The "impossible problem" thing rang a bell, and indeed I'd read about it in Stevenson and Stigler's book The Learning Gap (which is quite interesting). In it, they write:
We wanted to find out whether Asian students would in fact persevere longer than American students when given difficult problems. We planned to give children a mathematics problem that was impossible to solve, and see how long they would spend working on it before they gave up. Although the idea seemed reasonable, our Japanese colleagues convinced us to drop the task after they tried it out with several children. The difficulty? Japanese children, refusing to give up, kept working on the problem long beyond the time our colleagues felt they could justifiably allow the children to keep on trying.
So I think this isn't something we're likely to find in the published literature: it sounds as though they did a pilot for something that might have turned into a full study, and abandoned it as described.
On the next page of the book, they describe a different study that was carried out, though, in which American and Japanese children were asked to solve as many problems as possible in 20 mins. The American children attempted many more questions than the Japanese ones, but correctly solved a much lower proportion of them, getting a lower score overall.
As for what the impossible task could have been, I think if I were designing it, it might be something like this:
Find a number x (integer or fraction) such that x^2(x-3) = 3(x-1).
(Depending on the age of the children you might spell out the equation in terms of "the number multiplied by itself" etc. - provided the children can add and multiply fractions, they can attempt this, and provided they do not know enough algebra to have encountered or invented the rational zeroes theorem, they can't prove that there isn't one. They can get tantalisingly close, though, which might well keep them trying!)
The book I landed at when googling this, The Teaching and Learning of Mathematics at University Level: An ICMI Study
edited by Derek Holton, has a list of beliefs about mathematics that it says have been documented in American children, including:
Students who understand the subject matter can solve assigned mathematics problems in five minutes or less. Corollary: Students stop working on a problem after just a few minutes because, if they haven't solved it, they didn't understand the material (and therefore will not solve it). (Schoenfeld, 1988, p151)
This is key, I would suggest: it's not so much that the American children are lazy, more that they have simply never met the concept of a maths problem they can't solve quickly. The Schoenfeld reference supporting this is
Schoenfeld, A. H. (1988). When good teaching leads to bad results: the disasters of "well-taught" mathematics classes. Educational Psychologist 23(2) 145-166.
Which thanks to the wonders of google we can find
here. It looks to me like a must-read paper... but I have to get on with the day job now!
