Yet at the end of the term, on a surprise test, the students solved 72 percent of the problems that they’d studied in mixed sets, compared with 38 percent of those in blocked, homework-as-usual sets. The problems and teachers were the same, and the classes were taught as usual. The only change was in the homework.

In the jargon of the field, this strategy of mixed problem-sets is called interleaving. It is distinct from the end-of-unit reviews that teachers commonly give, because it’s self-guided and continual. It mimics a test in a crucial way, in that it forces students to distinguish between types of problems and decide which strategy is appropriate.

The beauty of broadening testing beyond basic assessment is that the approach can be applied at home, easily, for students of all ages. Most young children squirm through their homework, but many love to play teacher. By cutting short “study time” and asking them to be the teacher, parents can make the session more fun, more interactive and a richer learning experience. Teaching is self-testing of an especially potent kind.

Ditto for making an outline of a chapter (with the book closed), or discussing the material with a friend or roommate. One reason scientists suspect that studying in pairs or groups can be helpful is that students are forced to talk to one another about the material — or better yet, argue about it. These are all forms of self-examination, and as such deepen learning more than passively rereading or reviewing the material.

The brain is an exotic learning machine, to put it mildly. It does not take orders well. You can tell it to remember the major players in the settling of Manhattan, stress how crucially important that is, and on the test a week later very little comes back. And yet you might remember nearly every play in the San Francisco Giants’ Game 7 World Series victory. Why? Because the brain doesn’t listen to what you say; it watches what you do. And thinking often about Madison Bumgarner pitching, talking about the game, arguing about it: These are mental actions, as well as subtle forms of testing knowledge.

Testing in all its permutations, subtle and otherwise, convinces the brain that the knowledge is useful, and important. And by varying one’s testing strategies, the actual final exam — the dreaded assessment — isn’t nearly as scary.