ponder on (something)
To give great consideration to something; to ruminate or think about something very deeply. We sat pondering on various ways to improve our business model when Janet suddenly came up with a brilliant idea. Well, you're review has certainly given me plenty to ponder on.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
ponder (up)on something
to think on something; to consider something. (Upon is formal and less commonly used than on.) Ponder upon this awhile. See what you come up with. I need to ponder on this.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.