Credit: Paul Chinn/The Chronicle
Patricia Martinez Tejeda (left), Kismot Rakkat (center) and Phung Nguyen team up to solve a math problem in Mai-tien Nguyen's 4th grade class at Redding Elementary School in San Francisco.

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.

The opinions expressed in this commentary represent those of the author. EdSource welcomes commentaries representing diverse points of view. If you would like to submit a commentary, please review our guidelines and contact us.

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  1. Don 3 weeks ago3 weeks ago

    The overriding point to be made in response to Ms. Barnes article is that SFUSD's math achievement gap has grown larger in the past 3 years since the inception of the new math program despite her reference to a single and very limited assessment by SRI. The achievement stats are freely available at CAASPP and I can provide them if she wishes, though she is clearly aware of those results. In reference to the … Read More

    The overriding point to be made in response to Ms. Barnes article is that SFUSD’s math achievement gap has grown larger in the past 3 years since the inception of the new math program despite her reference to a single and very limited assessment by SRI. The achievement stats are freely available at CAASPP and I can provide them if she wishes, though she is clearly aware of those results.

    In reference to the article’s title “Encouraging students to make mistakes…” and not to be flip, I thought math educators are supposed to encourage right answers not wrong ones. That trial and error is part of learning goes without saying, though that does not mandate a focus on making mistakes. This is reveling in failure in the hope it will lead to success. Not necessarily! There is a downside to allowing students to err in the process of discovery. It spawns confusion which is the overriding feedback I have received from SFUSD parents and students, including my own son, as regards SFUSD’s math instruction. Because math was previously more wide than deep does not warrant throwing out the baby with the bathwater and starting anew with a district-wide experimental curriculum. Our children are not guinea pigs! I think it is SFUSD’s own policy makers who want to engage in a process of self-discovery for math instruction. They should not suppose students ought to do the same.

    In an effort to elicit a response from my own son without injecting my own opinions in the matter I had him read the article and give feedback. As an SFUSD student who experiences the math instruction first hand he had many comments which I will summarize as follows:

    1. Ms. Barnes does not understand that failing to model problem-solving first and leaving learning to self-discovery results in tremendous frustration on the part of students and is not conducive to effective group work.
    2. Cooperative learning is problematic in itself because invariably some students work hard and others do not, which results in less cooperative learning, especially in classrooms with wide variance in ability.
    3. Because of the two above, much time is wasted in this frustrating “discovery” process often without benefit.
    4. Teachers rely upon student self-discovery for learning and stop modeling correct problem-solving methodology. The instructional materials don’t provide examples on how to solve problems either. (Moreover, they lack the necessary reference materials to function according to standards set by the State Board of Education.)

    Those were his observations.

    I have some questions for Ms. Barnes.

    1. Why was this radical departure in math instruction not first piloted before subjecting the entire district to a curriculum and pedagogy that has been repeatedly altered to repair problems?

    2. Why are you relying on a single SRI test which was very limited in scope as an assessment tool and downplaying the terrible SBAC results? Under your math program the achievement gap in SFUSD has grown even larger and this district already has the highest gap among urban school districts.

    3. It is not mathematically logical to claim fewer student are forced to repeat math when you are comparing the current numbers with those from a time when students who had failed or nearly failed in math were forced by this district to take Algebra under the Algebra For All regime.

    SFUSD made the same math mistake in promoting the new math program when it then claimed students were failing Algebra 2 at high rates, not mentioning that they had misplaced underachieving math students first into Algebra 1 without adequate preparation and then promoted them to Algebra 2 after failing to achieve proficiency in the prerequisite. To then claim they were failing at high rates only highlighted the poor placement process by SFUSD. Ms. Barnes, are you saying that grades and course selection is now a substitute for demonstrating achievement on standardized tests?

    Finally, I must comment on Ms. Barnes’ point that “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.” This is an old canard often used to cover up for SFUSD’s poor performance. The fact is that SFUSD has held a false status as the highest performing district because it has an overperforming Asian population of about 6 times that of the state as a whole which skews the numbers. The devil is in the details. Without its particular demographics, SFUSD falls to the bottom of the pack. SFUSD’s subgroup performance of underperforming minorities is the worst in the state, even lower than Los Angeles Unified.

  2. John Golden 3 weeks ago3 weeks ago

    Does the district share its math curriculum with others?

    Replies

    • Lizzy Hull Barnes 3 weeks ago3 weeks ago

      Hi, John, thanks for asking. Much but not all of our curriculum is available online; for example the unit plans are freely available at http://www.sfusdmath.org/accessing-core-curriculum-unit-plans.html. I cut and pasted the fuller description of why there is limited access below: The SFUSD Core Curriculum contains materials from a variety of sources, including some that the district has purchased and some that are freely available on the internet. We only have the right to distribute … Read More

      Hi, John, thanks for asking. Much but not all of our curriculum is available online; for example the unit plans are freely available at http://www.sfusdmath.org/accessing-core-curriculum-unit-plans.html. I cut and pasted the fuller description of why there is limited access below:

      The SFUSD Core Curriculum contains materials from a variety of sources, including some that the district has purchased and some that are freely available on the internet. We only have the right to distribute within the district the proprietary material that the district has purchased. For this reason, we cannot share the full SFUSD Math Core Curriculum with anyone outside the district. Through the Math Portals (at the url above), anyone may view Unit Plans. Student pages and other materials are restricted to SFUSD students and teachers.