The CA Math Curriculum Conundrum
In case you missed it, a battle is raging over math curriculum in California, described at great length in a recent article in EdSource. The central controversies surround Algebra I in middle school and the potential substitution of “data science” courses for so-called “third-year” math (Algebra II or Mathematics III). The debate has been going on for at least four years, as the CA state board of education tries to develop a new math framework (hereafter called the CMF) to “help local educators as they work to diversify options and improve math outcomes for all students, including those who excel and those who struggle to successfully access math content and skills.”
So what’s an interested parent or educator to make of the controversy and shifting sands around what’s actually contained in the 1000-odd pages of CMF guidelines? Where did things land and what does it mean?
Where things landed
Unfortunately, based on my reading of the situation, the CMF does not provide definitive guidance on the two controversial topics – it punts things to school districts or the future:
Algebra I in middle school: Maybe…it’s up to school districts
Data science as a third-year-math substitute: Not the courses available today, but in the future, again, maybe
What it means for parents and educators
Here’s how I see the bottom line:
For Parents: For those with students in elementary school, your math learners will likely have different opportunities and pathways than those available today, depending on the school district. Algebra I might not be an option in your middle school; new data science courses might be offered as a substitute (or in addition to) Algebra II or Mathematics III. For those with students already in middle school, I’d say the outlook is also going to depend on the school district. While the guidelines are in principle available now, there’s no requirement to adopt them any time soon, and many districts may take a wait-and-see attitude to assess whether funding for training and implementation will be offered by the state in the coming years.
For Educators: In my opinion, the CMF as it currently stands is an unwieldy behemoth – who has the time to wade through 1000+ pages of guidelines? While the SBE web site provides a lot of information related to the guidelines, in addition to the CMF itself, it doesn’t provide easy on-ramps for different types of educators (e.g., middle- and high-school teachers, or those with varying amounts of experience, or guidance based on subject matter expertise). This means training will be critical to help math educators figure out how to implement new or modified approaches. And then there’s the data-science pink elephant – if districts start offering data-science courses, who exactly is going to teach these courses? If there’s no funding to hire dedicated teachers, then existing teachers of other subjects will likely be asked to step up and teach data science in addition to their existing course(s). New professional development opportunities and offerings become a critical need, in this case.
In short, despite the finalization of the CA math framework, these new guidelines exist only in the world of theory. In practice, it’s going to take years to understand the real impacts, and those impacts are likely to vary significantly across the 939 school districts in our huge and diverse state.
If you’re interested in digging into more of the details, read on!
All the gory detail
The EdSource summary article cited above is thought-provoking and very thorough, but also a bit complicated, which is perhaps a reflection of the debate itself. This article is long, too, so I’m one to talk! With that said, there are myriad players (see Appendix) and a raft of considerations, questions and issues that are tangled up like a Gordian Knot. The following sections are my attempt to re-organize and summarize.
Background
Most of the discussions of the CMF assume knowledge of the following context:
High-school math curricula have historically been uniform: For two decades, a math “trinity” has been considered the gold standard for college-prep math education: Algebra I, Geometry and Algebra II (or Mathematics III in CA, see below). There haven’t been explicit alternative pathways offered to students, especially those not headed into STEM or quantitative fields.
Assessments in CA reveal low proficiency and equity challenges: Student math assessments in CA have been poor and declining. In particular: “On California’s most recently reported Smarter Balanced assessment, only 33 percent of students met or exceeded math proficiency standards in 2022, and substantial achievement gaps exist, especially for Black, American Indian or Alaska Native, and Latino students” (from the Framework FAQ).
CA has established math content standards (referred to hereafter as CCSSM): California adopted the federal Common Core math standards in 2010, with its own amendments and revisions dating to 2013. In particular, CA created an additional “integrated pathway” for math that teaches all subjects at the same time over three years in the courses Mathematics I, II and III. NOTE: The CCSSM standards are intended to be curriculum-agnostic, which offers latitude to school districts when implementing them (hence the need for a curriculum framework).
CA already has a math framework, but it’s outdated: A framework was developed in 2013, presumably to go along with the (newly) adopted CCSSM (above).
The new CMF aims to provide updated implementation guidelines for the CCSSM (from the FAQ): Its goal is to “offer guidance for implementing (CCSSM) content standards. [It describes] the curriculum and instruction necessary to help students achieve proficiency, and [it specifies] the design of instructional materials and professional development. Further, [it provides] guidelines and selected research-based approaches for implementing instruction to ensure optimal benefits for all students.” In other words, the framework is aligned with and acts as a complement to the CA common-core standards.
CA is not replacing math content standards any time soon: The underlying CCSSM standards for math remain in place with the new CMF, though a working group has been created (the Intersegmental Committee of Academic Senates) to take a “broader” view of future content standards (which presumably means potentially replacing the CCSSM).
Fierce disagreement has reigned supreme: Many people have taken issue with the CMF, which generated a lot of back and forth and last-minute changes as the framework was being finalized. The SBE was making substantive changes to the framework right up until the last minute. The following quote from an article in The Atlantic is a pointed example of dissent:
“Armed with trendy buzzwords and false promises of greater equity, California is promoting an approach to math instruction that’s likely to reduce opportunities for disadvantaged students — in the state and wherever else educators follow the state’s lead.”
Debate I: Algebra in middle school
Should all school districts be required to offer Algebra I in middle school?
CMF guideline: As of the July 12 document, the CMF leaves this up to school districts, while asserting at length that it has provided extensive guidance and options for addressing the needs of more gifted students (e.g., acceleration paths) (see Chapter 8 of the guidelines).
NOTE: The San Francisco Unified School District (SFUSD) had a policy against offering Algebra I in middle school, with the goal being greater equity. The policy was to offer Algebra I in ninth grade, thus delaying geometry and other courses. A March 2023 longitudinal study of SFUSD students found that this policy did not achieve the desired outcome of greater equity.
Debate II: Data science as a course substitute for third-year math
How does data science fit in the new world of math education? This seems to be a much thornier question, with the outcome even murkier.
Can data science course(s) act as a substitute for Algebra II, from the standpoint of college admissions? Or will ditching Algebra II requirements in favor of data science hurt students who pursue this path, effectively closing off career options?
CMF guideline: Wishy-washy outcome…while the CMF said “no” to existing data science courses as substitutes (see next bullet), it left the door open to future data science courses that either require Algebra II as a pre-requisite or pass more stringent (possibly standardized) validation requirements
If data science can be substituted for Algebra II, how is the content for these courses (of which there are currently about 400 in CA) reviewed and approved? There are currently no standards for data science content and instruction in CA, and there’s no mention of data science per se in the CCSSM.
CMF guideline: The CMF revoked validation for data science courses currently in use as Algebra II substitutes. It says nothing about the establishment of future standards or how potential future courses will be vetted.
Should Algebra II be a pre-requisite for data science courses?
CMF guideline: Open question
In addition to data science considerations, is the approach to data literacy adequate (e.g., in the CCSSM standards for the “Measurement and Data” domain of K-8 instruction, along with the content for “Statistics and Probability”)? NOTE: The author of the previously cited Atlantic article believes the “data science” recommendations in the CMF are more accurately described as data literacy, which points again to the lack of data science standards in CA and the potential for confusion around these questions.
CMF guideline: Unclear. While the CMF removed language in the document related to “data literacy,” it’s still unclear whether its usage of “data science” is completely distinct.
Big questions remain unanswered
A few tactical considerations:
Is the CA SBE going to establish content standards for data science as a supplement to the CCSSM? In the absence of standards, is the current vetting and approval process for data science courses meaningful or arbitrary? Should UC continue to drive this process?
Who is going to teach any new data science courses that get created?
Will the state provide funding for school districts to help with training and rollout?
Some deeper philosophical concerns that come to mind:
What are some possible second-order effects / unintended consequences of the CMF?
Is it possible to simultaneously eliminate achievement gaps and maximize opportunity for all students? Are the goals and guidelines of the CMF idealized and unrealistic, given the finite budgets and resources within individual school districts? For more detail, check out the section on “Equity in implementation” in the EdSource article about the challenges behind rolling out the CMF.
What are the root causes of the achievement gaps in math education? Are those gaps a function of how math education is done, or are they driven by the broader forces of socioeconomic inequality? If it’s the latter, are claims about the positive benefits of math curriculum changes overstated (see SFUSD example above)?
Is there an underlying assumption being made in the CMF that most students should be getting a traditional four-year college education? How would things change if we acknowledged that, in today’s world, this may no longer be a pre-requisite for success or happiness for everyone? This notion is captured quite nicely by Pamela Burdman of Just Equations (a non-profit focused on equity in math education):
“There’s a tension between the interest in adhering to math standards and ensuring students learn math and also recognizing the changes that are happening in the uses of math in industry and the world in general”
It will take 6-7 years to know
At the risk of a bad pun, most of the things I've outlined above are probably academic for the time being.
In theory, it would seem the CMF is baked and schools can start putting the new guidelines into field. In practice, exactly how that will be done, and how long it will take, remain to be seen. According to another EdSource article on implementation challenges, “officials are still working on a professionally edited version of the framework, which can take about a year” and “it will still take up to two more years to have math materials that are vetted and approved by the state board that align with the framework.” It could take the next 6-7 years for things to settle into a state of equilibrium across California.
Final thoughts
The fierce debate around the CA math framework exposes the minefield involved when discussing the quality and relevance of math education, equity and achievement gaps. I believe many passionate, caring people are trying to do the right thing, but unfortunately, there’s never going to be a perfect solution. We live in the real world, where states and school districts have limited budgets, often an insufficient number of teachers and aides, and a population of students with needs as diverse as one can imagine. It’s aspirational to say a math framework can diversify and improve outcomes for all students, but it’s a goal worth striving towards.
So when it comes to the primary questions outlined above, here are my opinions, for what they’re worth:
Algebra I should be offered in middle-school: I believe all middle schools should offer an Algebra I course, and it should be accessible to the widest cohort of students possible. The implication is that elementary school math education needs to set high standards for everyone and do everything possible to help kids meet these levels of achievement. If we have low expectations of kids, then they will meet those low expectations. In addition, those with the socioeconomic means necessary can provide their kids with private instruction in Algebra I if it’s not offered in middle school; we shouldn’t punish those who don’t have the means by forcing them to wait until high school for that content even if their kids can tackle it in middle school.
Data literacy is implicit in the CCSSM – meet the existing standards: Everyone needs to be literate with data, and content standards exist. If taught properly, the “Data & Measurement” and “Statistics & Probability” domains of the CCSSM should cross an acceptable bar. Whatever CMF is in place should offer guidance on how to reach this basic level of data literacy, without conflating it and “data science” as the term is used in practice.
Data science is important and should complement, not replace, third-year math: Data science courses should be available in every high school for those students who would benefit from them, but they shouldn’t replace other math courses. Much of the knowledge obtained in Algebra II or Mathematics III courses is critical to keep career doors open for second-year students, many of whom don’t really know what they want to do in the future. Study of these subjects also promotes disciplined and critical thinking, and helps develop skills transferable to other subject areas and to life in general. It’s unreasonable to expect sophomore high school students to project into the future the consequences of dropping third-year math for data science. A “real” data science course, one that tracks with the practice of data science in industry, would necessarily require higher-level math (like Algebra II and Statistics) as well as computer science. I don’t see how a single course could teach data science (in the sense just articulated) and third-year math at the same time. NOTE: Is three years of high-school math essential for survival in the world, though? That’s a question for a different post.
It’s an important discussion and there are different arguments to be made, and I don’t have a crystal ball when it comes to predicting how the CMF will fare when it meets up with real teachers and schools. If I had to guess, I’d say this will all be an evolutionary work in progress for years to come, and I look forward to helping students where I can in their journeys.
If you have thoughts on the topic of math curriculum in CA (and elsewhere), please share them in the comments below!
Appendix
Extra stuff for those who are really interested!
The players
CDE: California Department of Education
SBE: CA State Board of Education
CFCC: SBE “Mathematics Curriculum Framework and Evaluation Criteria Committee”, the primary group responsible for the CMF
UCOP: UC Office of the President
BOARS: UC Board of Admissions and Relations with Schools (providers of policy oversight for UC)
BOARS working group: A newly established committee charged with clarifying the July 7 revocation changes to the CA Math Framework
Intersegmental Committee of Academic Senates: A second committee commissioned by BOARS, with math professors from CSU, community colleges and UC, charged with “taking a longer and broader view of math content”
UC “High School Articulation Unit”: A small group within UCOP charged with high-school course evaluation and vetting (e.g., for data science courses)
CSU Math Council
CSU “Academic Preparation and Education Programs Committee”: Group within the CSU academic senate
Barbara Knowlton: BOARS Chair and Professor of Psychology at UCLA
Jo Boaler: Professor of math education at the Stanford Graduate School of Education, co-author of CA Math Framework, and co-founder of YouCubed (a company that has developed at least one popular data science course, “Explorations in Data Science”)
Pamela Burdman: Executive director of the non-profit Just Equations
Quotes
A few more interesting snippets from the EdSource article cited above:
“A second group of UC, CSU and community college math professors is revisiting a more fundamental question: How much math knowledge is essential for any high school graduate with college aspirations, and separately for those interested in pursuing STEM, the social sciences or majors needing few quantitative skills?”
“Arguments about what content should be included in high school mathematics fail to acknowledge the elephant in the room: We haven’t yet figured out how to teach the concepts of algebra well to most students”
“Rick Ford, professor emeritus and former chair of the department of mathematics at CSU Chico, said that what once was a rigorous process for course approval had become a “horrendous” pro-forma exercise, “primarily reliant on the fidelity of submitters” to follow BOARS guidelines.”
“ You’re asking a 14- or 15-year-old kid to make a lifelong decision in the spring of sophomore year. Watering down content is creating a multitrack system instead of giving all students the greatest chance of success.”
“It’s been unfortunate that UC’s process of determining the rules has caused far more confusion than was needed”
