*Jo Boaler is a professor of math education at Stanford University and has written several books and research articles related to math education. She also co-founded youcubed.org, an organization and website that offers math education resources to students, teachers and parents. In addition, Boaler advises Silicon Valley companies and has given White House presentations on Girls and Science, Technology, Engineering and Math, or STEM. EdSource interviewed Boaler about her work and her latest book, “Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching.” Below are excerpts from the interview and her book.*

**Why is there a common belief in society that some people are naturally good at math and others are not?**

It seems that people in the U.S. believe this about mathematics, but not other subjects. In some countries, people believe that learning is a long and slow process that happens over time, in all subjects. Here in the U.S., and some other countries, people are quick to believe that if a math problem is hard to solve, then you are not “a math person.” It is difficult to know where this started, but I would say it is linked to the teaching of mathematics. That tends to be all about right or wrong answers and speed.

When we add to this the idea that people who can do math are (considered) “smart,” then any math struggle becomes truly devastating for students. My book attempts to debunk this myth, pointing out that all subjects are difficult in different ways and part of the reason people think math is so difficult is the faulty ways in which it is taught.

**Excerpt from “Mathematical Mindsets”:** “When I taught my online class, and I read all the responses from the people who took it, I realized more strongly than ever before that many people have been traumatized by math. Not only did I find out how widespread the trauma is, but the evidence I collected showed that the trauma is fueled by incorrect beliefs about mathematics and intelligence. Math trauma and math anxiety is kept alive within people because these incorrect beliefs are so widespread that they permeate society in the United States, the United Kingdom, and many other countries in the world.” *(From the introduction)*

**How does a person’s mindset affect his or her ability to excel in math?**

Research shows us that people with a “growth mindset” tend to be those who do well in math, and other subjects, and who keep increasing their achievement as they engage in learning, more than those with a “fixed mindset.” The likely cause ￼￼for this is that if you believe you are smart or not, and you struggle on a task, you are likely to conclude you are not smart and give up. If you believe that you can learn anything, and that struggle is part of the process of learning and you struggle, you keep going and keep learning.

**Excerpt from “Mathematical Mindsets”:** “People with a growth mindset are those who believe that smartness increases with hard work, whereas those with a fixed mindset believe that you can learn things but you can’t change your basic level of intelligence. Mindsets are critically important because research has shown that they lead to different learning behaviors, which in turn create different learning outcomes for students.” *(From the introduction)*

**How can teachers make math more interesting to students and encourage them to believe they can succeed?**

This is expanded fully in my book – but in a sentence, open up math, show math as an open, growth subject, not a closed, fixed subject. Ask questions and value the different thinking kids reveal – different routes through the problem, different ways of seeing the math.

**Excerpt from “Mathematical Mindsets”:** “Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people. Teachers can create such mathematical excitement in classrooms, with any task, by asking students for the different ways they see and can solve tasks and by encouraging discussion of different ways of seeing problems.” *(Chapter 5: Rich Mathematical Tasks –page 59)*

“Teachers can encourage students to use intuition with any math problem simply by asking them what they think would work, before they are taught a method.” *(Chapter 9: Teaching Mathematics for a Growth Mindset – page 188)*

**How can parents help their children to be successful in math?**

Here is some advice adapted and excerpted from information on the youcubed website:

1. Encourage children to play math puzzles and games. … Puzzles and games – anything with dice, really – will help kids enjoy math, and develop number sense, which is critically important.

2. Always be encouraging and never tell kids they are wrong when they are working on math problems. Instead find the logic in their thinking … .

￼￼￼￼

3. Never associate math with speed. It is not important to work quickly, and we now know that forcing kids to work quickly on math is the best way to start math anxiety for children, especially girls.

4. Never share with your children the idea that you were bad at math at school or you dislike it – especially if you are a mother. Researchers found that as soon as mothers shared that idea with their daughters, their daughters’ achievement went down.

5. Encourage number sense … having an idea of the size of numbers and being able to separate and combine numbers flexibly … .

6. Perhaps most important of all – encourage a “growth mindset” – let students know that they have unlimited math potential and that being good at math is all about working hard… use growth praise such as “It is great that you have learned that;” “I really like your thinking about that;” “You have worked really hard to learn that.”

**How does your work relate to Common Core math standards?**

My book and our website provide many mathematics tasks and advice on teaching that help teachers with Common Core mathematics. The tasks and advice are all consistent with the Common Core and the changes teachers need to make.

**Excerpt from “Mathematical Mindsets”:** “One of the most important contributions of the Common Core State Standards (CCSS), in my view, is their inclusion of mathematical practices – the actions that are important to mathematics, in which students need to engage as they learn mathematics knowledge. ‘Modeling with mathematics’ is one of the eight Mathematics Practices Standards … (using such tools as diagrams, two-way tables, graphs, flowcharts and formulas).”

“Modeling happens all through mathematics, but students have not typically been aware that they are modeling or asked to think about the process.” *(Chapter 9: Teaching Mathematics for a Growth Mindset – pages 195-196)*

“I speak to many groups of parents about Common Core math, and I am often asked, especially by the parents of high-achieving students, ‘Why should my child discuss his work in a group, when he can get the answers quickly on his own?’ I explain to parents that explaining one’s work is a mathematical practice, called reasoning, that is at the heart of the discipline. … Mathematicians propose theories and reason about their mathematical pathways, justifying the logical connections they have made between ideas.” *(Chapter 9: Teaching Mathematics for a Growth Mindset – pages 205-206)*

## Comments (20)

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Anna12 months ago12 months agoI would like to interact with you regarding mathematics education. I am a teacher educator working on mathematics education.

You site is a source of inspiration.

Al Dente1 year ago1 year agoWhen I went to college calculus was a prerequisite for physics. I was told that I couldn't understand college physics without first knowing calculus. I don't think this is the case. I was asking my son what he learned in school and he mentioned learning the quadratic formula. I asked him what sorts of problems he needed to know the roots of polynomials to solve. Other than questions on his … Read More

When I went to college calculus was a prerequisite for physics. I was told that I couldn’t understand college physics without first knowing calculus. I don’t think this is the case. I was asking my son what he learned in school and he mentioned learning the quadratic formula. I asked him what sorts of problems he needed to know the roots of polynomials to solve. Other than questions on his math homework and tests, he didn’t know any.

I think the problem is teaching math as a separate discipline. What if making students learn seemingly inscrutable math skills so they can later have an epiphany and understand their physics is the wrong approach? How about if we taught physics and the calculus it requires at the same time? The physics would make the math relevant while the math would make the physics clear. I understand that there would still be math as a discipline; for those who excel at symbolic understanding, it could be studied in its own right. But for everyone else, why not teach math along with the subjects that require it?

Gail Rosen2 years ago2 years agoAll of this explaining ideas is very difficult for brilliant children, who do not process the verbal skills to "explain." I find this curriculum needs a new way to accommodate children who happen to understand but have language disability and can not explain. I find some of the common core discriminatory against vey capable non-verbal/low verbal disorders. Math should not need to be explained to a group of peers. I'm pulling my student out … Read More

All of this explaining ideas is very difficult for brilliant children, who do not process the verbal skills to “explain.” I find this curriculum needs a new way to accommodate children who happen to understand but have language disability and can not explain. I find some of the common core discriminatory against vey capable non-verbal/low verbal disorders. Math should not need to be explained to a group of peers. I’m pulling my student out of his new geometry class because they are not taking notes, nothing is explained and it’s a disorganized mess that will not prepare him for the SAT or college.

Education should have Universal access and carefully mixed different methods rather that following trends like hemlines on a skirt. Common Core does not serve disabled populations of many minorities very well. This approach can be very limiting for inclusion of special education population that is very capable but does not learn in an overall verbal way. So what, if you can do the work and are unable to explain because you are speech impaired. In my son’s class, there are no lectures, no notes, and you sit with a group all period with a tile and talk about it and this is the 10th grade!

Karin Horne2 years ago2 years agoWhat is written is so true. Being a math teacher in junior grades I see how much children learn and cement their skills by trying to exlain verbally to their peers how they were thinking when they set out to solve a problem. They improve verbally every time! Some of the ‘weaker/slower’ children are very logical thinkers and as their confidence grows they become eager to explain their thinking too!

ann2 years ago2 years agoSo if, in five years after we have invested blood and treasure into Boalers belief system, the results are decreasing math proficiency, will she agree to give up her job at Stanford (or will the university have the integrity to fire her) and donate all the money she’s making pushing her ‘research’ to the CDE?

Norma2 years ago2 years agoAs a retired math teacher who loved teaching through my last day and still enjoys tutoring teens in algebra, geometry and trig, I so appreciated your words and share your ideas and practices! Thank you!

Kristin2 years ago2 years agoThat’s all “fine and good” but teaching math in this way to children who are not mature enough to get it causes frustration and sets them up for failure. I witness this almost daily. If parents can’t understand a 1st grade common core math worksheet without it being explained (including a parent who is a former college level math teacher), there’s something NOT RIGHT.

Melissa Clifford2 years ago2 years agoI was very fortunate to have some wonderful professors when I was pursuing my degree in Education. My math education teacher was my favorite (Dr. Raji). I was taught how to be a good teacher, to always question my methods, to try new methods with different students, to individualize assignments to meet the needs of varied students. Being a good teacher, however, is not compatible with today's schools. Teachers really can't "improve math education." They … Read More

I was very fortunate to have some wonderful professors when I was pursuing my degree in Education. My math education teacher was my favorite (Dr. Raji). I was taught how to be a good teacher, to always question my methods, to try new methods with different students, to individualize assignments to meet the needs of varied students.

Being a good teacher, however, is not compatible with today’s schools. Teachers really can’t “improve math education.” They may have the ability and the desire to do so, but if they don’t follow the curriculum as instructed, they can lose their job. When they get a high school student in their algebra class who doesn’t know the multiplication table, doesn’t know decimal rules, is afraid of fractions, they are told they still need to give the kid algebra work and expect the student to do it.

Administrators do not understand – for the most part – math instruction. Either that or they really just don’t care about getting kids to overcome math fear and to solidify their foundational skills. If a teacher wants to be a really good math teacher, that teacher is going to have to battle EVERY SINGLE DAY: principals, teaching coaches, parents who think their 17-year-old shouldn’t be taking home a multiplication table, etc., etc., etc. After 14 years of loving teaching math – and hating being a teacher – I am leaving my profession.

Renee Webster-Hawkins2 years ago2 years agoThis looks like important work, applying growth mindset principals into math and STEM curriculum. Does Professor Boaler study or adapt her recommendations specifically for kids with dyslexia (who have trouble with reading word problems ), dyscalculia or working memory struggles?

Sandra Stockall2 years ago2 years agoYour views and ideas about Mathematics strongly support my understanding of how our whole culture and not just our system or classrooms are affected by mathematically teaching in the last century. We are one small but passionate team in Moncton, New Brunswick, Canada that are working to change teachers ways of thinking. Thank you for your dedication to mathematics.

Sincerely

Sandra Stockall

Subject Coordinator of Mathematic K-5

Anglophone East School District

Barbara Flake3 years ago3 years agoMy mother once said to me, when I was struggling with math: “When you can understand the odds in poker like you do, you’ve already conquered math”.

Lynette3 years ago3 years agoI agree that math is a process and people approach it differently. I was excited for Common Core because I thought it would encourage students to look at problems differently that they could understand. So far, my daughter, who gets frustrated with math and believes she should not be in our family because math has always been easy, is more frustrated than ever. I see Common Core just the same … Read More

I agree that math is a process and people approach it differently. I was excited for Common Core because I thought it would encourage students to look at problems differently that they could understand. So far, my daughter, who gets frustrated with math and believes she should not be in our family because math has always been easy, is more frustrated than ever. I see Common Core just the same as it was but with more work. It still has to be done a certain way and not giving her the ability to understand her way. I think as long as she is able to show how her thought process, even though differently, should be allowed as long as she can come to the right conclusion. Once you see where she is thinking, you could correct or show her where she may have gone wrong.

Dr. Charles Wright III, MD, MS3 years ago3 years agoYou are truly a blessing to education. Trying to fix a nearly dead and dying system that once worked so well is a feat of infinite proportions. Getting parents, teacher, and kids excited is most of the battle....linking it to subjects that are creative and explorative is a genius idea. Thanks so much for rekindling the fire I once had. I got tired … Read More

You are truly a blessing to education. Trying to fix a nearly dead and dying system that once worked so well is a feat of infinite proportions. Getting parents, teacher, and kids excited is most of the battle….linking it to subjects that are creative and explorative is a genius idea. Thanks so much for rekindling the fire I once had. I got tired of fighting the system only to find out I just needed to change my perspective and those of others.

Replies

Alistair Windsor3 years ago3 years agoYou don’t need to link mathematics to subjects that are creative and explorative … mathematics itself IS creative and explorative!

Dr. Asher Wade3 years ago3 years agohttps://www.youtube.com/watch?v=UIKGV2cTgqA

ISELA3 years ago3 years agoBY FAR ONE OF THE BEST BOOKS EVER WRITTEN ABOUT MATH!!!!!! We’re introducing it at our upcoming kindergarten conference in Arizona! Thank you for writing this book!

John Densler3 years ago3 years agoI am an electrical engineer who taught business and algebra as a second vocation at a college level. The most important part was to convince students that they could actually do the work. My method was to explain that I could do the work in my sleep and I was going to share the easy way to get the correct results every time I used a very mechanistic methodology using an overhead projector with a three … Read More

I am an electrical engineer who taught business and algebra as a second vocation at a college level. The most important part was to convince students that they could actually do the work. My method was to explain that I could do the work in my sleep and I was going to share the easy way to get the correct results every time

I used a very mechanistic methodology using an overhead projector with a three step process. Step one was to go over a problem on the overhead; the students had a copy of the overhead. Second step was a similar problem where the students would do a step, then I would do the step, until the problem was solved. Next, a problem was presented and the students did all the steps, then I went over all the steps. My grading method, “0” for just the answer, 100% if all the steps were done as I showed the students. Homework was 5 – 8 of similar problems.

Each week a quiz. A 90 or above, no need to hand in homework, unless you did not maintain the 90% average.

Usually, the results were quite good. Part of the explanation was that there were situations in engineering where calculations became legal issues. For these cases, it was critical to show all the details as a defense in court!

Verinda3 years ago3 years agoI really like and understand the mindset, would love to know how to apply it to Adult Education GED.?

Monica Racz3 years ago3 years agoThis is not really a new concept. The reality is we expect children to learn math at the same rate and your research shows the opposite. Common Core has great ideas but we need time in school day to implement. Too much pressure is on parents for their children to keep up. Clearly disadvantaged students don't have that support. So the achievement gap increases. It is more than just trying harder. Yes that helps but … Read More

This is not really a new concept. The reality is we expect children to learn math at the same rate and your research shows the opposite. Common Core has great ideas but we need time in school day to implement. Too much pressure is on parents for their children to keep up. Clearly disadvantaged students don’t have that support. So the achievement gap increases. It is more than just trying harder. Yes that helps but we need to adjust our curriculum for different levels of learning. I am not a proponent of tracking but smaller class sizes allowing for creative differentiation could help a lot. We also need to look at assessment. We differentiate instruction but everyone takes the same standardized test. Why?

Felipe Razo3 years ago3 years agoCan we think of "re-engineering" our basic quantitative education in terms that make sense to the children, and their teachers? Today we seem to invoke "STEM" education, but seldom emphasize the nature and interrelationships of each of the subjects in the K-12 classroom. The simplest concepts of tools, systems, functions and numeric coding seem quite outdated and we still embrace old concepts as if they were untouchable. Do we need to really … Read More

Can we think of “re-engineering” our basic quantitative education in terms that make sense to the children, and their teachers? Today we seem to invoke “STEM” education, but seldom emphasize the nature and interrelationships of each of the subjects in the K-12 classroom. The simplest concepts of tools, systems, functions and numeric coding seem quite outdated and we still embrace old concepts as if they were untouchable. Do we need to really approach the “digital era” with a digital mindset? We (teachers, parents professionals, social activists) do know how to work in interdisciplinary teams, so why don’t we do what we preach?