Convergent vs. Divergent

Yesterday afternoon, we began the first part of a two part training on Questioning Strategies with our district Director of Advanced Academics Todd Kettler.  To say the least, the frequency and depth of a teacher's questioning during instruction can have a great effect on student learning!  A couple of stats to think about-

• 40% of our instructional time is spent questioning.
• 75-80% of questioning in elementary is at the memory/recall level.

We then began a discussion on Convergent vs. Divergent questioning.  Todd described Convergent questioning as generally having one possible response (doesn't stimulate critical thinking, not very engaging, designed to check for understanding).  Divergent questioning, on the other hand, allows teachers to check for understanding while at the same time promoting critical thinking AND stimulating student-generated questions.  Of course, Divergent questioning is what we should strive for, but more often than not we focus on the knowledge-based Convergent questioning.  This sparked a great question from one of our teachers-

     If students aren't successful with the Convergent questions (that is, if they can't correctly answer the recall/memory/low-level questions), is it instructionally appropriate to move on to more critical, deeper Divergent questions?

That's a tough question to answer!  Thoughts?  If you agree that it is appropriate, how do you asked those higher-level questions without that basic knowledge?  Hopefully, these are some questions that we'll be able to pursue when we meet again.