Range - David Epstein Page 0,37

2 pretzels.

Cheryl bought 1 bag of peanuts, 1 pretzel, and 1 milk shake.

What is the cost, in dollars, of 1 bag of peanuts? Show or explain how you got your answer.

What is the cost, in dollars, of 1 pretzel? Show or explain how you got your answer.

What is the total number of pretzels that can be bought for the cost of 1 milk shake? Show or explain how you got your answer.

For every problem like the first one, the simple formula “distance = rate × time” could be memorized and applied. The second problem requires the connection of multiple concepts that are then applied to a new situation. The teaching strategies that current teachers experienced when they were students are no longer good enough. Knowledge increasingly needs not merely to be durable, but also flexible—both sticky and capable of broad application.

Toward the end of the eighth-grade math class that I watched with Lindsey Richland, the students settled into a worksheet for what psychologists call “blocked” practice. That is, practicing the same thing repeatedly, each problem employing the same procedure. It leads to excellent immediate performance, but for knowledge to be flexible, it should be learned under varied conditions, an approach called varied or mixed practice, or, to researchers, “interleaving.”

Interleaving has been shown to improve inductive reasoning. When presented with different examples mixed together, students learn to create abstract generalizations that allow them to apply what they learned to material they have never encountered before. For example, say you plan to visit a museum and want to be able to identify the artist (Cézanne, Picasso, or Renoir) of paintings there that you have never seen. Before you go, instead of studying a stack of Cézanne flash cards, and then a stack of Picasso flash cards, and then a stack of Renoir, you should put the cards together and shuffle, so they will be interleaved. You will struggle more (and probably feel less confident) during practice, but be better equipped on museum day to discern each painter’s style, even for paintings that weren’t in the flash cards.

In a study using college math problems, students who learned in blocks—all examples of a particular type of problem at once—performed a lot worse come test time than students who studied the exact same problems but all mixed up. The blocked-practice students learned procedures for each type of problem through repetition. The mixed-practice students learned how to differentiate types of problems.

The same effect has appeared among learners studying everything from butterfly species identification to psychological-disorder diagnosis. In research on naval air defense simulations, individuals who engaged in highly mixed practice performed worse than blocked practicers during training, when they had to respond to potential threat scenarios that became familiar over the course of the training. At test time, everyone faced completely new scenarios, and the mixed-practice group destroyed the blocked-practice group.

And yet interleaving tends to fool learners about their own progress. In one of Kornell and Bjork’s interleaving studies, 80 percent of students were sure they had learned better with blocked than mixed practice, whereas 80 percent performed in a manner that proved the opposite. The feeling of learning, it turns out, is based on before-your-eyes progress, while deep learning is not. “When your intuition says block,” Kornell told me, “you should probably interleave.”

Interleaving is a desirable difficulty that frequently holds for both physical and mental skills. A simple motor-skill example is an experiment in which piano students were asked to learn to execute, in one-fifth of a second, a particular left-hand jump across fifteen keys. They were allowed 190 practice attempts. Some used all of those practicing the fifteen-key jump, while others switched between eight-, twelve-, fifteen-, and twenty-two-key jumps. When the piano students were invited back for a test, those who underwent the mixed practice were faster and more accurate at the fifteen-key jump than the students who had only practiced that exact jump. The “desirable difficulty” coiner himself, Robert Bjork, once commented on Shaquille O’Neal’s perpetual free-throw woes to say that instead of continuing to practice from the free-throw line, O’Neal should practice from a foot in front of and behind it to learn the motor modulation he needed.

Whether the task is mental or physical, interleaving improves the ability to match the right strategy to a problem. That happens to be a hallmark of expert problem solving. Whether chemists, physicists, or political scientists, the most successful problem solvers spend mental energy figuring out what type of problem they