math – Public Policy Institute of California

Governor Newsom Proposes New Investments in Math and Science Teachers

The governor unveiled his proposed 2020-21 budget last week, which includes record-high levels of K-12 and community college funding—a $3.8 billion dollar increase over last year. This includes $900 million for K–12 educator recruitment and development, building on a nearly $150 million investment from last year’s budget.

These new investments are an attempt to address the statewide teacher shortage, which is most acute in the high-need subjects of math and science (special education is also a high-need area). The hope is that these investments will pay dividends in improving the size and the quality of the teaching force in these subjects, which are important for college success and for jobs in the 21st century economy.

Most notably, the proposed funding includes one-time increases to address teacher shortages in key ways:

$350 million in competitive grants for teacher professional development
$193 million to address teacher shortages in high-need subjects
$175 million for residency programs to prepare and retain teachers in high-need subjects
$100 million to fund $20,000 stipends for teachers in high-need subjects at a high-need school for at least four years

Schools across the state face critical teaching shortages in math and science, leading many schools to increase their reliance on less-credentialed and less-experienced educators. Difficulty in staffing these subjects also means that some schools must reduce course offerings, impeding student access to math and science coursework. Indeed, the number of new math and science teaching credentials has not matched demand for such teachers in recent years. In fact, the number of new math credentials has actually fallen over the past two years, constraining schools in both hiring and course offerings.

$figure - Demand Outpaces Supply for New Math and Science Teachers$

These continued shortages have important implications for student opportunities in STEM fields. For example, nearly one-third of high school graduates do not meet current UC and CSU requirements for science coursework, and many schools do not have the number of teachers required to offer three or four years of math and science to all interested students. Proposed increases to science eligibility requirements for UC admission—and for math requirements at CSU—mean that increasing the supply of qualified new math and science teachers is more essential than ever. Continued shortages will make it difficult to both accommodate this increased demand and to address equity gaps in the availability of high-quality math and science coursework.

In this light, the governor’s proposal provides reason for optimism. Increased funding for teacher recruitment and retention should help to encourage young adults to enter teaching and retain those who do. And more money for training and development should help to ensure that schools are able to choose among qualified teachers. Whether this will be enough to truly make a dent in the state’s teacher shortage remains to be seen; it depends crucially on whether these investments will be continued in future years or end up as one-time relics from a strong budget year.

Proposed Changes in Admission Requirements at CSU

For the first time in over 15 years, California State University (CSU) and the University of California (UC) may have different course requirements for admission. CSU is currently considering changing its three-year high school math requirement to a quantitative reasoning requirement of four years that broadens the list of eligible courses.

The proposed change—scheduled for a November vote by the CSU Board of Trustees—would create a difference from UC’s three-year requirement, meaning that some students who would qualify for UC may not qualify for CSU. Both CSU and UC have historically defined their math requirements around algebra, geometry, and advanced algebra, as well as any advanced courses (e.g., pre-calculus and calculus) that require these subjects as prerequisites. Under the proposed change, students could continue with the traditional math sequence or take applied courses in the fourth year, including personal finance, laboratory science, computer science, or statistics. The new requirement would first apply to the high school graduating class of 2026.

The goal of the change is to better prepare students for success at CSU and to enable more students to pursue STEM majors once they enter college. But critics cite access and equity concerns, arguing that the changes may disproportionately affect low-income students in districts that are struggling to hire enough math teachers. CSU, which trains a large share of California’s K–12 teachers, has recently announced an expansion of its Mathematics and Science Teacher Initiative to increase the number of new math and science teachers.

CSU and UC have had the same course requirements since 2003, when UC adopted CSU’s visual and performing arts requirement, thus fulfilling “the long-sought goal of giving UC and the California State University a common set of subject requirements” (2000-05-24 Notice of the Meeting, Assembly of the UC Academic Senate).

The proposed change could cause confusion for students who may want to apply to more than one system. Complicating the issue, UC is currently considering adding another year to its science requirement but has not yet scheduled a vote by the UC Board of Regents.

Students in California would benefit from clearly organized admission requirements, but the state lacks an entity that could help K–12 and the higher education systems coordinate these requirements. A higher education coordinating body could provide expertise around this decision, clarify its goals, and help determine whether the proposed requirement is the best approach to meet those goals.

Exploring Math Pathways under Common Core

California adopted the Common Core State Standards (CCSS) in math and English in 2010. CCSS describes what students should know in math and English by the end of each grade. These standards also prepare students to be ready for college and beyond. Nearly nine years after its adoption, awareness of and support for CCSS remain strong among Californians. What do we know so far about the reach and effectiveness of this change, particularly in math?

One of the paradigm shifts introduced by CCSS is how math is organized and taught in high schools. CCSS standards are organized into two pathways:

Traditional, which follows the standard sequence and includes Algebra I, Geometry, and Algebra II.
Integrated, which consists of Mathematics I, II, and III, with each course containing standards from all conceptual categories. For instance, Mathematics I covers topics in numbers, algebra, geometry, and statistics.

Acceleration, which gives students the opportunity to reach higher-level math such as calculus earlier, is possible in both pathways. For instance, a 9th grade student may complete 9th grade math (Algebra I or Mathematics I) and 10th grade math (Geometry or Mathematics II) concurrently. Districts can decide when and how students may accelerate.

During the 2017–18 school year, 54% of districts followed the traditional pathway while 46% percent chose the integrated pathway. Significant and important differences in these choices exist across districts. Districts with more high-need students—low-income students, English learners and/or foster youth—were more likely to adopt an integrated model; districts with more certified math teachers, who are authorized to teach both pathways, were slightly more likely to choose the traditional pathway.

$figure - The Traditional Math Pathway Is More Popular Among Affluent and Well-staffed Districts$

Does the difference suggest that students in high-need districts may be left behind? Not necessarily. There was no significant variation based on student performance, such as the a-g completion rate. In addition, staffing, which tends to be worse in high-need districts, did not drive most of the differences in those decisions. Other factors, such as district capacity, pedagogical approach, and teaching philosophy may also be at play.

State assessment data does not seem to show any significant difference in student performance based on pathways; however, more formal evaluation is needed. So far, there have been no large scale studies that compare the effectiveness of these approaches. Doing so will require more and better data on a district’s chosen pathway (e.g., the first time these pathways were available) and student outcomes (e.g., postsecondary outcomes)—which the state currently does not collect. The governor’s proposal to create a statewide longitudinal database is a good first step toward building the capacity to evaluate one of California’s signature educational reforms.

Trends in Math Reforms at Community Colleges

The landscape of developmental (also known as remedial) math at California’s community colleges has changed dramatically in recent years. With the passage of Assembly Bill 705, community colleges will be required to maximize entering students’ likelihood of completing college-level math and English within a year. This is a critical goal. Our research has shown that developmental course sequences are lengthy, delaying students’ academic careers and sometimes affecting their ability to advance to college-level coursework.

The new law goes into effect in fall 2019, but many colleges have already started implementing reforms to improve the accuracy of placement into developmental education and to shorten developmental sequences while making them more relevant to students. In the 2017–18 school year, 83% of community colleges offered new developmental math courses in addition to or in place of traditional courses. Example course reforms include:

Offering statistics pathways for students in majors that only require statistics (e.g., liberal arts and humanities fields)
Compressing the traditional multi-course developmental sequence into a single course
Providing lab time or supplemental instruction in a co-requisite course while allowing students to enroll directly into college-level math
Designing curricula aligned with students’ programs of study
Dividing courses into modules that represent discrete math competencies

However, the availability of these new courses varies greatly within colleges and across the state. As illustrated in the map below, for every 100 traditional math courses offered in each region of California, less than 50 reform courses are offered, indicating that on the whole reform courses are still not as available as traditional courses. Moreover, reform courses tend to have fewer sections, which further limits enrollment.

Colleges that are adopting course reforms are mostly concentrated in highly populated regions such as the Bay Area and South Coast, which collectively serve about 56% of full-time community college students in the state. In contrast, the San Joaquin Valley stands out as having the smallest ratio of reform to traditional developmental math courses, while serving roughly 10% of full-time community college students in the state. Only six out of the thirteen colleges located in the San Joaquin Valley offer at least one course-level reform.

Although some California community colleges have already implemented developmental math reforms, overall, these efforts have reached only a small fraction of the students that could potentially benefit. Math guidelines for AB 705 are still pending, but the legislation may offer the leverage needed to implement effective reforms at scale and dramatically improve student completion of college-level math courses.

California Needs More Math and Science Teachers

Recent reforms in educational standards—including the Common Core math standards and the Next Generation Science Standards—have altered the expectations placed on California’s teachers. Other changes, such as requiring college prep courses for high school graduation, will further increase the demand for math and science teachers. The state’s teacher workforce has already changed significantly in the past 15 years, but it will need to further evolve to meet the demands of the future.

These are a few of the challenges ahead:

Although the number of math and science teachers has increased in the state, there are fewer of them than in other core subjects. As a result, the average class size in math and science at all levels is larger in California than in other states. For instance, the average class size for high school science in California is 27, well above the national average (22). Similarly, average enrollment in high school math is 25, which is again higher than the national average (21).
The teacher workforce in math and science is aging rapidly. In 2016, the median age of the state’s math and science teachers was 44, three years older than the national average. In the next five years, California will need to replace at least 11% of these teachers due to retirement. About 12% of districts will need to replace at least 20% of their teachers.
The composition of the teacher workforce in math and science has changed in recent years, yet it still does not reflect the diversity of California students. In the 2000–01 school year, only 10% of math and science teachers were Latino; today, 17% of them are (while 54% of the student body is Latino). The share of Asian teachers has increased slightly, while the share of African American teachers remains unchanged. Research shows that teachers of color play a critical role in helping students of color succeed.

As California’s schools continue to implement new math and science standards, the challenge of developing a larger and more diverse teacher workforce will loom large. There are examples of efforts both in California and in other states designed to address some of these challenges. For example, Call Me MISTER in South Carolina aims to recruit college students to increase the incoming teacher pool, while other programs—like Boston Public Schools’ High School to Teacher Program—reach out to students in high schools. In addition, some programs focus on recruiting members of the local community (e.g., Teach Tomorrow in Oakland, the San Francisco Teacher Residency program, and the Grow Your Own programs in Illinois).

These initiatives represent potential models, but they would need to scale up quickly to address the challenges ahead. PPIC’s ongoing research into the implementation of the Next Generation Science Standards suggests that the high demand for quality science teachers is an emerging implementation concern.

Video: Reforming Remedial Math in Community College

Developmental—or remedial—education is one of the largest barriers to student success in California’s community colleges. The good news is that reforms are underway, and a new report by the Public Policy Institute of California (PPIC) looks at the effectiveness of some of these reforms in math. PPIC researcher Olga Rodriguez presented the report in Sacramento this week. One reform the researchers studied is an alternative to traditional algebra-based courses and is designed for students in majors—particularly those in the liberal arts and humanities—that require only statistics. The report finds that students in this statistics sequence substantially outperform their peers who take traditional developmental math.

In a discussion following the presentation, panelists addressed the issue of why this math alternative is not more widely available. Myra Snell, math professor at Los Medanos College and cofounder of the California Acceleration Project, said the reasons range from the logistical to the cultural. Most math professors are not trained in statistics. Further, there is a deeply held belief among faculty that intermediate algebra is essential. She said that this “gets in the way of them rethinking what might be best for students.”

Laura Metune, vice chancellor of external relations at the California Community Colleges Chancellor’s Office, noted the necessary shift in emphasis from encouraging campuses to try multiple interventions to investing in alternatives with the best chance of helping more students achieve their academic goals.

Nikki Edgecombe, senior research scientist at the Community College Research Center at Teachers College, Columbia University, noted: “If we know that students who are completing a statistics-level pathway are completing their transfer-level math at a significantly higher rate, but we hold on to the old system as well, it’s safe to say we’re doing a lot of students a disservice.”

She continued: “To be honest, there are a lot of bad ideas out there. We need to have the moral courage to identify what those are and fashion solutions for students.”

Learn more

Read the report Reforming Math Pathways at California Community Colleges
Visit the PPIC Higher Education Center

Upgrading High School Math Requirements

California has not updated its math graduation requirements for 30 years and now lags behind other states in ensuring that high school graduates are ready for success in college and the workplace. Math graduation requirements can affect students’ participation in advanced math courses (e.g., algebra II), which in turn has an impact on their educational and economic outcomes over the long term.

Across the nation, California is one of three states that require only two years of math instruction for high school graduation. Other states typically require three years (27 states and the District of Columbia) or four years (17 states). From 2001 to 2016, 25 states made their graduation requirements more rigorous. In recent years, some states have even incorporated college- and career-readiness components, such as SAT or ACT scores, into their graduation standards. In contrast, California last updated its graduation requirements in 1986.

In the absence of changes at the state level, California’s public school districts and four-year institutions have taken the lead. Most of the state’s districts have independently updated their math graduation standards. During the 2015–16 school year, 63% of unified and high school districts supplemented the state minimum with an additional year of math, although larger districts with more than 20,000 students were somewhat less likely to do so. Moreover, both the California State University and University of California systems require three years of math, including algebra I, geometry, and algebra II (or equivalent).

For many students, taking only two years of math will not adequately prepare them for college and beyond. It’s time for California to update its graduation requirements to better align with district practices and other major statewide efforts to improve college readiness. Increasing the amount of math instruction required for high school graduation can encourage more students to take advanced math courses—which would increase their likelihood of graduating from high school and enrolling in college. It would also reduce the need for remedial education in college.

One concern is that more rigorous math requirements may prevent students from graduating high school. However, evidence from California districts and other states suggests that there is no correlation between high school graduation requirements and high school graduation rates.

Another concern is cost, as the state needs to fund any changes to graduation requirements (e.g., the cost of hiring more math teachers and offering more math courses). However, most districts already require three years of math, suggesting that funding may not be a big constraint. If the state sets higher minimum math requirements, the educational and economic benefits for California students will likely to outweigh the costs.

Learn more

Read the report College Readiness in California: A Look at Rigorous High School Course-Taking

Improving Math Placement Decisions

A new state law is intended to help ensure that all students—particularly those underrepresented in higher education—have access to rigorous math courses in high school. This is a key step to improving college readiness and closing achievement gaps. The centerpiece of the California Mathematics Placement Act is the requirement that districts create and implement a fair, objective, and transparent math placement policy. The law leaves many aspects of implementation up to the districts.

PPIC surveyed the state’s school districts during the 2015–16 school year to examine their placement policies and identify district needs right before the law took effect in 2016–17. In a new report, Math Placement in California’s Public Schools, research fellow Niu Gao and research associate Sara Adan found that districts face a number of challenges in implementing the law. Gao presented the report at a recent Sacramento briefing.

One issue is particularly complex: teacher recommendations. The new law calls for limiting their use due to concerns that they may be systematically biased against economically disadvantaged or Latino and African American students.

The PPIC report shows that teacher recommendations are among the most widely used measures in determining placement—and the way they are used now is complicated. Recommendations typically address both academic and “soft” skills, such as student maturity, persistence, and motivation, which are predictors of student success. The PPIC authors found cases in which teacher recommendations are biased against high-achieving minority students, but they also found cases in which teacher recommendations are advancing minority students who do not perform well on standardized tests. In other words, eliminating recommendations altogether may help some students but at the expense of others.

Gao said the critical issue is not whether teacher recommendations should be used but how they can be designed to complement objective measures, such as tests.