1. With disapproval, mistrust, or suspicion. Scornfully. She looked askance at the fine print on the contract.
2. With a side glance. Sidewise. Obliquely. The writer looked askance at the wall clock as he finished the last paragraph.
Obsure origin, but first known use 1520-1530, previously a scanche, a scance, a scaunce.
I'm not sure I like this word. Seems like there are plenty of more attractive ways to get these ideas across.