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In traditional schooling, time is a constant and understanding is a variable. A fifth-grade class will spend a set number of days on prime factorization and then move on to study greatest common factors — whether or not every student is ready.

But there is another way to look at schooling — through the lens of a method called “mastery learning,” in which the student’s understanding of a subject is a constant and time is a variable; when each fifth grader masters prime factorization, for instance, he moves on to greatest common factors, each at his own pace.

Mastery learning is not a new idea. It was briefly popular in the 1920s, and was revived by Benjamin Bloom in his paper “Learning for Mastery” in 1968. It has shown dramatic success — compilations of studies can be found here and here.

One of the advantages of mastery learning is that the student, not the teacher, leads — and we know that people learn far better when they are actively involved. The teacher provides materials, tools and constant support. Students set their own goals and manage their own time.

In a traditional classroom, the teacher must aim the lecture at the middle, leaving the faster learners bored and the slower ones lost. Differentiation and personalization are big challenges. But the mastery system allows each student to learn at her own pace.

Mastery also rewards students for actual learning. A student cannot simply turn in a shoddy paper, take the D and move on. If she turns in shoddy work, she can’t move on. She has to keep trying until she demonstrates she fully understands.

Despite these advantages, mastery learning never caught on, mainly because it was a nightmare for teachers. One problem was how to do direct instruction; a teacher can’t give five different lectures in one class. The other was how to test students. Multiple versions of a test were needed so students couldn’t pass them to friends who would be taking them later.

But some teachers are now reviving mastery learning. What is making it feasible is the flipped classroom, a method I wrote about in my most recent column.