WHAT DID YOU DO THIS SUMMER?

REFLECTIONS ON LEARNING MATH AND THE GROWTH MINDSET 

BY JENNIFER ADAMS

“What did you do this summer?”  I, like most people around a school, have been asked this question numerous times recently.  My first response surprises many people. I biked to school from my home in Novato. After they look at me askance, I quickly add that I got an early birthday present – a red, electric bicycle that makes the journey not only doable, but enjoyable. 

My second response, and the one that I have even more to say about, is that I took an incredible online course titled “How to Learn Math for Teachers,” taught by Dr. Jo Boaler, a professor of mathematics education at Stanford. Dr. Boaler, a recent celebrity in the mathematics education world, reinvigorated my teaching in countless ways.  

Two of Boaler’s lessons that guide my instruction the most these days are a focus on mindset and number sense. Dr. Boaler emphasizes the importance of setting students up for success by creating positive and encouraging class norms. The norms remind students what is true and important to be a growth mindset mathematician, one who sees intelligence and skill as mutable through effort. To foster the growth mindset I am spending the first weeks of class introducing Dr. Boaler’s “Positive and Encouraging Math Norms”:

  1. Everyone Can Learn Math to the Highest Levels. There is no such thing as a “math” person. Through believing in yourself, having a desire to learn, and hard work, you can reach the highest levels in math.

  2. Mistakes are Valuable. Brain research shows that mistakes grow your brain! It is good to struggle and make mistakes. Mistakes are growth opportunities.

  3. Questions are Really Important. Ask and answer questions. Continually ask yourself, “Why does that make sense?”

  4. Math is about Creativity and Making Sense. Math at its core is about visualizing patterns and creating solution paths that others can see, discuss, and critique.

  5. Math is about Connections and Communicating. Math is a connected subject, and a form of communication. Math can be represented by words, pictures, graphs, and equations that can all be linked together.

  6. Depth is much more Important than Speed. Most great mathematicians think slowly and deeply.  

  7. Math Class is about Learning not Performing. Math is a growth subject. It takes time to learn, and it is all about effort.

These norms will remain front and center throughout the year, encouraging our students to approach math with a growth mindset.

With norms in place, Dr. Boaler’s course reminded me of the importance of developing number sense. Boaler defines number sense as a student’s ability to “interact with the numbers flexibly and conceptually.” Number sense helps students see that there are numerous ways to solve a problem, giving them the confidence to experiment and even “play” with numbers, critical skills for more open-ended problem solving and higher level mathematics.  

One of the strategies for developing number sense that Boaler described, Number Talks, is something I know well from working with Kevin Marcovich last year. Kevin would write a number expression such as 8 + 5 on the board and ask the first graders to mentally find the sum. After all students had a moment to think, he would ask for solutions. Next, students had the opportunity to share their strategies for finding the sum. For example, one student said, “I added 10 + 5 and then subtracted 2 to get 13.” Another student said, “Since 8 is 3 + 5, I added 5 + 5 + 3 to get 13.” Excited to share their own strategies, the students were also learning new strategies from each other. They were developing flexible thinking while understanding conceptually that 13 can represented in many different ways.

Growth-mindset focused norms and developing number sense are just two of the many learnings Dr. Boaler had to offer. If you are interested in learning more about Dr. Boaler, I encourage you to explore www.YouCubed.org. On this site you will find articles, videos, activities, courses as well as parent resources.  

On one of my electrically assisted rides to MTS this summer, I reflected on the connection between Dr. Boaler’s course and all that we do at MTS. From math class to English class, we want our student to develop a growth mindset, to believe that intelligence can be positively impacted through effort. Furthermore, we want all of our students, regardless of subject, to develop flexible, conceptual understanding, to know the why, not just the how. I am excited to bring this to life in my math classes.

Jennifer Adams, Dean of Curriculum, 5th Grade Homeroom, Math Teacher