Stanford Professor Jo Boaler (right) and her colleague Cathy Williams (seated) discuss how new findings on the ways we learn are changing how teachers facilitate learning for students.
The noise level rose in the ballroom as excited teachers waved colleagues over, making room at their tables and eagerly awaiting the start of what promised to be a very inspirational day. After all, they were there to see Jo Boaler, the Stanford University mathematics professor, to learn about her groundbreaking work on growth-mindset approaches for teaching math.
Considered a “rock star” in the world of mathematics professional development, Boaler was invited to San Diego to present her “Mathematical Mindsets” workshop for the San Diego Math Network. The San Diego Math Network (SDMN), developed through a grant from the Bill and Melinda Gates Foundation, brings together regional K-14 educators and educational leaders who want to work together to improve mathematics education for all students through teacher professional development experiences and the sharing of collective resources. For several years, the SDMN has focused particularly on supporting successful transitions from elementary to middle school mathematics.
Some 150 TK-12 teachers and administrators from SDMN partner districts and schools, higher education, and regional K-12 schools attended the Mathematical Mindsets workshop on Saturday, March 10, 2018 at the Courtyard by Marriott at Liberty Station. The workshop was sponsored by SDMN partner Sweetwater Union High School District and focused particularly on grades five through seven.
Boaler kicked off the workshop with some brain science on learning mathematics. “Most people think of math as a set of methods…lots of math anxiety,” Boaler said. “We now know that in people who are anxious about math, a fear center lights up in the brain and the problem-solving center shuts down.” After math interventions, however, studies actually show a re-wiring of the brain in students.
“People think being good at math means being fast with numbers, which is not an important attribute in mathematical thinking,” Boaler said. “Speed comes at a cost of depth in connections. People think fluency means speed, when it’s really your flexibility and comfort with thinking about math.”
The terms “growth mindset” and “fixed mindset” were coined by fellow Stanford Professor Carol Dweck in her work on the development of a growth mindset for learning. According to Boaler, people who are given and believe negative messages about their math potential have a “fixed mindset” on what they can achieve. Ironically, using words like “smart” and “gifted” can also lead to a different kind of fixed mindset, as students come to fear any struggle suggests a lack of ability.
“Always praise what [students have] done, and never use the fixed praise like ‘you’re so smart,’ because it backfires later,” Boaler noted. With a growth mindset, students’ intelligence and ability is fluid; it grows through encouragement and struggle. “When you change your learning approach, you change who you are as a person,” she added.
To inspire a growth mindset, Boaler encouraged teachers to focus on several key areas.
Value creativity and depth over speed. Boaler presented a series of simple but rich, “low floor, high ceiling” math problems inspired by the work of 20th century artists Ellsworth Kelly, Frank Stella and Piet Mondrian.
Embrace change and mistakes. Boaler noted the most important thing teachers can do is to change their messaging when kids struggle. According to Boaler, those times are the most beneficial for brains, as brain synapses fire each time a mistake is made — as well as each time a mistake is recognized. With the correct answer, there is less brain synapses growth. “You want to continually push to the most difficult level you can, where you keep making mistakes. With a growth mindset, students’ brains are on fire; a fixed mindset is not on fire…it’s important to struggle.”
Encourage multiplicity. Mathematical creativity comes from opening up student thinking rather than everyone doing the same work in the same way. “When all work looks the same, no one is learning creatively,” Boaler said. Boaler and colleague Cathy Williams, co-founder with Boaler and executive director of youcubed at Stanford University, continued sharing the cognitive approach to math, by guiding teachers through an activity for making good brain connections. Students fold paper into a diamond with four sections and are asked to show four separate ways to solve one math problem: visually, in a story, in a cartoon or doodle, and another way. This exercise helps students think about math differently. “Taking just one initial step into doing multidimensional math with visuals or a story can change everything about your perceptions of students, and who is a ‘math person’ and who is not,” Boaler said.
In the afternoon, teachers experienced equitable group work by solving “Jo’s Favorite Tile Pattern” math problem. Teachers in groups of four and five were assigned a role (facilitator, recorder/reporter, resource manager, team captain and “spy”) and given a list of expected ways to work together to ensure problem-solving success (recognizing and depicting patterns, justifying thinking using multiple representations, leaning in and working in the middle of the table, equal air time, listening to each other, asking each other lots of questions).
The teachers had an hour to collaboratively solve the problem while Boaler and Williams walked around and interacted with the teachers.
Each group’s poster was then displayed gallery-style around the room and proved there was no one way to solve the problem.
Cathy Williams listens as Cristina Jimenez, math teacher at Albert Einstein Academy Charter Middle School (right), discusses one group’s solution.
Afterwards, teachers expressed enthusiasm for the workshop experience via an SDMN post-event survey.
A favorite part of the day was “…all of the hands-on math experiences,” noted one San Diego Unified School District elementary teacher. “Seeing Jo Boaler lead mathematical exercises was fantastic! I was hoping the workshop would be less of her telling how to teach math or what she has done to teach math, and more modeling of her teaching math – and it was!”
Another teacher from National School District hoped to “purposefully develop a mathematical mindset in all students. I feel I already encourage the ‘you can do it’ attitude; however, now I feel empowered and educated in the ‘why’ they can.”
“I think that my mindset has changed,” stated a teacher from Chula Vista Elementary School District. “I really want to challenge my students to change their mentality regarding math. I think many of them have no confidence in their ability to be a ‘math person.’ If I can change that, I/we win.”
For more information on the San Diego Math Network, contact firstname.lastname@example.org.