Calling on whomever you choose regardless of whether the student’s hand is up brings up several critical benefits to your classroom.
First, it allows you to check for understanding effectively and systematically. It’s critical to be able to check what any student’s level of understanding is at any time, regardless of whether he or she is offering to tell you. In fact, it’s most important when he or she is not offering to tell you.
Second, cold calling increases speed in both the terms of your pacing (the illusion of speed) and the rate at which you can cover material (real speed). Your pacing is a critical factor in how students engage in your classroom.
Third, cold calling allows you to distribute work more broadly around the room and signal to students not only that they are likely to be called on to participate, and therefore that they should engage in the work of the classroom, but that you want to know what they have to say.