"I'm not saying that the kids using it "should" know ... and the negative make up a small and interesting class."
"It happened in my lifetime also, since according Mark Israel's AUE FAQ, the variant "'Could care less', which is used ... care less'), developed in the U.S. around 1960." I don't remember noticing the transformation, however. The quote is from http://alt-usage-english.org/excerpts/fxcouldc.html"
Time to update the FAQ... last year I found a 1955 citation on Proquest:
This Morning . . . With Shirley Povich
The Washington Post, Sep 25, 1955, pg. C1
The National League clubs have always shied from pitching left-handers against the Dodgers, but Casey Stengel could care less about the Dodgers' reputation for beating southpaws.
OED2's earliest cite for "couldn't care less" is from 1946 ( I Couldn't Care Less , a book by Anthony Phelps of the British Air Transport Auxiliary). With the Chicago Tribune now available on Proquest, that can be pushed back to 1944, in a short story by the British mystery writer Christianna Brand:
'Danger List' by Christianna Brand
Chicago Daily Tribune, May 15, 1944, p. 18
"I couldn't care less, darling," said Frederica who, being on duty in the ward, could not go to the party.
And here's an interesting pre-idiomatic version, also found in a short story serialized in the Chicago Tribune:
'The Wrong Man' by May Edgington
Chicago Daily Tribune, Jun 11, 1934, p. 18
It was Benjamin who saw Cara off on the train in the morning. And he was wishing that he could care less, that he couldn't care at all.