Teaching someone a skill is not necessarily a difficult thing. Skills are concrete, task-like, discrete, and relatively well defined.
I have always tried to avoid teaching my students skills because it is my opinion that they need so much more than skill (although sadly they clamor for skills more than they clamor for background knowledge and understanding).
Instead, I try to help my students develop some degree of critical reasoning, problem solving ability, analytical capability, and appreciation. I believe that these attributes will carry them farther than will the mere acquisition of skills.
This is a stretch for many of my students - these demands take them places where they have not really been challenged before. As a result I notice that their confidence is dramatically decreased when they are taken beyond the stages of rote memorization. Because certitude is important I do not accept questions when I have asked them for answers. "Are you asking me or are you telling me?" are the most common words heard from me in the classroom.
I will never forget when my most quiet and passive student eeked out a hesitant and tentative response to a question asked of her... marked with the typical fading voice at the end of the statement, lack of eye contact, and raised intonation typically associated with a "is ______ the right answer...?" response.
Immediately, the class saw it coming as I rose and loudly questioned back, "I don't know; are you asking me or are you telling me?"
Then I heard something that I have not heard from her before. Right back at me she replied, "I think I am mentioning it. I'm not telling you, but I do think that I am mentioning it."
Stunned into silence, I nodded and accepted her response. This, I thought, is progress.