Tuesday, December 15, 2015


Earlier this year the Legislature passed Senate Bill 359, known as the California Mathematics Placement Act. Advocates of the new law, led by the Silicon Valley Community Foundation, say it is a big win for equity: providing all students equal access to courses culminating in Calculus in their senior year, giving them an advantage in admission to the University of California or a head start in majoring in science or engineering.

Past research indicated that low-income, African-American and Hispanic students were disproportionately held back from a more advanced course they should have been placed in. The new law was written to ensure that all students face the same objective criteria for determining the path to calculus. But they also acknowledge it’s too soon to say what the right criteria and the most effective pathway to advanced math will be; determining that may take years of experimenting and refining.

“The law is but the first step,” said Gina Dalma, special adviser to the CEO for public policy at the Silicon Valley Community Foundation. “We are hoping to see district leaders’ commitment to fairness and equity. Our concern is that the process will be done lightly instead of deeply.”

The new law coincides with the transition to the Common Core standards, which already have shaken up thinking about the timing and progression of math courses. The creators of the Common Core laid out a sequence of math standards for courses through middle school and presented several options for high school. California has left it to districts to decide how to accelerate courses and who should be eligible for those options. Many districts haven’t decided how that should be done, leaving it to the judgment of teachers.

Common Core math takes a deliberate, multi-year approach to Algebra, since it is the foundation for higher math. Algebra concepts are introduced in 7th and 8th grade, followed by a full Algebra course, with elements of Geometry, in 9th grade. The standard sequence would then be a Geometry course in 10th grade, Algebra II in 11th and Precalculus as a senior. An alternative approach to Common Core math combines elements of algebra, geometry and statistics in three progressively more difficult courses in 9th, 10th and 11th grades.  Many school districts have adopted this sequence, calling it Integrated Math I, Math II and Math III. 

The minimum course requirement for admission to the California State University and the University of California is math through Algebra II or Integrated Math III. But at least one year of Calculus or AP Statistics is needed for admission to competitive University of California campuses like UC Berkeley and UCLA. Therefore, either math sequence, traditional or integrated, requires students to accelerate the course sequences in high school – somehow compacting three years of math into two years to make room for higher-level courses in a student’s senior year.

In California, the math teachers and professors who drew up the Common Core math frameworks (see a summary of the options) suggested several acceleration options, but left it to districts to decide when and how. A new study of math in 10 California districts, coauthored by researchers Neal Finkelstein and Rebecca Perry of WestEd and expected out this month, has found great variations in timing of acceleration and course sequence with little evidence yet on which approach works best.

Teachers and math educators who developed California’s math frameworks, a blueprint for districts to develop a curriculum for the Common Core standards, suggested several options for accelerating the course sequence leading to Calculus in 12th grade. One option, pictured above, is to offer Algebra I or Integrated Math 1 in 9th grade, followed by Geometry or Integrated Math II in 10th grade. In 11th grade, Algebra II or Integrated Math III would be combined with Precalculus, leading to Calculus in 12th grade. A summer program between 11th and 12th grades is an option. Other options can be found here. 

The California Mathematics Placement Act, sponsored by Sen. Holly Mitchell, D-Los Angeles, will formalize that 9th grade placement process by requiring districts and charter schools to establish a “fair, objective, and transparent” policy for placing incoming 9th-graders in math courses.

The act “picked up on the critical issue that the criteria for identifying which students would be accelerated were often unevenly applied, inviting racial bias and equity concerns,” said Finkelstein, chief researcher on several math placement studies for WestEd.

The law requires districts to adopt “multiple objective academic measures,” which could include statewide standardized test results, student portfolios and other placement tests predictive of math readiness, interim assessments and grades. Those districts that currently have a uniform policy of placing all students in the same course in 9th grade but have an option for accelerating later in high school would meet the requirements, Dalma said.

Among the provisions, the law requires that districts:

Check within the first month of 9th grade to ensure that a student is in the right class;

Examine the data yearly to identify whether students who were qualified to move ahead in math had not been advanced and to quantify the numbers by race, ethnicity, gender and family income;

Report the data to the school board and post it on district websites;

Allow parents the right to challenge schools’ placement decisions for their children.

The law also encourages high school districts to work with feeder elementary and middle school districts to create uniform placement policies.

Supporters of the law hope that the provisions will prevent misplacing students who should be in advanced courses. But incorrect assignments also occur when students are pushed into a higher-level course before they’re ready. Research (here, here and here) has shown both instances were frequent in California.

The previous state math standards encouraged students to take Algebra I in 8th grade so they could be on track to take Calculus by their senior year.

Retreat from universal 8th-grade Algebra

By 2013, two-thirds of students were taking Algebra I in 8th grade, and passage rates on the state’s California Standards Test increased, although the passage rate was no higher than 40 percent.

But studies showed that student placement decisions were disjointed and subjective, often with a detrimental impact. Some schools designed 8th-grade Algebra classes that lacked rigor and left students unprepared for higher-level math in high school. A study of 24,000 California students by researchers at the Center for the Future of Teaching and Learning at WestEd found that one-third of students who took Algebra I repeated the course, with only a slim percentage passing it the second or even third time.

An oft-quoted 2010 study of Bay Area districts found that nearly half of students who had grades of B- or higher or passed standardized tests in Algebra I were held back for a second year in Algebra rather than promoted to Geometry. The study found significant differences in course placement correlated with students’ ethnicity or parental education – potentially indicating teachers’ unconscious bias in placement decisions.

Great variation in approaches

The new law applies only to 9th-grade placement, but acceleration decisions are starting in some districts, including Cupertino Union School District, in 5th grade, leading to accelerated classes in middle school,  and as late as 11th grade in other districts, such as San Francisco Unified.

Many options for accelerating math

In Appendix A of the California Mathematics Framework, which the State Board of Education adopted, the authors suggest multiple ways for districts to accelerate the math course sequence in high school so that students are able to take Calculus in 12th grade. The authors discourage acceleration before 7th grade “to ensure that students are developmentally ready for accelerated content.” High school options include:

  • Compacting three years of math into two years, without skipping standards, in 9th through 11th grades, so students take Precalculus in 11th grade, and Calculus in 12th grade.– Compacting four years of math into three years, leading to Calculus in the 12th grade.
  • Having students double up by enrolling in Geometry during the same year as Algebra I or Algebra II;
  • Offering summer courses that are designed to provide the equivalent experience of a full course in all regards.

Supporters of the new law hope that districts will apply the same principles of fairness and objectivity they will implement for 9th grade under the new law in whatever grades placement decisions are made. The Silicon Valley Community Foundation offers sample middle school and high school placement policies on its website.

The community foundation had proposed a bill covering more grades but, as a compromise, chose the start of high school partly to encourage elementary districts feeding into a high school district to adopt the same approach.

That will be critical in districts like the Modesto City High School District, which decides which freshmen from eight to 10 feeder districts will take an honors Integrated Math I course, a standard Math I course or a support class for students needing extra help. The district has not begun to set the criteria for placing students in these classes, said Mike Coats, senior director of educational services for the district.

The Jefferson Union High School District in Foster City and its four feeder districts, which formed a collaborative to work on placement issues several years ago, could offer a model. Starting in 7th grade, all students take a common multi-step performance assessment created by the Mathematics Assessment Resource Center, or MARS, that tests knowledge and a conceptual understanding of math.

They take another MARS performance test in 8th grade. The combined scores determine what course they will be placed in in 9th grade. A teacher’s recommendation can be used to advance a student whose test scores don’t qualify for acceleration. But to prevent potential bias, a teacher’s recommendation cannot be used to hold back a student whose scores qualify them for advancement, said Jefferson Elementary School District Superintendent Bernardo Vidales.

The district collaborative is also looking into using scores on interim Smarter Balanced tests given in the spring of 8th grade, or, if available in time for placement decisions, the end-of-year 8th-grade Smarter Balanced tests.

About 10 to 20 percent of students in the district collaborative have been determined to be eligible for a Math II course in 9th grade. He said those students need to demonstrate mastery of 8th grade standards to justify skipping Math 1.

Lack of statewide data and guidance

Critics, such as Ze’ev Wurman, a Palo Alto software engineer who helped draft the 1997 California math standards, deride the Common Core’s more gradual approach to Algebra I as punishing students capable of handling advanced math and dumbing down the curriculum. Defenders of the Common Core sequence assert that, with a better math foundation, more students will successfully complete Algebra II or Integrated Math III, the minimum requirements for admission to CSU or UC, and then take a fourth year of math in high school.

Who’s right won’t be known for at least several years. It’s widely assumed that fewer students, under the Common Core, are taking Algebra I in 8th grade, but no one knows for sure, since the state doesn’t require districts to report course enrollments by grade. All 8th graders now take the same Smarter Balanced test, and the state has stopped giving end-of-year subject tests in math to students in 9th and 10th grades.

But Cupertino, a K-8 district, and San Francisco Unified illustrate the vast differences in approaches and philosophy to math placement.

With a handful of exceptions, San Francisco has no acceleration option before 11th grade. All students are required to take Algebra I in 9th grade and Geometry in 10th grade. In 11th grade, students and their parents, in consultation with school counselors, will be able to decide whether to take an accelerated combined Algebra II/Precalculus course, said Jim Ryan, the executive director for science, technology, engineering and math education.

The exception was for incoming 9th-grade students from private schools who had taken Algebra I in 8th grade; they have been given a placement test to see if they were ready for Geometry in 9th grade. Last year, after parents of 8th-graders in the district protested the lack of an acceleration option in 9th grade for their kids, the district allowed all students to take the same test. Only 120 students in total passed and are now taking Geometry in 9th grade. They make up less than 4 percent of  9th-graders, Ryan said.

The district hasn’t promised to continue the test and has asked lawyers whether a uniform policy of placing all 9th-graders in Algebra I complies with the new law, Ryan said.

“We believe we will actually have more students in higher tracks and more advanced math,” Ryan said, because more students will have a stronger foundation in earlier grades and won’t have to repeat Algebra. They can then take an advanced course in their senior year.

Once you make advancement decisions in the younger grades, Ryan said, “students in the lower track are not prepared later on to make a choice.”

Cupertino Union Superintendent Wendy Gudalewicz said she too expected enrollment in Algebra I in 8th grade to decline with the Common Core. But the opposite has happened since the district focused resources on Common Core math and instituted objective, transparent placement criteria, which complies with the math placement act.

The district begins placement testing in 5th grade and continues each year, allowing middle school students to accelerate their  course sequence for those ready for a tougher math curriculum. Currently, more than half of 8th-graders are taking Geometry (triple the number two years ago), which is two years ahead of the standard sequence, and a quarter are taking Algebra I, with about 20 percent taking the standard 8th-grade Common Core math course.

Both districts have made progress using different models. Students in San Francisco Unified and Cupertino exceeded the average statewide scores on the initial Smarter Balanced math tests this year. But despite these efforts, significant gaps still exist between Hispanic and African-American students’ scores and those of Asians and white children in both districts.

“Math is a big deal” in her district, Cupertino’s Gudalewicz said. Denying a child who’s ready to advance would be like keeping a freshman star athlete off the varsity team or telling a pianist who plays concertos to learn scales again, she said.

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