A "thinking man's" term. When the call is given, dancers must decide whether they are in the proper formation to do the movement being called. If so, they perform the movement. If not, they stand pat and hope for the best. For example: From facing lines of four with couples half sashayed. "Those Who Can Do a Right and Left Thru." (Only the center couples are properly arranged to do it).
This definition is from The Handbook of Modern Square Dancing by Jay King.
It is provided here for informational and educational purposes only.