connive

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Merriam-Webster's Crossword Puzzle Dictionary, Third Edition.
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The Word of the Day for December 31 is:

connive   \kuh-NYVE\   verb
    *1 : to pretend ignorance of or fail to take action against something one 
ought to oppose
     2 a : to be indulgent or in secret sympathy : wink  b : to cooperate 
secretly or have a secret understanding
     3 : conspire, intrigue 

Example sentence:
     Did the professor connive at the cheating that was going on during the 
exam, or was he unaware that it was happening?

Did you know?
     "Connive" may not seem like a troublesome term, but it was to Wilson 
Follett, a usage critic who lamented that the word "was undone during the 
Second World War, when restless spirits felt the need of a new synonym for 
plotting, bribing, spying, conspiring, engineering a coup, preparing a secret 
attack." Follett thought "connive" should only mean "to wink at" or "to pretend 
ignorance." Those senses are closer to the Latin ancestor of the word 
("connive" comes from the Latin "connivere," which means "to close the eyes" 
and which is descended from "-nivere," a form akin to the Latin verb "nictare," 
meaning "to wink"). But many English speakers disagreed, and the "conspire" 
sense is now the word's most widely used meaning.