What's the point of reading a blog if you can't apply what you find?
Application is the subject of the third question: When does it make the most sense to ask divergent questions?
As a facilitator, I probably ask too many divergent questions, just because I like to get people thinking and generating ideas. But as a teacher (and a manager of the time of others) I see two distinctly appropriate "times": early in a process, and any time you are stuck.
Early in the process
This use is almost too obvious, and there are just too many benefits to do anything else.
-Ask a divergent question to generate fresh ideas: "What are some of the ways that we could drive additional revenue?"
-Ask a divergent question to get the juices flowing: "If you had unlimited resources, what kinds of things might you do to attack this problem?"
-Ask a divergent question to get people involved in whatever you are trying to accomplish: "What do you think might make a difference?"
Nothing you can do as a leader has a potentially more positive impact than asking a divergent question to open a dialogue (or a "multi-logue"). So start the process with a divergent question, carry out whatever process you have in mind, and go to closure by asking a convergent question.
For re-starts or re-groups: When you get stuck
Your conversation (or meeting, or class, or negotiation) has gone awry. You have hit an impasse, or an obstacle, but you are not ready to give up. You need to clear the air. Or you need to change the subject. Ask a divergent question: "If you were not sitting in this room working through this, where might you have been today?" Or, if you are the more serious type: "What are some of the ways you can imagine that we might come to an agreement?"
So finally, 4 posts later, that's the core I have to offer on divergent and convergent questioning. What do you think?