One of the most enduring conclusions from the new science of learning is the idea that people gain more if they mix up their practice. Researcher after researcher argues that people shouldn’t repeat a skill during a learning or training session. “The ultimate crime is practicing the same thing multiple times in a row,” psychologist Nate Kornell told me. “Avoid it like the plague.”
But despite a library’s worth of findings on the value of a mixed up approach, the strategy hasn’t taken hold. My daughter regularly comes up with math worksheets that use a blocked strategy (e.g. 7*6, 7*3, 7*8) instead of a mixed one (e.g. 7*6, 2*9, 5*3). Or I’ll come across a pianist who spends an entire afternoon just working on their Brahams. Even LeBron James isn’t immune, and instead of mixing up his practice and shooting a three-pointer and then a foul shot and then a hook shot, the basketball mega-star will work on the same shot multiple times in a row.
Psychologist Robert Goldstone introduced me to the power of a mixed up approach to learning in a pretty embarrassing way. One of the nation’s most esteemed cognitive psychologists, Goldstone is tall and bald with a wry smile. We met up in a Starbucks in downtown Washington a few years ago.
“You seem like a smart guy,” Goldstone said after we’d been talking for a bit. “Can I put you on the spot?”
“Sure,” I said, nervously fingering my notepad.
Goldstone then presented me with a version of this problem:
An aging king plans to divide his kingdom among his daughters. Each country within the kingdom will be assigned to one of his daughters. (It is possible for multiple countries to be assigned to the same daughter.) In how many different ways can the countries be assigned, if there are five countries and seven daughters?
I scribbled some of the key points on a piece of paper: “Does the answer have something to do with factorials?”
Goldstone shook his head. “Can I give you a hint?” he said. “If the king gives Germany to one daughter. He can still give France to the same daughter.”
I nodded but still struggled, and eventually Goldstone just explained the solution: “If there are seven options, or daughters, for each of the 5 things, or kingdoms, that need to be assigned to an option, there would be 7 X 7 X 7 X 7 X 7.”
Goldstone explained that the problem hinged on a math concept known as sampling with replacement. Typically taught in middle school, the concept boiled down to the formula: “The number of options raised to the power of the number of selections.”
So why did I get the “aging king” problem wrong? Well, the answer goes back to a mixed up approach to practice, and as we sat in the coffee shop, Goldstone argued that I did not develop the correct answer because I had been distracted by the superficial elements of a problem. Instead of thinking about the underlying concept (sampling with replacement), I had been focused on the surface details (like the lands and the daughters).
For Goldstone, this idea explains why a mixed up approach to practice is so important. Whether we’re learning how to knit or deep sea dive, a mixed up approach helps us see past the surface details and gain a richer understanding, and when people see multiple examples with different details, they’re far more likely to develop important insights into a skill or area of knowledge.
Psychologists sometimes call the practice “interleaving” or “jumbling,” and a wealth of research provides support for the approach. In one study from the 1990s, some young women learned to fire off foul shots. Some practiced only foul shots. Others took more of a mixed up approach—they practiced foul shots as well as eight and fifteen footers.
The results were remarkable: The mixed-shot group performed much better, with a much deeper sense of the underlying skill. The same is true in academic fields, from memory tests to problem solving skills: By mixing up practice, people develop a better sense of the underlying ideas, and they’ll sometimes post outcomes as much as 40% higher than those using a blocked approach.
Or take a look at this problem that also comes from Goldstone’s work:
A homeowner is going to repaint several rooms in her house. She chooses one color of paint for the living room, one for the dining room, one for the family room, and so on. (It is possible for multiple rooms to be painted the same color or for a color never to be used.) In how many different ways can she paint the rooms, if there are 8 rooms and 3 colors?
Now, unless you’ve had some experience in sampling with replacement, it’s not totally clear that the problem is also getting at the issue of sampling with replacement. But as Goldstone has shown, when people engage in additional problems with different features that revolve around sampling with replacement, they’re far more likely to understand the underlying concept of sampling with replacement.
One of the benefits of a mixed up approach to learning is that it pushes us to pay attention. It requires more focus. If you repeatedly read articles about the Trump administration, the reading can become robotic and monotonous. So, instead, read an article about Trump and then one about Obama and then one about Reagan and then return to Trump. The varied texts will do more to keep your attention, and so you’ll gain more in the end.
Sometimes people will take a jumbled up approach learning on their own. In skiing, for instance, someone might try to gain experience in different environments—twisty mountains, mogul-filled hills—along with different snow conditions, from powder to icy. In woodworking, people will try different tools and practice on various sorts of wood, oak, pine, fir.
But people don’t typically vary their practice—or examples—nearly enough. To spot deep connections, to really develop expertise, we need a lot of examples within the same field. In Goldstone’s experiments, for instance, people only really learned the deeper structure after doing at least a half-dozen sampling with replacement problems.
To develop expertise, we also need to mix up practice in a very direct way. The contrast needs to be immediate in order to be noticeable. In the skiing example, it’s not enough to ski a powdery slope one year and an icy hill the next year. The benefits of a more jumbled approach to learning comes from having the experience directly after each other. So, find an icy hill to shoot down right after skiing the powdery one.
Psychologist Brian Ross takes this idea one step further. He recommends that people be explicit when they’re facing a muddle of surface features, and in his research, Ross has found that people solve problems a lot more easily if they write the name of the concept—or deep structure—next to the problem. So if someone comes across a question like this:
A skateboarder enters a curved ramp moving pretty quickly, flying along at about a speed of 6.5 miles per second. Then the skateboarder leaves the ramp in a jump, slowing down slightly to 4 miles per second. The skateboarder, and the skateboard have a combined mass of 55 kilograms. What’s the height of the ramp?
They should write down the key concept alongside of the problem. In this case, something along the lines of: the total mechanical energy is the same in the first and final state. Or, if I come across another problem featuring a monarch with seven daughters and five lands, I should write down sampling with replacement. It will help me focus on the problem—and take a more mixed up approach.