Yet More on the California Framework (Part 2)

Previously on this topic:

  1. The California Math Framework Revision
  2. More on the California Framework
  3. Detracking, How To
  4. Yet More on the California Framework (Part 1)

In my last post (#4), I shared three important points raised by Boaz Barak, Edith Cohen, Adrian Mims, and Jelani Nelson in their open letter about the California Math Framework Revision (CMFR). I agreed with them on those three points. I appreciated that unlike the authors of the first open letter (discussed in #2), they did not complain about occasional word problems that address social issues, and that they avoided the vitriolic tone that is so often characteristic of the math wars.

Still, I cannot sign their letter. I’ll explain why in this post. There are two types of reasons: the context, and the specifics.

(All quotes below are from their open letter. I’ll refer to the authors as BCMN.)


There is a broad professional consensus in the math education community that the current use of tracking works well for the upper tracks, but poorly for the lower tracks. Those are plagued with low expectations, and are far from offering all students “a math curriculum with precision and rigor … that would enable them to pursue STEM degrees and careers if they so choose.” And the current version of acceleration often results in de facto tracking: for example, a typical 9th grade Geometry class is more challenging and rigorous than a typical 10th grade Geometry class — a fact which is justified by blaming the students for what is in fact a systemic failure.

Whether we want to acknowledge it or not, in the background of this discussion is a conflict between different social strata. Forgive the sociological jargon, but it is helpful to have a clear understanding of how this seemingly never-ending math war plays out in the real world. There is nothing new here. Some math educators have been trying over several decades to democratize math education, starting with the Algebra for All movement that started in the 1980’s. This has been met with ongoing resistance. Middle class parents felt threatened, and retaliated by promoting 8th grade algebra for the few. When that became more widespread, they stated pushing for 7th grade algebra for the few. And on it goes, an arms race between defenders and challengers of privilege. No one here is ill-intentioned: middle class parents, like all parents, care about their kids’ education, and worry that changes may undermine it. Many are convinced that their children are uniquely gifted, and cannot possibly be at the same level as everyone else. Sometimes they are deluded, but it does not stem from bad intentions.

I myself was in the middle of one of these skirmishes, when some parents and a math prof in Davis, CA rose up against the use of an Algebra 1 textbook I had co-authored. The School Board allowed the parents of middle school students to choose between a class that used my book and a class that used a traditional book. The results of the ensuing natural experiment was that my approach helped the less-prepared students at no cost to the better-prepared, who did equally well under either regime. Read the story here. But this is the key: it is absolutely possible to help the students who need the support, without harming their more advanced peers. In other words, it is possible to avoid the disastrous conflicts we allow ourselves to engage in.

Alas, sometimes, the reformers are their own worst enemy. In the 90’s, I attended meetings where reformers declared that fractions were obsolete (!), and were promoting an ill-defined “mathematical power” as a substitute for mathematical understanding and proficiency. It didn’t take long for the backlash to set the movement back for many years. Likewise, the currently fashionable bashing of Algebra 2 among some reformers will yield the same results if it is not challenged. 

In any case, I believe that the current version of the CMFR would make things worse, and lead to a powerful and unstoppable backlash. In the present highly polarized situation, criticizing the CMFR without challenging the current state of math education inequities comes across as defending an unacceptable status quo. 


To be clear, I do not claim or believe that BCMN want to defend the status quo. Their letter is narrowly focused on stopping the current version of the CMFR, which they see as undermining the preparation for STEM education at the college level. While I agree with them, I am playing a longer game. Whatever is included in the final version of the Framework will not change the need for a more nuanced understanding of how to move forward towards a high-quality math education for all students. BCMN do not provide that in their letter (nor do they claim to.)

I suspect that they are wrong in thinking that the CMFR is typical of a broad trend in math education. And I am disappointed that they carefully avoid mentioning geometry, in keeping with an actual many-decade trend in the US. But these are minor points. Here are my three main concerns with the letter. I will not call them “disagreements”, because I’m mostly reacting to omissions and vagueness. It would not be fair to expect people who are not math educators to come up with a fully-baked proposal for the California Math Framework. Still, the omissions and vagueness are sufficient to discourage me from signing, and they do give me an opportunity to spell out my views.

What about math educators?

BCMN “call on national, state, and local governments to involve college-level STEM educators and STEM professionals in the design of K-12 mathematics and science education curriculum.” Sigh. This leaves out math teachers and even math education academics. In other words, the people for whom the status quo has worked should be the ones to tweak it? The K-12 teachers for whom BCMN have “the utmost respect” apparently should just implement the ideas coming from STEM professionals? And the professors who have spent their careers researching what works and doesn’t in math education should not even be consulted? I realize I’m being oversensitive, as BCMN say nothing about excluding anyone, and they probably assume it goes without saying that math educators should be involved. I’ll just say that after decades of teacher-bashing in the US,  that cannot and should not be assumed.  

We’ve been there before. In the 1990’s, a Framework that triggered the ire of the STEM establishment and middle class  parents was replaced by California Standards that were written by university mathematicians who didn’t know a child from a chair, a curriculum that was essentially unteachable. (For example, the Algebra 2 standards could easily have taken two years in a normal classroom.) We are headed in that direction if the CMFR is not improved, and if the solution to its shortcomings is to just get the teachers and other math educators out of the way. 

It would not have been difficult for BCMN to get a hold of the National Council of Teachers of Math’s Catalyzing Change in High School MathematicsThis document is the result of massive input by people in the profession, and proposes a way forward to address the injustices that pervade the system as it is presently constituted. Because it is rooted in reality, it tries to initiate conversation, not make drastic changes all at once. This is consistent with BCMN’s belief that “changes to educational standards should be approached with care, using incremental experimentation building on lessons learned from both the US and abroad and using credible measures of success.” But NCTM’s document is forward-looking in a way that the open letter is not. I cannot summarize Catalyzing Change here but a key insight therein is that there are many structural obstacles to equity, and one of them is tracking.


Tracking is at the same time the central structure that enforces inequality in math education, and the one that is hardest to dismantle. It is not mentioned in BCMN’s letter, except perhaps that some of the vague language in the letter can be read to support tracking. (“There cannot be a ‘one size fits all’ approach to K-12 mathematical education.”)

Tracking is difficult to challenge for many reasons, different ones for different people: tradition, racism, not knowing of a workable alternative, belief that it is in the best interest of all, attachment to perceived privilege, fear that some students will be crushed by high expectations, and so on. Tracking is so embedded in our schools that it is profoundly counter-cultural to question it. Not only that, but tracking often involves an unfair and absurd division of labor in too many schools: the least experienced teachers (who are also the ones with the least power) are expected to teach the low tracks, which is of course more challenging. If you want to find out more about all this, a good place to start is the aforementioned Catalyzing Change document from NCTM, which includes copious footnotes.

Many reformers say that all students are natural mathematicians. They use this language in order to counter the demeaning descriptions of poorly prepared students as ‘low’, or ‘concrete thinkers’, or some other insulting and self-fulfilling euphemism. But still, everyone knows that students learn math at different rates. Denying this fact will convince no one — it only serves to reinforce the traditionalists’ campaign to keep things just as they are, because it makes it seem like reformers are detached from reality. The question is not whether there are differences, but how we deal with them. I agree with NCTM that in the long run, this has to include the elimination of tracking. I shared some ideas on how to do it in Detracking, How To. I believe the current version of the CMFR will not and cannot get us there.


“Students should be offered multiple pathways and timelines to explore mathematics.” Unfortunately, the vagueness of the statement lends itself to a defense of the status quo. I prefer NCTM’s formulation: multiple pathways should follow two to three years on a common path. As for different timelines, it’s tricky. As I mentioned before in this series, I believe many students in a given age cohort can successfully be in classes one year above grade level, starting with eighth grade Algebra 1. Acceleration beyond one year is very often a mistake. (A surprising number of students who are obedient and have good memory can appear more competent than they really are.) In any case, the number of students who should be accelerated by more than one year is not large enough to dictate policy. I discuss the unintended consequences of hyper-acceleration in this article. See also Penn mathematician Robin Pemantle’s article on More Calculus, Less Understanding?

One risk that is built into acceleration, even acceleration by just one year, is that if students in the accelerated class are segregated from their peers, it is just another form of tracking. Each course from Algebra 1 onward should include two years’ worth of students: half on grade level, and half who are “ahead” by one year. This guarantees that no one is in a low-expectations dead-end track. Of course, this would be challenging to teachers who are not accustomed to heterogeneous classes. There are ways to deal with that, including the ideas I suggest in Reaching the Full Range, as well as strategies such as Peter Liljedahl’s Thinking Classroom or the concepts behind Complex Instruction. But of course, getting teachers to buy into these techniques and become proficient at them cannot be done by fiat. In addition to those pedagogical changes, it requires a long-term strategy involving appropriate “low threshold, high ceiling” curricular materials, teacher training, and in-school structures for support and enrichment. 


I welcome interest in math education from members of the broader community, and as I made clear in my last post, I believe that BCMN are mostly correct in their opposition to the CMFR in its present form. I hope that both proponents and critics of the CMFR realize that this is not a zero sum situation where helping some students of necessity will harm others. Our goal should be and can be to find solutions that work for everyone. Of course, all participants in this conversation agree with this in theory. Finding a way to put this common goal into practice is where people part ways. Here are my suggestions for an approach that may work.

  • The next version of the CMFR should align with the professional consensus as articulated by the NCTM, not rush into drastic changes.
  • All students should learn the Essential Concepts outlined by NCTM in Catalyzing Change by the end of 10th or 11th grade. Data science should not displace fundamentals of algebra, geometry, and trigonometry.
  • After that, students should have a choice of pathways for their last year or two of high school. No pathway should be a low-expectations dead end. (Students should not be separated into different pathways too early, as that will almost certainly result in stealth tracking.)
  • Eighth grade Algebra 1 and 12th grade Calculus should be available to students who are adequately prepared. Other rigorous math courses should be available to seniors.
  • Strong students should not be segregated from others: courses should include students on grade level, along with students who are a year younger and ready for those courses.
  • California should aim for a multiyear detracking process. This must include appropriate curricular materials from various sources, adequate professional development for teachers, and an ongoing conversation among all stakeholders: teachers, other math educators, parents, and STEM professionals. Rushing this process can only result in failure. 
  • Outside of class, students should be offered support and enrichment, as needed.

If you agree with me on some or all of this, please share my posts with others, and let’s hope we are heard by the powers that be, and by their critics.

— Henri

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