Limitless Mind: Learn, Lead, and Live Without Barriers

by Jo Boaler

A similarly impressive result came from a study of pianists.7 Professional pianists were recruited to learn and perform a musical piece, but half of the pianists trained by imagining playing the music and the other half trained by actually playing it. The group who imagined playing the piece not only improved their performance so that they were almost indistinguishable from those who actually played it, but they improved in all of the same ways as the actual players, in movement velocity, movement timing, and movement-anticipation patterns. Scholars point out that imaginary practice is beneficial for pianists, because it can save them from overuse of their hands, which may lead to physical strain.8

I will highlight some incredible new work that the mindset team has been conducting on people’s ability to move out of conflict and become more peaceful. I first met David Yeager when he was a doctoral student at Stanford; he is now a psychologist at the University of Texas at Austin. He and Carol Dweck have conducted important research on mindsets and conflict. They found that people with fixed mindsets (individuals who believe that their abilities and qualities are static and can’t be changed) have a heightened drive for aggressive retaliation during conflicts. Yet when they are given information that causes them to change their mindset, these aggressive tendencies fade away.9 The researchers point out that people with a fixed mindset are more likely to be aggressive, since they believe that people—including themselves—cannot change and that any failure they have experienced themselves is an indication of their own weakness. This causes them to harbor more negative feelings about themselves. Those with a fixed mindset feel more shame, view their adversaries as bad people, and express hatred toward them.

Their improved response to conflict comes about because they view others as being capable of change. Importantly, the aggressive feelings that those with a fixed mindset experienced were not fixed, and when they were helped to develop a growth mindset, they became more forgiving and wanted to help people act in better ways in the future.

In other studies, researchers have found that people with growth mindsets are less prejudiced about race.10

We now know that the idea that some people are “math people” and some are not is a harmful myth.

Considerable evidence exists showing the relevance of the progress that can be made when students believe in their learning potential and let go of ideas that their achievement is genetically determined.

One of Dweck’s studies showed that children’s mindsets, which had come from the type of praise given by parents, were developed by the time they were three years old.

When children are told they are smart, they at first think that is good, but when they mess up on something, they decide they are not smart, and they keep evaluating themselves against that fixed idea.

One of Dweck’s studies revealed the immediate impact of the word “smart.” Two groups of students were given a challenging task. On completion, one group was praised for being “really smart,” and the other was praised for working hard. Both groups were then offered a choice between two follow-up tasks, one that was described as easy and one that was described as challenging. Ninety percent of the students praised for working hard chose the harder task, whereas the majority of the students praised for being “smart” chose the easy task.14 When students are praised for being smart, they want to keep the label; they choose an easy follow-up task, so they can continue to look “smart.”

In the interview study we conducted for this book with sixty-two adults who reported change, it became clear that people can change at any age. The interviews also revealed the detailed ways that fixed ideas can lock people up and, conversely, the ways that mindset and growth ideas can unlock them.

Even students in advanced groups believe they are not good enough if they are not at the top of their group.

Fixed-brain thinking leads to these rigid beliefs and unproductive comparisons.

brains are growing and changing every day. Every moment is an opportunity for brain growth and development.

When students become disillusioned because others are ahead of them or complain that they don’t understand something, a word that Carol Dweck champions using with them is “yet.”

When I ask adults to visually represent an idea, I often hear them say, “I am terrible at drawing.” I tell them, “You mean you have not learned to draw well yet.” This may seem like a small linguistic change, but it is an important one. It moves the focus from the perceived personal lack to the process of learning.

Social comparison is particularly damaging when it is based on supposed genetic endowment. When children think that their sibling or classmate was born with a better brain and that brain will always be superior, it is demoralizing. It would be better if, instead, children saw a peer’s or sibling’s ability as a challenge and an opportunity—“Because they can do it, I can too.”

Part of the process of change and of becoming limitless involves letting go of the idea that your past failures came about because there was something wrong with you. A similarly important change is realizing that you do not have to live your life as an “expert,” that you can go into situations and proudly share uncertainty.

The feeling of paralyzing stress Jesse described, the fear of being asked something he could not answer, is a feeling shared by millions of people in different situations and jobs, and it is a feeling that I hope this book can change.

Carol talks about the importance of being in touch with your different mindset personas, because the more you can be on the lookout for your fixed-mindset thinking, the more you can be ready to greet it and warn it to stop.

She explains that “false growth mindset” thinking is telling students they simply need to try harder and praising them for effort even if they fail. She says that this backfires because students know that the praise is a consolation prize. Instead, teachers and others should praise the learning process and, if students are not making progress, help them find other strategies and different approaches. Crucially, praise should be linked to effort that leads to something important.

Neural pathways and learning are optimized when considering ideas with a multidimensional approach.

Carol Dweck herself has written that the information on the value of changing mindsets needs to be accompanied by a different approach to teaching, one that enables students to learn differently.

As she says, “Effort is key for students’ achievement, but it is not the only thing. Students need to try new strategies and seek input from others when they are stuck.”

Alfie Kohn, a great educational writer and leader, has criticized the mindset movement, saying it is unfair to tell students to change—to tell them to try harder—without changing the system.

The solution is a multidimensional approach to teaching and learning.

We can learn mathematical ideas through numbers, but we can also learn them through words, visuals, models, algorithms, tables, and graphs; from moving and touching; and from other representations. But when we learn by using two or more of these means and the different areas of the brain responsible for each communicate with each other, the learning experience is maximized.

Because of research showing the relationships between fingers and mathematical thinking, neuroscientists highlight the importance of “finger perception”—knowing your individual fingers really well.

Neuroscientists know that it is important for young children to develop the finger area of the brain, which comes about when they use their fingers to represent numbers.

careful consideration of Mozart’s upbringing shows that from the age of three he engaged in the activities that develop a perfect pitch.8

Albert Einstein, probably the person most thought of as a “genius,” embraced mistakes and approached learning in a particularly productive way. Some of my favorite quotes from Einstein include: A person who never made a mistake never tried something new. It’s not that I am smart. It is just that I stay with problems longer. I have no special talent. I am only passionately curious. In the middle of difficulty lies opportunity. These and other quotes from Einstein suggest strongly that he had a growth mindset, even though mindset was not a concept at the time that he was alive. Einstein talked about embracing struggle, staying for a long time with difficult problems, being curious, and making mistakes and rejected fixed ideas of talent and giftedness.

Einstein also engaged with ideas visually. Einstein often said that all of his thinking was visual—and he struggled to then turn his visual ideas into words and symbols.

What is different in the brains of people who “are trailblazers in their fields” is that they have more active connections between different brain areas, more communication between the two hemispheres of the brain, and more flexibility in their thinking.

One of the ways we encourage this multidimensional approach is through what my colleague and fellow youcubed director Cathy Williams calls “diamond paper.”

I will never understand the narrow teaching of science—as a list of facts and rules. That is the perfect way to turn students away from a subject that, at its heart, is about discovery, experimentation, and the possibility of multiple causes and outcomes.

One of my favorite approaches to science comes from John Muir Laws, a passionate nature enthusiast and educator. I love his book The Laws Guide to Nature Drawing and Journaling.

He proposes that people study events by collecting data; finding patterns, exceptions, and changes over time; recording events; and making maps, cross sections, and diagrams. He then shows the multiple ways to dig into data, including writing, diagramming, recording sound, making a list, counting and measuring, using data tools, and building a “curiosity kit,” which is filled with items such as a magnifying glass, a compass, and binoculars.

I always try to be very supportive of my daughters’ teachers, because I know teaching is one of the most demanding jobs possible and teachers are almost always wonderful and caring people. One evening, however, I decided I needed to intervene. My youngest daughter, around nine at the time, had come home with a worksheet of forty questions. She sat in front of the worksheet looking deflated. I was immediately concerned that this sort of worksheet would turn my daughter against math, so I asked her to work on only the first five questions. Then I wrote a note to the teacher on the worksheet that said: I have asked my daughter to only work on the first five questions, and I can see that she understands them. I have asked her not to complete this worksheet, because I do not want her to think this is what math is.

Just over a year ago one of the county instructional coaches for mathematics, Shelah Feldstein, came to visit me at Stanford. She asked me about an idea she had to enroll all of the fifth-grade teachers in several districts in my online class “How to Learn Math.” She also had wonderful plans to organize the teachers to take the course in groups and to sit together and process the ideas in school groups, with funded time. Many amazing things happened over the next year that have been detailed in research papers,16 but one I was particularly pleased with was that the teachers changed their own relationships with math.

He talked about a concept in Judaism called tikkun olam, “healing the world,” and how he sees this as related to having a growth mindset. Marc reflected: “It’s almost, to me, ‘Why am I on this planet? Why am I here? Why am I in this classroom?’ There has to be a reason.” Marc’s positive approach to life, even in times of extreme adversity, is inspiring.

Speed of thinking is not a measure of aptitude. Learning is optimized when we approach ideas, and life, with creativity and flexibility.

Beilock and her team also found that the amount of math anxiety female elementary-school teachers have predicts their female—but not male—students’ achievement.5 I imagine this result comes about because female teachers share their feelings about math through statements I have heard like the obvious, “I was not good at math in school,” but also, “Let’s just get through this quickly, so that we can move to reading time.” Girls are affected by this more than boys, because they identify more with their same-gender teachers. Both studies show that parent and teacher messages about math can reduce students’ achievement. This highlights again the relationship between our beliefs and our achievement.

Some of the strongest mathematical thinkers are very slow with numbers and other aspects of mathematics. They do not think quickly; they think slowly and deeply.

I no longer look at math problems as something to answer quickly, but as something to think about deeply and creatively.

One of the ways that fast learning damages us is when slower learners compare themselves to those working more quickly. This usually results in feeling inadequate at the task at hand.

it is important to give students access to the reasons why methods work, not just give them methods to memorize. In the last chapter I spoke of the value of asking students how they see an idea, which can really help with understanding it conceptually.

“number talks,” was devised by educators Ruth Parker and Kathy Richardson and developed by Cathy Humphreys and Sherry Parrish. The method involves talking about different approaches to number problems. In a number talk, students are asked to work out a number calculation in their heads, without using paper and pencil, and then teachers collect their different methods.

One particularly useful approach in mathematical problem solving is called “taking a smaller case.” When we approach a complex problem by trying it with smaller numbers, the patterns inherent in the problem often become clearer and more visible.

Instead of grading tests with pluses and minuses and giving them back to students, a process that conveys fixed messages to students about their achievement, Nina started to write comments on the students’ work, pointing out what they understood and what they were only beginning to understand.

Nina also gave students more open and conceptual mathematics problems.

In every country the students taking a memorization approach were the lowest achievers, and countries that had high numbers of memorizers—the US was one of these—were among the lowest achieving in the world.