Encouraging students to make mistakes to improve math outcomes

November 19, 2017

Fourth-grade students in a math class at San Francisco's Redding Elementary School.

Nearly two decades ago, international math and science tests revealed mathematics instruction in the United States as an inch deep and a mile wide. Since then, we have grappled with how to get depth over breadth in classrooms. This is confirmed every time I work with teachers or parents, most of whom remember the procedural, answer-based mathematics that they were taught, and the results of that approach. I often hear phrases like: I was really good at math, and then I just didn’t get it anymore; I was never good at math; I was dumb.

Lizzy Hull Barnes

Classroom teachers, education professors and psychologists are working to help us recapture mathematics as discipline that involves sense-making and reasoning, not just memorizing steps. No one has all the answers, but in the San Francisco Unified School District, our math curriculum emphasizes teaching students to persist using a mindset that allows them to make and learn from mistakes. Often, that involves creating a classroom atmosphere that allows students to take risks with their thinking without fear of being laughed at or corrected.

We want to hear mathematical thinking as students talk in class. Teachers ask students: How did you approach the problem? Why didn’t it work? How is your thinking the same or different from the ideas we just heard?

Our PreK-12 math curriculum is taught using principles of “growth mindset,” a concept developed by Carol Dweck, a professor of psychology at Stanford University. Taught with this framework, students learn mathematical reasoning; embrace mistakes as learning opportunities; and work together to build the flexibility and resiliency required for success in math. The goal is to help students stay motivated in the face of challenging work. We’re working to reframe the question, “What does it mean to be good at math?”

Another component is that students must be flexible in their approaches to problem-solving. The units that make up each grade’s scope and sequence are built on rich math tasks that take time to solve and invite collaboration. The old-school silence of an answer-based classroom is now re-energized with students asking each other questions and building on one another’s ideas.

Math is notorious for turning kids off to school. Even students who take calculus in high school to get into college might never take another math class. But, if we can promote the idea that “mistakes are gifts” and that you can learn from your mistakes, we can counter that outcome.

We don’t pretend the correct answer doesn’t matter. That is not our message. But if we only present questions that can be answered with a single correct computation, students never think about more complex situations or explore alternative ways to find answers.

Four years ago, as we launched our curriculum and professional learning for teachers, we were responding to the urgency of the moment and the opportunity to change approaches presented by California’s adoption of the Common Core State Standards. The timing also coincided with a growing movement across the nation to expand curriculum and instruction to better reflect how students learn, incorporating components of social and emotional learning and applying new research about the brain’s ability to change throughout life.

In fact, other schools and networks across the nation have joined our district in teaching with curricula that encourage the kind of group problem-solving and risk-taking classroom climate that we’re using. A case study by the Aspen Institute National Commission on Social, Emotional, and Academic Development spotlights SFUSD’s efforts and how educators in other schools and districts are incorporating social and emotional learning to provide richer academic lessons that can help all students reach their potential. Learning, research has shown, is itself a social and emotional activity.

Since its launch, we have revised and refined SFUSD’s Math Core Curriculum based on teacher feedback. We are not finished, but our curriculum gets better every year. Now, we want to provide more technology to support educators.

In the meantime, we see encouraging evidence. Data from a 2016 report by SRI Education show that our students are developing stronger math skills, particularly in their ability to apply concepts and explain their thinking. Teachers report that students are cooperating more as they discuss tasks and compare solutions. They also see higher levels of student engagement and confidence in math. As a district, we are happy to report that more students are gaining access to rigorous math courses.

San Francisco Unified is the only large urban school district in California with more than half of its students meeting or exceeding standards on both the math and English language arts portions of the Smarter Balanced assessments. Perhaps more significantly, we have cut from 40 percent to 8 percent the proportion of students who are repeating Algebra 1.

Although state tests show we still have much work to do in closing the achievement gap for African-American and Latino students, our district’s other measurements such as middle school math course grades and course-taking patterns at high school indicate that our African-American and Latino students are beginning to bridge the gap on those measures at least.

We are hitting the reset button for thousands of students who have developed new confidence and are less likely to believe that they are not smart enough to do math. Years ago, students might have said, “I am smart because I got the right answer.” Now they would say, “This was a really hard problem, but I stuck with it until I understood how to find the answer.”


Lizzy Hull Barnes is the mathematics supervisor at San Francisco Unified School District, working with teachers and other staff to develop and implement a shared vision of effective math instruction across the district.

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