Here's something to think about:
When engaging someone in a discussion or debate, should you focus on their understanding of their own worldview, not the "correct" or "accepted" understanding of their worldview?
Greg Koukl (in his book Tactics) says to focus on the person's understanding. His reasoning is that focusing on another understanding (whether its "correct" or not- it makes no difference) will make the person believe that you are either ignoring their concern, or trying to belittle them by telling them how to believe what they believe.
Part of me wants to disagree for the simple reason that I think one should always focus on the understanding with the strongest evidence and arguments. I say this because it helps prevent committing the "straw man" fallacy (see my previous post "This Argument Is Full of Crap!"). For those who are unfamiliar with the "straw man", it is a misunderstanding of a view that is easy to argue against and tear down. The problem with it is that even though that understanding has been destroyed, the argument doesn't touch the true issue.
But, when I think about it a little further, I realize that the person (whom I'm attempting to persuade my direction) may have a "straw man" of his own worldview in his mind. If I were to attack another view (say, the "correct" view), I would be committing the "straw man" fallacy by not understanding his view and attacking that. So, by attacking the "correct" view, I would be committing the "straw man" fallacy on a "straw-man" view. (Confused yet?)
Simply put, I must agree with Koukl. Focus on the person's understanding. After you provide enough doubt to abandon the view, they may move closer to the "correct" view. As they move closer to the "correct" view, you can focus on the new understanding. Eventually, you will have placed enough doubt in them for all their understandings (including the "correct" one) that they will have no choice but to abandon the all understandings of that worldview. Now, that's not to say that they will jump on board with your view. If there is another possible worldview and they are committed against the worldview you are offering, expect them to adopt another alternative for a while and the process starts all over again. This may happen many times. If this is happening constantly with a specific person, see the future post "Can You Argue Someone Into The Kingdom?".
Of course, during this whole time, don't forget to provide positive evidence for your own point of view. See my previous post "Positive vs. Negative Arguments" for more on this. Many times, its difficult to tell if someone is searching for truth or if they are just searching for anything, that makes even the slightest bit of sense, except a specific worldview- especially since the person is not likely to admit the latter, and since we may misperceive the former as the latter.
Further resources:
Podcasts
Stand to Reason
Straight Thinking
Websites
Stand to Reason
Books
Tactics by Greg Koukl
Come, Let Us Reason by Norman Geisler