Credit: Allison Shelley for American Education
A group of high school students work together to solve an algebra problem during their precalculus class.

The recent debate over California’s proposed math framework is missing the forest for the trees. In its myopic focus on which advanced math courses best prepare high school students for their futures, it glosses over a glaring fact: More than half of California seniors take no advanced math course at all. In fact, California requires students to take only two years of math, through Algebra 1.

As recently as 2018, nearly 40% of schools in the state had no seniors at all enrolled in advanced math, according to a 2019 report. More than 200,000 students left high school without the benefit of any advanced math. These students were more likely to be Black, Latino and low income than students taking advanced math.

Against this backdrop, California educators can ill afford to disagree over the value of a more traditional precalculus or calculus course versus a rigorous course in statistics, data science or mathematical modeling. Both are valuable — the former as preparation for the fields of science, technology, engineering and math, or STEM, with the others aligning well with an interest in fields such as psychology, law or political science. Rather than prejudge students’ choices — or preclude them from making choices — educators should focus on making multiple rigorous options available.

To be sure, STEM majors and careers should be accessible to all students, and that has traditionally not been the case. Special attention must be placed on expanding STEM preparation for groups that have historically been excluded — particularly students who are Black, Latino, and/or experiencing poverty — so that students can authentically opt in.

But not all students want to enter STEM fields. Nor do these professions have room for every student. Ensuring that all students develop mathematical maturity requires making more than one type of math available in high school, as advocated by the National Council of Teachers of Mathematics and others — not requiring each student to prepare for STEM entry, regardless of their interest.

Will California’s math framework solve all of these problems? No. But it can help advance a two-fold agenda: improving math preparation for STEM fields, particularly for historically excluded students, and ensuring that students focused on other pursuits also have opportunities to deepen their mathematical skills in relevant and engaging ways.

Efforts to promote advanced math opportunities have begun. The state and private foundations have supported several new courses designed to improve math learning and college readiness among California graduates. These range from teaching the fundamentals of data science and discrete math to strengthening understanding of traditional algebra-intensive math.

Such courses aim to serve students who historically didn’t continue in mathematics through new content and professional development. And though data science and statistics are not recommended for students committed to a STEM path, preliminary evidence points to their potential to reengage students who had previously ruled one out.

California university policies have reinforced such changes. Some individual courses, such as this and this in the Los Angeles district, have been accepted for admission to the University of California and California State University since at least 2015 and 2017. In 2020, the UC’s Board of Admissions and Relations with Schools clarified its definition of courses that qualify as “advanced math” options for high school juniors and seniors.

Faculty as well as administrators at CSU, which uses the same A-G course requirements as UC, have also endorsed the importance of honing students’ quantitative reasoning skills throughout high school, whether through traditional content or more innovative courses (and their proposal to require a fourth year of such courses is undergoing research).

Both universities require students to enter with at least three years of mathematics but recommend four years. Still, college admissions policy is not the best strategy for upgrading students’ high school math preparation, especially when the state only requires two years of high school math, less than 40-some other states. Some California districts have raised the bar to three or four years, but that exacerbates gaps across schools.

Shouldn’t California catch up to the 21st century and equalize opportunity within the state by requiring at least three years of math preparation for students to complete high school?

Of course, requiring courses is not enough, if access remains inequitable. The California Mathematics Placement Act of 2015 attempted to ensure objective placement measures in the transition from middle to high school. Given the importance of equitable access to advanced math courses generally and STEM-oriented math, research is needed into its implementation and outcomes.

University and K-12 educators undoubtedly share the vision for experiences that nurture students’ quantitative skills and prepare them for a rich future, in STEM as well as other fields. To achieve that vision, there is much work ahead — and one element must be ensuring the availability of multiple high-quality advanced options, while doubling down on equitable access to each.

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Pamela Burdman is executive director of Just Equations, a nonprofit that promotes policies that prepare students with quantitative skills to succeed in college.

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  1. Maya K 2 months ago2 months ago

    This is very interesting in light of Dr Conrad's (Professor of Mathematics Director of Undergraduate Studies in Math, Stanford University) exhaustive look in to the problems with the CMF. I urge people to read it : https://sites.google.com/view/publiccommentsonthecmf/#h.cckogmmiz8sw Tom Loveless wrote about his concerns that this framework will not help struggling math students: https://tomloveless.com/posts/evidence-struggling-math-students-and-californias-2022-math-framework/ Meanwhile, a CPRA request to UCLA garnered emails between Dr. Boaler and Dr. Gould and in these emails Dr. Gould admits that those who want … Read More

    This is very interesting in light of Dr Conrad’s (Professor of Mathematics Director of Undergraduate Studies in Math, Stanford University) exhaustive look in to the problems with the CMF. I urge people to read it :

    https://sites.google.com/view/publiccommentsonthecmf/#h.cckogmmiz8sw

    Tom Loveless wrote about his concerns that this framework will not help struggling math students:

    https://tomloveless.com/posts/evidence-struggling-math-students-and-californias-2022-math-framework/

    Meanwhile, a CPRA request to UCLA garnered emails between Dr. Boaler and Dr. Gould and in these emails Dr. Gould admits that those who want to go in to Data Science need more math than the high school course they propose:

    https://www.scottaaronson.com/cmf-documents/Jo_Boaler_Emails.pdf

    From Page 3

    ‘4) They’re right to some extent. We call DS an “intro” course because there’s lots you can do
    without the math they mention, and that stuff is more important (in my humble opinion) than the math. In addition, that stuff is difficult, challenging, and subtle and takes practice and time to be learned. One course isn’t enough. And so I hope our IDS students go to college and take another intro course, which will go a bit deeper, but also strengthen what they know. Then they’re ready for “citizenship” (or at least tentatively ready). those who wish to major in that or a related field will need more math.”

    We need a diverse STEM professional workforce. I’m a 57 year old electrical engineer and I’ve seen firsthand how not having diversity in the room leads blind spots. We need more Black, Latinx, Indigenous and other under represented voices to bring their experiences to solve the many problems facing us.

    Semiconductor Digest raised the alarm that we need more STEM graduates, not less.
    https://www.semiconductor-digest.com/u-s-is-keystone-of-the-worlds-science-and-engineering-ecosystem/

    “Addressing the persistent educational inequities that exist across geography, race and ethnicity, and socioeconomic status is both an ethical and economic imperative for our country,” says Julia Phillips, Chair of NSB’s Science and Engineering Policy Committee. “To meet our workforce needs and ensure the U.S. remains globally competitive, we must break down the systemic barriers that too many Americans face and nurture the next generation of domestic STEM talent from K-12 through doctoral degrees.”

    My son graduated last week with his MS in electrical engineering. My daughter is a college junior in Biotechnology. I had to battle with SFUSD to get her access to Algebra 1 in 8th grade as she fell in to the SFUSD’s delayed Algebra experiment. This was widely celebrated in the first draft of the CMF but oddly after this report showing that these claims were not reproducible with CPRA data, they were removed from the second draft.

    https://static1.squarespace.com/static/60412a3a51d4863950d1bdf2/t/616e2f823696906267609f3f/1634611077888/Report-+Inequity+in+Numbers.pdf

    We need to overhaul math education but I don’t believe this draft is the way forward.

  2. Richard Rasiej 2 months ago2 months ago

    My sense is that we will not be able to make substantial progress on this until we finally get around to improving the quality of math instruction in the earlier grades, particularly K-5. Too many students of all backgrounds are falling out of the potential pipeline to advanced math through poor instruction provided by ill-prepared teachers who, even if they have a full traditional multiple-subject teaching credential, have poor math content knowledge. We … Read More

    My sense is that we will not be able to make substantial progress on this until we finally get around to improving the quality of math instruction in the earlier grades, particularly K-5. Too many students of all backgrounds are falling out of the potential pipeline to advanced math through poor instruction provided by ill-prepared teachers who, even if they have a full traditional multiple-subject teaching credential, have poor math content knowledge. We need to convince policymakers that better math teaching is fundamental to better math learning.

    Replies

    • Neepa Parikh 1 month ago1 month ago

      I agree with Richard. My son is senior and he has done well in all his math classes from K to 12 since he started early from preschool. He has taken all advance math class available at LAUSD. LAUSD has lots of resources available where parents and students can get help. Parents' involvement is most important. If you plan to go for STEM degree, 4 years of math is very very crucial. In name of … Read More

      I agree with Richard. My son is senior and he has done well in all his math classes from K to 12 since he started early from preschool. He has taken all advance math class available at LAUSD. LAUSD has lots of resources available where parents and students can get help. Parents’ involvement is most important.

      If you plan to go for STEM degree, 4 years of math is very very crucial. In name of equity and justice, you can’t lower the standards. Best you can do it to give help who needs it and make math classes more interesting and fun. 2 years of math is not enough for STEM degree and that could be the reason students drop out since it gets harder in college.

    • Pamela Burdman 1 month ago1 month ago

      Good point.

  3. el 2 months ago2 months ago

    "nearly 40% of schools in the state had no seniors at all enrolled in advanced math" That is a shocking statistic. Like how is that even possible? What does a school with that statistic look like and why do we allow it to continue? Is it possible that these are just counting a lot of small continuation high schools and other alternative programs? I do think data science and statistics have value, and probably more value than … Read More

    “nearly 40% of schools in the state had no seniors at all enrolled in advanced math”

    That is a shocking statistic. Like how is that even possible? What does a school with that statistic look like and why do we allow it to continue? Is it possible that these are just counting a lot of small continuation high schools and other alternative programs?

    I do think data science and statistics have value, and probably more value than high school calculus, even for STEM majors. (Note: I have a STEM degree and work in a STEM field.) They are also hard to teach well, and our teachers will need support to be able to handle those topics appropriately. The good news is, it is much easier and much more interesting to teach these topics now that we have computers and learning the material doesn’t involve laborious hand calculations to work with a data set of any size, as it did when I was a student. The potential to play with this data – and yes, it can make complex mathematics feel like play – IMHO can indeed bait the interest of students who have come to think of math as boring or pointless.

    Calculus is a big break in even “what math is” from the algorithmic rules we teach in algebra and before. It’s good stuff but only if well taught.

    I would also like to see more advanced math made available for dual enrollment through online and otherwise accessible courses at the community colleges. It’s hard to learn advanced math online and it’s not for everyone, but these are valuable options for gifted students who are not in large high schools with a cohort of other gifted students. If we have gifted kids stuck at high schools without a strong advanced math teacher, we need to figure out ways to get them access to the material, even if they live in rural areas. This doesn’t relieve us of the obligation to get good math instruction at every school everywhere, but more options are better.

    Replies

    • Pamela Burdman 2 months ago2 months ago

      Some, but not all, are non-traditional high schools.

  4. Replies

    • Pamela Burdman 2 months ago2 months ago

      Thanks for the note. I have only skimmed your commentary, but it appears it reflects the 2021 version, not the current one. I believe many of the issues you’re raising have been addressed.

      • Zeev Wurman 2 months ago2 months ago

        Actually I think you are wrong, Pamela. The current (2022) version of the Framework removed its previous claim that "there is no such thing as talent and hence all students should take identical math for as long as possible" but retained most everything else such as focus on data science, trauma-informed pedagogy, sociopolitical consciousness, social justice and similar. Peter Martinson's essay provides links to specific criticisms of the current version of the Framework and, … Read More

        Actually I think you are wrong, Pamela. The current (2022) version of the Framework removed its previous claim that “there is no such thing as talent and hence all students should take identical math for as long as possible” but retained most everything else such as focus on data science, trauma-informed pedagogy, sociopolitical consciousness, social justice and similar. Peter Martinson’s essay provides links to specific criticisms of the current version of the Framework and, in particular, details about cherry-picked and misinterpreted research widely used to support Framework’s ill-supported recommendations.

        • Pamela Burdman 1 month ago1 month ago

          Thanks. I wasn’t commenting on the entire Framework, only the need for multiple options for the third and fourth years of high school. I said the paper isn’t addressing the current version is because it has one or more broken links and analyzes at length a document re equitable math instruction that is not even listed in the citations.