I know some people would rather play RPGs as if they’re a skirmish version of Warhammer 40K (and I respect their right to do that if it’s fun for them) but I’m not one of them.
If it were a practical option to pull all the character sheets and rulebooks off the table and keep them behind a screen, and communicate with the players without referencing any stats, then believe me I’d be playing like that.
Practically however, that isn’t a viable option.
As it is, I encourage players to try and put the rules out of their head when they decide what their characters are doing, and base their actions on narrative value first and *then* use the rules to calculate the actual result. Use the rules to calculate how the story turns out, don’t sit and treat it like a boardgame where you base your decisions on what result the rules say they’ll give you.
Update: This line of thought is continued (to some degree) in my short study of Story, Rules, and Realism so I’m going to lock this post to comments and redirect you there.