The California State Board of Education voted to adopt a new—and much-debated—math framework on Wednesday, concluding a years-long process that involved three drafts, prompted hundreds of suggested revisions, and reignited decades-old arguments over the purpose of math education and the meaning of equity.
The 1,000-page framework aims to put meaning-making at the center of the math classroom, promoting a focus on problem-solving and applying math knowledge to real-world situations. It also encourages teachers to make math culturally relevant and accessible for all students, especially students of color who have been traditionally marginalized in the subject.
“The United States has not been teaching math effectively or equitably. We are one of the lower-achieving countries … and California is below the national average in its achievement in mathematics,” said Linda Darling-Hammond, the president of the California State Board of Education, during the board’s meeting on Wednesday. “This is an area of great need, and change is imperative. The same old, same old will not get us to a new place.”
The framework is guidance, not a binding document, but it influences instructional practices, professional development, and materials adoption in California—one of the largest education markets in the country, with just under 6 million students in its K-12 public schools. Its reach has already been felt beyond the state’s borders.
In essence, the framework has become a proxy both for longstanding debates over math education—such as the teaching techniques teachers should use and whether to track students into different course sequences—and newer ones, such as if, and how, coursework should address social issues and politics.
Long before its adoption, the framework had been the subject of vociferous public debate. Scholars from Stanford University, the University of California Berkeley, and the California Institute of Technology, among others, had challenged it in public letters; others tracked down its research citations, disputing how they were used in the document. (Some citations were later removed from the draft the committee voted on.)
Despite revisions since the first draft of the framework was released in early 2021, Wednesday’s meeting saw nearly two hours of public comment, including from critics.
“The process has taken a long time, but it has allowed many voices to be heard and has resulted in a deeper, important understanding, better conversations, and provided insight into the complexities that we all must grapple with as we roll this out,” said Ellen Barger, the chair of the curricular and improvement support committee.
With the framework adopted, board members referenced the months- and years-long work ahead.
“What’s most important beyond this framework is going to be the professional development, the determination of the instructional materials that will support instruction. That’s where the rubber’s going to really meet the road,” said Cynthia Glover Woods, the state board’s vice president.
Here are four core themes to understand about the new framework.
The framework proposes a fundamental shift to how math content is structured throughout the grades. Instead of organizing curricula and instruction around individual standards, the framework outlines “big ideas in mathematics” for each grade that are designed to drive instruction.
The standards still exist, with several discrete goals living under each big idea. But the organizational change is designed to help illustrate the connections across topics, both within the grade and between grades.
Teachers are encouraged to use inquiry to explore these “big ideas” designing “student investigations of intriguing, authentic problems.” The goal, the framework explains, is to get students engaged in problem-solving that feels interesting to them and that demonstrates the real-world relevance of math, something everyone from parents to the Bill and Melinda Gates Foundation say they want to see in math class.
These problems, the framework says, should challenge students with “productive struggle”—being asked to grapple with complex ideas and novel situations as part of the learning process. Much of this approach is shaped by the work of Stanford education professor Jo Boaler, a popular but controversial figure in the math education landscape.
The National Council of Teachers of Mathematics endorses this kind of reasoning and sense-making in the teaching of the subject. And some teachers who have moved to this problem-based method say that it can make students see why learning math matters for their lives.
Teaching this way is complex, requiring careful sequencing to ensure that students have the content knowledge and skills that they need to attack these challenging problems.
Some critics of the framework have questioned research cited in the document, claiming that some of the studies referenced don’t back up claims about the efficacy of specific instructional choices.
Outside of the debate about the framework, other math education experts have argued against the notion that inquiry-based learning is the most effective way to teach.
In 2021, a group of professors and other math educators formed the “Science of Math,” a movement challenging some of the most closely held tenets in the field. These researchers, most of whom study students experiencing math difficulties, have pointed to studies that show the benefits of explicit instruction and scaffolded practice. They warn that struggle in the math classroom isn’t always productive, and can lead to frustration that alienates students from the subject.
Researchers generally agree that students need to master basic math fact fluency, and that they need explicit supports as they transition into more conceptual work in story problems and word problems.
In Wednesday’s board meeting, Darling-Hammond said that the adopted version of the document struck this balance. Some commenters, she said, “have claimed the framework would abandon math facts for young students in favor of what they characterize as inquiry—an either-or characterization that is not accurate in the framework.”
Equity and cultural responsiveness
Beyond these debates about teaching strategies, problem-based learning has long faced political critiques—often from conservatives, who oppose the idea that math class could be a venue to discuss social justice themes or solutions to public policy problems.
The California framework encourages teachers in this work on two fronts. First, the collaborative, inquiry-based approach is meant to support students from all backgrounds to find a sense of belonging in math classrooms and to engage their participation in meaningful conversations about math. Second, math content itself can help students use math to examine inequities and address important issues in their lives and communities.
Such an orientation toward social justice has faced sharp criticism from some members of the math community. In an open letter in 2021, over a thousand signatories—many of them math and science professors and business professionals—outlined pieces of a prior draft of the framework that they said would politicize the subject in a “potentially disastrous way.”
While some of these aspects have since been revised, the focus on social justice remains throughout the document.
High school course sequencing
One major course-taking milestone has consumed much of the debate about the framework: when students take algebra, a decision that can influence the trajectory of their high school math career.
Algebra I is regarded as a gateway course in high school math. The class is a prerequisite for higher level math courses and students are generally required to pass it to graduate.
The original version of the framework recommended that all students take Algebra I in 9th grade, a strategy designed in part to reduce the potentially harmful effects of tracking, in which some students were relegated to lower-level courses as early as middle school and never caught up.
The idea was deeply influenced by work in the San Francisco district, which not only began de-tracking its math classes but also moved to more inquiry-based lessons. Research on the city’s experiment showed that it increased Black students’ access to some higher-level courses, but that racial inequities at the most advanced levels of high school math remained unchanged.
It was also hugely controversial.
Critics, including many parents of high-achieving students, worried that students would be prohibited from taking appropriately challenging courses—and that delaying Algebra until 9th grade wouldn’t leave students enough time to take calculus, generally viewed as a prerequisite for competitive colleges, by their final year in high school.
That language has since been revised. The approved framework still suggests that most students take Algebra I or equivalent courses in 9th grade, through either a traditional pathway or an “integrated” pathway that blends different math topics throughout each year of high school.
But the framework notes that “some students” will be ready to accelerate in 8th grade. It cautions that schools offering Algebra in middle school assess students for readiness and provide options for summer enrichment support that can prepare them to be successful.
If students don’t take Algebra I in 8th grade, though, there are a few options for them to take Calculus by the end of high school. The framework notes that schools can organize summer options or support for concurrent coursetaking, and it suggests that the board work to develop a compressed high school math sequence to allow students to reach Calculus in high school.
These kinds of alternative options can make a pathway to calculus accessible for students who might not be ready for Algebra in 8th grade, said Darling-Hammond. “We should be thinking about how we get most students to higher-order math, not only those who in early elementary school are already obviously on a path,” she said.
Data science as a priority
The framework also steps into ongoing conversation about the role of data literacy in math education—and whether statistics-focused courses could, or should, replace calculus as the terminus of high school math.
“The high demand for data science has been linked to the rise of big data and its increasing importance to businesses and other organizations,” said Kyndall Brown, the executive director of the California Mathematics Project, a statewide network to support math teaching and learning, during the California State Board of Education meeting. “You’d be hard pressed to find an organization, a government entity, a business that doesn’t use large data.”
Brown cited findings from California, showing that students who took data science courses earned slightly higher grade point averages than their similar peers who took precalculus.
The ubiquitous use of data in society, alongside the idea that it may be a more accessible advanced math course, have prompted some in the math education field to push for greater availability of statistics-oriented pathways in high school mathematics.
The original draft of the framework included such a pathway as an alternative to both the traditional math sequence through Algebra II and the state’s integrated math sequence, which combines geometry and algebra instruction into three merged courses.
This, too, sparked controversy.
More than 400 academic staff at California colleges and universities signed a letter arguing that students who took a data science course instead of Algebra II would be “substantially underprepared for any STEM major in college,” referring to the fields of science, technology, engineering, and mathematics.
In response, the framework writers removed references to this alternative pathway. The final framework encourages teaching data science throughout all course pathways.
It suggests that students should be able to choose from a wide variety of course offerings in their third and fourth years of high school—though it does note that taking courses other than Algebra II on a traditional pathway, or Mathematics III on an integrated pathway, could take students off the path to calculus that is expected for careers in STEM.
One additional wrinkle complicated these recommendations at the 11th hour just as the framework neared approval.
On Tuesday, the Chronicle of Higher Education reported that a faculty committee governing the University of California system admissions voted to end a policy that would allow high school data science courses to count toward UC’s math requirement. Data science courses would no longer satisfy its college admissions standard.
Data science classes will continue to count for this year’s applicants, and the UC system’s academic senate plans to study what criteria are necessary for a high school class to be deemed “advanced.”
Still, the K-12 framework’s emphasis on data science proved popular during Wednesday’s public comment on the document, with several teachers, professors, and former California public school students speaking in favor of expanded pathways.