How to Build Deep Understanding and Stop Fooling Yourself

How does someone ace a hard physics course and then fail a test made of simple questions about the same subject?

In 1990, Eric Mazur had been teaching introductory physics at Harvard for seven years, and by every normal measure he was good at it. His lectures were clear and polished, his demonstrations worked, his students gave him high marks on their evaluations, and the class, mostly premed and engineering students, was solving complicated problems.

Then he came across a set of research papers by two physics education researchers, Ibrahim Halloun and David Hestenes. They had built a test called the Force Concept Inventory, and they’d found something that bothered them. After a few months of physics, most students could recite Newton’s third law and use it to solve number problems, but when the same idea was asked about in plain, everyday terms, a lot of them got it wrong.

The questions look almost too easy. Say a big truck and a small car crash head on. During the crash, which one pushes harder on the other? Newton’s third law says the forces are equal, and students who’d been through a semester of physics could tell you that law word for word. But the answer that feels right is the truck, because it’s bigger, and that’s the one a lot of students pick.

Mazur’s first reaction was that his students wouldn’t have that problem. These were Harvard students, picked through one of the toughest admissions processes in the country, and they’d been handling problems far harder than anything on this test. So he gave it to his class.

Before they even got going, one student raised her hand and asked whether she should answer “according to what you taught me, or how I usually think about these things.” It was the first sign something was wrong. When Mazur looked at the results, his students had done hardly better on this simple test than on his midterm, which covered material he’d considered much harder.

About two-thirds of the class still thought about motion the way people did before Newton. Aristotle taught that an object only keeps moving as long as something keeps pushing it, while Newton showed that a moving object keeps going on its own until a force stops it, and after a semester of Mazur’s physics, most of his students still believed Aristotle.

Mazur later described that moment as the time the house of cards collapsed. In his own telling, his students had been memorizing physics and solving problems by rote without ever really learning it. These were some of the best students in the country, so whatever separates people who barely understand from people who really get it, raw intelligence isn’t the whole answer.

That student had two sets of answers in her head. One set was for the class, the formulas and laws she could write down on an exam. The other set was what she actually believed about how things move, and nothing she’d learned in the class had ever changed it. She could pass every test Mazur gave her and walk out of the room still believing what she believed before she walked in.

You’ve probably got some of this too. You might have passed algebra in high school and still not be able to use it on a real problem today, or you might remember the main points of a business book you read last year without ever having used one of them when it counted. Even at work, plenty of people know a procedure by heart and couldn’t tell you why it’s done that way. So ask yourself how much of what you “know” would still be standing if someone asked it in a way you didn’t expect.

Why do the study habits most people rely on feel like they’re working when they aren’t?

Most people learn the same way they learned in school. You read the chapter, highlight the parts that look important, maybe write a summary, and then read it all again before the test. By the second or third time through, you recognize everything on the page, so you figure you’ve got it. Most of us have never had a better way to tell, so we go with it.

In 2013, a team of psychologists led by John Dunlosky of Kent State University went through the research on ten of the most common study techniques and rated how useful each one actually was. Two came out on top: practice testing, which means quizzing yourself or answering questions without looking, and distributed practice, which means spreading your studying out over days and weeks.

Five were rated low, and three of those five were habits most students say they rely on: highlighting, rereading, and summarizing. The review found that students lean heavily on rereading and highlighting, and that those habits don’t reliably improve how well students actually perform. Dunlosky said he was shocked at how little the most popular strategies helped.

So why do highlighting and rereading feel so productive? Two psychologists at Yale, Leonid Rozenblit and Frank Keil, found part of the answer in 2002. They asked people to rate, on a scale of 1 to 7, how well they understood how everyday things work, like zippers, flush toilets, speedometers, and piano keys. Then the researchers asked them to write out, step by step, exactly how each one worked.

After trying, people rated their own understanding lower. Rozenblit and Keil even warned some people ahead of time that they’d be asked to explain, and their ratings still dropped. They called it the illusion of explanatory depth:

Try it yourself right now. Picture a zipper and explain how it actually holds together. What do the teeth do when the slider moves up, and why can’t you just pull the two sides apart once it’s closed? You’ve used zippers your whole life, and if you’re anything like us, you got about two sentences in before you started guessing.

Rozenblit and Keil were testing everyday objects, so their study doesn’t measure studying directly. Our take is that the same thing happens when you reread a chapter. Every time you go back over it, the words start to look like something you already know, and from the inside, that feels exactly like understanding it.

Highlighting works the same way. If you’ve ever highlighted so much of a page that it would’ve been faster to highlight the parts you didn’t want, you already know that highlighting only marks what looks important, and it doesn’t tell you whether you could explain any of it.

When you reread or highlight, the book is open the whole time, so you’re never forced to come up with the idea on your own. Even a summary can be written while you’re looking right at the page. None of it shows you what you’d actually be able to do without the book in front of you.

So part of the reason some people study for years and still barely understand a subject is that the habits they rely on mostly make information easy to recognize. Practice testing works differently, because it makes you pull the answer out of your own head with nothing to look at, which shows you right away what you can’t do yet and gives you something to fix.

Flash cards are the version most people already know, and they count, as long as you actually answer before you flip the card. Being able to explain something from memory, and say why it works, is the first real test of whether you understand it.

How can someone know every definition in a subject and still not recognize it when it’s sitting right in front of them?

When Richard Feynman was a kid, another boy pointed at a bird and asked him what kind it was. Feynman had no idea. The boy told him it was a brown-throated thrush and said Feynman’s father didn’t teach him anything. Feynman thought it was the other way around. His father had already pointed at a bird with him, rattled off made-up names for it in a few different languages, and told him that you could learn its name in every language in the world and still know nothing about the bird itself.

You’d only know what people in different places called it. So instead, they watched what the bird was actually doing. Feynman later wrote that this was where he learned “the difference between knowing the name of something and knowing something.”

Decades later, he saw this play out in a classroom. In August 1951, Feynman took a sabbatical to teach at the Brazilian Center for Physics Research in Rio de Janeiro, and he stayed until June 1952. One of his courses was electricity and magnetism for students who were training to become teachers themselves. He found that he could ask the class a question and get the answer back instantly, but if he asked the same thing again worded a little differently, nobody could answer it.

When the class got to polarized light, he handed out strips of polarizing filter, the same kind of material that’s in polarized sunglasses, and asked how you could tell which direction light was polarized using just one piece of it. Nobody knew. He gave them a hint and told them to look at the light bouncing off the bay outside, and nobody said anything.

So he asked if they’d ever heard of Brewster’s Angle, and they answered right away, reciting that light reflected off a material like water at a certain angle comes off completely polarized, and even which direction it’s polarized in. Feynman then told them to look at the bay through the filter.

When they did, they were amazed to see that the light coming off the water was polarized, even though they’d just recited that fact to him. He had handed them the problem and told them exactly where to look, and the definition they’d memorized still didn’t connect to anything they could see. In his own telling, after looking into it more, he concluded they had memorized everything without understanding what any of it meant.

He saw the same thing in a lecture he sat in on. The professor talked about moments of inertia, which is the idea that weight placed farther from the point something turns on makes it harder to spin, without ever mentioning the most obvious example of it. A door with heavy weights on its outer edge is much harder to push open than the same door with the weights near the hinges. At the end of his stay, he stood in front of a room of students and professors and told them that, as far as he could see, no science was being taught in Brazil. People were passing exams and teaching others to pass exams, and nobody understood the physics.

Those students had learned physics the opposite way from how Feynman’s father taught him, with the names first and nothing after. This is one man’s account of one group of students more than seventy years ago, and it doesn’t tell us anything about Brazil today. So was this just a case of bad teaching, or does it happen to ordinary people too?

In 1980, two psychologists at the University of Michigan, Mary Gick and Keith Holyoak, ran an experiment that suggests it happens to ordinary people too. They gave people a medical problem. A patient has a tumor that has to be destroyed with rays, but a ray strong enough to kill the tumor will also kill all the healthy tissue it passes through on the way in, and a weak ray won’t do anything. Only about one in ten people solved it on their own, so if you’re stuck on it right now, you’re with most of the room.

Another group first read a story about a general who needed to capture a fortress. Every road leading to it was mined, so a whole army marching down one road would set off the mines, but small groups could pass safely. So he split his army up and sent small groups down every road at once, and they all arrived at the fortress together. The tumor problem has the same answer. You send a lot of weak rays from different directions at the same time. Each one is too weak to hurt the healthy tissue it passes through, but they all meet at the tumor, and that’s the one spot where their strength adds up. Even after reading the story, only about thirty percent of people made the connection. When people read the story and were told outright that it would help, about seventy-five percent solved it. Most of them had the answer in their heads the whole time and didn’t use it until someone pointed out where it applied.

Being able to explain something is one test of whether you understand it. This is a second one: when you’re handed a problem, can you actually use what you know to solve it? Feynman’s students and most of Gick and Holyoak’s subjects failed it even though they knew the answer. Our take is that knowledge stays attached to the place you learned it. If you learned a definition off a page to answer questions on a test, then it’s a page answer, and most of the time it won’t jump out at you in the real world on its own, even if you know it perfectly.

The British philosopher Alfred North Whitehead warned about this in 1916, in a talk called “The Aims of Education.” He called them inert ideas, meaning ideas you take into your head without ever using them, testing them, or combining them with anything new. Feynman never used Whitehead’s term, but his students in Rio were full of exactly what Whitehead was describing. The words still matter, since you can’t really think about polarized light without a name for it. Feynman’s father gave him the name too, after they’d watched the bird.

If you took two or three years of Spanish or French in school, you’ve lived this. You could conjugate verbs on a test, and then the first time someone actually spoke it to you at normal speed, or you tried to order food somewhere it’s spoken, almost none of it came out. You knew the language on paper and had never used it anywhere else. So pick a term from your own work that you could define right now, and ask yourself when you last actually saw it happen in your own life.

When something you’ve learned doesn’t work for you, how do you know whether the problem is you or what you were taught?

In May 1899, Wilbur Wright sent a letter from his bicycle shop in Dayton, Ohio, to the Smithsonian Institution asking for whatever it had published on flight. He and his younger brother Orville had been interested in flying since they were kids, and Wilbur wanted the Smithsonian to know he was serious. He described himself as “an enthusiast, but not a crank,” meaning he didn’t come with pet theories of his own about how a flying machine should be built.

The Smithsonian sent pamphlets that included work by Otto Lilienthal, the German glider pioneer, and Samuel Langley, who ran the Smithsonian, along with a reading list that included Octave Chanute’s history of flying machines. Wilbur sent back a dollar for Langley’s book.

In 1900 and again in 1901, the brothers took gliders to the sand dunes at Kitty Hawk, North Carolina, for the steady wind, and along with the gliders they brought instruments to measure wind speed and the angle of the wings. They wanted to compare what the glider actually did with what the math said it should do. Everyone at the time used the same formula to figure out how much lift a wing would make. It took the size of the wing, the speed of the wind, a number for how much lift that wing shape made at a given angle, which the brothers took from Lilienthal’s published tables, and a number called Smeaton’s coefficient.

That number came from John Smeaton, an 18th-century English engineer who’d worked it out while designing windmills, and people had been using it for almost 150 years. The brothers designed their 1901 glider with that formula, so in a 15 mile per hour wind, it should have been able to lift its own 100 pounds plus a 150-pound pilot. By their measurements, it made about a third of the lift the formula predicted.

On the train home to Dayton, Wilbur told Orville he didn’t think people would learn to fly in their lifetime. Orville later remembered him putting it even more strongly, that man wouldn’t fly for a thousand years. A few weeks later, Octave Chanute invited Wilbur to speak to the Western Society of Engineers in Chicago, and getting ready for that speech made him go back through everything they’d measured. Their numbers fit much better if Smeaton’s coefficient was about 0.0033 instead of the accepted 0.005. In the speech, Wilbur also told the room he thought Lilienthal’s tables were wrong.

So they tested it. First they mounted a bicycle wheel sideways on the front of a bicycle, attached a small curved wing and a flat plate to it, and rode it through the streets of Dayton to make their own wind. When that was too rough to give them reliable numbers, they built a wind tunnel in the bicycle shop. It was a long wooden box with a fan at one end, run off the same engine that powered their shop tools, and the scales inside that measured lift and drag were made from old hacksaw blades and bicycle spokes.

That fall, they tested around 200 small wing shapes and wrote the results down on scraps of wallpaper. By mid-December, they knew Smeaton’s number was wrong, and that Lilienthal’s tables, the ones Wilbur had called wrong in front of a room full of engineers, were mostly right. They had been made for Lilienthal’s wing shape, and the brothers had been using them on a different one.

They kept the formula and replaced the one number that was wrong. They designed the 1902 glider with their own data, and it made very close to the lift they predicted. They flew it almost a thousand times that fall, and on December 17, 1903, they flew a powered airplane at Kitty Hawk.

The brothers’ knowledge failed the applying test. The formula they’d learned didn’t predict what the real glider did, but that alone didn’t show them which part was wrong. Instead of trusting the formula and deciding they were bad at building gliders, or throwing the whole thing out and guessing, they went through it one assumption at a time and tested each one against what actually happened. That included Wilbur’s own doubt about Lilienthal, which turned out to be wrong.

Today, people call this first principles thinking. You find the assumptions behind an accepted explanation, test them against reality, and rebuild where the evidence says it’s wrong. The term goes back to Aristotle, who described a first principle as the first basis from which something is known. Most people have heard it from Elon Musk, who said in a 2012 interview that everyone assumed battery packs would always cost around $600 per kilowatt hour. He asked what the materials inside them would cost on the metals market and got roughly $80. The Wright brothers never called it first principles, and their work wasn’t the only reason they got off the ground, since their engine, their control system, and three seasons of practice as pilots mattered too.

The Wright brothers also put in the work before they doubted anyone. For every person who doubted the experts and turned out right, there were plenty who doubted and were just wrong, and the difference was the measuring. By the time the Wrights said Smeaton’s number was off, they had read what the field had published, flown their 1900 and 1901 gliders, and measured everything. If something you’ve learned doesn’t make sense to you yet, that’s usually a sign you need more of the basics, and it’s only worth questioning once your own careful evidence says it’s wrong.

Say you start the 50/30/20 budget everyone online swears by: half your income to needs, thirty percent to wants, twenty percent to savings. Three months in, it isn’t working. Before you decide budgeting doesn’t work or that you’re bad with money, check two things. Did you actually track your spending, or did you guess? And which one assumption in the method doesn’t fit your life? If rent alone takes forty-five percent of your paycheck in your city, the fifty percent for needs was never going to hold. The idea of the budget can still work for you with that one number changed.

If being smart isn’t the whole answer, what else separates people who really understand something from people who don’t?

Most people would say experts just know more. They’ve read more, done more problems, and seen more situations, so they have more to pull from when something comes up. Experts do know more, but in 1981, the psychologist Michelene Chi and her colleagues Paul Feltovich and Robert Glaser found a difference in how experts organize what they know.

They took 24 problems from an introductory physics textbook and gave them to two groups: eight students who had just finished a semester of mechanics, and eight advanced physics PhD students. Each person was asked to sort the problems into piles that would be solved the same way. Both groups made about the same number of piles, but they sorted the problems in completely different ways.

The beginners sorted by what the problems were about on the surface. Every problem with a block sliding down a ramp went in one pile, and every problem with a rope over a pulley went in another.

The PhD students sorted by the principle you’d need to solve the problem, like conservation of energy or Newton’s second law. A ramp problem and a spring problem could end up in the same pile, because both were about energy being converted from one form into another, even though one has a block on a slope and the other has a coiled spring.

The study has been cited thousands of times, but it hasn’t held up as cleanly as its reputation. In 2011, Andrew Mason and Chandralekha Singh gave a similar sorting task to introductory physics classes with more than a hundred students each, and they found a wide range of skill, with a lot of overlap between the best introductory students and the graduate students.

Another team found that how cleanly experts and beginners separate depends heavily on which problems you hand them, and part of Chi’s original set of problems has been lost. So the difference between seeing surface details and seeing principles is real, but beginners and experts aren’t two clean groups. It’s a skill people have in different amounts.

There’s also a limit to what the study can tell you. It shows how experts sort problems, but it doesn’t show that sorting by principle is what made them experts. They might sort that way because they’re already experts.

Gick and Holyoak, the same psychologists behind the tumor experiment, worked on that question in 1983. First they tried to help people pull the principle out of a single story. Some were asked to summarize the fortress story, some were given a written statement of the principle, and some were shown a diagram of it. None of it made much difference.

Then they gave people two stories that looked nothing alike but had the same solution, the general splitting up his army and a fire chief who put out a fire by spraying it from many hoses at once, and asked them to describe what the two had in common. In one version, roughly six in ten solved the tumor problem on their own, compared with about one in ten in their earlier study who’d read no story at all. The written statement of the principle and the diagram, which hadn’t helped people with one story, helped a lot when they were paired with two.

Researchers at Northwestern University found the same thing outside of lab puzzles. In a 1999 study, they taught business school students a negotiation strategy using two example cases. Some students compared the two cases and wrote down what they had in common, and others read the same two cases separately. When it came time to negotiate, the students who compared were nearly three times as likely to use the strategy. In a later study with negotiation teams, reading the cases separately was no better than getting no training at all.

Our take is that this is what’s going on with the people who seem to grasp a subject at a completely different level. They organize what they know around the principle underneath instead of what things look like, so when a new problem doesn’t match anything they’ve seen before, they still recognize it.

That’s what makes it possible to pass the applying test, using what you know on a problem you’re handed. And based on these studies, being told the principle mostly isn’t enough to get there. You have to find it yourself, and one way that works is to compare two examples that look different and work out what they share. You do need the basics first, since you can’t spot conservation of energy under two problems if you’ve never heard of it.

If you’ve ever worked in sales, you’ve seen this. A new salesperson hears “it’s too expensive,” “I need to think about it,” and “let me talk to my spouse” as three different problems, each with its own script. Someone experienced listens for the question underneath first, and a lot of the time it’s the same one: whether this is worth it. So the next time you learn something from an example, whether it’s a video, a case study, or a deal you worked, put a second one from a completely different situation next to it, and write down in one sentence what’s the same underneath.

If you really understand something, shouldn’t you be able to explain it?

Most people assume so, and figure that if you can’t put something into words, you don’t really get it. But some people make the right call over and over in situations where they couldn’t tell you why if you asked them in the moment.

Starting in the mid-1980s, the psychologist Gary Klein interviewed firefighters about how they make decisions under pressure. He found that the experienced commanders mostly didn’t line up their options and compare them, the way decision-making textbooks said they should. They looked at a situation, recognized it as something they’d seen before, and acted on the first plan that came to mind. One interview became the best-known example from his work.

A lieutenant led his crew into a house where the fire seemed to be in the kitchen at the back. They stood in the living room spraying water on it, and the fire barely changed. The lieutenant started to feel that something was wrong. He didn’t know what, but he ordered everyone out, and right after they cleared the building, the floor they had been standing on collapsed. The real source of the fire was in the basement directly under them, and the lieutenant hadn’t even known the house had a basement.

When Klein asked him how he knew to get out, the lieutenant said it was extrasensory perception, a sixth sense. He couldn’t explain it at the time. As Klein went back through the fire with him, the cues came out one by one. The water wasn’t knocking the fire down, the living room was much hotter than a small kitchen fire should have made it, and it was too quiet, because the floor was muffling the fire burning below.

The lieutenant wasn’t guessing, since the living room being too hot, the fire being too quiet, and the water not working were all right there in front of him, and he’d been to enough fires that his mind noticed they didn’t fit before he could say what was off. This is the third test of understanding, judging. When nobody tells you what the problem is, can you recognize what’s going on, make a call, and check afterward whether you were right? Nobody handed the lieutenant a question, and he had to notice on his own that something about the fire didn’t add up. He passed that test while failing the explaining test at the time, which is one reason to treat these as three separate abilities.

Chick sexing, which means sorting newborn chicks into males and females, might be the strangest example of this. [Yes I know, weird topic if you aren’t in the industry] Egg farms only want hens, so hatcheries need someone to do it, and at that age, males and females look almost identical. Professional sorters are known for doing it fast and nearly perfectly, with industry accounts putting them at around 98 percent accuracy and up to a thousand chicks an hour.

In Japan, the training school ran two-year courses, and many experts said they couldn’t explain what they were looking at, only that they looked at a chick and knew. In 1987, the psychologists Irving Biederman and Margaret Shiffrar studied the skill, worked out the small difference in shape the experts were picking up on, and gave beginners a short lesson on exactly where to look. The beginners got much closer to the experts’ level.

That might sound like it goes against what Gick and Holyoak found, where being handed the principle barely helped people. The difference is in what’s being taught. Telling someone exactly where to look works for anything you judge by seeing, hearing, or feeling.

An abstract idea is different, and people mostly need examples to compare before it sinks in. So if what you’re learning is something you judge by looking, ask an expert exactly what they look at. If it’s an idea, get examples and compare them.

None of this means your gut feeling is always right. In 2009, Klein wrote a paper with Daniel Kahneman, the psychologist who spent his career showing how gut judgments go wrong.

They set out to find where they disagreed and found they mostly didn’t. Their conclusion was that a gut feeling is worth trusting only in a field with reliable cues, and only for someone who’s had a lot of practice there with fast, honest feedback.

Firefighters and doctors can build that kind of judgment. People picking individual stocks or making long-range political predictions mostly can’t, because those fields don’t have reliable patterns to learn, no matter how long you practice. They also found that how confident someone feels says nothing about whether their gut is right. We hear about the lieutenant who pulled his crew out seconds before the floor gave way, and nobody retells the time someone pulled everyone out over a bad feeling and nothing happened.

You already have this kind of judgment somewhere. If you’ve been driving for years, you’ve probably hit the brakes before you consciously noticed the car drifting into your lane. You got thousands of hours of instant feedback to build that.

Now think about a gut feeling you had about someone after a twenty-minute job interview. You may never find out if you were right, and if you do, it’ll be months later, so there’s almost nothing for your gut to learn from. The next time you have a strong gut feeling at work, write the call down before you find out how it turns out, and check back later.

If smart students can ace a class and still hold the wrong ideas, what actually changes their minds?

Starting in 1991, Eric Mazur stopped lecturing straight through his classes. Every so often, he’d stop and put up a short question about the main idea he’d just covered, the same kind of plain, everyday question that had tripped up his students on the 1990 test. Every student had a minute or two to think it through alone and commit to an answer, at first by holding up a flash card and later by clicking a handheld device. Then he told them to turn to the person next to them and try to convince them they were right. After a few minutes of arguing, everyone answered the same question again, and only then did Mazur explain it. He called it Peer Instruction.

He kept giving his students the same concept test at the start and end of every semester, so he could see whether it was working. To measure progress, he used a number called the normalized gain. Say a student scores 60 out of 100 at the start of the semester. That leaves 40 points they could still pick up. If they score 80 by the end, they picked up 20 of those 40, so their gain is 0.5.

In his last semester of straight lecturing, his class averaged about 0.25, so his students closed about a quarter of the gap between what they knew and a perfect score. In his first semester of Peer Instruction, it was about 0.49. By the sixth time he taught that way, it was about 0.74. Those are Mazur’s own numbers from his own classes, so on their own they don’t prove much beyond Harvard.

There’s an obvious reason to be suspicious of the arguing part, too. When scores go up after students talk to each other, maybe the few who already knew the answer just talked everyone else into it.

In 2009, a team of researchers tested that in a college genetics course. After students discussed a question and answered it again, they got a second question on the same idea, written around a different situation, and answered it alone.

Students did better on the new question than they had on their first try at the original, and that held even in groups where nobody had the right answer to begin with. The arguing itself built understanding, so it wasn’t just the students who knew convincing the ones who didn’t.

In 2014, Scott Freeman’s team at the University of Washington checked whether this held up beyond one teacher. They combined 225 studies of college science, engineering, and math classes that compared straight lecturing with classes where students actively worked through problems, with Peer Instruction as one of many ways of doing that.

In the lecture classes, 33.8 percent of students failed, compared with 21.8 percent in the active classes, so lecture students were about 1.5 times as likely to fail. Active learning also raised scores on concept tests, the same kind of test Mazur gave in 1990, more than it raised scores on regular exams. Only 16 of those studies randomly assigned students to one kind of class or the other, but those showed the same results as the rest.

At Harvard in 2019, Louis Deslauriers and his colleagues in the physics department ran a test on 149 students in an introductory physics course. For two class meetings, they randomly split the students into two rooms. Each student sat through one class as a polished lecture from an experienced, highly rated instructor, and spent the other class working through problems in small groups, with the same handouts and the same two instructors teaching both ways.

After each class, the researchers tested how much the students had learned and asked how much they felt they’d learned. The students scored higher after the active classes and felt like they’d learned less. After the lectures, they felt like they’d learned more and had actually learned less.

The researchers concluded that the students took the extra effort of the active classes as a sign they weren’t learning. Robert Bjork, a psychologist at UCLA, had a name for this back in 1994. He called it desirable difficulties, meaning conditions that make learning feel slower and harder while it’s happening but make it last longer and carry over to new problems better.

Our take is that this is the other half of what made Mazur’s students so sure they understood physics. Listening to a clear lecture feels like learning because everything makes sense while you’re hearing it. Committing to an answer and then having someone push back on it feels awful, because it shows you right away what you don’t actually get. The effort behind that feeling is part of what makes it stick, which is what Bjork’s research found.

It only works if the question is hard enough to be worth arguing about and you know enough to have a real opinion, so this doesn’t replace learning the basics.

Think about the last class, video, or podcast that felt really clear and easy to follow, and ask yourself how much of it you could explain right now without looking. If you want to do what Mazur’s students did, find one person who’s learning the same thing as you. Both of you write down an answer before you talk, then argue it out until you agree or figure out exactly where you disagree. If there’s nobody around to argue with, write down the best case you can for a different answer than yours, and see if your own answer still holds up.

So what do you actually do, starting tomorrow, to understand something this deeply?

Most people think the answer is more hours. Read more, watch more, study longer, and eventually it’ll sink in. Mazur’s students and Feynman’s students in Rio had put in plenty of hours and still didn’t understand the basics of their subjects, because they’d spent those hours memorizing answers without ever testing whether they could use them.

The system below is ours. Every step comes from the research and stories you’ve already read, but nobody has tested these seven steps together as one package, so treat it as our best reading of the evidence, not a proven method.

To keep it concrete, we’ll run two examples through every step. One is learning to cook without a recipe, which is a skill you judge with your senses. The other is learning robotics, which is built on math and logic you can’t see or taste. Those are the two kinds of learning the chicken story and Gick and Holyoak showed us, and the system has to work for both.

Before you can reason about a subject, you need its foundations. In the preface to his 1968 textbook on educational psychology, David Ausubel summed this up in one line: “The most important single factor influencing learning is what the learner already knows.”

This step also tells you when doubting what you’ve been taught is worth it. The Wright brothers read the field and flew two seasons of gliders before they questioned anyone. If something doesn’t make sense to you yet, that usually means you’re missing a foundation, and it’s not time to question it yet.

In cooking, the foundations are physical. If you can’t cut an onion into even pieces, half of it burns while the other half stays raw, and you’ll blame the recipe for something your knife did. If you don’t know how hot your pan gets on medium, you can’t tell whether a dish failed because of the ingredients or because of the heat. Get those two things down before you try to improvise anything.

In robotics, the foundations are on paper. You need enough algebra and trigonometry to figure out where a robot arm ends up when its joints turn, enough programming to tell it what to do, and enough about circuits to understand why a motor stops when its battery drops. Someone who skips this and jumps straight into building usually ends up copying code they can’t fix when it breaks.

Every subject rests on a handful of principles, and everything else is those principles showing up in different forms. The way to find them is what the people in Gick and Holyoak’s study did when they got two stories instead of one, and what the business students did in the negotiation study: put two examples side by side that look nothing alike, and figure out what they have in common.

In cooking, the chef Samin Nosrat built her book Salt, Fat, Acid, Heat on the idea that good cooking comes down to managing four things. Salt brings out flavor, fat carries flavor and creates texture, acid balances flavor, and heat decides texture. A pot of chili that tastes flat and a tray of roasted vegetables that tastes heavy look like two different problems, but a lot of the time they can both be fixed the same way, with a squeeze of lime or a splash of vinegar. Once you see that, a recipe becomes one way of balancing those four things, and you can start making your own calls about what a dish needs.

In robotics, one of the core ideas is feedback control. A robot measures where it is, compares that to where it’s supposed to be, and corrects the difference, over and over, many times a second. A thermostat on your wall does the same thing with temperature, turning the heat on when the room gets too cold and off when it’s warm enough. A self-balancing robot does it with tilt, driving its wheels forward or back every time it starts to tip. One hangs on a wall and the other rolls around the floor, but they work on the same principle, and once you see it, you’ll start noticing it in cruise control, autopilot, and anything else that corrects itself.

This is the explaining test. Once you think you understand something, close the book and explain it from a blank page, then predict what will happen before you check. Do it again a few days later, because Dunlosky’s review found that spreading your studying out over time was one of the two most useful study habits, along with testing yourself.

A lot of people know this as the Feynman technique, explaining something in simple words until you find where you get stuck. Feynman never called it that. The name came from a writer named Scott Young in 2011, built on Feynman’s habits. The idea itself is a form of testing yourself, the other habit at the top of Dunlosky’s list.

In cooking, this means making the dish again a few days later without the recipe in front of you. Before you start, say out loud why each step is there. Why does the garlic go in after the onions and not before? If you can’t answer, that’s the gap, and it’s probably the step you’d get wrong.

In robotics, try explaining why a robot overshoots its target. When its correction is set too strong, it moves toward the target so fast that it passes it, then corrects back too hard and passes it the other way, and it ends up wobbling back and forth. Write that explanation out without looking anything up, then predict what will happen if you turn the correction down, and test it. If your prediction was wrong, your explanation was missing something.

This is the applying test. Take what you learned and use it on a problem that looks different from anything you studied, and look for it in your own life. That’s what Feynman’s students never did with Brewster’s Angle, and it’s why the answer sitting in Gick and Holyoak’s subjects’ heads stayed there.

In cooking, buy an ingredient you’ve never cooked, like a vegetable you’ve walked past at the store for years, and cook it without looking up a recipe. Use what you know about salt, fat, acid, and heat to decide what to do with it, then see how close you got.

In robotics, take the feedback idea you learned on a motor that holds a steady speed and use it to build a robot that follows a line on the floor. Nobody tells you it’s the same problem. You have to see that a sensor measuring how far the robot has drifted from the line is the same as a sensor measuring how far the motor has drifted from its speed.

This is the Wright brothers’ step, and it comes fifth on purpose. Only start questioning what you’ve been taught once the first four steps are in place, and only when your own careful evidence says something doesn’t fit. Then do what they did: find the one assumption that doesn’t match what you’re seeing, and test that one instead of throwing everything out.

In cooking, a recipe says to roast potatoes for 40 minutes at 425 degrees, and yours keep coming out pale. Before you decide the recipe is wrong or that you can’t cook, check which assumption doesn’t fit your kitchen. Maybe your oven runs cold, maybe your pan is crowded so the potatoes steam instead of browning, or maybe your potatoes are cut bigger than the recipe meant. An oven thermometer costs a few dollars and settles the first question in ten minutes.

In robotics, your line-following code works perfectly in a computer simulation, then drifts off course on a real floor. Engineers call this the sim-to-real gap, and it’s a well-known problem in robotics. The simulation made assumptions the real world doesn’t follow, like wheels that never slip or sensors that never give a noisy reading. Instead of rewriting the code, figure out which of those assumptions is wrong for your floor and your robot, and fix that.

Decide what you think the answer is first, then talk it through with someone who might see it differently, before either of you checks who’s right. That’s what Mazur’s students did, and it’s how the genetics students in the 2009 study did better on new questions, even in groups where nobody had the right answer at the start. It checks your explaining and your applying against another person who sees it differently.

In cooking, have someone taste what you made and ask them what they think it needs before you tell them what you were going for. If they say it tastes kind of flat and you thought it was perfect, talk it through, figure out together whether it needs more salt or a squeeze of lemon, and taste it again.

In robotics, explain your design to a teammate before you test it, and both of you write down whether you think it’ll work and why. If you disagree, argue it out before you run it, and when you test it, you’ll both find out which part of your thinking didn’t match what the robot actually did.

This is the judging test. Make your call before you find out the answer, write it down, and keep track of how often you’re right. Klein’s lieutenant built his judgment over years of fires with fast, honest feedback, and Kahneman and Klein found that’s the only kind of gut call worth trusting. Keeping score is how you find out whether your gut is getting there.

In cooking, before you take the first bite, guess what the dish needs. Then taste it and see if you were right. After a few months of doing this, you’ll know whether your guesses are getting better or staying about the same.

In robotics, watch the robot move and call what’s wrong before you look at the data. Something like “it’s correcting too hard” or “the left sensor is reading wrong.” Then check the data and see if you were right. Your record will tell you how much to trust your eye on the next robot.

Picking What’s Worth Going Deep On

Nobody can run this on everything, and you shouldn’t try. Go deep on the things you use all the time, the things a lot of other things rest on, and the things your important decisions depend on. For everything else, knowing it at the surface is fine, as long as you know that’s all you know.

Each of the three tests has its own signs.

• Explaining: you can come up with your own examples instead of repeating the book’s, and you can spot what’s wrong in someone else’s explanation.
• Applying: when a new problem comes up, you can tell which principle it’s really about, even when it looks nothing like what you studied.
• Judging: your predictions keep getting more accurate, and your written record shows it, so you aren’t just going by how sure you feel.

Most people don’t have hours a day to study, so here’s our suggestion for twenty minutes, which no study has tested: explain one thing from memory, use it on one new problem, and write down one prediction to check later. Save the full system for the few things you decide to go deep on.

Pick one thing you’d like to understand this deeply, whether it’s for your job, a skill you’ve been putting off, or something you’ve always wanted to figure out. This week, just do step one. Ask yourself what you’d need to know first for it to make sense, and start there.

Back in 1990, a student in Mazur’s class asked whether she should answer his test the way he’d taught her or the way she usually thought about these things. She had two sets of answers, one for the class and one for what she actually believed, and nothing in the class had ever made them meet.

When you understand something deeply, you don’t have two sets of answers anymore. What you were taught and what you actually believe have turned into one, so the answer you’d give on a test is the same one you’d act on in real life.