When the Wall Street Journal's editorial board and the New York Post endorse your efforts, that should ring warning bells.

Several members of the theory and mathematics community and have written and endorsed an Open Letter on K-12 Mathematics that attacks the proposed revisions to the California Mathematics Framework. I have mixed feelings about these efforts.

Certainly the CMF has its issues, and the FAQs protest too much. But the letter goes too far in the other direction, arguing mainly for the status quo that worked well for those who signed the letter, very few of which have significant experience in K-12 education. The open letter allows for only incremental change unlikely to lead to any significant improvements.

Before you sign the letter, take a look at the CMF introduction

To develop learning that can lead to mathematical power for all California students, the framework has much to correct; the subject and community of mathematics has a history of exclusion and filtering, rather than inclusion and welcoming. There persists a mentality that some people are “bad in math” (or otherwise do not belong), and this mentality pervades many sources and at many levels. Girls and Black and Brown children, notably, represent groups that more often receive messages that they are not capable of high-level mathematics, compared to their White and male counterparts. As early as preschool and kindergarten, research and policy documents use deficit-oriented labels to describe Black and Latinx and low-income children’s mathematical learning and position them as already behind their white and middle-class peers. These signifiers exacerbate and are exacerbated by acceleration programs that stratify mathematics pathways for students as early as sixth grade.

Students internalize these messages to such a degree that undoing a self-identity that is “bad at math” to one that “loves math” is rare. Before students have opportunities to excel in mathematics, many often self-select out of mathematics because they see no relevance for their learning, and no longer recognize the inherent value or purpose in learning mathematics.

You may or may not agree with the CMF approach, but it's hard to deny the real challenges they are trying to address and students they are trying to help. If you don't agree with the CMF, work with them to come up with a good alternative that helps create a more inclusive mathematical citizenry. An outright rejection of the approach won't fix problems and probably won't be taken seriously, except from the conservative press.

Update (1/12/22): Boaz Barak and Jelani Nelson respond to this post.

Interesting point of view. But I'm wondering why is it that being endorsed by Conservative outlets is a "warning bell", while being promoted aggressively by Liberal media and activists, such as in the case of the CMF, is apparently not a warning bell, in your opinion? Is there something inherently sinister about being a Conservative? Voting for the Republican party? Is it now considered outright illegitimate to hold Conservative views in American academia, that "you shouldn't (even) be taken seriously" anymore, as you write?

ReplyDeleteOne can't be an expert in everything, or take the time to study every proposal in detail. So, the opinions of others can be useful. Knowing the history of the person or organization that is offering an opinion provides information as to the reliability of the opinion. Since the Wall Street Journal's editorial board and the New York Post generally are in favor of things that are good for rich people, and not so good for others, their support of a proposal does suggest that one should scrutinize the proposal more carefully to understand it and why they are supporting it.

DeleteThis is a gross generalization, not to mention that it assumes anything "good for rich people" must be inherently bad. (Isn't preventing climate change good for everyone?)

DeleteFor me, using the abomination "Latinx" rings warning bells.

ReplyDeleteCertainly the reasonable among us agree that California's goals are just, and many of their opponents villainous.

ReplyDeleteBut do avoid the casual taint of logical fallacies like Automatic-Guilt-By-Association, or Doing-Something-Is-Better-Than-Nothing, that weaken your arguments. The burden to find the right solution does not fall upon those that speak up to disavow a bad solution.

Perhaps, in your position and experience, you could give insights as to whether the specific, proposed actions will affect the equity of your undergrad/graduate programs? For example, from your observations, have public school students who do not have the opportunity to learn Algebra before high school, or Calculus before college (as the framework suggests) fared well as your students?

Hope you are doing well and staying safe in these trying times!

I work now at a university that has a tradition of providing a tech education to those who might normally not get one. Many of our students didn’t have the opportunity for advanced math courses in high school. Some struggle but most do well and graduate into a solid job. I do not believe high school calculus is needed to succeed in college.

DeleteWe’ll just have to disagree about whether those who put only barriers to change are really willing to accept any significant change.

I signed that letter.

DeleteThe CMF seems to me to be about providing equality of opportunity (which is a good thing) in a terrible way, viz. enforcing mediocrity in mathematics. I cannot think of a better way to encourage talented kids to abandon math. "From each according to their ability" will not work out well if that ability is not developed and rewarded. And "to each according to their needs" will entail defining needs downward in that event.

If a HS taught the rudiments of computational complexity and probability instead of calculus it would be great. I know (from producing and giving extra credit lectures) that this is possible within the confines of a class at or even below the level of precalculus, though it is demanding.

It's terrible that any topic is discussed through the lens of political views. I would assume education should be above that.

ReplyDeleteI find the open letter unhelpfully vague about what it objects to in the new proposal. Reading some of the blog posts and analysis behind the open letter, I think there are some good critiques, but also points I disagree with and places where I think the some of the critiques don’t actually match my reading of the proposal.

ReplyDeleteFirst, there is a fundamental problem that standard math sequences have 6 notional years of content (7th grade math through Precalculus) but only 5 years to teach it in for students who will take Calculus in their senior year. The “traditional” solution is to have a tracked system where some students take that standard sequence (and so in 7th grade are filtered out from being able to take Calculus) and another track where students cover 3 years of content in 7th and 8th grade. The revisions as I understand them propose to instead cover parts of what would traditionally be Algebra 1 for middle school for all students, so effectively having all students cover something like 2.5 “years” of content in the two years of middle school. Then students who will take Calculus need to cover 3.5 “years” of content in their first three years of high school. This seems a plausible approach to me. I think what the letter misses, and the revision does a poor job explaining (because it spends most of its focus on integrated pathways) is that even though it says students won’t start “Algebra 1” until 9th grade this won’t be the same “Algebra 1” taught in 8th grade today – it can’t be because large chunks of that content are being moved to middle school for all students. I think it makes much more sense to think of the proposal in terms of the integrated pathway, where the content of Algebra 1, Geometry, and Algebra 2 has already been rearranged into Integrated 1, Integrated 2, and Integrated 3. In that sort of structure, it feels clearer how you can fit the content in without the sort of “compression” course the letter complains about. I haven’t analyzed the specific topics they allocate to each course, so I could be convinced that the revision as currently specified fails to actually deliver on this pathway, but I haven’t seen such a case made. Furthermore, the large number of students currently taking AP Calculus as juniors (or earlier) certainly suggests such as thing is possible as they are already compressing by a further year.

Second, I think the revision makes a plausible case (although stated too universally) that the push for high school calculus may have gone too far. The number of students taking the AP calculus exam has tripled since I was in high school (Peak AP Calculus, What Comes Next? Part I — MATH VALUES). Certainly part of this increase is likely a good thing in the form of expanding access, but I can certainly believe there a substantial fraction of those students who despite completing the course do not actually adequately learn the material. Those students might well be better served, and still able to be perfectly successful in STEM careers, by having a pathway that gives them a firmer foundation through Precalculus leaving them well prepared to start with Calc 1 in college. Again, I could be convinced that the revision is wrong in its diagnosis of the existence of a group of students for whom this is true, but I don’t see anything in the supporting materials behind the letter that makes a case it actually is.

I do agree with the letter on one significant point – the emphasis on flavoring the integrated pathway with data science feels trendy and does not seem particularly well-motivated by evidence. I’m more agnostic on the detracking claims. I haven’t seen strong evidence presented either way on whether switching to the 2.5 / 3.5 structure for students on the “advanced” track too is better or worse than the current 3 /3 structure. So while a bit experimental it also doesn’t seem so unreasonable that I would raise a strong objection to it.

There is a bait-and-switch in the discussion of 8th grade math that tricked you: the CMF speaks of a "new" 8th grade math course but there is nothing new for 8th grade. The content standards for grade 8 are not changing in any way at all since the entire grade-level standards are remaining exactly the same as since 2013: it's the same California Common Core State Standards for Math. If you look closely at Chapter 7 on grades 6-8, you'll see that chapter has no discussion of content changes at all: it just discussing things like examples of new ways of teaching some topics.

DeleteWhen the CMF speaks of the "former" Algebra 1 course, that is actually referring to what was done before 2013. Look at the 2013 Common Core document for California: its topic coverage for grades 8 and 9 is exactly what is still being proposed for grade 8 content and for the traditional pathway in grade 9. There is absolutely nothing being moved into grade 8 from grade 9. Seriously. This is why the claims that all options remain within reach in grade 12 (including calculus) without any compression are false. `

If you look at Chapter 8 on the high school material, the proposed way to reach calculus is through misrepresentation of papers that CM claims demonstrate precalculus is unnecessary (but the cited papers say nothing of the sort). This is spelled out in detail in the critique document if you look in it towards the end.

If the CMF's claims were true then ever since 2013 students in California would have been able to reach calculus in 12th grade with no compression, no doubled-up classes, etc. because the 8th grade class is not changing in its content at all. Yet it is widely documented that students in SF have had to go through many types of work-arounds to deal with the elimination of the option of actual Algebra 1 in 8th grade since 2014.

If the People's Republic of California decides on K-12 Math Ed "from each according to their ability" and "to each according to their needs" then so be it.

ReplyDeleteTwo words for those who believe that the status quo promotes inequality:

Piper Harron

https://beforetheabstract.com/piper-harron/

The fact that mathematical education in the US (and California in particular, which is doing worse than many other states) is not great or equitable, doesn't mean that proposed changes can't make it much worse. While the CMF might have a nice introduction, the actual changes it makes will be negative, and are likely to make math education *less* equitable. See for example this analysis by a K-12 math teacher and education consultant with 42 years of experience https://blog.mathed.page/2021/12/14/yet-more-on-the-california-framework-part-1/

ReplyDeleteAs Adrian Mims says (a co-leader of this effort with extensive experiment in math education for low-income students and students of color https://thecalculusproject.org/ ), California math education is like "a ship with a hole in the bottom and a few people on the ship come up with an idea to create another hole in the bottom of the boat to drain the water flooding the boat."

Now I don't think that a letter written mostly by University STEM faculty should dictate how to teach K-12 math, and this is why the letter is not endorsing a particular alternative. But I do think we should speak out when people are proposing changes that would put obstacles for lower-resourced students to reach STEM majors, particularly when these majors provide the best job opportunities and potential for growth in the foreseeable future.

I wrote the following to Lance in an email, but figured I might as well post it here too:

ReplyDeleteI empathize with the positive intentions behind the CMF, which are presented in the introduction, but the practical effect will actually be worse for students of fewer means. See our analysis on https://gdoc.pub/doc/e/2PACX-1vQvuzlJ8MWthsqOhRLxQc5akGS0JkgThz3umqO3K-WQiXFhWiq9qw-9iYdTyC652Ftjvv5nHvgGYTEv which was agreed by several experts on education we discussed it with.

In particular, the way the system is set up, they are creating a "data science pathway" that does not enable to reach to calculus (maybe not even pre-calculus) but

(1) it's only one of three pathways, and students can choose the others,

(2) while it's recommended and supported by the state, school districts that have enough resources can and will reject this pathway altogether.

The net effect will be that this will be a de-facto lower track in math, and in some sense a worse than traditional tracking. In the current state, if you didn't get to calculus but only to pre-calculus or Algebra II, then if you decide to major in STEM, you have one or two courses to make up, which are very standard courses offered everywhere. If you went through this data science pathway then you might be even more behind. This is coupled with the fact that K-12 math teacher quality and training is already a huge issue, and there isn't any supply of teachers that are qualified to teach data science.

I think on the college end, we should be (and many universities are) making sure not to penalize in admission students who didn't have as much access to advanced math as others, and to also support these students with programs like https://www.math.harvard.edu/undergraduate/emerging-scholars-program/ once they are admitted. But making them come in with even less math will only make the problem worse.

As I wrote on Twitter https://twitter.com/boazbaraktcs/status/1466799637638139912?s=20 , in many ways students need more math these days rather than less. It used to be you didn't need to know any math if you wanted to do applied CS. These days, you better know your gradients and your matrices if you want to get that machine learning internship. Similarly, it used to be that only a small fraction of college students majored in STEM, but these days STEM and other quantitative majors such as Econ account in many universities for the majority of students, and are also the best paths toward social mobility.

I have to agree with Boaz. We live in a world where it's trendy to throw the terms 'equity' and 'DEI' around, but all that glitters is not gold. An introduction stating that the proposal is pro-equity doesn't mean that it actually is -- one has to dig deeper into the details. My opinion is that this proposal is actually a step in the opposite direction. Making the path to advanced mathematics more difficult in public schools simply means that those with resources can work around the obstacle (private schools, math circles, tutoring, etc.). I already see this with my wife's 11th grader brother: supposedly he can take advanced courses in community college, but high schoolers have last priority and the classes he's interested in always fill up before high schoolers can enroll. So, next summer he'll just pay the thousands of dollars required to enroll in similar courses at UC Berkeley, and he's also entered into a local math circle starting Spring'22 which also costs money. These are options students without resources don't have, and delaying algebra and making it harder to graduate having taken calculus will simply exacerbate the problem. Not to mention these students will then be at a disadvantage once they start college if they decide to pursue a STEM major.

ReplyDeleteThe major problem with K-12 education is the content. Until grade-appropriate mathematical content is being taught, fiddling with the course structure won't make much difference. Are there textbooks that implement the Common Core in a mathematically sound way? Or are they basically the same old textbooks that have been slightly edited so that they can claim they are Common Core?

ReplyDeleteThe main author of the latest version of the California Mathematics Framework is Jo Boaler. Regarding her past work, see

DeleteA Close Examination of Jo Boaler's Railside Report

https://nonpartisaneducation.org/Review/Articles/v8n1.pdf

https://web.stanford.edu/~joboaler/