Credit: Allison Shelley for American Education

Even in the birthplace of microchips and iPhones, unequal access to advanced math starts early for many California students.

Luis Castro Limon, an incoming senior in Pomona Unified, has seen the inequity play out firsthand. Limon excels in math, but when he transferred to a new middle school in eighth grade, a counselor rejected his request for advanced math because he didn’t take the school’s seventh-grade math course.

“Math is his forte. When I requested the honors class because I knew my son was capable, the counselor said he didn’t qualify,” Limon’s mother, Yésica Limon, told EdSource through a Spanish translator. “But she never explained why or that we could talk to a teacher or do anything else. At that point, I made an appointment with the principal, but they didn’t explain anything.”

Limon was later accepted into the course, placing him on a fast track to advanced math in high school, but only after a teacher backed up his and his mom’s requests. The whole situation left him feeling slighted and frustrated, he said.

“The counselor seemed irritated that I wanted to get into this class. She said I would struggle and fall behind,” said Limon, who has excelled in math since then and is now enrolled in the Pomona College Academy for Youth Success, a college-prep program that helps prepare first-generation and underrepresented students for highly selective colleges and universities.

Limon’s story is not uncommon across California, where Latinos make up more than half of the state’s total student enrollment but only 30% of those enrolled in calculus in 2018-19, according to an analysis of the most recent California Department of Education data by EdSource. Black students are just over 5% of the state’s total K-12 enrollment, but they make up 2% of those enrolled in calculus across the state.

Now, California has a rare opportunity to shift expectations regarding how students learn math, who is deemed gifted and which students should be given a chance to take advanced courses. The state is currently rewriting its official mathematics guidance for schools and teachers, known as the California Mathematics Framework, a process that happens every seven years. The framework is voluntary. However, districts are expected to align staff development and learning materials with what it outlines.

But one of the framework’s major proposals — encouraging students to take the same math classes in middle school through sophomore year, rather than placing students into advanced or traditional math courses beginning in sixth grade — has been met with fierce opposition from some parents and teachers who fear it could hold students back.

“As teachers, we want to grow all of our students to their potential and each of them receive the attention they need. That’s our students on grade level, those who need help and those who are ready for acceleration,” said Lori Meyers, a public school parent and private school math teacher in California. “The recommendations in this framework would not allow for that.”

Others have criticized elements of the framework that incorporated elements of social justice into practical applications for math lessons. A previous version of the framework cited a report titled “A Pathway to Equitable Math Instruction,” which calls for dismantling racism and white supremacy that surfaces in mathematics through tracking and intervention rosters, as well as practices such as finding only one right answer.

However, the framework authors agreed to remove the report after parent complaints. The framework still calls on teachers to make math lessons relevant to students’ cultural backgrounds and rejects the notion of giftedness, saying “there is no cutoff determining when one child is ‘gifted’ and another is not” and that the idea has led to inequities in math education.

“For all the rhetoric in this framework about equity, social justice, environmental care and culturally appropriate pedagogy, there is no realistic hope for a more fair, just, equal and well-stewarded society if our schools uproot long-proven, reliable and highly effective math methods,” reads an open letter signed by nearly 500 math teachers and professors addressed to Gov. Gavin Newsom, State Superintendent of Public Instruction Tony Thurmond, the State Board of Education and the Instructional Quality Commission.

On July 14, the California State Board of Education voted to push back its timeline for revising the framework. That was done almost two months after a decision by the Instructional Quality Commission to make changes to the framework following a 60-day public review period that solicited more than 500 comments from teachers, parents and math education experts.

Experts say stark gaps among some ethnic groups, which exist throughout the state and country, start as early as elementary school, when students are typically tested for math placement for middle school. Course enrollment data analyzed by EdSource shows that white and Asian students are frequently overrepresented in calculus and the pathways that lead to advanced math courses. Native American, Black and Latino students are more likely to take Algebra 1 later in high school compared with white and Asian students, who are more likely to take it in eighth grade, according to data from the U.S. Department of Education’s Office of Civil Rights.

Studies have also shown mixed outcomes for students who speed through or skip math courses, which students often do in accelerated math pathways. One recent nationally representative study of gifted programs found that students’ reading scores improved only slightly in this model, by 2 percentile points, and that math score gains for students who got into gifted programs were even smaller.

The study also showed that students in gifted programs have much higher socioeconomic status and that students from wealthy backgrounds benefited the most, likely due to private tutoring, parental support and programs tailored to their needs.

“The caution around accelerating students beginning in middle school to get to calculus is appropriate,” said Pamela Burdman, the founder of Just Equations, which researches and advocates for equitable math education opportunities. “What’s important to remember is that no one is trying to forbid students from taking calculus in high school.”

Burdman noted that the proposed framework does not eliminate calculus. She sees it as a chance for schools to increase their advanced math course offerings, like data science and statistics, and give students a more equal footing to take them.

Old problems, new answers

Debates over how to teach math have been ongoing in California for decades, and unequal opportunities to take rigorous courses date back even earlier. As the public education system expanded in the 19th century, students were frequently and explicitly separated into academic programs based on race.

The adoption of the Common Core State Standards in math and English language arts in 2010 marked a turning point for math education. The new standards shifted instruction away from rote memorization to focus more on real-world application. Rather than separating math into discrete subjects, the new standards interweave topics and introduce Algebra much earlier than previous standards.

California’s public universities are now moving in a similar direction. In 2016, the University of California stated that high school students do not need to take calculus to be eligible for admission. And in 2020, it added more math courses, such as data science, to the list of courses it accepts for students’ third and fourth year of high school math.

As a result, many districts have moved away from traditional math course sequences and now offer integrated courses that combine topics, such as algebra, geometry and trigonometry. Those integrated courses also lead to calculus and other advanced math in a student’s junior and senior years of high school. And a small but growing number of school districts, such as San Francisco Unified, have abandoned the tracking system altogether.

In San Francisco Unified, students typically take the same integrated math courses from grades six to 10 and then select from a variety of options, including AP Calculus, their junior and senior years. Students looking for additional math opportunities can take two math courses their freshman or sophomore year to make room in their schedules for more advanced courses later, or they can take a “compressed” version of Algebra 2 and pre-calculus their junior year.

After passing a new course sequence policy in 2014, the percentage of district students who failed and had to repeat Algebra 1 decreased from 40% with the class of 2018 to 8% for the class of 2019. The percentage of students meeting application requirements for the state’s public universities increased for Black, Latino, Asian and white students alike, and total enrollment in AP math courses increased from 1,641 in 2016-17 to 1,819 in 2020-21.

During the same time period, overall enrollment in the district ticked up slightly. Racial demographics stayed similar for Black and white students, but the portion of Latino students grew by 2 percentage points and Asian students decreased by about 4 percentage points, according to data from the California Department of Education.

Melissa Daar Carvajal, a parent of twins about to enter their senior year in San Francisco Unified, is pleased with the math experiences her sons have had at Mission High School. One son, Tomas, is planning to take calculus and computer science this year as he prepares to apply for STEM college programs. Carvajal’s other son, Samuel, will be taking statistics and plans to apply to a UC campus. Both took the same courses during their freshman and sophomore years, as well as in middle school, as part of the district’s reform.

“I think this idea that my child will be held back could be informed by some of our own prejudices that even liberals still carry in the back of our head about other people,” said Daar Carvajal, who is also president of the Parent Teacher Student Association. “I don’t see any evidence that my children were held back in any way in any of these classes.”

Now in his senior year, Limon, the student at Pomona Unified, is taking AP Statistics after a successful year of calculus as a junior. He’s weighing his options for what comes next with college but says math will be part of his plan. A student activist, he’s already used some of his math skills by analyzing local budgets and advocating for funding for foster youth and other student-focused programs.

“It’s annoying,” he said about his math experience in middle school, “not even because they thought I wouldn’t be able to do it, but they think ‘you’re a kid’ so they wouldn’t take serious what I had to say.”

Limon’s mother is now struggling with middle school math placement for her daughter, after a year of remote learning with the same district. She’s open-minded about de-tracking efforts she’s seen at other districts, but she fears the slower pathway in her district could hold her daughter back from opportunities later.

“Even if I don’t speak the language, I’ll find the help for my kids so they can continue to advance, but a lot of parents don’t have that capacity,” she said, noting that her involvement with her children’s education has helped her advocate. “Education here is designed for the average American, but we’re not counting the Latinx experience as part of this.”

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  1. Timo Timo 2 months ago2 months ago

    I don't see the experience of Limon and most of this article's info as providing any evidence of racial bias or any support of a thesis. When my white/asian daughter changed schools, the new high school would not recognize her 8th grade honors Algebra course from a different, better school district and she was tracked 'regular' and restricted from taking Calculus despite A grades. Children generally achieve at the educational level of their parents. It's … Read More

    I don’t see the experience of Limon and most of this article’s info as providing any evidence of racial bias or any support of a thesis. When my white/asian daughter changed schools, the new high school would not recognize her 8th grade honors Algebra course from a different, better school district and she was tracked ‘regular’ and restricted from taking Calculus despite A grades. Children generally achieve at the educational level of their parents. It’s a slow process that requires patience and work, not weird logic.

  2. Logical Parent 2 months ago2 months ago

    Math is a tool, not something some people should be woked about. You cannot force students into higher math levels if they are not into it. But this also means you shouldn't force people into lower levels of math education who shouldn't be there. Mixing low and high performing students together into the same math classes does not result in desired results. Every student has equal opportunity to learn, but their education outcome depends on … Read More

    Math is a tool, not something some people should be woked about. You cannot force students into higher math levels if they are not into it. But this also means you shouldn’t force people into lower levels of math education who shouldn’t be there. Mixing low and high performing students together into the same math classes does not result in desired results. Every student has equal opportunity to learn, but their education outcome depends on them, not some theoretical model of equitable outcome that has not been proven and actually peer reviewed by various math education experts.

    Have a standard math program for those who are not into STEM. Also, something for those who are into STEM.

    When it comes to sports, there are no equitable outcomes. You have to train a lot to get what you want. There are no secret system here to get results.

    There is nothing wrong with taking pre-calculus later at a community college for some who are not into math in high school.

    As for the ethnic groups from the graphs above, there are no details on their culture, economic, parental and educational backgrounds to make a comparison. I have met some native Americans, blacks, Latinos, and other different ethnic groups are are very educated.

    As for the CAASPP results, this should be a warning to improve CA public education system when compared to other high performing states and countries:

    http://caaspp.edsource.org/sbac/california-00000000000000

    https://factsmaps.com/pisa-2018-worldwide-ranking-average-score-of-mathematics-science-reading/

  3. Paul Muench 2 months ago2 months ago

    There are copious amounts of excellent math instruction available for free to anyone with a computer and internet access. Enjoy yourself!

  4. Dr Math 2 months ago2 months ago

    The story starts with a Latino boy whose family had to push hard against administrative barriers to get him into advanced math and then the story talks positively about a report that would get rid of such accelerated math courses. Which one is socially just? Is it having accelerated courses for the few who handle them (including good Latino and Black math students) or getting rid of them completely?

  5. Maya K 2 months ago2 months ago

    San Francisco has implemented this sequence for 7 years. My son had 8th algebra while my daughter was one of the first who didn't. I paid for her to take it on line concurrently with Math 8 when she was in 8th grade. My son is now an electrical engineer. My daughter is a STEM college sophomore. These types of articles calling it a "rush" is misleading and creates … Read More

    San Francisco has implemented this sequence for 7 years. My son had 8th algebra while my daughter was one of the first who didn’t. I paid for her to take it on line concurrently with Math 8 when she was in 8th grade. My son is now an electrical engineer. My daughter is a STEM college sophomore.

    These types of articles calling it a “rush” is misleading and creates a strawman. This is no more a rush than allowing children drawn to literature, art and all other manner of topics to follow their bliss.

    Lost in this is that science requires advance math and data science in college requires calculus. This idea that because some students repeat high school calculus in college so why bother baffles me no end. If the majority of students in a calculus class in college are familiar with the material and then a handful of students are new to this, the class is going to move at the speed of the majority, this is akin to credit recovery for students who repeat (anecdotally neither of my children who took Calculus BC in 12th had to repeat).

    Those of us in San Francisco have lived this and seen on the ground that it does not work. We have filed FOIA for data, the claims the district make fall apart on scrutiny. Especially the reduction of repeat rate when Algebra was delayed a year to 9th grade.

    The district has only recently acknowledged that prior to the class of 2019 (this cohort was the first with delayed Algebra) students had to pass a state exam to advance past Algebra 1. The actual grade distribution between the class of 2018 (last with 8th algebra) and Class of 2019 are the same. If students in the class of 2018 were allowed to advance on grades as Class of 2019 was the repeat rate would have been the same. Meanwhile many of us have asked where 40 % repeat rate came from because it isn’t reproducible from the data received in the FOIA request.

    This pathway turns access to higher level math and science in to the path for the private and privileged. Bob Moses who died this week, the founder of the Algebra Project, had it right that access is a civil rights issue.

    We need to go forward not back as California is attempting to do and San Francisco has done. We need more Black, Latino and Indigenous voices in STEM, and this path will derail talented students from underserved communities. I’ve asked for years why San Francisco’s data isn’t audited and why people are accepting their claims of success without asking to see the data behind it.

    I am a huge proponent of what has been branded as CRT. There is systemic racism. Black, Latino and Indigenous communities face challenges which need to be addressed, the opportunity gaps are real and addressing it in high school makes no sense. I’m of the opinion that the key is reading gaps in 3rd grade (stop with this leveled reading fascination) and if we can get everyone reading at the same level we can begin to fix foundational inequities.

  6. Dan Plonsey 2 months ago2 months ago

    I've taught public school math in CA for 17 years. This article hardly does justice to attempts by some of us involved in math education to address extremely inequitable outcomes – and bad pedagogy. To begin with, the example of Luis Castro Limon's experience perhaps reflects racial bias by administrators – but the issue of bias is not central to the remedies suggested in the framework. The framework responds to the high correlation between success … Read More

    I’ve taught public school math in CA for 17 years. This article hardly does justice to attempts by some of us involved in math education to address extremely inequitable outcomes – and bad pedagogy. To begin with, the example of Luis Castro Limon’s experience perhaps reflects racial bias by administrators – but the issue of bias is not central to the remedies suggested in the framework. The framework responds to the high correlation between success in education, particularly in math, with family income – unmentioned as usual in EdSource (and, to be fair, in pretty much all such articles nationwide). Thus, in a district like mine which has large variation in income, we have a much greater disparity.

    In a typical year, of ~160 students in Advanced Math, only one or two are Black (~12% of students overall are Black). Thus, our Advanced Math program serves to increase the existing gap. It also damages many students who don’t work well in classes which privilege speed over deep understanding; I actually don’t recommend it for any student.

    In my experience, students who real love math do just fine in a regular math class! They enjoy deepening their knowledge as they work with peers. They get many chances to explain their thinking. I occasionally get a student who aces tests and acts bored – but a real mathematician always has something to think about.

    In my 17 years, I’ve never been bored, because each time through I make new discoveries, because math is far more than solving problems: it’s about finding connections, noticing patterns, and comparing sometimes radically different approaches to problems. (See for example the solutions to the current math puzzle in fivethirtyeight.) When parents insist that their child should not be “held back,” I’m sure they mean well, but I don’t think they understand the impact of economic inequality, and I don’t think they know much about math. The only real fix to the education gap is to dramatically reduce economic inequality.

    Replies

    • JudiAU 2 months ago2 months ago

      I’ve met many teachers like you through my daughter’s journey. My daughter doesn’t learn like other children. She does not need a lot of repetition. She prefers larger assignments with more challenging problems. She becomes disinterested in watching the teacher explain for the third week the concept she learned on the first day, and explaining it with no greater depth. She has no natural skills or desire to explain concepts to other children in ways … Read More

      I’ve met many teachers like you through my daughter’s journey. My daughter doesn’t learn like other children. She does not need a lot of repetition. She prefers larger assignments with more challenging problems. She becomes disinterested in watching the teacher explain for the third week the concept she learned on the first day, and explaining it with no greater depth. She has no natural skills or desire to explain concepts to other children in ways they understand. And most of all, as a well behaved girl, her teachers expect her to be someone’s (usually a bright and unruly boy) emotional support animal.

      After year after year of slow and tedious “instruction” while she was expected to be someone’s aide, she is finally free to learn through an appropriate and free education.

  7. JudiAU 2 months ago2 months ago

    My daughter was ready to take Algebra I as a 6th grader and did in our district. She could not and will not be held back. Children progress at very different rates in math and American math curriculum is often slow and boring. The only change this racist and biased curriculum change will bring is that bright public schools students will be left out of the continued development of STEM jobs. Math doesn’t end … Read More

    My daughter was ready to take Algebra I as a 6th grader and did in our district. She could not and will not be held back. Children progress at very different rates in math and American math curriculum is often slow and boring. The only change this racist and biased curriculum change will bring is that bright public schools students will be left out of the continued development of STEM jobs. Math doesn’t end at Calculus.

    The changes in SF have reduced the number of Black and Hispanic completing Calculus. Why isn’t Edsource reporting this?

    Russian Math School ($2000/year/no financial aid) opened 12! new branches in Bay Area after the change. Report that.

    AOPS ($1500/year/no financial aid) is booming. Report that.

    CTY ($600 a class, financial aid offered) is booming and the only reliable math program that offers aid.
    The numbers of advanced learners repeating classes is low. Report that.

    There are large numbers of POC in advanced math classes. Report that.

    Many districts, including our state’s largest, LAUSD, have model “big tent” programs that make access to advanced classes available and welcoming. They offer four math tracks that meet the needs of their students. Report that.

    In four hours of public testimony, every single parent, teacher, and advocacy group supported accelerated math tracks. The only group that spoke in favor of eliminating was the CTA. Report that.

    This new document portrays Asian students as outsiders, other, sneaky, and not serving of legitimate support. The hatred was so obvious that my son reported it to groups tracking Anti-Asian hate crimes. Report that.
    The report has profound bias against gifted student, which both the state and federal government recognizing as having unique needs. Report that.

    Yes Black and Hispanic students have low math achievement. This is a tragedy that the state needs to be resolved. Report on that. More.

    But hanging bags of rocks around the necks of children who want and need to learn helps no one and will make public schools less equitable as wealthy people leave, students with means get access other places, and the poor no longer have access.

  8. SD Parent 2 months ago2 months ago

    First, Limon encountered racism. You don't fix that problem by slowing the math sequence. Second, given the CAASPP scores in Math, it's clear that a large percentage of students – particularly students of color – don't have the basic foundation in Math that would prepare them for success in higher math. Is the solution really de-tracking and slowing down the higher math sequence for all students – or better instructional practices in Math across all … Read More

    First, Limon encountered racism. You don’t fix that problem by slowing the math sequence.

    Second, given the CAASPP scores in Math, it’s clear that a large percentage of students – particularly students of color – don’t have the basic foundation in Math that would prepare them for success in higher math. Is the solution really de-tracking and slowing down the higher math sequence for all students – or better instructional practices in Math across all grade levels?

    Third, concluding that de-tracking and slowing the math sequence is what caused the presumed success in San Francisco Unified is presumptive. From what I understand, in addition to de-tracking and slowing the math sequence, SFU also provided significant professional development to teachers to improve overall math instruction. As such, one could just as easily conclude that combatting intrinsic racism and providing effective PD in Math have been the reason for SFU’s results – and would be a better way to improve the outcomes for all students and especially students of color.

    Finally, the idea that de-tracking math and slowing it down does not come as a cost is magical thinking. Doubling-up in math courses in the sophomore year only works in the Algebra 1-Geometry-Algebra 2 sequence (not an integrated math sequence, such as used in San Diego Unified). Taking the extra math class in high school also causes the missed opportunity for another class in a student’s schedule, such as an elective in VAPA, CTE, or an AP course, which has a host of consequences.

    And for those students who don’t make it to Calculus while in high school, good luck gaining freshman admission into the competitive UC and private university engineering programs. They more or less require you to have had Calculus while in high school, which isn’t as publicly stated as it once was but that you can still find if you go looking.

    For example:
    Harvey Mudd requires Calculus https://www.hmc.edu/admission/apply/first-year-students/eligibilty/
    See UC Berkeley for an example of the toned-down “suggestion” of Calculus: https://mae.ucsd.edu/undergrad/ugadmissions

    California has tried many times over the decades to “solve” the math learning problem. I’m just not convinced that de-tracking and slowing down the math sequence is the panacea it’s made out to be.

  9. David Patterson 2 months ago2 months ago

    It is unfortunate that the headline for the article is so misleading. A well structured math sequence, with choices, does provide a rich and appropriate paths to calculus. The core challenge is providing the educational opportunities and support for students who traditionally have not had support and opportunities so they too can reach and excel at high math. The answer is not one size and dumbing it down.

  10. Jeff Camp 2 months ago2 months ago

    This subject will be of great interest to many middle school parents who want to know how their child can “get ahead”. More about it on Ed100. https://ed100.org/blog/slow-down