The Mathematics of Waiting

Always winter.  Never Christmas.  That’s how C.S. Lewis describes the reign of Narnia’s evil White Witch.  Not a bad metaphor to express the agony of expectation in the concrete language of childhood.  Mathematics offers another language for describing the torment of waiting.

Imagine you’re five.  You’ll spend one-sixth of your life waiting for your next birthday.  But the life percentage for a fifty-year old is much, much smaller.  Thus, grandparents bemoan the brevity of life while twelve-year olds can hardly wait to get a driver’s license.  This offers professors [frequently-untapped] leverage during class discussions.

“Who’s first?” you ask brightly.  You scan the room with hopeful eyes.  Surely a motivated junior in the second row will volunteer to present an idea from last night’s homework:  a Marxist deconstruction of Arrested Development.  But the room is silent.  Students look at their desks or their phones or their friends.  They look anywhere but in the teacher’s direction.  The seconds tick by.  One one thousand.  Two one thousand.  Three one thousand.

“Did anyone maybe have a quote from Lee Barron’s book?” you ask.  Perhaps alluding to an assigned reading from Social Theory in Popular Culture will grease the wheels of discussion.  But no one reaches for the life line you’ve tossed them.  One one thousand.  Two one thousand.  Three one thousand.

You turn your back on the class (they exhale) for the time it takes to write “Marx” on a whiteboard.  “Okay, Karl Marx was concerned that media might affirm… what?”  Now you write what you say aloud: “Class and Capitalism.”  You are devolving to first principles, but you have to fill the silence with something, don’t you?  An athlete near the back of the class half-remembers having heard the word “Capitalism” in last week’s lecture.  He flips half-heartedly through a notebook.  One one thousand.  Two one thousand.  Three one thousand.

The clock inside your head ticks its way to boredom.  Your course evaluation scores slide lower with every second.  “No volunteers?  Okay.”  The bile of panic rises.  Your strategy shifts from invitation to threat.  “Shall I… call on someone?”  You survey the herd.  You can pick off the weak at the perimeter, or choose a popular opinion leader, hoping the rest will follow.  One one thousand.  Two one thousand.  Three one thousand.

I keep counting to three as if that were standard practice.  But let’s face it:  three seconds is eternity.  When the concept of “wait time” was first quantified by Mary Budd Rowe in the early seventies, it rarely lasted more than 1.5 seconds.  Successive studies have watched it shrink to between 0.7 and 1.4 seconds.

Never fear.  This isn’t another diatribe against the Gen-Z attention span.  Instead, I’m thinking about the secret, mathematical weapon of age.  Three seconds might be uncomfortable for an 18-year old, but it’s an appreciably smaller percentage of a professor’s life.  Letting a well-formed question hang for a full three seconds produces measurable positive outcomes:

  • The length and correctness of student responses increases.
  • The number of “I don’t know” and no answer responses decreases.
  • The number of volunteered, appropriate answers by larger numbers of students greatly increases.
  • The scores of students on academic achievement tests tend to increase.

Developing this discipline of patience will also change your teaching style.  A three-second “think-time” (a preferred term suggested by educational researcher Robert J. Stahl) tends to

  • make questioning strategies more varied and flexible.
  • decrease the quantity while increasing the quality and variety of questions.
  • produce additional follow-up questions that require more complex information processing and higher-level thinking on the part of students.

So, raise a glass of an aged libation.  A toast to mature waiting.  To Us: the patient old folks in no hurry to teach well.

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