ponder on

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.
See also: on, ponder
References in classic literature ?
I like to ponder on all kinds of problems, though I can't solve 'em," said Captain Jim.
My mother would never suffer him to ponder on the subject if she could help it.