The California Mathematics Framework Discourse

It’s Time for Humility

Welcome to the California Mathematics Framework Discourse Explainer that nobody requested, that nobody wants, that nobody needs, and that I truly did not enjoy writing.

Before I even tell you what the California Mathematics Framework (CMF) is, I want to address an important point, as prompted by this exchange I had on Twitter X Whatever-It-Is.

This is a legitimate and important question, and the answer is: I’m not. I have no interest in defending the CMF because I don’t know enough about it to render substantive judgment. Which is exactly the point of today’s post.

What is the California Mathematics Framework (CMF)

If you really want to know, go straight to the source. Here’s my own summary based on the limited amount I have read.

The CMF provides guidance for implementing the content standards of the California State Board of Education and is meant to support teachers, administrators, and parents. The CMF aims to outline the curriculum and instruction of mathematics in a comprehensive manner and includes a range of resources to facilitate the effective teaching and learning of mathematics.

Here are some key components and objectives of the CMF:

• It is aligned with the California Common Core State Standards for Mathematics (CA CCSSM). These standards define what students should understand and be able to do in their study of mathematics.
• It emphasizes instructional practices that are based on research and thought to be effective in helping students understand mathematical concepts and skills.
• It includes information on how to assess students’ understanding and abilities, including formative and summative assessments, to inform instruction.
• It addresses issues related to equity and access to quality mathematics education for all students, including those from marginalized backgrounds and those with special needs.
• It emphasizes the importance of applying mathematical knowledge in real-world contexts to enhance understanding and relevance for students.

What Is The Capital-D Discourse

Some people are really displeased with the CMF. I’m not, and it’s difficult (and undesirable) for me to get inside the heads of those who are. But if you insist, I can make some guesses about the displeasure.

Equity Focus. The CMF has a strong focus on equity and social justice in mathematics education, aiming to address disparities in mathematics achievement among different groups of students. If you’re not for that, you are not going to be a fan of the woke CMF.

Diversity and Inclusion. There is an emphasis on making mathematics education more inclusive and diverse, integrating cultural and societal contexts into mathematics learning. Ditto my above point.

Teaching Approaches. The CMF recommends various teaching strategies intended to make mathematics more accessible and engaging to all students. Traditionalists might not like this and could prefer “direct instruction” (lecturing).

Grouping and Tracking. The CMF has suggested moving away from ability grouping and tracking, where students are placed in different mathematics courses based on their perceived abilities. My anecdotal sense is that this is a real trigger for research-intensive professors in mathematics and related fields, who might take it as a devaluation of their own talents and priorities.

Curriculum. The CMF still acknowledges traditional subjects like algebra as a core component, vital for imparting essential skills and knowledge to students, but it tries to create space to address the rising significance of statistics and data science. If you believe that the traditional pre-college pathway is the right one — algebra leading to geometry leading to algebra II leading to precalculus leading to calculus — then you may not be a fan of the CMF.

I’m not suggesting that every critic of the CMF shares all these concerns; they might have only a few, just one, or entirely different critiques.

Where Is The Capital-D Discourse

Good lord, it’s everywhere. On social media. In the news. In open letters like this one and this one. In online manifestos. And now, in The Atlantic.

Who Is The Capital-D Discourse

To me, this is the million dollar question. From what I’ve observed, the voices of individuals deeply rooted in evidence-based, scholarly work on K-12 mathematics education — including those who played a critical role in the CMF’s design — are often drowned out. It’s not uncommon to see college professors and individuals with advanced degrees leading the charge in these conversations. Their insights are valued, yet I find it essential to remember — and I remind myself of this too — that holding a Ph.D. in mathematics or possessing extensive experience in collegiate teaching doesn’t translate to expertise in the K-12 mathematics education landscape. Understanding K-12 mathematics education demands a distinct blend of knowledge, skills, and experience. It’s those who are armed with this specialized expertise who need to be amplified, ensuring that the conversation is nuanced and well-informed.

In the Atlantic piece, the author — an esteemed mathematician — shares his qualifications. I choose not to mention his name, not out of dis respect, but rather, out of courtesy and the assumption that privacy in online discussions is generally appreciated. He shares:

I am a professional mathematician, a graduate of the public schools of a middle-class community in New York, and the son of a high-school math teacher. I have been the director of undergraduate studies in math at [fancy school] for a decade.

I’m prompted to reflect on the degree of connection between these commendable achievements and expertise in K-12 mathematics curriculum, pedagogy, and policy:

• Professional Mathematician: An accolade-worthy accomplishment, yet its translation to K-12 mathematics education expertise remains unclear.
• Graduate of Public Schools: Valuable lived experience, but not a direct indicator of K-12 mathematics education expertise.
• Son of a High School Math Teacher: Offers potential insights, but, like my relationship to my father’s publishing career, might not translate to in-depth knowledge.
• Director of Undergraduate Studies in Math: A role certainly requiring insight into higher education, a role likely given because of mathematical credentials, and yet the applicability to K-12 mathematics education is not obvious.

I acknowledge that this individual has dedicated a considerable amount of time and effort towards critiquing the CMF — an issue he is passionate about — and there’s no doubt that he has garnered some level of expertise from this hard work. I hold his commitment in high regard. However, it’s worth noting that both his online manifesto and The Atlantic piece are single-authored by him. For me, the resonance of these works would have been significantly amplified had they been co-signed as the collective insights of a group of experts specialized in K-12 mathematics education, representing a consensus.

But The Critiques

I’d like to circle back to the Tweet/X/Whatever-It-Is with which I began this post. I sense an expectation from some readers for me to take a clear stance on the CMF. However, as previously stated, I’m abstaining.

People are indeed presenting critiques of the CMF. That’s undeniable. But here’s the rub: when such critiques originate from individuals not steeped in the specific nuances of K-12 mathematics education, addressing them requires sifting through conjecture and misinformation. It’s akin to battling a straw man — an exercise in futility and a diversion of valuable time and energy. The amplification of voices, authoritative yet lacking in relevant expertise, poses a significant challenge to an objective, fact-based discourse. To be clear, this isn’t an endorsement of the CMF; rather, it’s an acknowledgment that parts of The Discourse mired in non-expert opinions are not always conducive to an informed evaluation of the framework’s merits or shortcomings.

Case in point: I was directed to a lengthy document from the author of the Atlantic piece, purportedly showcasing the CMF’s misrepresentation of scientific literature. You can believe me or not on this, but I picked one point out of it at random. I scrolled through and suddenly on page 12 thought “this seems fun to look into.”

I looked up the first paper (Liang et al., 2012). Here’s a direct quote from the authors:

The significant deterioration between the number of eighth graders taking the CST for Algebra I and the number of ninth graders taking the CST for Geometry signifies a decline and leads us to suggesting this idea of a leak in the pipeline. It appears that simply encouraging more students to take eighth-grade algebra does not by itself lead to significantly more students taking advanced mathematics in high school, nor does it lead to substantial increases in performances in higher mathematics CSTs.

And here’s another:

Our longitudinal data analysis (Table 2) indicates that Subgroup A members have much less chance of passing the CST for Algebra I in 9th grade compared to Subgroup B members (9.61% vs. 31.46%, see Tables 3 and 5). In other words, those students who failed the CST for Algebra I in 8th grade and retook the same test in 9th grade had a 69% (1–0.0961 / 0.3146) less chance of passing the test compared to those students who passed the CST for General Mathematics in 8th grade and took the CST for Algebra I in 9th grade for the first time. This striking failure rate is highlighted in a California Department of Education press release that states that for grades 8 through 11, only 15% of students repeating the CST for Algebra I scored proficient or above compared to 26% of first time algebra test-takers in all grades for the 2007 test administration. More recent data from the 2011 test administration show that 36% of first-time Algebra I CST takers scored proficient or above compared to 24% of the retakers scoring proficient or above (Torlakson, 2011, Table 6). The difference between first-time algebra test takers and repeaters in success rates and the fact that it appears to be continuing through 2011 raise serious questions about giving algebra 1 year sooner to those students who scored below proficient. These rates also suggest that such a practice may not help them succeed in algebra in following years.

I haven’t evaluated this paper for its scientific merit, but all I can say is that the authors’ description of their own work seems consistent with the claim made by the CMF, and I think portraying that claim as a misrepresentation is not correct. I brought this all to the person who had originally directed me to the catalog of alleged misrepresentations, and they did some digging and replied to me:

Shrug.

Let’s Be Humble

I’m really not in the market for a public spat with the author of The Atlantic piece. Honestly, I bet we’d get along. So hey, if you’re reading this, let’s grab a coffee or a beer.

More generally, I don’t want to have a public fight with anyone.

We all have a stake in public education; it’s a universal concern that impacts our society at every level. It’s appropriate and necessary for everyone to have a voice in this conversation.

However, caution is warranted. We must be mindful of the way we leverage our academic and professional credentials in these discussions. There’s a risk of conflating expertise in higher mathematical study with a nuanced understanding of K-12 mathematics education, which is a field all its own.

For my peers in academia who support the CMF, I encourage transparency and humility. Share your insights and perspectives as informed citizens, not as mathematical authorities. Those who oppose the CMF should approach the discussion with the same level of candor.

To the research mathematicians out there who oppose the CMF, I understand where you’re coming from. The CMF might feel like it’s turning your world upside down. It’s poking at the values and structures that have shaped your professional life. And if you’re one of those delving deep into the CMF, I believe you’re coming from a place of care and concern for the field of mathematics. I respect that.

I can’t say how the new CMF will pan out; we’ll need to give it time. What I do know is that up until now, the status quo system hasn’t exactly been knocking it out of the park, especially when it comes to equitable outcomes. Justice demands a change. If the current CMF turns out to be a misstep, perhaps we pivot to another approach. If it shines, heralding a generation of students armed with revitalized quantitative acumen and a diversified demographic landscape, that’s great, and for Ph.D.-carrying mathematical scientists, it doesn’t need to invalidate our identity, our values, or the significance of our work.

Your neighbor,

Chad