Silence is golden, some say.  But when silence replaces class discussion, it doesn’t feel so golden! When that dreaded, long silence appears in your class, what do you do? Fear? Panic? How do we work ourselves out of that terrible black hole?

Maybe your students need to discuss how “(all polynomials of degree-2) is a single vector space”. Puzzling, right!?!  Or maybe your kiddos need to think about a story: its characters and their actions. We need to hear and guide our students’ thoughts. But what if the students say nothing?

Where do we start? Are there tools we can employ to excite the intellectual energy of our students and direct it toward the lesson at hand? Is there a way to engage every student? The answer is a resounding yes.  The answer is the five common topics.