Fire those synapses

Hi. Mrs. Sanford Speaking.

I hope everyone had a fun and festive 4th of July. The great thing about a Tuesday 4th is that there’s a very long weekend followed by a very short week 🙂

Anyways, back to summer reading.

Another book I’m currently reading is Mathematical Mindset by Jo Boaler. If I were to tell my past self that I’d be thoroughly enjoying a book about Math, my past self would have a heart attack. I’m not just enjoying the read though, I’m gobbling it up, and telling friends about it, and taking notes, and digging into all of Boaler’s tangential resources (many of which I’ve shared in the Resources page). And I’ll tell you what, it is changing my views, not only on math education, but also on mindset and on homework. There is so much packed into this book. In this post, I’m going to focus only on the Math Mindset piece. “Revolutionizing Math Education” and the “Homework Battle” will come later.

Let’s begin with just a little overview of the book. In Mathematical Mindset, Boaler explains that, despite what is commonly believed and what people often say, there is no such thing as a “math person” or a “math brain.” On the contrary, we all have the ability to learn high levels of math. Boaler says “We need to free young people from the crippling idea that they must not fail, that they cannot mess up, that only some students can be good at math…” (Boaler, 2016). She gives examples of how to open up problem sets in math to make them more meaningful and accessible, as well as techniques to change the language we use and the classroom culture from one of fearing mistakes to one of embracing mistakes. There is also a huge Appendix in the back that provides many wonderful examples of the ideas and exercises that Boaler explains in the book. This resource isn’t just for teachers though. I know a hand full of parents who say that reading this book is just as beneficial with their approach to parenting as it is in directing their teaching in class. 

So…. Mindset!

Carol Dweck, a friend and colleague of Boaler’s, and the author of the forward of this book, is a leader in the discussion on the power of Mindset (you may recognize her name from my first post about Summer Reading). According to Dweck, there are two different types of mindsets: Fixed Mindset and Growth Mindset. You can find a more detailed definition on Dweck’s website, Mindset online, but here’s a quick synopsis in regards to math:

  • Kids (and adults) with fixed mindsets believe that they are either good at math or bad at math and that very little they do is going to change that. For example, someone who has never really thrived in math may believe that he is just “not a math person,” when really he just hasn’t been given the opportunity to connect with math in a meaningful way. People with fixed mindsets believe that mistakes are bad. They are often terrified of making mistakes because they fear that making mistakes will result in them being labeled as stupid.
  • Kids (and adults) with growth mindsets, on the other hand, believe that intelligence grows and that the more they learn, the smarter they become. They are encouraged by mistakes because, as Boaler points out, mistakes make synapses in our brain fire, resulting in brain growth.



“A lot of evidence suggests that the differences 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 opportunity they have to learn” (Boaler, 2016).

People aren’t born with these mindsets, they are learned. They’re learned by experiences with teachers and schools, exposure to language, observations of parents and friends, etc. Schools, unfortunately, often perpetuate the idea of fixed mindset by grouping students into high and low levels, by giving monotonous worksheets filled with problems with only one right answer, and by grading based on the number of mistakes made on assignments and tests. Fostering a growth mindset in students takes a lot of work. Boaler provides ample examples of ways to change your language and change the nature of your class (or home life) to foster this growth mindset.

One idea is to use language such as “It’s great that you’ve learned that” or “I love how you’re thinking about this problem.” These are two examples of praising what the students have done and learned, instead of praising them as a person. Notice the difference between these responses and “You are so smart.”

It may not seem problematic to tell a kid she’s smart. In fact, it seems kindof nice, right? People love hearing that they’re smart. The problem is, labeling someone as “smart” often puts so much pressure on the kid to stay “smart” that they are terrified of making mistakes and losing their status as “smart.” Research shows that kids who are labeled as smart by parents or teachers choose to do less rigorous work in order to not fail, because failing would take away their “smartness.” Whereas kids who are praised for their determination and grit chose to attempt more difficult work. What do we want to value, kids who are afraid to take on the challenge of more difficult problems just to maintain their status as smart, or kids who are continually willing to challenge themselves and recognizing that their effort is paying off?

Another example in the book that Boaler gives as the type of language that she uses with her students is: “Do you know what just happened? When you got that answer wrong, you’re brain grew.” I love how she’s flipped that around and turned mistakes into fabulous learning and growth opportunities instead of failures to avoid at all costs. 

Changing your language in order to foster a growth mindset is not easy. I tried to be mindful of the language I was using with my math students at the end of this school year, and I noticed that I often used phrases such as “Look at you! So smart!” I made a concerted effort to change these messages to ones where the kids were able to recognize their own hard work and effort on tasks. I had the pleasure of witnessing my colleague, who was also reading Mathematical Mindsets, implement many of Boaler’s strategies a little bit earlier in the school year, and it was really fun to see the difference in the attitude of the kids in her class. 

This mindset and language aspect of the book really struck me because I was one of those students who said “math just isn’t my thing” and I grew up absolutely accepting that I’m just not a “math person.” It’s one way of writing off a failure or briefly explaining away a weakness. And it’s a perfectly accepted excuse in this day and age. All the time, I hear teachers say to students “It’s okay, math was never really my thing, either – you just have to get through it.” What kind of message does this send to kids?

Evidence suggests that this attitude and language among teachers, especially female elementary teachers (which make up a very large percentage of that subset), is a major contributing factor for why young girls lose interest in math. We should all be working extra hard to reverse the downward trend of women and girls in STEM disciplines.

I’m not sure I’ll ever teach math again (remember, I’m in a big transitional phase), but encouraging a growth mindset is cross-curricular. Wherever the future brings me in my teaching career, I will be sure to start off with heavy growth mindset building and strive to practice better language and encouragement with the kids. Mathematical Mindset provides much of what you’d need in order to preparation for this type of setup. 

Boaler provides many ways for teachers and parents to build student’s growth mindsets in class and at home. Here are her 7 “norms”:

positive norms

Another example is that she likes to start classes by telling students what she values and what she does not value:

I value

  • displaying your work in multiple different representations (graphs, pictures, charts, sequence, color coding, etc)
  • deep thinking
  • the ability to explain your thought process and your answer to a skeptic
  • questions and mistakes

I do not value

  • speed*

*speed is often the measure of ability in math. Kids who quickly solve math equations are thought to be smart. Boaler stresses that it is important to praise deep thinking and discussion over speed, and giving open ended problems instead of simple equations naturally encourages deep thinking and discussion.

albert einstein

The mindset aspect is integral to Boaler’s approach to successful mathematics experiences. Check out this quick video that Boaler made with some of her grad students at Stanford. 


I can’t express how incredibly resourceful this book is. It’s packed with “Aha” moments and I believe that if it was required reading for all math (and other subject) teachers, kids would be more confident with their abilities, more competent in their problem solving skills and the US would not be 35th in the world in math scores.

There are a few more links to some amazing resources from Boaler and her Stanford YouCubed organization on the Resources page, such as videos, activities and some online professional development courses. Check ’em out.

-Mrs. Sanford



Mindset chart created by Reid Wilson; icon by

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