Passing Grades Can Hide the Gaps That Break Math Later

Educator Salman Khan was describing what happens after a math exam to show why capable students with good teachers stumble later in algebra and calculus.

Even a student who scores 95 percent, he noted, may have missed one small thing. He asked what that absent 5 percent was. Maybe, he offered, the student never grasped what happens when a number is raised to the zeroth power. Then, as Khan put it, "the class moves on to the next topic."

Each new concept builds on the last, so those small unknowns accumulate. Khan likened the result to Swiss cheese, with holes running through the foundation.

To show how strange that grading bargain looks outside school, he turned to learning to ride a bicycle. As Khan put it, "I give you a bicycle for two weeks," then return to judge you. You wobble on left turns and cannot quite stop, and you are told, in his words, "You're an 80 percent bicyclist." You get a C and are handed a unicycle.

That sequence, he said, is "that's exactly what's happening in our classrooms right now."

The fix is to treat math like riding, by persisting, in his words, "as long as necessary, until you have mastery." In his framing, conventional schooling punishes missteps yet lets learners advance without full command, while his approach welcomes missteps yet insists on full command before moving ahead.