The Power of Yet

 

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.

Beliefs vs Brains

 

In order to study the impact of our beliefs on our health, Stanford researchers Alia Crum and Octavia Zahrt collected data from 61,141 people over an extensive time span, twenty-one years. The researchers found that those people who thought they were doing more exercise were actually healthier than those who thought they were doing less, even when the amount of exercise they were doing was the same.

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If you enter a challenging situation believing in yourself, but then mess up, your brain will react more positively than if you go into a situation thinking, “I don’t think I can do this.” If we have a difficult job or a problematic situation at home, this result should prompt us to go into those situations believing in ourselves. If we enter difficult situations with positive beliefs, our brains will become more resilient and adaptative when we make errors than if we are doubting ourselves. This change in belief alters the physical structures of the brain and creates avenues for higher-level thinking and creative problem solving. Just as those who believed they were engaging in healthy exercise became healthier, those who believe they are learning more productively actually learn more.

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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. 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.”

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It is just as important to take on ideas about social comparison with students as it is to make them aware of the value of struggle. I have had many conversations with learners of all ages who argue that brains must be fixed, because some people appear to get ideas faster and to be naturally “gifted” at certain subject areas. What they do not realize is that brains are growing and changing every day. Every moment is an opportunity for brain growth and development. Some have simply developed stronger pathways on a different time line. It is critical that students understand that they too can develop those pathways at any time—they can catch up with other students if they take the right approach to learning.

Mathematical Mindsets [Jo Boaler] (3):The Power of Mistakes and Struggle

Every time a student makes a mistake in math, they grow a synapse. (Carol Dweck)

Psychologist Jason Moser studied the neural mechanisms that operate in people's brains when they make mistakes (Moser et al., 2011).

Moser's study shows us that we don't even have to be aware we have made a mistake for brain sparks to occur. When teachers ask me how this can be possible, I tell them that the best thinking we have on this now is that the brain sparks and grows when we make a mistake, even if we are not aware of it, because it is a time of struggle; the brain is challenged, and this is the time when the brain grows the most.

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In Moser and his colleagues' study, the scientists looked at people's mindsets and compared mindsets with their ERN and Pe responses when they made mistakes on questions. Moser's study produced two important results. First, the researchers found that the students' brains reacted with greater ERN and Pe responses—electrical activity—when they made mistakes than when their answers were correct. Second, they found that the brain activity was greater following mistakes for individuals with a growth mindset than for individuals with a fixed mindset. Figure 2.1 represents brain activity in individuals with a fixed or growth mindset, with the growth mindset brains lighting up to a much greater extent when mistakes were made.

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The fact that our brains react with increased activity when we make a mistake is hugely important. I will return to this finding in a moment.

The study also found that individuals with a growth mindset had a greater awareness of errors than individuals with a fixed mindset, so they were more likely to go back and correct errors. This study supported other studies (Mangels, Butterfield, Lamb, Good, & Dweck, 2006) showing that students with a growth mindset show enhanced brain reaction and attention to mistakes. All students responded with a brain spark—a synapse—when they made mistakes, but having a growth mindset meant that the brain was more likely to spark again, showing awareness that a mistake had been made. Whether it is mathematics, teaching, parenting, or other areas of your life, it is really important to believe in yourself, to believe that you can do anything. Those beliefs can change everything.

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Moser's study, showing that individuals with a growth mindset have more brain activity when they make a mistake than those with a fixed mindset, tells us something else very important. It tells us that the ideas we hold about ourselves—in particular, whether we believe in ourselves or not—change the workings of our brains. If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make a mistake. This result is highly significant, telling us again how important it is that all students believe in themselves—and how important it is for all of us to believe in ourselves, particularly when we approach something challenging.

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“Peter Sims, a writer for the New York Times, has written widely about the importance of mistakes for creative, entrepreneurial thinking (Sims, 2011). He points out: 

“Imperfection is a part of any creative process and of life, yet for some reason we live in a culture that has a paralyzing fear of failure, which prevents action and hardens a rigid perfectionism. It's the single most disempowering state of mind you can have if you'd like to be more creative, inventive, or entrepreneurial.”

He also summarizes the habits of successful people in general, saying that successful people:

Feel comfortable being wrong

Try seemingly wild ideas

Are open to different experiences

Play with ideas without judging them

Are willing to go against traditional ideas

Keep going through difficulties”

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One of the most powerful moves a teacher or parent can make is in changing the messages they give about mistakes and wrong answers in mathematics.

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Another strategy for celebrating mistakes in class is to ask students to submit work of any form—even test papers (although the less we test students the better); teachers then highlight their “favorite mistakes.” Teachers should share with students that they are looking for their favorite mistakes, which should be conceptual mistakes, not numerical errors. Teachers can then share the mistakes with the class and launch a class discussion about where the mistake comes from and why it is a mistake. This is also a good time to reinforce important messages—that when the student made this mistake, it was good, because they were in a stage of cognitive struggle and their brain was sparking and growing. It is also good to share and discuss mistakes, because if one student makes a mistake we know others are making them also, so it is really helpful for everyone to be able to think about them.

Mathematical Mindsets [Jo Boaler] (2):The Brain and Mathematics Learning

In the last decade we have seen the emergence of technologies that have given researchers new access into the workings of the mind and brain. Now scientists can study children and adults working on math and watch their brain activity; they can look at brain growth and brain degeneration, and they can see the impact of different emotional conditions upon brain activity. One area that has emerged in recent years and stunned scientists concerns “brain plasticity.” It used to be believed that the brains people were born with couldn't really be changed, but this idea has now been resoundingly disproved. Study after study has shown the incredible capacity of brains to grow and change within a really short period (Abiola & Dhindsa, 2011; Maguire, Woollett, & Spiers, 2006; Woollett & Maguire, 2011).

When we learn a new idea, an electric current fires in our brains, crossing synapses and connecting different areas of the brain.

 
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If you learn something deeply, the synaptic activity will create lasting connections in your brain, forming structural pathways, but if you visit an idea only once or in a superficial way, the synaptic connections can “wash away” like pathways made in the sand. Synapses fire when learning happens, but learning does not happen only in classrooms or when reading books; synapses fire when we have conversations, play games, or build with toys, and in the course of many, many other experiences.

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The new findings that brains can grow, adapt, and change shocked the scientific world and spawned new studies of the brain and learning, making use of ever-developing new technologies and brain scanning equipment. In one study that I believe is highly significant for those of us in education, researchers at the National Institute for Mental Health gave people a 10-minute exercise to work on each day for three weeks. The researchers compared the brains of those receiving the training with those who did not. The results showed that the people who worked on an exercise for a few minutes each day experienced structural brain changes. The participants' brains “rewired” and grew in response to a 10-minute mental task performed daily over 15 weekdays (Karni et al., 1998). Such results should prompt educators to abandon the traditional fixed ideas of the brain and learning that currently fill schools—ideas that children are smart or dumb, quick or slow. If brains can change in three weeks, imagine what can happen in a year of math class if students are given the right math materials and they receive positive messages about their potential and ability.

 
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The new evidence from brain research tells us that everyone, with the right teaching and messages, can be successful in math, and everyone can achieve at the highest levels in school. There are a few children who have very particular special educational needs that make math learning difficult, but for the vast majority of children—about 95%—any levels of school math are within their reach. And the potential of the brain to grow and change is just as strong in children with special needs. Parents and teachers need to know this important information.

 
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I am often asked whether I am saying that everyone is born with the same brain. I am not. What I am saying is that any brain differences children are born with are nowhere near as important as the brain growth experiences they have throughout life. People hold very strong views that the way we are born determines our potential; they point to well-known people who were considered geniuses—such as Albert Einstein or Ludwig van Beethoven. But scientists now know that any brain differences present at birth are eclipsed by the learning experiences we have from birth onward (Wexler in Thompson, 2014). Every second of the day our brain synapses are firing, and students raised in stimulating environments with growth mindset messages are capable of anything. Brain differences can give some people a head start, but infinitesimally small numbers of people have the sort of head start that gives them advantages over time. And those people who are heralded as natural geniuses are the same people who often stress the hard work they have put in and the number of mistakes they made. Einstein, probably the most well known of those thought to be a genius, did not learn to read until he was nine and spoke often about his achievements coming from the number of mistakes he had made and the persistence he had shown. He tried hard, and when he made mistakes he tried harder. He approached work and life with the attitude of someone with a growth mindset. A lot of scientific evidence suggests that the difference between those who succeed and those who don't is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunities they have to learn. The very best opportunities to learn come about when students believe in themselves. For far too many students in school, their learning is hampered by the messages they have received about their own potential, making them believe they are not as good as others, that they don't have the potential of others. 

When students are given fixed praise—for example, being told they are smart when they do something well—they may feel good at first, but when they fail later (and everyone does) they think that means they are not so smart after all.

 
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The impact of the praise students receive can be so strong that it affects their behavior immediately. In one of Carol's studies, researchers asked 400 fifth graders to take an easy short test, on which almost all performed well. Half the children were then praised for “being really smart.” The other half were complimented on “having worked really hard.” The children were then asked to take a second test and choose between one that was pretty simple, that they would do well on, or one that was more challenging, that they might make mistakes on. Ninety percent of those who were praised for their effort chose the harder test. Of those praised for being smart, the majority chose the easy test (Mueller & Dweck, 1998).

Praise feels good, but when people are praised for who they are as a person (“You are so smart”) rather than what they did (“That is an amazing piece of work”), they get the idea that they have a fixed amount of ability. Telling students they are smart sets them up for problems later. As students go through school and life, failing at many tasks—which, again, is perfectly natural—they evaluate themselves, deciding how smart or not smart this means they really are. Instead of praising students for being smart, or any other personal attribute, it's better to say things like: “It is great that you have learned that,” and “You have thought really deeply about this.”

 

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There is no preordained pace at which students need to learn mathematics, meaning it is not true that if they have not attained a certain age or emotional maturity they cannot learn some mathematics. Students may be unready for some mathematics because they still need to learn some foundational, prerequisite mathematics they have not yet learned, but not because their brain cannot develop the connections because of their age or maturity. When students need new connections, they can learn them.