A friend of mine who teaches English in Asia asked me about a quirk of American speech. Since he's been asked to teach American English rather than English English, he wants to know which is best.

He has heard Americans, on TV and in real life, saying "I could care less" - instead of "I couldn't care less". Now I've only lived here in the States a little while, but I have never heard anyone say that. However, it's a big country. So my question to you is, do you hear American's saying "could" instead of "couldn't" in this phrase, indeed, do you say it yourself, and if so, which version is more common where you live?

Of course they do!

<<<sigh>>>

Still doesn't make it right though

Americans: always in my experience "could care less"
but your friend needs to teach that this is just wrong!

I hear it all the time. It makes me want to punch people.

"What do you think of my new <<insert insignificant purchase here>>?"

"I could care less."

"Oh, so you do quite like it then?"

"What?"

"Don't you mean 'pardon'?"

"Whaaaaa . . . ?"

*thump* - as my head falls off and rolls away in protest.

I have heard it in speech and on TV, so I guess "could care less" is right in American usage even if it doesn't make sense.

It's not correct even in America, it starts a whole host of complaints and arguments on another (US) site I go to, it's a pet peeve of many Americans even, if you could care less you would.
There are a lot of them, someone hears the saying wrong, takes it wrong, uses it in the wrong way and then says they are the right one

This is why I prefer to stick to 'I couldn't give a shit.' No confusion there

No. It is incorrect. Americans who know how to speak/read/write recognize it as wrong and will make fun of them behind their back. Teach it the correct way, the way that makes logical sense, and be done with it.

Or the more polite: "I'm sorry, you appear to be confusing me with someone who gives a f**k" ...

I save that one for when I want to be extra specially nice!

This analysis on World Wide Words is interesting.

The writer suggests that it may be a typical American "sarcastic inversion of apparent sense" with its possible roots in Yiddish phrases etc.;

"There’s a close link between the stress pattern of I could care less and the kind that appears in certain sarcastic or self-deprecatory phrases that are associated with the Yiddish heritage and (especially) New York Jewish speech. Perhaps the best known is I should be so lucky!, in which the real sense is often “I have no hope of being so lucky”, a closely similar stress pattern with the same sarcastic inversion of meaning. There’s no evidence to suggest that I could care less came directly from Yiddish, but the similarity is suggestive. There are other American expressions that have a similar sarcastic inversion of apparent sense, such as Tell me about it!, which usually means “Don’t tell me about it, because I know all about it already”. These may come from similar sources."

I figured it was probably just the first half of a phrase like:
"I could care less, but I don't"

That's similar to the one that irks the snot out of me: when speaking of an unusually cold person (usually a woman), it's said, "butter would melt in her mouth". Now, I know what they really mean is that she's so icy in her demeanor that even butter wouldn't melt in her mouth, but........

We use that phrase for someone who is 'too good to be true'.

My dear old Granny had that beaten with her classic, which I shall re-state for you now (To a person who made an extraordinary claim or the like):

"If you'd a square arsehole you'd shit bricks"