How to respond to a question when you don't know the answer.

What if I don't know the answer to a student’s question?

It’s curious that what students most fear is what teachers fear as well—not knowing. Our students hesitate when we turn from the board and say, “Any questions?” They don’t want to appear stupid, to let others know they still don’t understand.
Many graduate teaching fellows’ biggest fear in teaching for the first time is facing a question from a student that they are unable to answer. Some full professors have the same fear.

And yet not knowing is what learning is all about.
You might consider addressing this issue from the get go. Talk about a process your community of learners will use when a question arises that no one can answer. Talk about how exciting it is to discover a new area of learning. Talk about how a good learner approaches questions. Teach your students the skills of how to begin investigating what they don’t know, don’t understand, or cannot yet do. Where would you look? What resources are available to you? From what you do know, can you make an educated guess? Can you phone a friend?

Not knowing the answer to a student question once in a while is very different from not preparing well. You risk your credibility when you are poorly prepared and unable to facilitate the class well.

When you have prepared well and students are having a productive learning experience with you, they will accept that you don’t have answers for everything. They will appreciate your efforts to improve their skills in finding answers for themselves.

- University of Oregon Teaching Effectiveness Program