With unanimity and generally high praise on Wednesday, the State Board of Education passed the new California Mathematics Framework that took nearly four years and three versions to adopt.
The new framework, which will guide teachers and spell out what publishers must adopt, comes at a critical time, said Ellen Barger, an assistant superintendent for Santa Barbara County who has participated in the framework process. Flocks of new teachers relying on outdated textbooks and struggling to help students recover from the pandemic “all create a sense of urgency,” she said during a two-hour presentation by the California Department of Education.
“Teachers are seeking clarity and guidance to ensure mathematics that is engaging, enjoyable, meaningful and inclusive.”
That is the promise of a nearly 1,000-page framework, which calls for significant shifts in instruction. It will stress approaches that seek to engage all students by emphasizing problem-solving and creating context and the relevance of math to students’ daily lives. The goal is to build a conceptual understanding of what students will learn before delving into math procedures and algorithms that traditionally have come first.
That is what state board member Gabriela Orozco-Gonzalez, an elementary school teacher in Montebello Unified, said appeals to her in the framework. “The framework’s focus on fundamental concepts, open-ended tasks, justice, student inquiry, reasoning and justification aligns with effective mathematics teaching practices,” she said. “I am encouraged by the incorporation of strategies to support diverse learners, such as promoting multilingualism, facilitating group work, employing visual aids, and establishing cultural connections.”
Board member Kim Pattillo Brownson also praised the focus in early elementary years “on student-centered learning, experiential learning and conceptual understanding, which is oftentimes a little bit harder for many parents — I’ll count myself in this category — who learned more on an algorithmic sort of set of principles.”
“Starting with the logic of math, the decomposing numbers of understanding how to manipulate them then moving to fluency and rapid recall is fantastic,” she said.
The three hours of public testimony that preceded the vote mirrored discord over the framework that inspired 1,500 public comments in response to two extensive revisions. The three main disagreements were over the wisdom of centering instruction around “big ideas” while, critics said, diminishing direct instruction and fluency from teaching math facts and algorithms; wording that discouraged taking algebra in eighth grade, giving advanced students a head start to calculus in 12th grade; and the framework’s approach to data science in high school.
Though the divisions of opinion are deep, the board did approve a series of amendments to the framework suggested by the California Department of Education that addressed the issues, though likely they won’t mollify critics.
In commenting on each area, Board President Linda Darling-Hammond said some commenters “who see the world through a polarized math war lens” falsely pitted “investigation and inquiry against solid learning of math facts in ways that assure fluency and proficiency.” She pointed out the balance that inquiry and teaching standard algorithms both were mentioned four dozen times in the same framework chapter; math fluency was mentioned 23 times. The amendment clarified that math facts for addition and fluency with the algorithms for multiplication and division will meet the grade requirement set by the Common Core standards.
Tom Loveless, a former senior fellow at the Brookings Institution, the author of a book on the Common Core standards, who said the imbalance would hinder students’ growth, gave a “tip of the hat” to the change but said the framework’s “message that math facts can be treated lightly remains.”
Darling-Hammond said that the position on eighth-grade algebra also was misconstrued. The framework emphasizes the ability of students to accelerate in middle school or high school at different times, at their own pace; what must end is tracking, starting in early elementary school that locks mostly low-income, Latino and Black students, on a track to nowhere, she said. The framework encourages acceleration options, whether geometry in a summer program, personalized learning, or a compressed course in high school. She cited an example in New York, where support classes and a redesigned curriculum enabled an entire class of middle schoolers to take algebra in eighth grade.
The approved amendment is a simple one-sentence reaffirmation as an asterisk to a diagram on high school course pathways in the chapter on high school math (chapter 8) — “Students may take Algebra 1 or Mathematics 1 in middle school.”
Commenters from the public, however, insisted that the language in the same chapter and the diagram reinforce the view that ninth graders should take a “common course” in Algebra I. While applauding the intention of “finding ways to help struggling math students attain greater proficiency,” Kathy Jordan said that approach will fail, as it did in San Francisco Unified. It has abandoned a policy of mandating all students take ninth-grade algebra after evidence that it held back advanced students while failing to narrow inequities.
In some districts in the Bay Area, a sizable portion of eighth graders take algebra in order to avoid having to compress four courses of math – Geometry, Algebra II, Precalculus and Calculus – into three through summer school or a compressed Algebra II and Precalculus course. The framework drafters are calling for a work group by mathematicians to reduce redundancies in standards and prune less important standards to enable Calculus by senior year without extra courses.
Data science became a focus of the framework, which framework authors initially proposed as a separate high school pathway, then withdrew in the final draft amid opposition from CSU and UC STEM professors. High school courses in data science have become popular in the past several years, and CSU has designed several as a way to encourage students who were ready to quit math after the minimum two-year requirement to continue for a third or fourth year.
Commenters reiterated its importance.
“This course transformed my own teaching practices and transformed the lives of many students,” said one teacher. “Data science by nature brings equity into the classroom. Students who had a dislike for math suddenly were transformed in to math lovers. They became skilled in statistical analysis, computer programming and critical thinking, valuable skills needed to navigate this world.”
Said a math teacher from Merced County, “I’ve watched students wrestle with creating and manipulating formulas to solve open-ended problems, but doing so through equity-connected topics such as skin-tone representation (in the) media, community water usage, and other topics that are engaging. They’ve developed their critical thinking skills, and analytical skills as they endeavor to make sense of calculations and results from large databases.”
Update on data science
The flashpoint was the approval by a Senate faculty committee, called BOARS, crediting data science courses that included minimum math for satisfying Algebra II. Faced with criticism that students taking them would be unprepared for harder courses and a major in STEM in college, BOARS changed its mind at a meeting last Friday, and withdrew the Algebra II credit. Without disclosing that decision, the chair wrote to the state board, asking that it delete references in the framework that tied data science to Algebra II.
Breaking the silence, the executive director of the UC Faculty Senate partially clarified the confusion Wednesday in a statement to Darling-Hammond, which she read. It said, in part, “There’s been continued discussion about the adequacy of a small number of data science courses, not data science broadly, in the context of our systemwide student preparedness expectations.”
The UC statement said BOARS would establish a working group “to examine the criteria that determine whether a course is considered advanced math and to draft a charge for their undertaking over the coming months.”
Meanwhile, the university “will still recognize the existing advanced math courses approved to fulfill the subject requirement,” including data science, “for this year’s applicants to the university.”
The two most popular data science courses that grant credit for Algebra II and are taught in several hundred high schools are Introduction to Data Science, designed by UCLA Statistics Professor Rob Gould, and Explorations in Data Science by YouCubed, an organization established by Jo Boaler, a Stanford University math education professor and one of the authors of the original framework. Various speakers praised both at the meeting.
The process of approving curriculum materials for the new framework, which will have to be written from scratch, could take two years or longer. Meanwhile, teachers are awaiting word on a rollout of training. Speakers stressed the critical need for extensive professional development; the Department of Education has not yet released plans.