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© Jo Boaler 2019

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DEDICATION

I dedicate these pages to the people I interviewed for the book who opened their hearts and shared their journeys—I could not have written this book without you. I also dedicate this book to my two amazing daughters. Thank you for being you, Jaime and Ariane.

CONTENTS

Cover

Title Page

Copyright

Dedication

INTRODUCTION The Six Keys

CHAPTER 1 How Neuroplasticity Changes … Everything

CHAPTER 2 Why We Should Love Mistakes, Struggle, and Even Failure

CHAPTER 3 Changing Your Mind, Changing Your Reality

CHAPTER 4 The Connected Brain

CHAPTER 5 Why Speed Is Out and Flexibility Is In!

CHAPTER 6 A Limitless Approach to Collaboration

CONCLUSION Living Without Limits

Acknowledgments

Resources to Help Change Mindsets and Approaches

Appendix I: Examples of Numerical and Visual Approaches to Math Problems

Appendix II: A Sample Rubric

Notes

Credits and Permissions

Index of Searchable Terms

Also by Jo Boaler

About the Publisher

INTRODUCTION

THE SIX KEYS

IT WAS A SUNNY DAY and I stopped to appreciate the sunlight playing on the columns of the San Diego museum as I walked into my presentation. A flutter of nerves passed through me as I climbed the steps of the auditorium, ready to share the latest science on the ways we learn to a room packed with medical professionals. I speak regularly in front of teachers and parents but was uncertain how a different audience would relate to my latest discoveries. Would my ideas fall flat?

I needn’t have worried. The response from the group of medical professionals was the same as that of the many students and educators I regularly work with. Most were surprised, some were shocked, and all could immediately see the crucial connections of these ideas to their work and lives. Several even started to see themselves in a new light. Sara—an occupational therapist—rushed up to me afterward to tell me how she dropped out of a math major many years ago when the work got difficult and she felt as if she didn’t belong. She recalled an experience of being held back by damaging and incorrect beliefs about her ability. She believed, as most people do, that there were limits to what she could do.

But what if the opposite is true, and we can all learn anything? What if the possibilities to change our expertise, to develop in new directions, to form different identities as people are actually endless and continue throughout our lives? What if we wake up every day of our lives with a changed brain? This book will share evidence that our brains—and our lives—are highly adaptable, and that when people fully embrace this knowledge and change their approach to their lives and their learning, incredible outcomes result.

Almost every day I meet people who believe damaging ideas about themselves and their learning, and they come from all ages, genders, jobs, and walks of life. Typically people will tell me that they used to like math, art, English, or another subject area, but when they started to struggle, they decided they did not have the right brain for the work and gave up. When people give up on math, they also give up on all math-related subjects, such as science, medicine, and technology. Similarly, when people get the idea they cannot be a writer, they give up on all subjects in the humanities, and when people decide they are not artistic, they give up on painting, sculpture, and other aspects of the fine arts.

Every year millions of children start school excited about all they will learn, but quickly become disillusioned when they get the idea they are not as “smart” as others. Adults decide not to follow pathways they had hoped to pursue because they decide they are not good enough for them, or they are not as “smart” as other people. Thousands of employees enter meetings in the workplace anxious that they will be found out, and exposed for not “knowing enough.” These limiting and damaging ideas come from inside us, but they are usually sparked by incorrect messages sent by other people, and by institutions of education. I have met so many children and adults whose lives were limited by incorrect ideas that I decided it was time to write a book dispelling the damaging myths holding people back on a daily basis; it was time to offer a different approach to life and to learning.

A large number of people are told directly that they are not a “math person” or an “English person” or an “artist” by teachers or parents. In an attempt to be helpful, adults tell young learners that a particular subject is “just not for them.” This happens to some when they are children. For others, it happens later in life when they are taking college courses or interviewing for their first job. Some people are given negative messages about their potential directly; others assume it from culturally embedded ideas—that some people can achieve and some cannot.

When we learn the new science in this book and the six keys of learning I will present, our brains function differently, and we change as people. The six keys not only change people’s beliefs about their reality, they change their reality. This is because as we begin to realize our potential, we unlock parts of ourselves that had been held back and start to live without limiting beliefs; we become able to meet the small and large challenges we are faced with in life and turn them into achievements. The implications of the new science are important for everyone. For teachers, leaders, and learners, the changed possibilities created by this new information are far reaching.

I am a Stanford professor of education who has spent the last few years collaborating with brain scientists, adding their knowledge of neuroscience to my knowledge of education and learning. I regularly share the new knowledge that is in this book, and invite people to think differently about problems, and it changes the way they think about themselves. I have spent the last several years focusing on mathematics, the subject with the most damaging ideas held by teachers, students, and parents. The idea that math ability (and a host of other capabilities) is fixed is a large part of the reason that math anxiety is widespread in the US and the world. Many children grow up thinking that either you can do math or you can’t. When they struggle, they assume they can’t. From that point on, any struggle is a further reminder of their perceived inadequacies. This affects millions of people. One study found that 48 percent of all young adults in a work-apprentice program had math anxiety;¹ other studies have found that approximately 50 percent of students taking introductory math courses in college suffer from math anxiety.² It is difficult to know how many people walk around in society harboring damaging ideas about their math ability, but I estimate it to be at least half of the population.

Researchers now know that when people with math anxiety encounter numbers, a fear center in the brain is activated—the same fear center that lights up when people see snakes or spiders.³ As the fear center of the brain becomes activated, activity in the problem-solving centers of the brain is diminished. It is no wonder that so many people underachieve in mathematics—as soon as people become anxious about it, their brains are compromised. Anxiety in any subject area has a negative impact on the functioning of the brain. It is critical that we change the messages that are given to learners about their ability and rid education and homes of anxiety-inducing teaching practices.

We are not born with fixed abilities, and those who achieve at the highest levels do not do so because of their genetics.⁴ The myth that our brains are fixed and that we simply don’t have the aptitude for certain topics is not only scientifically inaccurate; it is omnipresent and negatively impacts education and many other events in our everyday lives. When we let go of the idea that our brains are fixed, stop believing that our genetics determine our lives’ pathways, and learn that our brains are incredibly adaptable, it is liberating. The knowledge that every time we learn something our brains change and reorganize comes from perhaps the most important research of this decade—research on brain plasticity, also known as neuroplasticity.⁵ I will be sharing the most compelling evidence on this topic in the next chapter.

When I make the point with adults—often teachers and educators—that we should reject ideas of fixed thinking and instead see all learners as capable, these adults invariably tell me about themselves as learners. Almost all of them can recall their own experience and realize the ways in which they themselves were limited and held back. We have all been fully immersed in the damaging myth that some are smart—they have a gift or special intelligence—and some are not, and these ideas have shaped our lives.

We now know that ideas about limits to potential or intelligence are incorrect. Unfortunately, they are persistent and widespread in many cultures across the world. The good news is that when we challenge these beliefs, incredible results follow. In this book, we will upend these ingrained and dangerous self-limiting beliefs and reveal the opportunities that open up when we adopt a limitless approach. The limitless approach starts with knowledge from neuroscience and expands into a different approach to ideas and to life.

The original discovery of neuroplasticity is decades old, and the groundbreaking studies that have shown brain growth and change—among children and adults—are well established.⁶ The science, however, has for the most part not made its way into classrooms, boardrooms, or homes. It has also not been translated into the much-needed ideas for learning that this book will share. Fortunately, a few pioneers who have learned about brain change have taken it upon themselves to spread the news. Anders Ericsson, a Swedish-born psychologist, is one of those people. He first became aware of the brain’s incredible ability to grow and change not from the neuroscience that was emerging at the time, but from an experiment he tried with a young athlete, a runner named Steve.⁷

Ericsson set out to study the limits of people’s ability to memorize a random string of digits. A study published in 1929 found that people could improve their ability to memorize. The early researchers managed to train one person to memorize thirteen random digits and another person, fifteen. Ericsson was curious to know how people improved, so he recruited Steve, whom he describes as an average Carnegie Mellon undergraduate. On the first day that Steve began working with the researchers to memorize digits, his performance was exactly average: he could remember seven numbers consistently, sometimes eight. On the following four days, Steve improved to just under nine numbers.

Then something remarkable happened. Steve and the researchers thought he had reached his limit, but he managed to push through the “ceiling” and memorize ten numbers, two more than had seemed possible. Ericsson describes this as the beginning of what became the two most surprising years of his career. Steve continued to steadily improve until he had successfully memorized and could recall a string of eighty-two random digits. Needless to say, this feat was remarkable, and it was no magic trick. This was an “average” college student unlocking his learning potential to accomplish a rare and impressive feat.

A few years later, Ericsson and his team tried the same experiment with a different participant. Renee started off much like Steve, improving her memory beyond the level of an untrained person, and she learned to memorize close to twenty digits. Then, however, she stopped improving, and after another fifty hours of training without improvement, she dropped out of the study. This set Ericsson and his team on a new quest—to work out why Steve had managed to memorize so many more digits than Renee.

This is where Ericsson began to learn more about what he called “deliberate practice.” He realized that Steve’s love for running had made him highly competitive and motivated. Whenever he hit what seemed like a limit, he developed new strategies to become successful. For example, he hit a barrier at twenty-four digits, so he developed a new strategy of grouping numbers into four four-digit strings. At regular intervals, Steve developed new strategies.

This approach illustrates a key takeaway—when you hit a barrier, it is advantageous to develop a new approach and come at the problem from a new perspective. Despite how logical this sounds, far too many of us fail to make adjustments in our thinking when we run into those barriers. We often decide, instead, that we cannot overcome them. Ericsson has studied human performance in many fields and concludes: “It is surprisingly rare to get clear evidence in any field that a person has reached some immutable limit on performance. Instead, I’ve found that people more often just give up and stop trying to improve.”⁸

For the skeptics reading this—and deciding that Steve’s incredible memory feat meant that he was in some way exceptional or gifted—there’s more. Ericsson repeated the experiment with another runner named Dario. Dario memorized even more than Steve—more than one hundred numbers. Those who study remarkable feats performed by seemingly ordinary people find that none of the people have a genetic advantage; instead, they put in a lot of effort and practice. Not only are ideas of genetic ability misguided; they are dangerous. And yet many of our school systems are built on a model of fixed-ability thinking—limiting potential and preventing students from incredible achievement.

The six keys of learning I will share in this book create opportunities for people to excel in the learning of different subjects, but they also empower them to approach life in a different way. They allow people to access parts of themselves that were previously unavailable. Before the journey I will set out in this book, I had believed that learning about brain science and the limitless approach would change how educators approached the teaching and learning of school subjects. Through the interviews I have conducted for this book—with sixty-two people from six different countries, people of different ages, jobs, and life circumstances—I discovered the limitless approach means much more than that.

A woman who has done an enormous amount to change people’s ideas about what they can do is a colleague of mine at Stanford, Carol Dweck. Dweck’s research reveals that how we think about our talents and abilities has a profound impact on our potential.⁹ Some people have what she has termed a “growth mindset.” They believe, as they should, that they can learn anything. Others have a damaging “fixed mindset.” They believe that their intelligence is more or less fixed, and although they can learn new things, they cannot change their basic intelligence. These beliefs, she has shown through decades of research, change the scope of what we can learn—and how we live our lives.

One of the important studies Dweck and her colleagues conducted took place in mathematics classes at Columbia University.¹⁰ The researchers found stereotyping to be alive and well: young women were being given the message that they did not belong in the discipline. They also found that the message hit home only with those who had a fixed mindset. When students with a fixed mindset heard the message that math was not for women, they dropped out. Those with a growth mindset, however, protected by the belief that anyone can learn anything, were able to reject the stereotypical messages and keep going.

Throughout this book, you will learn about the importance of positive self-beliefs and ways to develop them. You will also learn about the importance of communicating positive beliefs to yourself and others, whether you are a teacher, parent, friend, or manager.

One study conducted by a group of social psychologists dramatically showed the impact of positive communication by teachers.¹¹ The study focused on students in high-school English classes, all of whom had written an essay. All of the students received critical, diagnostic feedback (the good kind) from their teachers, but half of the students received an extra sentence at the end of the feedback. Remarkably, the students who received the extra sentence—especially students of color—achieved at significantly higher levels in school a year later, with higher GPAs (grade point averages). So what was the sentence that those students read at the end of the feedback that caused such a dramatic result? It simply said: “I am giving you this feedback because I believe in you.”

When I tell teachers about this research, I do so to show the importance of teachers’ words and messages—not to suggest that they put this message at the end of every student evaluation! One teacher in a workshop raised her hand and said, “Does that mean I don’t put it on a stamp?” Everyone laughed.

Studies in brain science present a very clear case for the importance of self-beliefs and the role of teachers and parents in influencing them. Yet we are living in a society where the widespread message we receive through the media on a daily basis is one of fixed intelligence and giftedness.

One of the ways children—even those as young as three—develop a damaging fixed mindset is from a small, seemingly innocuous word that is used ubiquitously. The word is “smart.” Parents regularly praise their children by telling them how smart they are in order to build up their self-confidence. We now know that when we praise children for being smart, they at first think, “Oh good, I am smart,” but then later when they struggle, fail, or mess up in some way, as everyone does, they think, “Oh, I am not so smart”; they end up constantly evaluating themselves against this fixed idea. It is fine to praise children, but always praise what they did and not them as people. Here are some alternatives for use in situations where you may feel the need to use the word “smart.”

Fixed Praise | Growth Praise
You can divide fractions? Wow, you are smart! | You can divide fractions? That is great that you have learned how to do that.
You solved that tricky problem like that? That is so smart! | I loved your solution to the problem; it is so creative.
You have a degree in science? You are a genius! | You have a degree in science? You must have worked really hard.

I teach an undergraduate class at Stanford called “How to Learn Math” to some of the most highly achieving students in the country. They too are vulnerable to damaging beliefs. Most have been told, over many years, that they are smart, but even that “positive” message—“you are smart”—damages students. The reason it makes them vulnerable is that if they believe they are “smart” but then struggle with some difficult work, that feeling of struggle is devastating. It causes them to feel they are not smart after all and give up or drop out.

Regardless of your experience with the fixed-brain myth, the information in these pages will change your understanding of ways to raise your and other people’s potential. Taking a limitless perspective is about more than a change in our thinking. It is about our being, our essence, who we are. If you live a day with this new perspective, you will know it, especially if it is a day when something bad happens, you fail at something, or you make a serious mistake. When you are limitless, you feel and appreciate such moments, but you can also move past them and even learn new and important things because of them.

George Adair lived in Atlanta after the Civil War. Originally a newspaper publisher and cotton speculator, he went on to become a highly successful real-estate developer. His success was probably spurred by an important insight that has since been widely shared: “Everything you’ve ever wanted is on the other side of fear.” Let’s think together now about ways to become limitless and move to the other side of negative beliefs and fear.

1

HOW NEUROPLASTICITY CHANGES … EVERYTHING

THE SIX KEYS all have the potential to unlock different aspects of people. The first key, however, is perhaps the most critical and the most overlooked. It originates from the neuroscience of brain plasticity. Although aspects of the evidence may be familiar to certain readers, many practices in schools, colleges, and businesses are based upon ideas that are the opposite of those I will share. The result of fixed-brain thinking is that we have a nation (and world) filled with underachieving people who have been limited by ideas that could and should be changed.

LEARNING KEY #1

Every time we learn, our brains form, strengthen, or connect neural pathways. We need to replace the idea that learning ability is fixed, with the recognition that we are all on a growth journey.

Nestled in a part of California that has been described as “a piece of Tuscany transplanted into North America” is the villa that is the home of one of the world’s leading neuroscientists—Michael Merzenich. It was Merzenich who stumbled upon one of the greatest scientific discoveries of our time—by accident.¹ In the 1970s, he and his team had been using the newest technologies to map out the brains of monkeys. They were making what he called “mind maps,” maps of the working brain. It was exciting, cutting-edge work. The scientists hoped that the results of their studies would send ripples through the scientific community. But what Merzenich and his team discovered did not send ripples; it sent crashing waves that would go on to change people’s lives profoundly.²

The team successfully made mind maps of the monkeys’ brains and then set the maps aside to continue on with other aspects of their work. When they returned to the mind maps, they realized the monkey’s brain networks, which they had sketched out in the mind maps, had changed. Merzenich himself reflected: “What we saw was absolutely astounding. I couldn’t understand it.”³ Eventually the scientists drew the only possible conclusion they could—the brains of the monkeys were changing and they were changing quickly. This was the birth of what came to be known as neuroplasticity.

When Merzenich published his findings, he received pushback from other scientists. Many simply would not accept an idea they had been so certain was wrong. Some scientists had believed that brains were fixed from birth, and others that brains became fixed by the time people became adults. The evidence that adult brains were changing every day seemed inconceivable. Now, two decades later, even those who were the most vehemently opposed to the evidence from neuroplasticity research have conceded.

Unfortunately our schools, colleges, businesses, and culture have, for hundreds of years, been built around the idea that some people can and some people can’t. This is why putting young students into different groups and teaching them differently made perfect sense. If individuals within a school or company weren’t reaching their potential, it was not due to teaching methods or environmental factors, but to their limited brains. But now, with decades of knowledge about brain plasticity, it is time that we eradicate this damaging myth about learning and potential.

Energized by the new evidence showing brain plasticity in animals, researchers began to look at the potential of human brains to change. One of the most compelling studies of the time came from London, the city where I had my first teaching and university job. London is one of the most vibrant cities in the world—and it is always filled with millions of residents and visitors. On any day in London you will see “black cabs” zipping around the thousands of major thruways, streets, and lanes. The drivers of these iconic taxicabs hold themselves to very high professional standards. Londoners know that if they get in a black cab and tell the driver a road to find, and the driver does not know it, the driver should be reported to black-cab authorities.

Knowing all the roads in London is quite a feat—and drivers go to huge lengths to learn them. In order to become a black-cab driver, you need to study for at least four years. The most recent cab driver I traveled with told me he had studied for seven years. During this time drivers must memorize every one of the twenty-five thousand streets and twenty thousand landmarks within a six-mile radius of the centrally located Charing Cross station—and every connection between them. This is not a task that can be accomplished through blind memorization—the drivers drive the roads, experiencing the streets, landmarks, and connections, so they can remember them. At the end of the training period, the drivers take a test that is aptly named “The Knowledge.” On average, people have to take the test twelve times in order to pass it.

The extent and focus of the deep training needed by black-cab drivers caught the attention of brain scientists, who decided to study the brains of the black-cab drivers before and after the training. Their research found that, after the intense spatial training, the hippocampus of the cab drivers’ brains had grown significantly.⁴ This study was significant for many reasons. First, the study was conducted with adults of a range of ages, all of whom showed significant brain growth and change. Second, the area of the brain that grew—the hippocampus—is important for all forms of spatial and mathematical thinking. Researchers also found that when black-cab drivers retired from cab driving, the hippocampus shrank back down again—not from age, but from lack of use.⁵ This degree of plasticity of the brain, the amount of change, shocked the scientific world. Brains were literally growing new connections and pathways as the adults studied and learned, and when the pathways were no longer needed, they faded away.

These discoveries began in the early 2000s. At around the same time, the medical world was stumbling upon its own revelations in the realm of neuroplasticity. A nine-year-old girl, Cameron Mott, was suffering from a rare condition that gave her life-threatening seizures. Doctors decided to perform a revolutionary operation, removing the entire left hemisphere of her brain. They expected Cameron to be paralyzed for many years or possibly life, as the brain controls physical movement. After the surgery, they were absolutely stunned when she started moving in unexpected ways. The only conclusion they could draw was that the right side of the brain was developing the new connections it needed to perform the functions of the left side of the brain,⁶ and the growth happened at a faster rate than doctors had ever thought possible.

Since then, other children have had half of their brains removed. Christina Santhouse was eight when she had the operation—performed by neurosurgeon Ben Carson, who later would run for president. Christina went on to make the honor roll at her high school, graduate from college, and go on to achieve a master’s degree. She is now a speech pathologist.

We have multiple forms of evidence, from neuroscience and from medicine, that brains are in a constant state of growth and change. Every single day when we wake up in the morning, our brains are different than they were the day before. In the next chapters you will learn ways to maximize brain growth and connectivity throughout your life.

A few years ago we invited eighty-three middle-school students to the Stanford campus for an eighteen-day math camp. They were typical students as far as their achievement levels and beliefs went. On the first day each of the eighty-three students told interviewers that he or she was “not a math person.” When asked, they all named the one student in their class whom they believed to be a “math person.” Unsurprisingly, it was usually the student who was quickest to answer questions.

We spent our time with the children working to change their damaging beliefs. All students had taken a math test in their district before coming to us. We gave them the same test eighteen days later at the end of our camp. The students had improved by an average of 50 percent per student, the equivalent of 2.8 years of school. These were incredible results and further evidence of the brain’s learning potential when given the right messages and forms of teaching.

When the teachers and I were working to dispel the negative beliefs the students held, we showed them images of Cameron’s brain, with only one hemisphere, and told them about the operation she underwent to have half of her brain removed. We also described her recovery and how the growth of the other hemisphere had shocked doctors. Hearing about Cameron inspired our middle-school students. As they worked over the next two weeks, I often heard them say to each other, “If that girl with half a brain can do it, I know I can do it!”

So many people harbor the damaging idea that their brain is not suited to math, science, art, English, or any other particular area. When they find a subject difficult, instead of strengthening brain areas to make study possible, they decide they were not born with the right brain. Nobody, however, is born with the brain they need for a particular subject. Everyone has to develop the neural pathways they need.

Researchers now know that when we learn something, we grow the brain in three ways. The first is that a new pathway is formed. Initially the pathway is delicate and fine, but the more deeply you learn an idea, the stronger the pathway becomes. The second is that a pathway that is already there is strengthened, and the third is that a connection is formed between two previously unconnected pathways.

These three forms of brain growth occur when we learn, and the processes by which the pathways are formed and strengthened allow us to succeed in our mathematical, historical, scientific, artistic, musical, and other endeavors. We are not born with these pathways; they develop as we learn—and the more we struggle, the better the learning and brain growth, as later chapters will show. In fact, our brain structure changes with every different activity we perform, perfecting circuits so they are better suited to tasks at hand.⁷

The Fixed-Brain Message

Let’s imagine how transformative this knowledge can be for the millions of children and adults who have decided they cannot learn something—and for the teachers and managers who see people struggle or fail, and decide they will never succeed. So many of us believe or were told by teachers that we were incapable of learning in a particular area. Teachers don’t impart this idea to be cruel; they see their role as providing guidance on what students should or shouldn’t pursue or study.

Others give this message to be comforting. “Don’t worry if math isn’t your thing” is, tragically, a common refrain heard by girls. Other students receive this message through faulty and outdated teaching measures, such as the separation of young children into ability groups or an emphasis on speed in learning. Whether it is through the educational system or in conversations directly with educators, far too many of us have been conditioned to believe that we don’t have the capacity to learn. Once people get this terrible idea in their heads, their learning and cognitive processes change.

Jennifer Brich is the mathematics lab director at California State University San Marcos. She lectures in mathematics as well as directing the center. Jennifer works hard to dispel the damaging beliefs that her students hold about mathematics and their brains, one of very few university-level mathematics teachers doing so. Jennifer used to think that “people were born with certain talents, and you were restricted to those talents.” But then she read the research on brain growth and change. Now Jennifer teaches the research on brain growth not only to her own students, but also to graduate students who teach other classes. Teaching the new science can be difficult, and Jennifer tells me that she gets a lot of pushback from people who want to believe that some people are born with math potential and others just don’t have it.

A few months ago, she was sitting in her office going through emails when she heard the sound of sobbing coming from the office next door. Jennifer describes paying attention to the sound and then hearing the professor say: “It’s okay. You’re a female. Females have different brains than men, so you may not get this right away, and it’s okay if you don’t get it at all.”

Jennifer was horrified and took the brave step of knocking on the door of the other professor’s office. She poked her head in and asked if she could talk to the male professor. She discussed the incorrect messages he was giving with him, which caused him to get upset and report Jennifer to the department chair. Fortunately, the department chair was a woman who also knew that his messages were incorrect and supported Jennifer.

Jennifer is taking on the myths about math and learning, and she is just the person for it. She recently told me about her own challenging experience of being discouraged by a professor when she was in grad school:

I was a grad student, finishing my first year. I had started some research for my thesis. I was doing great; I was working really hard and getting good grades. I was in this class, it was topology, and it was really challenging for me, but I was working really hard, and I had done really well on an exam. I was really proud of myself. We had gotten the exams back, and I had gotten like a 98 or something, really close to perfect. I was so happy. Then I flipped to the back of the exam, and there was a note from my professor that said to see him after class. And I was like, “Okay, well maybe he’s excited too.” I was so happy and proud of myself.

When I sat down in his office, we began this conversation about why I wasn’t cut out for math. He wanted to know if maybe I cheated or memorized, to do so well on the exam. He pretty much told me that he didn’t think that I was a mathematician, that it shouldn’t be my future, and encouraged me to consider my other options.

I told him I was starting my thesis that summer and what my grade point average was. So he pulled up my grades and saw that I did both undergrad and my master’s there. Then he pulled up my grade record and started looking at some of my grades. And he just kept asking me questions that all implied that I didn’t earn those grades myself. It tore me apart when he did that, because he was a man I respected, someone I thought was so smart, who was very well known in the math department, very respected. A lot of the male students loved him. After that I went to my car and cried, I was so upset. I just bawled my eyes out.

My mom’s a teacher, so I called my mom. When I reported the conversation, she of course got really defensive and angry. She told me to really just think about it and think about people who do well in math and why they do well. And she made me think about all these different things. I think that was the planting of the first seed that really helped me to start to understand what a growth mindset is. And following that, luckily the fierceness in me kicked in, and the feistiness, and I used that to motivate myself to do even better in that course and in my career. And I made sure to give that professor a big smile as I walked across the stage at graduation.

Jennifer’s encounter tells us of a person, a professor responsible for students’ lives, who believes that only some people belong in mathematics. Sadly, this professor is not alone in his incorrect thinking. The Western world, in particular, is filled with the deeply ingrained cultural belief, pervasive in all subject areas and professions, that only some people can be high-achievers. Many of us have been told this, and we have been conditioned to believe it. Once people believe that only some can reach high levels, it affects all areas of their lives and stops them from choosing fulfilling pathways. The belief that only some people can be high-achievers is insidious and damaging and prevents all of us from reaching our potential.

When teachers and others give people the idea that they don’t have the brain to learn something, it is because they do not know or they refuse to accept the new scientific evidence. More often than not these are STEM (science, technology, engineering, and mathematics) teachers and professors, an issue I will return to. I think of these people as stuck inside the “fixed-brain regime.” It is not surprising that so many people are stuck inside this negative place. The neuroscience showing brain growth did not become established until about twenty years ago; before that everyone believed that people were born with certain brains and those brains never changed. Many of the teachers and professors inside the fixed-brain regime have not seen the scientific evidence. University systems of reward mean that professors are most valued for publishing in scientific journals, not writing books (such as this one) for the public or sharing evidence widely. That means the most important evidence is “locked” up in journals, which are often behind paywalls, and does not get to the people who need it—in this case, educators, managers, and parents.

Changing Perceptions and Brains

It is the lack of opportunities for important knowledge to get to the people who need it that prompted Cathy Williams and me to start youcubed. This is a Stanford center and website (youcubed.org) dedicated to getting research evidence on learning to the people who need it—especially teachers and parents. We are now in a new era, and many neuroscientists and doctors are writing books and giving TED Talks in order to bring people new information. Norman Doidge is one of the people who has done a great deal to change perceptions and share the new and important brain science.

Doidge is a medical doctor who has written an incredible book with the title The Brain That Changes Itself: Stories of Personal Triumph from the Frontiers of Brain Science. The book is exactly what the title describes; it is filled with inspiring examples of people with severe learning disabilities or medical conditions (such as a stroke) who, although written off by educators and doctors, have undergone brain training and recovered completely. Doidge works to shatter a number of myths in the book, such as the idea that separate brain areas are compartmentalized and don’t communicate or work together and, most important, the idea that brains don’t change. Doidge describes the “dark ages” when people believed that brains were fixed, says that he is unsurprised that people are slow to understand the plasticity of the brain, and suggests that it will take an intellectual “revolution” for them to do so.⁸ I agree, because over the last few years in my teaching about the new brain science I have met many people who seem unwilling to make the shift in their understanding of the brain and human potential.

The vast majority of schools are still inside the fixed-brain regime. Schooling practices have been set over many years and are very difficult to change. One of the most popular is tracking, a system in which students are placed in groups based on their supposed ability and then taught together in those groups. A study in Britain showed that 88 percent of students placed into tracks at the age of four remained in the same track for the rest of their school lives.⁹ This horrific result does not surprise me. Once we tell young students they are in a lower-track group, their achievement becomes a self-fulfilling prophecy.

The same is true when teachers are told which tracks students are in; they treat students differently whether they intend to or not. Similar results were found in a study of nearly twelve thousand students from kindergarten to third grade in more than twenty-one hundred schools in the US.¹⁰ None of the students who started out in the lowest reading group ever caught up to their peers in the highest group. Such policies of placing students in groups based on their supposed level of ability may be defensible if it resulted in higher achievement for the low-, middle-, or high-achieving students, but it does not.

Studies of schools’ tracking policies in reading show that those schools that use tracked reading groups almost always score lower on average than schools that do not.¹¹ These results are echoed in mathematics. I have compared students learning mathematics in middle and high schools in England and the US, and in both school levels and countries the schools that taught students in mixed achievement groups outperformed those that used ability groups.¹²

San Francisco Unified is a large and diverse urban school district whose school board voted, unanimously, to remove advanced classes until eleventh grade. This prompted a lot of controversy and opposition from parents, but within two years, during which all students took the same mathematics classes until tenth grade, algebra failure rates fell from 40 to 8 percent of students in the district and the number of students taking advanced classes after tenth grade went up by one-third.¹³

It is hard to imagine that the teaching practices of the district teachers changed dramatically in two years, but what did change were the opportunities students received to learn and the ideas students believed about themselves. All students, instead of some students, were taught high-level content—and the students responded with high achievement. International studies of achievement in different countries across the world show that countries that use tracking the latest and the least are the most successful. The US and the UK, two countries in which I have lived and worked, have two of the most highly tracked systems in the world.

Nobody knows what children are capable of learning, and the schooling practices that place limits on students’ learning need to be radically rethought. Someone whose story illustrates most clearly for me the need to change our expectations of young children is Nicholas Letchford. Nicholas grew up in Australia, and in his first year of school his parents were told that he was “learning disabled” and had a “very low IQ.” In one of his mother’s first meetings with teachers, they reported that he was the worst child they had seen in twenty years of teaching. Nicholas found it difficult to focus, make connections, read, or write. But over the next few years Nicholas’s mother, Lois, refused to believe that her son could not learn, and she worked with Nicholas, teaching him how to focus, connect, read, and write. The year 2018 was an important one for Lois Letchford. It was the year that she published a book describing her work with Nicholas, called Reversed,¹⁴ and it was also the year Nicholas graduated from Oxford University with a doctoral degree in applied mathematics.

Research and science have moved beyond the fixed-brain era, but fixed-brain schooling models and limited-learning beliefs persist. As long as schools, universities, and parents continue to give fixed-brain messages, students of all ages will continue to give up on learning in areas that could have brought them great joy and accomplishment.

The new brain science showing that we have unlimited potential is transformative for many—and that includes those diagnosed with learning disabilities. These are individuals who are born with or develop, through injury or accident, physical brain differences that make learning more difficult. For many years, schools have traditionally put such students into lower-level classes and worked around their weaknesses.

Barbara Arrowsmith-Young takes an entirely different approach. I was fortunate to meet Barbara on a recent visit to Toronto, during which I toured one of the incredible “Arrowsmith” schools she has set up. It is impossible to spend time with Barbara and not realize that she is a force to be reckoned with; she is passionate not only about sharing her knowledge of the brain and how we develop it, but in using her knowledge to change the neural pathways of those diagnosed with special educational needs through targeted brain training.

Barbara is someone who was herself diagnosed with severe learning disabilities. As she was growing up in Toronto in the 1950s and 1960s, she and her family knew she was brilliant in some areas, but they were told she was “retarded” in others. She had trouble pronouncing words and could not engage in spatial reasoning. She could not follow cause-and-effect statements, and she reversed letters. She was able to understand the words “mother” and “daughter,” but not the expression “mother’s daughter.”¹⁵ Fortunately for Barbara, she had an amazing memory and was able to memorize her way through school and hide what she knew was wrong.

As an adult her own disabilities prompted her to study child development, and eventually she came across the work of Alexander Luria, a Russian neuropsychologist who had written about stroke victims who had trouble with grammar, logic, and reading clocks. Luria worked with many people with brain injuries, produced an in-depth analysis of the functioning of various brain regions, and developed an extensive battery of neuropsychological tests. When Barbara read Luria’s work, she realized she herself had brain injuries, became quite depressed, and started to consider suicide. But then she came across the first work on neuroplasticity and realized that particular activities could produce brain growth. She began months of detailed work on the areas she knew she was weakest in. She made herself hundreds of cards with clock faces and practiced so much she was reading them faster than “regular” people. She started to see improvements in her symbolic understanding and for the first time began grasping grammar, math, and logic.

Now Barbara runs schools and programs that give brain training to students diagnosed with learning differences. Chatting with Barbara on my visit, I found it hard to imagine that this woman herself had had such severe disabilities in the past, as she is an impressive communicator and thinker. Barbara has developed over forty hours of tests that diagnose students’ brain strengths and weaknesses and a range of targeted cognitive exercises that enable students to develop brain pathways. Students come to her Arrowsmith schools with severe disabilities and leave without them.

When I visited one of the Arrowsmith schools for the first time, I saw students sitting at computer screens intensely concentrating on their cognitive tasks. I asked Barbara if the students were happy doing this, and she replied that students stay motivated because they can feel the effects of the program very quickly. Many of the students I spoke to talked in the same terms—after they started on the cognitive tasks, they felt a “fog lifting” and were able to make sense of the world. When I visited the Arrowsmith school for the second time, I sat and talked to some adults going through the program.

Shannon was a young lawyer who had become concerned after criticism for the length of time it took her to produce her work, as people typically pay for lawyers’ time by the hour. She was referred to Arrowsmith and decided to enroll for a summer. When I met her, a few weeks into the program, she told me that it was already “life changing” for her. Not only was Shannon thinking a lot more efficiently, but she was able to make connections she had not been able to make before. She was even making sense of events that had happened in her past, even though she had not been able to make sense of them at the time. Shannon, like the others, talked about a “fog lifting” from her mind; she said she used to be a passenger in conversations, but now “everything is clear” and she is able to participate fully.

Barbara not only offers brain training for students who go to Toronto and enroll in the school; she has now developed a program that educators can be trained in and take back to their schools. Some students stay in the program for a few months, some for a few years, and now a remote program is being developed for students to work in different locations. Barbara is somebody who is leading the world in her brain-training approach. Like many groundbreakers, she has had to endure critiques from the people who do not accept the idea of neuroplasticity or that brains can be exercised and developed, but she has continued fighting for the rights of students who have been made to believe they are “broken.”

Most of the students who contact Arrowsmith have been given the idea there is something terribly wrong with them, and many of them have been rejected by the school system. They leave Arrowsmith transformed. One of the results of my visits to the school was that I became determined to help spread the news of what is possible with brain training and share the Arrowsmith methods with our army of teachers and parents who follow youcubed (they call themselves youcubians). As mentioned, the approach of special education in schools has been to identify students’ weaknesses and teach around them, essentially teaching to their strengths. Arrowsmith’s approach is the opposite. The teachers work to identify brain weaknesses and then teach to them—building up the brain pathways and connections that students need. My hope is that all students with learning differences will be exposed to brain training and freed from the labels and limits they have been forced to live with, replacing these instead with hope engendered by a transformed brain.

Many amazing individuals who were written off and told not to pursue particular studies have excelled in them. Dylan Lynn was diagnosed as having dyscalculia, a particular brain condition that makes learning mathematics hard. But Dylan refused to accept that she could not learn math and pursued and achieved a degree in statistics. She did this by refusing to listen to all the people who told her to drop her mathematics courses, instead working out her own approach to mathematics. Dylan now collaborates with Katherine Lewis, a professor at the University of Washington, in telling her story to inspire other learners who were told they could not achieve their desired goal.¹⁶

It is time to recognize that we cannot label children and have low expectations for them. This is true regardless of any diagnosed learning difference. As we ourselves are learning in these pages, the most notable quality of our brains is their adaptability and potential for changing and growing.

In addition to children with genuine learning disabilities, many other students are either told or made to believe they have a learning disability when they do not—particularly when it comes to mathematics. For decades, teachers everywhere have identified children who do not memorize math facts as well as their classmates and labeled them as having a deficiency or disability.

One study, conducted by neuroscientist Teresa Iuculano and her colleagues at Stanford School of Medicine, clearly shows the potential of children’s brains to grow and change as well as the danger of misdiagnosing students.¹⁷ The researchers brought in children from two groups—one group had been diagnosed as having mathematical learning disabilities and the other consisted of regular performers. The researchers used MRI scans to look at the brains of the children when they were working on math. They found actual brain differences. This is where it gets interesting. The difference was that the students identified as having disabilities had more brain regions lighting up when they worked on a math problem.

This result is counterintuitive, for many people think that students with “special needs” have less going on in their brains, not more. However, we do not want all of the brain lighting up when we work on mathematics; we want a few focused areas to light up. The researchers dug further and gave one-on-one tutoring to both sets of students—those who were regular performers and those identified as having a mathematical learning disability. At the end of the eight weeks of tutoring, not only did both sets of students have the same achievement; they also had the exact same brain areas lighting up.

This is one of many important studies showing that after a short period of time—research interventions are often eight weeks long—brains can be completely changed and rewired. The “learning disabled” students in this study developed their brains to an extent that allowed them to function in the same way as “regular performers.” Let’s hope they returned to school and lost their “mathematical disability” labels. Just imagine how everything could change for those young children in school and in life.

High-Achieving Students

The importance of knowing about brain growth is not limited to students diagnosed with learning differences. It extends across the entire achievement spectrum. Students come to Stanford with a history of school success; often they have only ever received As in school. But when they struggle in their first math (or any other) class, many decide they cannot learn the subject and give up.

As mentioned, for the last several years I have been working to dispel these ideas with students by teaching a class called “How to Learn Math.” The class integrates the positive neuroscience of learning with a new way of seeing and experiencing math. My experience of teaching this class has been eye-opening. I have met so many undergrads who are extremely vulnerable and too readily come to believe they don’t belong in STEM subjects. Unfortunately, they are almost always women and people of color. It is not hard to understand why these groups are more vulnerable than white males. The stereotypes that pervade our society based on gender and color run deep and communicate that women and people of color are not suited to STEM subjects.

One study published in the premier journal Science showed this powerfully.¹⁸ Sarah-Jane Leslie, Andrei Cimpian and colleagues interviewed university professors in different subject areas to see how prevalent the idea of a “gift” was—the concept that you need a special ability to be successful in a particular field. Their results were staggering. They found that the more prevalent the idea of a gift was in any academic field, the fewer women and people of color were in that field. This held across all thirty subjects they looked at. The following graphs show the relationships the researchers uncovered; the top chart (A) shows the science and technology subjects, and the chart below (B) shows the arts and humanities subjects.

The question I always ask when I see data like this is: If the idea of giftedness is harmful to adults to this extent, what does it do to young children?

The idea of giftedness is not only inaccurate and damaging; it is gender and racially biased. We have many different forms of evidence showing that those who believe in fixed brains and giftedness also believe that boys, men, and certain racial groups are gifted and girls, women, and other racial groups are not.

One of the forms of evidence that shows this clearly was collected by Seth Stephens-Davidowitz, who focused his attention on google searches.¹⁹ His study revealed something very interesting and disturbing. He found that the most commonly googled word following “Is my two-year-old son …” is “gifted.” He also found that parents search the words “Is my son gifted?” two and a half times more than the words “Is my daughter gifted?” This is despite the fact that young children of different genders have equal potential.

Sadly, the problem is not limited to parents. Daniel Storage and his colleagues conducted analyses of anonymous reviews on RateMyProfessors.com, and they found that students were twice as likely to call male rather than female professors “brilliant” and three times as likely to call male rather than female professors “geniuses.”²⁰ These and other studies show that ideas of giftedness and genius are intertwined with racist and sexist assumptions.

I am convinced that the majority of people who have gender or racial biases do not think about them consciously or perhaps even realize they have them. I also contend that if we were to dispel the idea that some people are “naturally” gifted and instead recognize that everyone is on a growth journey and can achieve amazing things, some of the most insidious biases against women and people of color would disappear. This is needed in the STEM fields more than anywhere else; it is no coincidence that STEM subjects evidence the strongest fixed thinking and the starkest inequities in participation.

Part of the reason so many students are dissuaded from thinking they are capable of learning math is the attitudes of the teachers and professors who teach them. I have now met a few amazing mathematicians who devote large parts of their lives to dispelling the elitist ideas that pervade mathematics. University mathematician Piper Harron, one of my own heroes, is one of those people. On her website, called The Liberated Mathematician, she writes: “My view of mathematics is that it is an absolute mess which actively pushes out the sort of people who might make it better. I have no patience for genius pretenders. I want to empower the people.”²¹ It is wonderful to have voices like Piper’s to help dispel the myths about who can achieve in mathematics.

Unfortunately, there remain too many academics and teachers who continue to transmit false elitist ideas and willfully and openly state that only some people can learn their subjects. Just last week I learned of two examples that are typical. A community college professor started her class by telling the students that only three of them would make it, and a high-school math teacher in my local school district announced to his eager fifteen-year-old students who were placed in his high-level math class: “You may think you are hot shit, but no one gets above a C in this class.” These are the words of elitists who revel in the low number of students who are successful in their classes, as they think it shows that they are teaching really difficult content. It is this sort of thinking and speaking to students that has kept so many amazing people from pursuing pathways that would have been rewarding for them. Such ideas harm people, and they harm the disciplines, because access is denied to the diverse thinkers who would have provided beneficial insights and breakthroughs in these fields.

One of these thinkers was the incredible mathematician Maryam Mirzakhani. The story of Maryam’s life and work appeared in newspapers worldwide when she became the first woman in the world to win the coveted Fields Medal—the equivalent of the “Nobel Prize” for mathematicians. Maryam grew up in Iran and, like many others, was not inspired by school math classes. In seventh grade, Maryam was told by her math teacher that she was not good at math. Fortunately for the world, Maryam had other teachers who believed in her.

At age fifteen things changed for Maryam when she signed up for a problem-solving class at Sharif University in Tehran. She loved mathematical problem solving and went on to study advanced mathematics. During her PhD studies she proved several previously unproved theories in mathematics. Her approach was different from that of many mathematicians, and her work almost entirely visual. The field would be narrower—less rich, visual, and connected—without Maryam’s contribution, one that could so easily have been lost if she had listened to the teacher who told her that she was bad at math.

When Maryam came to Stanford, we found many occasions to meet and discuss mathematics learning, and I enjoyed chairing a PhD exam for one of her students. At age forty, she tragically died. The world lost an incredible woman, although her ideas will always live on and continue to broaden mathematics.

The American Mathematical Society recently devoted the November issue of its journal to Maryam, and one of those reflecting on Maryam’s amazing contribution to mathematics was Jenya Sapir, the doctoral student whose thesis defense I chaired, now a mathematician herself. Here are her reflections on Maryam:

Maryam would paint beautiful, detailed landscapes in her lectures. If she were giving a talk about concepts A, B, and C, she would not just explain that A implies B implies C. Rather, she would paint a mathematical landscape where A, B, and C lived together and interacted with one another in various complicated ways. More than that, she made it seem like the rules of the universe were working harmoniously together to make A, B, and C come about. I was often amazed by what I imagined her inner world to be like. In my imagination it contained difficult concepts from disparate fields of mathematics all living together and influencing one another. Watching them interact, Maryam would learn the essential truths of her mathematical universe.²²

The world is filled with cases of people who think differently—often more creatively—and are dissuaded from pursuing careers in sports, music, academics, and many other fields. Those who persist despite the negative messages they receive often go on to achieve incredible feats.

But how many are there who do not go forward, who believe negative judgments and who turn away from fields and dreams? One of the people who thought differently and received extensive rejection is the author of the Harry Potter series, J. K. Rowling, now the most successful author in history. Shortly after the death of her mother, she was at a very low point in her life; she was recently divorced, a single mother, living in poverty, but she focused on something she cared deeply about—writing. Rowling (also called Jo) sent her Harry Potter manuscript to twelve different publishers, all of whom rejected it.

She began to lose confidence in her book when the editor at Bloomsbury Publishing sat down to read the book; she also gave it to her eight-year-old daughter. The young reader loved it and encouraged her mother to publish it. Rowling’s books have now sold over 500 million copies, and she is a role model for any who face rejection yet believe in their ideas. Today she actively works to end poverty and support children’s welfare. I love many of her words, but this is perhaps my favorite quote of all:

It is impossible to live without failing at something, unless you live so cautiously that you might as well not have lived at all—in which case, you fail by default.

The Problems of Giftedness

The teachers, professors, and parents who maintain that only some people can learn subjects are all reflecting the misinformation of the fixed-brain era. It is perhaps not surprising that so many people still cling to the idea of fixed brains, as most of them lived during the years when this was all anyone knew. The fixed-brain myths have been devastating for students of all ages who have been written off in schools, classrooms, and homes, millions of children who have been made to believe they cannot achieve. But there is another side to this story as well. Fixed-brain thinking has also had negative consequences for the students who have been held up as being “gifted.” This may seem nonsensical—how can being labeled as gifted possibly harm anyone? I have already mentioned the research showing that the idea of giftedness—that you need some inherited gene to do well—is harmful for women and students of color, but how does it harm individuals who are given the label?

A few months ago, I was contacted by a filmmaker who was making a film on giftedness with a social justice angle. That, I thought, sounded interesting, so I looked at the trailer he sent me. I was disappointed to find that his argument was that more students of color should be identified as gifted. I understand the motives for such a film, as there are serious racial disparities in gifted programs. But there was a larger issue at play, and that was the continued practice of fixed-brain labeling.

I decided in those moments to make my own film, with the help of my youcubed team and an amazing filmmaker, Sophie Constantinou, from Citizen Film. I asked the Stanford students I knew to reflect upon their experiences of being labeled as “gifted.”²³ The twelve Stanford students who speak in the film give a consistent message—they received advantages, but at some costs. The students talk about feeling that they had a fixed thing inside them, and when they struggled, they thought it had “run out.” They say they learned that they could not ask questions; they could only answer other people’s questions. They say that they tried to hide any struggles, in case people found out that they did not have a “gift.” At the end a student named Julia strikingly says, “If I grew up in a world where no one was labeled as gifted, I would have asked a lot more questions.”

The gifted movement has the worthy ideal of ensuring that high-achieving students get a rich and challenging environment, which I agree is needed. But they have done so by perpetuating an idea that some students are worthy of this because they have a fixed “gift”—like a present they have been given. Although the programs point out that some students need especially challenging material because they have reached an elevated point, they omit the fact that others can also reach that point if they work hard. The message is that some people are born with something that others cannot achieve. This, in my view, is damaging, both for those who get the idea they have no gift and for those who get the idea they have a fixed brain.

One of the reasons that it can be damaging to receive the gifted label is that you do not expect to struggle, and when you do, it is absolutely devastating. I was reminded of this when chatting with my education students at Stanford last summer. I was explaining the research on brain growth and the damage of fixed labels when Susannah raised her hand and sadly said, “You are describing my life.”

Susannah went on to recall her childhood, when she was a top student in math classes. She had attended a gifted program and had been told frequently that she had a “math brain” and a special talent. She went on to enroll as a math major at UCLA, but in the second year of the program she took a class that was challenging and that caused her to struggle. At that time, she decided she did not have a math brain after all, and she dropped out of the program. What Susannah did not know is that struggle is the very best process for brain growth (more on that later) and that she could grow the neural pathways she needed to learn more mathematics. If she had known that, Susannah would probably have persisted and graduated with a math major. This is the damage that is caused by fixed-ability thinking.

The story Susannah told me relayed her experience of being labeled as gifted, with a “math brain,” and the ways this fixed labeling led her to drop the subject she loved. This could be repeated with any subject—English, science, history, drama, geography—anything. When you are valued for having a brain that you did not develop, one you were just given at birth, you become averse to any form of struggle and start to believe you do not belong in areas where you encounter it. Because of my field of specialty, I have met many people who have dropped out of STEM subjects because they thought they did not have the right brain, but the problem is not limited to STEM subjects. It comes about whenever people are led to believe that their intellect is fixed.

Although I decry the labels given to students—of giftedness or the opposite—I do not maintain that everyone is born the same. At birth everyone has a unique brain, and there are differences between people’s brains. But the differences people are born with are eclipsed by the many ways people can change their brains. The proportion of people born with brains so exceptional that those brains influence what they go on to do is tiny—less than 0.001 percent of the population. Some have brain differences that are often debilitating in some ways, such as those on the autism spectrum, but productive in other ways. Although we are not born with identical brains, there is no such thing as a “math brain,” “writing brain,” “artistic brain,” or “musical brain.” We all have to develop the brain pathways needed for success, and we all have the potential to learn and achieve at the highest levels.

Bestselling author Daniel Coyle, who has spent a lot of time in “talent hotbeds,” agrees. He has interviewed teachers of the most “talented”—the people Coyle describes as having worked in particularly effective ways. Their teachers say that they see someone they regard as a “genius” at a rate of one person per decade.²⁴ To decide that 6 percent of students in every school district have a brain difference that means they should be siphoned off and given special treatment is ludicrous. Anders Ericsson has studied IQ and hard work for decades and concludes that the people regarded as geniuses—people like Einstein, Mozart, and Newton—“are made, not born,” and their success comes from extraordinary hard work.²⁵ Importantly, we should communicate to all students that they are on a growth journey, and there is nothing fixed about them, whether it is called a “gift” or a disability.

We are no longer in the fixed-brain era; we are in the brain-growth era. Brain-growth journeys should be celebrated, and we need to replace the outdated ideas and programs that falsely deem certain people more capable than others, especially when those outdated labels become the source of gender and racial inequalities. Everybody is on a growth journey. There is no need to burden children or adults with damaging dichotomous thinking that divides people into those who can and those who cannot.

The idea that women have to work hard to be successful whereas men are naturally brilliant was a notion I myself encountered in high school—not from my math teacher, but from my physics teacher. I remember it clearly. It was at the time when all students took a practice exam, known as a “mock exam,” in preparation for the high-stakes exam all students take at age sixteen in England. Eight students—four girls and four boys—received borderline scores, and I was one of them. At this point my physics teacher decided that all the boys had achieved their scores without trying, but all the girls had achieved their scores from working hard—and so they could never do any better. As a result, he put all the boys in for the higher exam and the girls were entered for the lower exam.

Since I did hardly any work in high school (I was bored a lot of the time from just having to memorize facts) and skated by with minimal effort, I knew he was wrong about the girls having worked harder. I told my mother about the teacher’s decision based on gender. My mum, being the feminist she was, complained to the school, so they grudgingly put me in for the higher exam, telling me it was a stupid risk on my part, because the only grades given for the higher exam were A, B, C, or failing. I said I would take the risk.

Later that summer I received my result—an A. I was fortunate that I had a parent who got the sexist decision the teacher made overturned, and countering his thinking gave me a reason to work especially hard for the exam. The unfortunate impact for me, however, was that I decided I would not go any further in physics. I just did not want any more to do with the man (who was the department chair) or the subject.

Luckily, I did not receive such sexist dissuasion in math, and some of my best and highest-level math teachers and professors were women. I chose to take advanced mathematics instead—I took all the sciences at advanced levels except physics. This is an example of the particularly insidious impact that men like my physics teacher have when they limit pathways based on gender (or race or other characteristics).

A group of young women recently shared with me their experience of approaching their mathematics professor with a question after one of their first classes at a top university. When they asked their question, the professor said it was too basic and they should take a class at the local community college. The women, all African American students, decided at that moment to leave STEM subjects for good. They had experienced enough of these messages and, like many other students before them, they walked away.

Mathematics is, of course, not the only subject that fuels damaging ideas about who can achieve. Art, English, music, sports—all of these are areas where students are initially interested until they begin to struggle and decide they don’t have the right kind of brain (or body). In all cases when students get these damaging ideas, some portion of their future potential is foreclosed. And not only in school. Fixed ideas about potential impact their work lives as well.

I have now talked with many professionals who tell me that before they learned about brain science, they were too nervous to offer ideas in meetings, in case they were wrong, and they were always living in fear of being judged. This is not surprising, as we have grown up in a fixed-brain world that judges everyone on their “smartness.” Many of us have grown up feeling judged for everything, often feeling “not good enough” and worrying about being found out. When people let go of fixed-brain ideas, they become unlocked, especially when they combine this knowledge with other findings from neuroscience that we will explore shortly.

Workers suffer the effects of fixed-brain thinking, but often managers do as well. Managers in companies are just as likely to write off an employee as not having a good brain or being smart enough. If, instead, managers saw the limitless potential of the people they work with, they would talk to them differently and open up opportunities rather than close them down. Instead of deciding that some workers are of limited value, managers might decide that they could be given different opportunities for learning—some may need something to read or study or build (more on this in later chapters). This would change the ways many companies operate and empower many more employers to create important ideas and products.

The first step in living a limitless, unlocked life is to know brains are constantly reorganizing, growing, and changing. Remembering that every day of our lives, we wake up with a changed brain. In every moment of our lives our brains have opportunities to make connections, to strengthen pathways, and to form new pathways. When we face a challenging situation, rather than turn away because of fear of not being good enough, we should dive in, knowing that the situation presents opportunities for brain growth. As we start to recognize the huge implications of the adaptability of our brains, we will start to open our minds, and live differently. The key information that will enable our new pathways and approaches to be enhanced further will be shared in the remaining chapters.

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WHY WE SHOULD LOVE MISTAKES, STRUGGLE, AND EVEN FAILURE

OUR LIVES are filled with mistakes. We make them all the time, and they are simply part of everyday life. Even though mistakes sometimes make no difference or end up producing fortuitous results, most of us instinctively respond to mistakes by mentally beating ourselves up and feeling terrible. It is not surprising that large sections of the population respond negatively to mistakes. Most of us have grown up with the idea that mistakes are bad, especially if we attended test-driven schools, where we were frequently marked down for making mistakes, or our parents punished mistakes with harsh words and actions. This is unfortunate, and this is why.

LEARNING KEY #2

The times when we are struggling and making mistakes are the best times for brain growth.

When we are willing to face obstacles and make mistakes in the learning process, we enhance neural connections that expedite and improve the learning experience. The research on the positive impact of mistakes and struggle is emerging from both neuroscience¹ and behavioral studies of high-achieving people.² Some of this work is counterintuitive, as we have believed for so long in the absolute necessity that everything be “correct.” Releasing people from the idea that they must always be correct and not make any mistakes turns out to be transformative.

The Science of Mistakes

I first became aware of the positive impact of mistakes when I was hosting a workshop for teachers and Carol Dweck, the pioneer of mindset research, joined us. The teachers attending the workshop that day had gathered in a large group and listened attentively to Carol. She announced that every time we make mistakes, synapses fire in the brain, indicating brain growth. All the teachers in the room were shocked, as they had all been working under the premise that mistakes are to be avoided. Carol was drawing from work that has researched the brain’s response when we make mistakes, particularly investigating the different ways brains respond when people have a growth or a fixed mindset.³

Jason Moser and his colleagues extended Carol’s work investigating the brain’s response when we make mistakes. Moser and his team found something stunning. They had asked participants to take tests while they monitored the participants’ brains with MRI technology. They looked at the scans when people got questions correct and when they got them incorrect. The researchers found that when people made mistakes, brains were more active, producing strengthening and growth, than when people got work correct.⁴ Neuroscientists now agree that mistakes positively contribute to the strengthening of neural pathways.

This learning key is particularly significant because most teachers design classes so that everyone is successful. Curricula and textbooks are designed with trivial, unchallenging questions, so that students will get a high percentage of answers correct. The common belief is that getting most answers correct will motivate students toward greater success. Here’s the problem, though. Getting questions right is not a good brain exercise.

For students to experience growth, they need to be working on questions that challenge them, questions that are at the edge of their understanding. And they need to be working on them in an environment that encourages mistakes and makes students aware of the benefits of mistakes. This point is critical. Not only should the work be challenging to foster mistakes; the environment must also be encouraging, so that the students do not experience challenge or struggle as a deterrent. Both components need to work together to create an ideal learning experience.

Author Daniel Coyle studied “talent hotbeds,” places producing a larger proportion than normal of high-achievers, and concludes that achievement comes not from any natural-born ability, but rather from a special kind of work and practice. He has studied examples of those who excel at learning in music, sports, and academic subjects. His research reveals that all of the people who achieved at very high levels engaged in a particular kind of practice that caused the coating of brain pathways with myelin.

Our brains function through an interconnected web of nerve fibers (including neurons), and myelin is a form of insulation that wraps around fibers and increases their signal strength, speed, and accuracy. When we revisit an idea or kick a soccer ball, myelin coats the neural pathways involved, optimizing the particular circuits and making our movements and thoughts more fluid and efficient in the future. Myelin is vital to the learning process. Most learning takes time, and myelin aids the process by reinforcing signals and slowly strengthening pathways. Coyle gives a number of examples of the highest-achieving mathematicians, golfers, soccer players, and pianists practicing their craft and describes the role of myelin in wrapping layers of insulation around their neural circuits. He characterizes the world’s experts as having “super-duper pathways” wrapped in layer upon layer of myelin, which makes them very effective.

So how do we all develop “super-duper pathways”? This occurs when people are working at the edge of their understanding, making mistake after mistake in difficult circumstances, correcting mistakes, moving on and making more mistakes—constantly pushing themselves with difficult material.

Coyle starts his book with an interesting story of learning. He describes the case of a thirteen-year-old girl he calls Clarissa, who is learning the clarinet. Clarissa, he says, has no musical “gifts,” lacks a “good ear,” and has only an average sense of rhythm and subpar motivation—yet she became famous in music circles, because she managed to accelerate her learning by ten times, according to the calculations of music psychologists. This amazing learning feat was captured on video and has been studied by music experts. Coyle describes watching the video of Clarissa practicing and suggests that the video be given a title of “The Girl Who Did a Month’s Worth of Practice in Six Minutes.” He describes the practice session this way:

Clarissa draws a breath and plays two notes. Then she stops. She pulls the clarinet from her lips and stares at the paper. Her eyes narrow. She plays seven notes, the song’s opening phrase. She misses the last note and immediately stops, fairly jerking the clarinet from her lips. … She starts over and plays the riff from the beginning, making it a few notes farther into the song this time, missing the last note, backtracking, patching in the fix. The opening is beginning to snap together—the notes have verve and feeling. When she’s finished with this phrase, she stops again for six long seconds, seeming to replay it in her mind, fingering the clarinet as she thinks. She leans forward, takes a breath, and starts again.

It sounds pretty bad. It’s not music; it’s a broken-up, fitful, slow-motion batch of notes riddled with stops and misses. Common sense would lead us to believe that Clarissa is failing. But in this case common sense would be dead wrong.⁵

A music expert watching the video commented on Clarissa’s practice, saying it was “amazing” and, “If somebody could bottle this, it’d be worth millions.” Coyle points out: “This is not ordinary practice. This is something else: a highly targeted, error-focused process. Something is growing, being built. The song begins to emerge, and with it, a new quality within Clarissa.”⁶

In each of the learning cases Coyle reviews, he says that the learner has “tapped into a neurological mechanism in which certain patterns of targeted practice build skill. Without realizing it, they have entered a zone of accelerated learning that, while it can’t quite be bottled, can be accessed by those who know how. In short, they’ve cracked the talent code.”⁷

One of the significant characteristics of the highly effective learning described is the presence of mistakes and the role of struggle and error in transforming people from beginners into experts. This is consistent with the brain research showing increased brain activity when people struggle and make mistakes and decreased activity when they get work correct.⁸ Unfortunately, most learners think they should always be getting work correct, and many feel that if they make mistakes or struggle, they are not good learners—when this is the very best thing they can be doing.

Practice is important for the development of any knowledge or skill. Anders Ericsson helped the world understand the nature of expert performance and found that most world-class experts—pianists, chess players, novelists, athletes—practiced for around ten thousand hours over twenty years. He also found that their success was not related to tests of intelligence but to the amount of “deliberate practice” they undertook.⁹ Importantly, although people succeed because they are trying hard, the people who become experts are trying hard in the right way. A range of different researchers describe effective practice in the same way—people pushing at the edge of their understanding, making mistakes, correcting them, and making more.

A Different View of Struggle

Every four years an international test of mathematics and science called TIMSS (Trends in International Mathematics and Science Study) is conducted in fifty-seven countries. In the last round of testing, Singapore was the highest-performing country in mathematics. The information from such tests is not very useful if we do not know what approach countries use to bring about their results. Accordingly, a group of researchers studied the nature of math teaching by going into classrooms and recording a representative sample of the teaching in seven countries. This teaching study uncovered a number of noteworthy outcomes.¹⁰ One finding was that the mathematics curriculum in the US is “a mile wide and an inch deep” compared to the curriculum in more successful countries.

Japan has always scored well in mathematics—it has always finished in one of the top-five TIMSS positions—and was one of the countries visited in the study. The researchers found that Japanese students spent 44 percent of their time “inventing, thinking, and struggling with underlying concepts,” whereas students in the US engaged in this kind of behavior less than 1 percent of the time.

Jim Stigler, one of the authors of the study, writes that the Japanese teachers want the students to struggle—and recalls the times when they would purposely give the wrong answer so that students would go back and work with foundational concepts. In my thousands of observations of classrooms over many years in the US and the UK, I have never seen this kind of practice; more typically I have seen teachers who seem to want to save students from struggle. Many times I have observed students asking for help and teachers structuring the work for students, breaking down questions and converting them into small easy steps. In doing so they empty the work of challenge and opportunities for struggle. Students complete the work and feel good, but often learn little.

I saw a very similar teaching approach, focused on struggle, in a visit to classrooms in China, another country that scores highly in mathematics. I had been asked to visit China to give a talk at a conference and managed, as I like to do, to sneak away and visit some classrooms. In a number of high-school math classrooms, lessons were approximately one hour long, but at no time did I see students working on more than three questions in one hour. This contrasts strongly with a typical US high-school math classroom, where students chug through about thirty questions in an hour—about ten times more. The questions worked on in Chinese classrooms were deeper and more involved than the ones in US classrooms. Teachers would ask provocative questions, deliberately making incorrect statements that students would be challenged to argue against.

One of the lessons I watched was on a topic that is often uninspiring in US classrooms—complementary and supplementary angles. The teacher in China asked the students to define a complementary angle, and the students gave their own ideas for a definition. Often the teacher would push the students’ definition to a place that made it incorrect and playfully ask, “Is this right, then?” The students would groan and try to make the definition more correct. The teacher bantered with the students, playfully extending and sometimes twisting their ideas to push the students to deeper thinking. The students probed, extended, clarified, and justified for a long time, reaching depths that were impressive.

Contrast this with the standard US lesson on the same topic. Teachers often give definitions of complementary and supplementary angles to students, who then practice with thirty short questions. The defining characteristic of the lesson in China was struggle—the teacher deliberately put the students in situations where they became stuck and had to think hard. The lesson was entirely consistent with researchers’ description of targeted, mistake-focused practice. As Coyle says, the best way to build a highly effective circuit is to “fire it, attend to mistakes, then fire it again.” This is what the teachers in China were enabling their students to do.

Elizabeth and Robert Bjork are scientists at UCLA who have studied learning for decades. They point out that a lot of learning that happens is very unproductive, as the most important learning events often go against intuition and deviate from standard practices in schools. They highlight the importance of “desirable difficulties,” again suggesting that the brain needs to be pushed to do things that are difficult. They particularly highlight the act of retrieving information from the brain, as every time we retrieve something, it changes in the brain and is more accessible when needed later.¹¹

Many people study for tests by rereading materials, but the Bjorks point out that this is not very helpful for the brain. A much more helpful way of reviewing material is to test yourself, so that you keep having to recall the material—and hopefully make mistakes and correct them along the way. Learning scientists point out that these tests should not be performance events, as these cause stress and reduce the learning experience. Nonevaluative self-testing or peer testing is most beneficial.¹²

Teaching the Value of Mistakes

As neuroscience becomes more established as a field, it seems that more and more evidence is revealing the value of mistakes and struggle. Good teachers have known this intuitively and impressed upon learners that mistakes are really good opportunities for learning. Unfortunately, I have found that this message is not strong enough to keep students from feeling bad when they make mistakes—often because of the performance culture in which many good teachers work. Even when the message is phrased more powerfully—that mistakes are good not only for learning, but for brain growth and connectivity—it is hard for teachers to send it in a system in which they are made to give students tests that penalize them every time they make a mistake.

This highlights the challenge of changing education—it is a complex system that has many different parts, all of which impact each other. Teachers can give the right messages to students, but then witness their messages being undermined by a practice that is imposed by their school district. This is why I encourage any teacher who learns about effective messages and teaching ideas to share them not only with their students, but with administrators and parents as well.

When teachers encourage students to make mistakes and struggle, it is incredibly freeing. New Zealand second-grade teacher Suzanne Harris began teaching in an era of procedural teaching and timed testing. When she read one of my books, she knew that what she felt was right was backed up by research and asked her principal if she could teach the “Jo Boaler way”! He agreed. Suzanne went on to make many changes, one of which was to explain the positive benefits of mistakes and struggle to her students. In my interview with Suzanne, she described how this and other messages had changed things for a young boy in her class.

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