A group of students work together during their math class to solve algebra problems in their textbook.
The decision to offer eighth grade algebra — and when, how and for whom to accelerate math education — is for individual school districts and charter schools to make, the latest version of the California Mathematics Framework made clear this week. The 900-page document was never intended as a mandate.
Now that that controversy has been clarified, the addition of a few chapters and the removal of politically charged references to racism behind past mathematical policies and practices, the framework has now embarked on its third, and presumably final, 60-day review process.
It took 10 months, with hundreds of rule edits and more substantial rewrites based on public comments and recommendations by a committee advising the State Board of Education, to review it. The Council of State is expected to adopt the final version in July.
Proponents of the new guideline hope the changes will shift the focus from criticism that its drafters wanted to sacrifice rigor in the name of social justice. The goal, they say, is to make math interesting and relevant to students who have found it inaccessible and impenetrable.
“We truly see equality as the future for better math education for all students in California,” said Brian Lindaman, co-faculty director of the Center for Science and Mathematics Instruction at Chico State, and the leader of five authors of the framework. The goals of making math more accessible and better performing are an artificial dichotomy, he said.
“My hope is that the outcome (of the framework) will be that schools and districts have more leeway to develop math courses and sequences that will get students excited and help draw more of them into STEM areas or advanced math, no matter what they get for it.” choose to do in life,” said Pamela Burdman, executive director of Just Equations, a nonprofit organization that promotes policies that prepare students with quantitative skills to succeed in college.
The framework provides voluntary guidelines to educators and textbook publishers on how to teach state academic standards. The new math framework replaces the framework passed in 2013 that served a specific purpose: to differentiate for teachers between the newly adopted Common Core math standards and the previous state standards.
The new framework has a more student-centered goal: to build understanding of mathematical concepts and relationships between classes and subjects, while developing students’ critical thinking and reasoning.
That’s a tall order, but achievable, said Rebecca Pariso, a teacher on assignment for the Hueneme Elementary School District, north of Los Angeles, who sat on the educators’ committee that recommended the first draft of the framework. “The framework provides solutions to engage students more in math, to see the context of math in their lives and where they belong in a world of numbers,” she said.
Others question some of the framework’s principles, including the elimination of grouping students by ability, and point to the recommendation not to offer algebra until ninth grade as a source of their skepticism.
That issue was a flash point in the first draft. Critics interpreted that position as a signal that the state was watering down math education, delaying those ready for advanced math because of misplaced uniformity.
They said it would be unnecessary for students who want to major in science, technology, engineering or math in college to take an additional math course to fit into math as a senior. This could discourage black and Latino students from pursuing those majors in which they are already underrepresented.
By recommending that all students take Algebra I in ninth grade, the authors of the first draft heralded the success of San Francisco Unified. The district, which made the switch in 2014, released data showing an immediate improvement in math performance in the ninth grade compared to the eighth grade the previous year, and in the number of students who subsequently enrolled as seniors in more advanced math courses. . The district continued to insist that it was a good policy.
But the district declined to release the data behind its findings, and two analyzes by critics of the policy, one by Ze’ev Wurman, a researcher at the Independent Institute in Oakland, and the other by a San Francisco parent group with access to some undisclosed information, concluded that the data was flawed. The latest version of the framework removed the mention of the success in San Francisco.
“It’s an advancement that the writing team now recognizes the need for better roads to calculus in California public schools. But this second revision of the framework just repeats the same arguments from the first revision, while removing all references to (San Francisco’s) discredited claims of success,” said Elizabeth Statmore, a math teacher at Lowell High School in San Francisco. “Maybe it’s time for the California State Board of Education to stop wasting taxpayers’ money on magical thinking.”
A newly formed San Francisco school board, with appointees by Mayor London Breed after last month’s recall of three of its seven board members, is expected to reconsider the district’s algebra placement policy.
What’s the best way to accelerate?
The revised framework recognizes that offering Algebra I, also referred to as Integrated Math I under Common Core, in eighth grade is an option for math acceleration. But it adds the caveat that districts should assess students’ willingness to take it and consider requiring a summer school or additional preparation.
As another alternative to eighth grade algebra, the framework proposes that math experts design a new high school course that combines four-year courses into three by eliminating repetitive material. This would also lead to further education in mathematics in the final year.
At the same time, in a new chapter, “Structuring School Experiences for Equality and Engagement,” the framework urges districts not to create an advanced pathway for some students and a “separate pathway that filters most high-level math students from a young age.” This approach has historically denied opportunities to underrepresented minorities. “Any system that includes acceleration options for some students should do so without excluding most students from reaching a higher level of math by the end of high school.” ,” it said.
Burdman said research is clear that a “race to calculus” can undermine the mastery and conceptual knowledge of mathematics. The framework makes it clear that students starting a standard math series in the ninth grade should have options other than calculus to take as seniors – data science, financial algebra, and statistics, which relate to “how math is used in the real world, what it means to be quantitatively literate,” Burdman said.
“It’s unfortunate that many see these as inferior pathways when they are central to our future,” she said.
Ellen Barger, assistant superintendent of curriculum and instruction at Santa Barbara County Office of Education, agrees.
“It would be helpful, instead of fighting over theoretical dichotomies, that we start with common aspirations for children. We need to expand access to high-quality math, including data science and statistics, as more students will need these applications in their careers.
California ranks in the bottom third of states in math in the National Assessment of Educational Progress, or NAEP. It now ranks 32 in the world, well below average, on the international student assessment program.
Math mindset is important
The authors of the framework emphasize that improving achievement in math statewide starts with increasing students’ confidence in math and their interest in it.
“All students deserve powerful math; high-level math achievements do not depend on rare natural gifts, but rather can be cultivated,” reads the framework’s opening chapter.
Much of the framework describes what equality in math looks like in the classroom — and what it takes to build a math mindset, especially among students of color who have internalized that they are incapable of doing it right. The writings of Jo Boaler, professor of mathematics education at the Stanford Graduate School of Education and one of the framework’s five authors, is often quoted.
Pleasure, the framework says, “comes when students are actively engaged with mathematical concepts — when they develop mathematical curiosity, ask their own questions, reason with others, and encounter mathematical ideas in multidimensional ways.”
Teachers should give students open tasks that “enable all students to work at levels that are an appropriate challenge for them”. They should use examples related to the students’ own lives because, the framework says, “mathematics is a quantitative lens through which to look at the patterns that exist around the world.”
Many teachers have not personally experienced math this way and will find it challenging to change the way they teach math, Pariso acknowledged. “What will be important is to help teachers see the value of what’s in the box; then they will want to make changes in the classroom,” she said.
Lindaman said the teachers will determine whether the framework is having an effect.
“I hope the framework will spark conversations about how to improve math education for more students,” Lindaman said. “Mathematics is a lively, beautiful subject. We show how it can be made empowering.”
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