about-face".
One the other hand, my impression is that the customer was more interested in scoring points (maybe to get fame through YouTube) than in making the reps see the light. As you said, pointing out the unit switch would have clarified the issue much better.
I didn't have a problem with the customer because he's not a math teacher.
ReplyDeleteThat was my take-home message: if you're going to handle a billing dispute with a customer rep you probably ought to know a little something about how to teach math.
This is also an illustration of why it's a very bad idea to leave math reteaching up to parents.
Teaching math IS brain surgery. Basic arithmetic may be easy, but teaching basic arithmetic is not.
This customer, a rank amateur when it comes to teaching arithmetic, tried at least two different strategies.
He used numerous comparisons and he had the reps take out a piece of paper and write things down.
My analysis is that where he went wrong was in failing to "diagnose" why the reps weren't getting it.
Of course I don't know why they weren't getting it, but I have a reasonable hypothesis I could test and then abandon if it proved incorrect.
Before I made the call I'd write down some simple versions of:
.6033 dollars
60.333 cents
(Something like that. I'd have several examples in which decimal numbers that "look like" dollars are atually cents, and decimal numbers that "look like" cents are actually dollars.)
I'd probably also have a few problems written out in which you start out with dollars and you end up with dollars; you start out with cents and you end up with cents; etc.
(I'd also ask the rep to write everything down. No one's working memory can hold that many numbers & steps when he or she isn't proficient in the concept.)
I explained the story to Christopher just now, and he seemed to get it.
I told him the reps were reading numbers like .06 as cents and 60.033 as dollars, because that's what they're used to seeing.
It was great, because for a couple of seconds he didn't get why it's possible to have a dollar figure like $60.033. Then he said, "Oh, because the calculator keeps on going."
Christopher also knew how to write "1/2 of 1 cent" in decimal form, thank God.
I suspect that even if the customer had come up with a strategy to show the reps that they'd switched units mid-stream he still couldn't have made his point with the first guy.
The first rep just didn't sound like he'd had enough practice with unit conversions and decimals to grasp what the customer was saying no matter what.
I would also have made the difference in terms of the bill VERY concrete.
ReplyDeleteInstead of saying .002 dollars is 100x the amount of .002 cents, I would point out that the difference in my bill is 71 cents versus 71 dollars.
I would see whether it worked to say, "You told me .002 cents, so the bill should be in cents not dollars."
It should be 71 cents, not 71 dollars.
I'm sure that would have added to the confusion, BUT I think it would also have given both reps pause.
I suspect that both of them would have thought that if they quoted "cents" and then billed in "dollars" that might be a problem.
Part of the difficulty, possibly, is that neither rep is convinced that the mistake might be on their end not the customer's.
AND I would have thought about using a "friendlier" decimal.
ReplyDeleteSuppose the quote was .5 cents per kilobyte versus .5 dollars per kilobyte.
The question of how you might get the reps to see what you're talking about is pretty fascinating, I have to say.
ReplyDelete"The question of how you might get the reps to see what you're talking about is pretty fascinating, I have to say."
ReplyDeleteSometimes you are just hitting a wall, no matter what you do.
In the Kettle clip, the gentleman tried every rational approach, and see how far that got him. (grin)
Sometimes you are just hitting a wall, no matter what you do.
ReplyDeleteIs the Kettle clip the one we watched?
I have a question about how "far you can go" with superb explanation.
ReplyDeleteThe parent math teacher I've been talking to, who's taught math for 34 years, says he can explain fairly complicated material ONCE and have kids get it.
He may be right.
He's teaching Ms. K's class to his son, and his son has an A-/B+ average in the class.
It's made the round.
ReplyDeleteThis is the one: http://video.google.com/videoplay?docid=7106559846794044495
The Kettles made up their own algorithm. They must have been early constructivist. They should get credit for having been on the cutting edge before their time.
oh right!
ReplyDeleteI saw that one!
I think Carolyn posted it awhile back on ktm-1