Questioning assumptions is one aspect of mathematical endeavour that is useful in other areas of society to improve or understand why things are the way they are, or change to how they might be. Having faith in logic and one's conclusions is also useful, and is often used in diagnosing problems and finding what are root causes of certain situations, or solutions to certain problems.
Another aspect which may be omnipresent outside of mathematics and which mathematicians and others alike would do well to use is multiple perspective. Being able to process several views of a situation often leads to an increase in understanding, an abillity to modify, and possibly achieve an outcome which is desired in many of the viewpoints.
And, of course, trying to communicate well the particular sequence of ideas requires a well-timed orchestration of abstraction, generalization, specialization, and shifting of viewpoints. However, it might be even better to relate such information by telling a story ("You mean my English literature class applies to real life?").
Gerhard "Yes, It Really Does Apply" Paseman, 2011.09.06