“Those who can, do. Those who can’t, teach. And those who can’t teach, teach teaching.”

WHOEVER coined that caustic aphorism should have been in a Harlem classroom last week where Bill Jackson was demonstrating an exception to the rule. Jackson, a 31-year classroom veteran, was teaching the mathematics of ratios to a group of inner-city seventh graders while 15 young teachers watched attentively. Starting with a recipe for steak sauce — three parts ketchup to two parts Worcestershire sauce — Jackson patiently coaxed his kids toward little math epiphanies, never dictating answers, leaving long silences for the children to fill. “Denzel, do you agree with Katelyn’s solution?” the teacher asked. And: “Can you explain to your friend why you think Kevin is right?” He rarely called on the first hand up, because that would let the other students off the hook. Sometimes the student summoned to the whiteboard was the kid who had gotten the wrong answer: the class pitched in to help her correct it, then gave her a round of applause.

After an hour the kids filed out and the teachers circled their desks for a debriefing. Despite his status as a master teacher, Jackson seemed as eager to hone his own craft as that of his colleagues. What worked? What missed the mark? Should we break this into two lessons? Did the kids get it? And what does that mean?

“Does ‘get it’ mean getting an answer?” Jackson asked. “Or does it mean really understanding what’s going on?”

At that point Deborah Kenny, the founder of the Harlem Village Academies charter schools, leaned over to me: “That right there, that is why we’re starting a graduate school.”