Limitless Mind

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.

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.

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.

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.

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.”

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.”

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.

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.”

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.

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.

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.