Having worked in the San Francisco Unified School District for 18 years, Marcy Johnson knows what works best for her students heading off to middle school.
“I get a lot of kids in fifth grade who come in saying they hate math, they’re horrible at math, they don’t get it. I feel like by the end of the year, they understand a lot more and they are more confident in math, so I think I’m doing something right,” Johnson said.
Not everyone, however, is as satisfied with the math program at SFUSD. For years, parents and teachers have argued that because of the school board’s 2014 adoption of a Common Core-aligned math sequence that shifted Algebra I from eighth grade level to ninth grade — with the goal of reducing disparities among ethnic groups — students wishing to enroll in advanced placement classes have faced more obstacles. Similar questions have been raised at the state level, as the California math framework enters its third round of revisions.
Among the pieces of data that educational experts are sifting through in California’s so-called “math wars” are student outcomes on standardized tests and the percentages and demographics of students reaching high-level math courses.
In San Francisco, preliminary results from the 2021-22 Smarter Balanced Assessments show that 45.5% of students were at or above proficiency in mathematics, down from 50.6%, where proficiency had hovered since the test was first administered in 2015. Racial disparities are evident, with only 9% of African American students and 17.8% of Latino students having met the Smarter Balanced standard in 2021-22. As for high-level math achievement, only three African American students in San Francisco schools took an Advanced Placement math test in 2020-21, down from 42 in 2019-20.
But San Francisco is not an outlier. Statewide, only 30% of students are proficient in math, according to 2021-22 Smarter Balanced Assessments results.
The birth of the Common Core
To improve those scores, William McCallum — a former professor emeritus at the University of Arizona — said multiple factors need to align: standards, curriculum that meets those standards, a coherent instructional system based around those standards and a willingness to learn from one another.
The first piece to the puzzle — the standards — was born in 2010 out of an effort to standardize learning across the nation and allow American students to measure up to their international peers. Before then, each state was required to come up with its own standards under the No Child Left Behind Act of 2001.
In 2009, the Council of Chief State School Officers and the National Governors Association hired McCallum, Phil Daro and Jason Zimba to write a set of standards that all states could adopt, called the Common Core. The mathematics standards of the Common Core specified what should be taught each year from kindergarten through eighth grade, but not how to teach it. The adoption of the Common Core in SFUSD shifted Algebra 1 from eighth to ninth grade, though McCallum noted a lot of what used to be in Algebra 1 was incorporated into Common Core 8th grade math.
While the Common Core specified high school standards for Algebra 1, geometry and Algebra 2, the writers did not want to adjudicate the order they should be taught.
When Johnson started teaching at SFUSD’s Jefferson Elementary School in 2003, the school was known for being strong at teaching math. This is why, when the Common Core standards came out, she was excited — they aligned perfectly with what she had been teaching.
“When I grew up, teaching math was learning an algorithm, memorizing it and practicing it over and over and over again,” Johnson said. “The way I was taught how to teach math — which was really just developing number sense and understanding how numbers work so that you could figure out ways to solve problems — seemed more realistic to me because that’s what I do as an adult. If I’m cooking and I have to divide a recipe, I’m not using an algorithm that I memorized in sixth grade, I’m figuring it out because I understand fractions.”
Translating those standards into curriculum, however, proved to be more difficult than anticipated. While some textbook companies scrambled to write new material, others simply slapped a Common Core-aligned sticker on what they had and called it a day, making it hard to differentiate.
So in 2012, SFUSD began to develop its own Common Core-aligned curriculum with the help of Daro. Over the next two years, 120 teachers studied the standards to create a unit-based curriculum for pre-kindergarten through the Algebra 2 + precalculus compression course. They referred to existing materials and other newly created Common Core-aligned materials to assemble the curriculum and had 180 teachers pilot and give feedback.
Following three additional years of feedback and improvement, SFUSD’s curriculum was released, though ultimately it has been up to teachers to decide whether they want to use it.
Johnson decided she did not.
“It took a lot of really good lessons, but they’re kind of from all over the place and the sequencing doesn’t make a lot of sense to me,” Johnson said. “I actually get kind of angry sometimes. I wish that they had just bought a researched curriculum that had already been developed — something that was already proven to meet these standards — but they didn’t do that.”
Framing California math education
Although SFUSD continues to revise the curriculum each year, it was originally created around the time of the 2013 California math framework, which emphasized a standard-by-standard approach to teaching rather than content connections, according to Brian Lindaman, who chaired the committee that drafted the most recent framework and serves as co-faculty director of the Center for Science and Mathematics Instruction at Chico State.
“A lot of teachers interpreted that to mean, ‘I need to cover standard number one, and then I need to cover standard number two and then I need to cover standard number three,’ and that builds to … an instrumental understanding of mathematics — this belief that mathematics are these discrete individual ideas that aren’t connected to one another,” said Kyndall Brown, executive director of the California Mathematics Project statewide office, at a July 28 EdSource roundtable discussion.
The California math framework, similar to the nationwide Common Core standards, is meant to serve as guidance, not mandate. Unlike the standards, however, the framework specifies how to teach, rather than what.
The most recent framework, which is set to be finalized in 2023, has drawn criticism from many, including Brian Conrad, a professor of mathematics and director of undergraduate studies in math at Stanford University.
Conrad said the assertions of some of the research papers used in the article were misrepresented and need to be fixed. He also criticized the framework for its lack of emphasis on calculus, saying that the preparedness to learn calculus early in college, if not in high school, is important beyond traditional science, technology, engineering and math majors. Eight members of Congress also expressed concern over the recommendation that schools phase out any accelerated math options prior to sophomore year.
The framework is centered in part around grade-level big ideas and content connections that span the grades.
“For example, one big idea is this notion of representation, that you can represent the solution to a problem in words, numbers, symbols, pictures or graphs,” Brown said. “If a student is able to represent the solution to that problem in four different ways and see the connections between those representations, then they are demonstrating a full understanding of the concept and you’re covering multiple standards.”
In covering multiple standards in one fell swoop, SFUSD math teacher and coach Rori Abernethy said that teachers may not have to rush through the curriculum trying to get through everything, something that Johnson said she struggles with every year.
At a time when only 18% of African American students and 20% of Latino students are proficient in math statewide, the new framework also emphasizes equity. One of the key stances is that all students, regardless of background, language of origin, differences or foundational knowledge are capable of achieving success in mathematics.
‘Detracking’ for equity
To ensure that that stance is reflected in classrooms, Abernethy emphasized the importance of detracking while still promoting acceleration. Detracking takes teachers out of the equation and leaves it up to students and parents to decide which pathway they want to pursue in mathematics.
“What I like about the framework is that it ... at least alludes to the fact that as teachers we need to have these conversations and not make assumptions about our students when they come into the room,” Abernethy said. “You have to have the intrinsic belief that all students can do mathematics and that all students can do mathematics with rigor.”
As a Black woman, Abernethy was told in middle school that there was no room for her in the algebra track, even though she qualified. Her Black and brown friends were told the same, and by the time she became a math teacher, few barriers had been removed.
In contrast, the lack of tracking at SFUSD was one of the reasons Abernethy was excited to teach there. According to Lizzy Barnes and Ho Nguyen, supervisors for SFUSD curriculum and instruction, the district makes sure all options are clear to counselors who make student schedules, but ultimately the choice is up to the student and their family.
This effort to detrack, however, also included the elimination of advanced math courses through 10th grade, a policy that was immediately controversial when instated in 2014. Now, in order to get to AB or BC calculus by senior year, students must double up on math courses in freshman and sophomore year or take an Algebra 2 + geometry compression course their junior year.
Given the sheer number of pathways that students can choose and schools can create, McCallum still thinks that schools have to incorporate standards-based curriculum, professional learning and implementation support into their rollout. Yet none of that can happen without funding.
“We can’t keep trying to make $1 out of 15 cents. At some point, these great ideas in the framework ... need to be funded and need to be supported,” Abernethy said. “Teachers are not doing well — people are overstretched and overworked post-COVID — and so the more boots on the ground, the more math bodies in classrooms that we can get, I think will be the best for our students in the long run.”