One notable early finding, Ms. Phillips said, is that teachers who incessantly drill their students to prepare for standardized tests tend to have lower value-added learning gains than those who simply work their way methodically through the key concepts of literacy and mathematics. Teachers whose students agreed with the statement, “We spend a lot of time in this class practicing for the state test,” tended to make smaller gains on those exams than other teachers. “Teaching to the test makes your students do worse on the tests,” Ms. Phillips said. “It turns out all that ‘drill and kill’ isn’t helpful.”

To date, education research shows that good teachers matter a lot, class size may be less important than once thought and nothing improves student performance as much as one-on-one human tutoring.

The potential benefits of technology are greater as students become older, more independent learners. Making that point, Mr. Gates said in an interview that for children from kindergarten to about fifth grade “the idea that you stick them in front of a computer is ludicrous.”