Traditionally, educators and psychologists in the U.S. were not fans of allowing students to flounder. B.F. Skinner, the hugely influential 20th century behavioral psychologist, didn’t even like his lab rats and pigeons to err and constructed experiments to shape their behavior toward always getting the task right. “He thought if they made a mistake, the mistake would get entrenched, and you’d have to backtrack to erase it,” explains Janet Metcalfe, a professor of psychology at Columbia University, and the author of an impressive scientific review titled “Learning from Errors,” published earlier this year in Annual Review of Psychology.

American educators, perhaps influenced by Skinner, have tended to see things the same way. Classic studies by psychologists James Stigler of UCLA and the late Harold Stevenson, detailed in their 1994 book The Learning Gap, compared videotaped lessons in eighth-grade math in several countries. They found that American teachers emphasized specific procedures for solving problems, largely ignored errors and praised correct answers. Japanese teachers, by contrast, asked students to find their own way through problems and then led a discussion of common errors, why they might seem plausible and why they were wrong. Praise was rarely given and students were meant to see struggle and setbacks as part of learning. The difference, the authors believed, is one reason that Japanese students outperform Americans in math.

“Learning about what is wrong may hasten understanding of why the correct procedures are appropriate,” they wrote, “but errors may also be interpreted as failure. And Americans … strive to avoid situations where this might happen.”

'Being in this environment where we are openly discussing mistakes, where mistakes are good, really opened the door for certain kids who had math phobias.' Kushal Patel, teacher, Columbia Secondary School for School for Math, Science and Engineering, New York City

The American allergy to errors began to ease with a burst of new studies by cognitive psychologists beginning this century. They showed clear benefits to engaging with mistakes—in both verbal and math tasks. For instance, Nate Kornell of Williams College conducted a word-pair experiment in which people were cued with a word (say, tree) and then asked to pair it a related “target” word (say, oak). He found that they remembered the target word significantly better if they had made a wrong guess (like maple or pine) and were corrected than if they were simply given the correct pairing and asked to memorize it.

Numerous other studies have confirmed and expanded upon this finding. Metcalfe and others have shown that on tests involving general knowledge (What’s the capital of Australia?), a wild guess doesn’t help with learning. “They have to be making a serious stab at the answer,” she notes. And it was Metcalfe and colleagues who showed that the more certain you are of your wrong answer, the better you will learn the right one after being corrected.

Why is this? The answer isn’t completely clear but it likely involves the fact that making an error rallies your attention — and even more so if you’re surprised that you got it wrong. In addition, it is easier to learn something new after you’ve summoned up your prior knowledge — a process neuroscientists call memory reconsolidation.

There’s hard, biological evidence for some of this. By placing electroencephalogram caps on subjects as they play video games or do other tasks, scientists have identified specific signals in the brain linked to making errors. The first one, known as Error-Related Negativity or ERN, occurs just 50 millionths of a second after the error. That’s well before you are even conscious of the mistake! A second wave, called error positivity (Pe for short), comes 50 to 550 milliseconds later and is believed to reflect conscious attention to the error, usually followed by an effort to avoid repeating it.

As an undergrad at Michigan State, Hans Schroder became so obsessed with error-related brain signaling that, he recalls, “I actually ‘married’ it on Facebook.” He also did serious work on the subject in psychologist Jason Moser’s lab there. Past research had shown that these signals relate to academic performance.

“The ERN tends to correlate with grade-point average. It’s linked with the ability to recognize when things don’t go as expected and to better working memory,” Schroder explains. “The Pe is more linked to effort, becoming aware of mistakes and rebounding.” While both signals emanate from a brain region called the anterior cingulate, the Pe involves more widespread activity as you allocate mental resources to improve your performance.

'By taking the grade off their test I thought they might spend more time looking at what they got right and what they got wrong. I wanted to refocus them on actually learning the content.' Leah Alcala, math teacher in Berkeley, Calif.

Schroder was especially interested in this effort-related activity and wanted to know if it was linked to a person’s attitude or mindset about his or her own ability. Stanford University psychologist Carol Dweck kicked off a wave of research in education and psychology with her work — and popular 2006 book, Mindset— defining two distinct “mindsets”: the belief that one’s intelligence is fixed or that it is fluid and can grow with effort. People with a fixed mindset (as measured on a standard questionnaire) tend to see errors as signs that they are not good at something. Those with a growth mindset see them as signs they need to work harder.

Schroder theorized that people with a growth mindset would have a stronger Pe signal following an error. This proved to be true in studies with both children and adults. Just as important, growth-minded people raised their game more in the wake of an error. For instance, he reports, growth-minded children playing a videogame in which they had to round up escaped zoo animals “were more accurate after making a mistake than kids who were fixed-minded.”

How do these psych lab results translate to the messier world of the classroom? A number of researchers are attempting to answer that question with studies that more closely mimic educational situations or by conducting research within schools.

Carnegie Mellon psychologist Robert Siegler, an expert on how children learn math, has delved deeply into the best way to give feedback on student errors. He has shown, for instance, that asking third and fourth graders to explain how someone got the wrong answer and also how someone got the right answer is enormously effective – more so than just asking the child to explain the correct procedure, as teachers so often do. Dislodging wrong ideas is important, he notes: “These wrong approaches are like crab grass, they are hard to get rid of and often have deep roots. You really have to undermine the roots of the misconception as well as strengthen the correct conception.”

Metcalfe is exploring that approach in an experiment with eighth-grade math teachers at the Columbia Secondary School for Math, Science and Engineering — a New York City public school affiliated with Columbia University. For the past two years, her team has been monitoring what happens to performance on the state’s Common Core Regents algebra test when teachers give frequent practice quizzes followed each time by a review of the students’ specific errors, in a continuous cycle four days a week for four weeks prior to the statewide exam.

The results, which have not yet been published, seem promising. “We had a 100% pass rate on the Algebra 1 Regents for eighth grade, which was pretty awesome,” says Kushal Patel, a participating teacher. Patel notes that even though the passing grade for special education students is 55 rather than the typical 65, all of the special ed students passed with the higher grade. Performance across the class was even stronger the second year than the first. Metcalfe’s team is now analyzing videos of class sessions second by second, looking at exactly what teachers did and how it relates to the errors individual children made. Preliminary results suggest that the improvement in performance was closely tied to the error-focused feedback.

“Being in this environment where we are openly discussing mistakes, where mistakes are good, really opened the door for certain kids who had math phobias,” Patel observes.

And in keeping with a growth mindset, students began to see errors as a path to learning rather than humiliation. When he shared students’ errors anonymously with the class, he says, “the kids got really good about saying ‘Hey, that’s my mistake! Let me talk about what I did wrong.’ It was incredible. They got past the shy moment of, ‘Oh, I screwed up.’”

Next year Metcalfe will be testing a new system for reviewing errors that combines computerized feedback with teacher-led instruction.

In Berkeley, Calif., math teacher Leah Alcala witnessed a similar change in middle school and high school students when she began spotlighting what she calls her “favorite errors.” Alcala likes to hand out test results without grades but with highlights indicating the precise spots in a math problem where things took a wrong turn.

“By taking the grade off their test I thought they might spend more time looking at what they got right and what they got wrong,” she explains. “I wanted to refocus them on actually learning the content.” You can see her method in an online Teaching Channel video.

Like Patel, Alcala says she was influenced by Dweck’s mindset framework. While not everyone in her economically and ethnically diverse classes masters all the math, “what I know for sure is that my kids never give up on my class.”

Such robust examples of teaching kids how to learn from their errors remain the exception in U.S. classrooms. Probably the biggest reason, Siegler suggests, is that “the people who write the textbooks don’t know about the research findings. There’s a lot of knowledge in the psychology of learning that hasn’t been incorporated into education.” Also, he notes, there’s a “common sense wisdom” to focusing almost exclusively on correct procedures. It’s what American teachers have always done.

And it’s what most of us believe in, the evidence be damned. Metcalfe has found that people are generally unaware of the benefits of bumping up against mistakes. This is true even after they participate in studies in which, again and again, they improve their performance after getting something wrong and being set straight. When asked if they did better in trials where they were given the answer or those in which they erred and were corrected, they chose the former.

“Isn’t that amazing!” she says of this metacognitive blind spot. No wonder so many educators err when it comes to errors. “If teachers don’t realize that making errors will help learning, they will be like Skinner and say ‘I’ll just teach them the right thing.’ ”