The high school band problem experiment is an instance of Chinese Remainder Theorem [1]. I didn't actually read the cited study, but from the summary given in

The high school band problem experiment is an instance of Chinese Remainder Theorem [1]. I didn't actually read the cited study, but from the summary given in this article, I thought that experiment was poorly conducted. The subjects weren't encouraged to engage with the material on all levels. The instructions might lead many subjects to focus on grammar and style rather than mathematical content. I would have told the subjects that one of the four example problems has a numerical error and they have a half hour or so to find it and write a paragraph explaining the issue, when in reality none of the example problems had an error. [1] http://en.wikipedia.org/wiki/Chinese_remainder_theorem http://en.wikipedia.org/wiki/Chinese_remainder_theorem