Math scores of California's average eighth graders on standardized tests in 2021 were in line with the knowledge and skills of fifth graders, according to a new analysis of the state's Smarter Balanced tests.

The results raise doubts whether traditional strategies like summer school and tutoring can succeed in making up such a huge gap in learning.

The analysis, which looks at performance over time, shows that students fell behind each year incrementally even before the pandemic, starting in third grade when tests were first given.

Progress completely stalled last year, when most students were in remote learning. Eighth graders overall scored at the same level that they did when they took the sixth grade test two years earlier.

The state canceled Smarter Balanced tests in the spring of 2020 because of the Covid pandemic, so there are no results from seventh grade for these students.

Progress in math builds on knowledge accumulated in previous years. Missing instruction and skills compound the challenges that elementary and middle school math teachers face moving forward after another disruptive year dealing with Covid variants.

“The results highlight massive gaps in math learning that existed long before pandemic,” said Rick Miller, CEO of the CORE Districts, a multidistrict data and improvement collaborative. “Responding with a one-time fix misunderstands what is happening.”

The analysis was produced by David Wakelyn, founder of Union Square Learning, a nonprofit with offices in San Francisco and Washington, D.C., that works with education organizations on improvement strategies. Wakelyn formerly was executive director for policy development for The College Board, an education policy adviser to former New York Gov. Andrew Cuomo, and program director for the National Governors Association.

First drop in five years

Wakelyn viewed the test scores with a different yardstick from the California Department of Education. As it has every year, the state measured the percentage of students who met or exceeded standards, noting that for the first time in five years, the percentage dropped.

Wakelyn tracked the scores of the students as they progressed from third to eighth grade and compared the results with the pre-pandemic cohort that took the eighth grade test in 2019, two years earlier. Smarter Balanced makes this possible since scores progress on a vertical scale from 2350 to 2700. Making standard -- passing the test -- requires a score of 2436 in third grade, 2485 in fourth grade and so on.

Last year, the average scores of all groups in eighth grade were below standard except for Asian students, the only group whose scores significantly increased last year; their average score was in the upper range of exceeding standards. Black and Latino eighth grade and low-income students in all eighth grade groups averaged far below standard, with a score approximating what fourth graders need to meet that grade's standards.

Miller, state officials and others caution against overinterpreting the 2021 test scores and against comparing them with prior years.

Fewer than one-quarter of students in grades three through eight and 11, the grades given the assessments, took the tests. Because of the pandemic, the state gave districts the choice of giving Smarter Balanced or a local assessment; as a result, only 24 percent of students statewide took the Smarter Balanced test.

Since eighth graders didn't actually take a fourth or fifth grade test, one can only say their scores were indicative of the knowledge of fourth or fifth graders. Some may know elements of what they were taught in sixth or seventh grade.

Even though those students generally reflect the state's demographics, experts said it would be improper to generalize from that number. Additionally, although Smarter Balanced is an online test, not enough is known about the students who took the test and the conditions under which they took it.

Online fatigue impacts scores

“There was a fatigue and resistance to spending more time online" and to take seriously something they were not invested in, said Peg Cagle, a mathematics teacher and department chair at Reseda High School in Los Angeles Unified School District.

Adverse conditions have continued this year, with widespread staff shortages, crippling rates of student absences and worrisome data on students' declining mental health. When most students return from spring break, they will take this year's Smarter Balanced tests.

Natomas Unified Superintendent Chris Evans is among those who question the value and accuracy of taking standardized tests this year. Given all that students have gone through, he said, big declines in scores may be false negatives that don't reflect students' and teachers' hard work.

Wakelyn pointed out that the math results in 2021 contrasted with the students' scores in English language arts. Reading and writing scores were only slightly below grade-level standards and took a small dip in 2021. He described math scores as "a five-alarm fire" that should be taken seriously, caveats notwithstanding.

Miller agreed. “I have no argument with the spirit of what he found. It mirrors the data we have been looking at.”

A revised math framework

Organizations like the California Mathematics Council are counting on the proposed California math framework, now its second revision, to help teachers bridge the knowledge gaps they see in their classrooms. The framework's writers spend much of the 900 pages explaining and giving examples on how to make math engaging and challenging - and how to weave multiple standards and concepts into "big ideas" of math that can put math into context.

A key element is building a math mindset by showing that all kids can think like a mathematician - especially those who have convinced themselves they're just no good in math.

First introduced in the California Digital Learning Integration and Standards Guidance, which the State Board of Education adopted in 2021, the approach was folded into the new framework, said one of the authors, Jo Boaler, a professor at the Stanford Graduate School of Education. The framework encourages the use of visualizations and manipulatives through "rich, open tasks" that create "space to learn," Boaler said. "Kids who miss knowledge can begin to get it. That's the magic of big ideas."

A classroom in Oak Grove, an elementary school district in San Jose, may hint at what's to come. Working with researchers from youcubed, a center at Stanford University that Boaler co-directs, a dozen teachers are receiving all-day training on the framework and then trying out what they've learned in their classrooms. After a morning of giving students hands-on exercises around a big idea, a third grade teacher announced it was time for lunch.

“But when do we start math?' the kids asked her,” reports Jenay Enna, the director of curriculum, instruction and assessment. “They were used to seeing math as exercises in a workbook.”

The State Board is expected to adopt the framework, last adopted in 2013, this summer. In his commentary, Wakelyn wrote that help can't come too soon for besieged teachers.

“The materials and know-how to embed support for prerequisites from several earlier grades does not exist," he wrote. "To expect teachers, especially in middle and high school, to figure this out on their own places unnecessary stress on an already exhausted workforce.”

Disagreements on remedies

Perspectives differ on what can be done to make up for the lost math instruction and learning.

“We have long known that elementary school teachers struggle to teach math and as a result focus the bulk of their attention on literacy,” said Arun Ramanathan, CEO of Pivot Learning, an Oakland-based nonprofit working in two dozen states to raise academic achievement in public schools. “But we lack a state strategy to get high-quality instructional materials in the hands of teachers and support their ongoing professional learning with high-quality coaching.”

Gov. Gavin Newsom has included $500 million in his 2022-23 budget proposal to hire and train literacy coaches and reading specialists in high-needs schools; a task force on early childhood literacy created by State Superintendent of Public Instruction Tony Thurmond echoed support for that and other initiatives last week. Newsom is proposing no comparable effort for math or science.

With record state funding expected to generate billions of dollars of additional K-12 funding in the May budget revision, organizations like the California Partnership for Math and Science Education, the California Mathematics Council and the advocacy organization Education Trust-West are pushing for Assembly Bill 2565, authored by Assemblymember Blanca Rubio, D-Baldwin Park.

The Assembly bill calls for spending $388 million over three years to create statewide professional learning networks in math and science and fund teams of teachers and administrators at the district and school levels to lead training and adopt high-quality materials. The first hearing on the bill is today, April 6.

Angela Gunderson, a sixth to eighth grade math coach in Norwalk-La Mirada Unified, criticized the lack of a systemic approach to training at a recent news conference on the bill. Amid the pandemic, she said, there was an immediate focus on social and emotional learning, with massive attention and materials.

“I was thinking, wouldn't it'd be nice if the same approach was taken that fast for math and science,” Gunderson said. “It is possible if made a priority.”

Morgan Polikoff, an associate professor at the University of Southern California's Rossier School of Education, said “the pat answer -- tutoring -- is fine,” but simply offering it after school won't assure students who need help will show up.

“I think lengthening the school day and year is the likeliest approach to improving student learning. Just offering interventions -- especially if many who need them won't take them -- is not enough.”

Research is clear that tutoring is most effective when done in school, individually or in groups of up to three students, several times each week, by trained staff. The Partnership for Los Angeles Schools, an independent nonprofit organization that runs a network of schools within Los Angeles Unified, is deploying staff from federally funded AmeriCorps program City Year, trained in the math curriculum, to work in concert with teachers in some of its 19 campuses.

Alternative to tracking

It's time to consider a basic structural reform, rethinking “organizing kids by age in a system where gaps have widened this dramatically," Polikoff said.

“If kids are three to four years behind, why are we teaching them grade-level standards now?” he asked. “Why are we grouping kids who are on-grade with kids who are so far behind? How is that sustainable for teachers?"”

Dividing students based on skills raises the prospect of tracking -- a dead-end path for low-income children of color. It's a concern Polikoff said he shares but also a line that many districts won't be willing to cross. Nor should they, said Ian Guidera, chief academic officer of the Partnership for L.A. Schools.  “Our theory has always been your math block should be on grade-level instruction. You can have a two-tier rotation, but extra and pullout time (for remediation) should be supplemental to grade-level instruction,” he said.

Critical to that effort, he said, are well-trained teachers and a standards-aligned curriculum, he said.

The latest survey by EdReports, which evaluates math textbooks and materials, found that 59 percent were either not aligned or partially aligned with standards. And the curriculum should be centered on solving problems and strengthening math reasoning, he said.

Guidera, Raman and others refer to "low-floor, high-ceiling" tasks that challenge students at various skill levels simultaneously while building confidence and interest in those who might give up. For an exercise in Raman's sixth grade class on ratio and proportions, some students may add fractions with uncommon denominators, a fourth grade standard, while another student may learn slopes, an eighth-grade task.

John Fensterwald is a reporter with EdSource, which partners with Bay Area News.