California Moves Closer to Passing New Guidelines for Teaching Math

The State Board of Education is poised to approve a nearly 1,000-page guidance for math instruction this week with the ambitious, much-contested goal of transforming how math is taught in California, where only a third of students ­— and 1 in 5 low-income students — met standards in the latest state standardized test.

With the adoption of new textbooks, it may take years of intensive teacher training on a magnitude the state has not funded in decades before it becomes clear whether the revised Mathematics Framework for California Public Schools will move the needle of student engagement and achievement. Many teachers are confident it will, but there are skeptics.

The revised framework is nearly four years in the making. The third and likely last version, in response to more than 900 comments and petitions pro and con, took 14 months to complete. It was drafted by a new set of writers connected with the Region 15 Comprehensive Center of WestEd, the San Francisco-based research and service organization contracted by the California Department of Education.

The state board released the new draft on June 26; it accepted comments only through noon on July 7. After a final hearing scheduled for Wednesday, the board is expected to pass it, perhaps with minor changes.

Among those who will urge the board to adopt the final draft is Kyndall Brown, a former high school math teacher who is the executive director of the state-funded California Mathematics Project Statewide Office. Saying he was pleased that the “spirit” of the framework remains intact, Brown added, “This is the most equity-focused math framework I have ever seen as an educator in California.”

“The biggest and strongest part of this framework are the chapters on teaching and structuring school experiences for equity and engagement,” he said. “The math ed community, the people I interact with on a regular basis, support the framework, and we are ready to move forward and get this implemented.”

The framework’s recommendations are voluntary, but they heavily influence districts’ and teachers’ decisions and serve as guidelines for textbook publishers. The first two drafts have stirred national interest, in part because California, with 5.8 million students, is the nation’s largest and most lucrative market for textbook publishers, who, the framework’s authors make clear (see Chapter 13), will have to hew to its guidelines to make the list of approved publishers.

But the proposed framework also adds another twist in the decades long debate over math instruction. Math traditionalists are warning that a proposed student-centered, inquiry-based, “big-ideas” driven instructional strategy, which de-emphasizes memorization and attention to procedures, will fail most students.

Thousands of university STEM professionals signed petitions criticizing a proposed high school pathway that appeared to favor data science over the traditional course sequence to calculus, which is required for college students majoring in science, technology, engineering and math. Parents of students with advanced math skills and 6,000 others who signed a related petition were angry that the framework discouraged districts from starting algebra in eighth grade. The early start would give students a leg up on fitting in calculus before high school graduation.

In response, the new writers did eliminate the call for a new data science pathway; instead, they wove data skills into math instruction throughout grade spans. They also made some effort to clear up confusion conflating courses in data literacy, which all 21st-century students need, with a more rigorous, math-intensive data science course that, together with calculus, would prepare students for a data science major in college.

What the framework didn’t discuss, however, is a related controversy roiling the University of California and California State University faculties over whether a growing list of UC-authorized data science courses, with minimal advanced math content, will leave students unprepared for math-intensive courses in college.

Last week, a committee of the UC faculty senate, called BOARS, which oversees high school course qualifications, publicly acknowledged it is having second thoughts on the approved courses. In a July 7 letter to the state board (PDF), the chair of BOARS asked that the revised framework delete references in the text and in a diagram (see below) indicating that data science courses can substitute as a math requirement for Algebra II. The letter indicated that BOARS planned to look into the issue further.

The writers of the latest revision rephrased or removed some citations of works in the prior version, on neuroscience and other topics. Some of the citations of work support the instructional methods promoted by math instruction experts, including Stanford University math education professor Jo Boaler, one of the original framework’s team of authors.

At least some critics who had hoped that a year of work would fix the numerous problems they raised remain dissatisfied. The most prolific, if not most influential of them, Brian Conrad, professor of mathematics and director of undergraduate studies in math at Stanford, once again called for rejection of the framework due to shortcomings he cited.

In a nine-page update of his dissertation-length critique from a year ago, he pointed to remaining citation misrepresentations, and inconsistencies that could lead to contradictory interpretations of the framework and data science issues. “Critical concerns remain, and the (framework) does not live up to the standards of a document that sets state-wide education policy,” he wrote in a public comment last week.

Philosophy intact

Most of the past year’s effort went into clarifying, shortening and reorganizing the massive document. The focus of rewriting was on a half-dozen chapters, including the first two, laying out how to develop positive mindsets about math, like the belief that all students can succeed in math, and use students’ diverse backgrounds as “cultural assets.” Vignettes useful for teachers that lengthened chapters were moved to an appendix.

“Just the idea of the big ideas is huge, so that teachers aren’t feeling they’re teaching things in isolation,” said Vicki Murray, a learning coordinator in Buellton Unified who has taught elementary grades math, agrees. “Jo Boaler has really done an amazing job showing the mile-high view, that this idea connects to all these different other pieces of math.” Buellton is a 600-student district north of Santa Barbara.

“A lot of K-6 teachers are super excited about it, and it makes sense to them,” Stevenson said. “It’s actually asking them to teach math the same way they teach a lot of other things,” like the Next Generation Science Standards. But high school teachers may feel disoriented with the approach and burdened by the complex set of rubrics around which teachers should design lessons.

“I support the idea that we need to teach differently. I do agree that what we’re doing right now is not working. We’re trying to teach too much too fast,” Stevenson said. “I wonder if there isn’t a simpler formulation of what they (the authors) are trying to get at.” At the end of a class, she said, students may walk away with a “muddy sense of what they were to have learned.”

Tom Loveless, an education researcher who now lives near Sacramento, a former senior fellow at the Brookings Institution and the author of a book on the Common Core standards, gave a harsh assessment of the framework’s philosophy. The authors, he said, created a “false dichotomy” about the need for “conceptual understanding before procedural fluency. Good teachers teach both.”

The math framework should be organized around the content of the Common Core standards, not around “rather fuzzy ideas about process,” he said.

He said he is sympathetic with the critics that math facts and procedures have been taught poorly. “But there will be a toll paid for pushing them in the background.”

“The previous framework was very clear that math fluency involves speed and accuracy. The proposed framework rejects speed as being even part of fluency, and that’s a problem,” he said.

Math facts learned and stored in long-term memory can be retrieved effortlessly when students take on more-complex cognitive tasks, he wrote in a recent article. Contrary to the requirements of the Common Core standards, the framework calls for pushing back fluency in multiplication and division tables until late elementary grades. The delay will carry forward, and he expects fewer students will be prepared for algebra in ninth grade.

That has been the experience of Jane Molnar, who has been teaching math for 43 years as a math specialist working in classrooms and as a tutor. “If you don’t master certain things in first grade, second grade, third grade and instead you’re just exploring and talking about numbers, kids just can’t keep up. And when the same thing continues through middle school, students who wouldn’t know how to divide with ease using the division algorithm would find trying to divide polynomials in algebra way too complicated.”

Training is essential

Advocates of the framework agree that intensive training will be critical and a heavy lift for teachers who lack strong content knowledge.

“There’s going to be some discomfort for sure at the front end for those who really have a very regimented routine about how math should be taught,” said Sampson.

Brown said his biggest hope is that the framework “will really influence the way that teachers think about teaching and engaging their students.” His biggest fear is that “the state will not really fully fund the rollout and provide teachers with the support they need to really implement it.”

Like Brown, the framework’s original authors said the payoff would be huge.

“One of the missions of this framework is to get rid of ways of thinking that only some students can do mathematics to high levels and open up this beautiful subject of mathematics for everyone,” said Boaler.

Ben Ford, a math professor at Sonoma State University, said, “If my students start arriving at university understanding mathematics as a set of lenses for exploring questions that they’re actually interested in, I would be ecstatic. And that is one of the goals of this framework.”

Loveless, however, predicts history will repeat itself.

Just as more parents now are demanding an end to whole-language instruction and adoption of reading curricula with basic literacy skills, parents seeing poor results in math will demand change in a few years, as they did in the ’90s, he said.

“Math facts are to math as phonics is to reading,” Loveless said.

This story was originally published by EdSource.