Though the interleaved homework took longer at first, most of the students adjusted. “I usually need a lot of time to study for tests,” said Marigny Duga, who was a student in Mr. Paul’s class, “but doing this mixed homework, I felt like, when the test was coming I needed less time than usual, because everything was still pretty fresh in my head.”

Over nine weeks, each student in the study got 10 assignments with 12 problems each. Same students, same problems. But each student got half a semester of mixed homework, and half a semester of blocked.

Two weeks after the last homework assignment, the researchers gave a surprise cumulative test.

The results were striking. Students scored 72 percent, on average, on the interleaved material. They scored 38 percent on the homework-as-usual problems. This is a large difference, but it’s not unheard of in laboratory studies of interleaved practice, experts said.

Psychologists are not sure why mixed problem sets can improve learning. One possibility is that studying mixed platters of items makes a student ask, first, “What kind of problem am I looking at?” rather than blindly applying a single procedure to every problem in the assignment.

“Contrast this to a typical homework assignment, which might say ‘The Quadratic Formula’ right there at the top of the page,” Dr. Rohrer said. “They know what strategy to use before they read the problem.”

Another possible explanation is that interleaving reinforces the brain’s associations between specific types of problems (say, calculating slope) and a matching solution strategy (dividing the vertical change by the horizontal change, or “rise over run”). The problem and the solving strategy become a linked pair.

Can these kinds of results hold up across school districts and over time?

It is far too early to know, experts said. “You have to think of the classrooms as single units, so it’s a sample size of eight, which is small,” said Daniel T. Willingham, a psychologist at the University of Virginia. “The effect of interleaving is exceptionally robust in the lab, in terms of aiding memory, and there is certainly nothing to object to in this particular study.