scratch one's head

To show that one is puzzled, doubtful, or uncertain; to show that one has trouble understanding something. Literally scratching one's head can indicate the same thing. His decision to pull the plug on the lucrative program has everyone scratching their heads.

Express puzzlement or perplexity, think hard, as in They scratched their heads over this vexing question, but no one knew the answer. Although literally scratching one's head may simply betoken the fact that it itches, it also may indicate mental mystification or bewilderment. The term's figurative use dates from the first half of the 1900s.