Brian Conrad on the California Mathematics Framework

Brian Conrad has been doing the state of California a great service by taking a careful look at the drafts of the proposed California Mathematics Framework and the research they are supposedly based on.   He has recently created a website where he has been writing up commentary on what he has found. Conrad is known among his colleagues as one of the most careful and level-headed research mathematicians around, and these characteristics show through in what I have read on his new site.

I should make it clear that personally I have zero expertise on the topic of K-12 math education, so my own views on the matter aren’t worth much (and, I think anyone commenting on this should ask themselves about the same issue). Conrad has put a huge amount of his time and effort into learning about the subject and the extensive relevant math education research, and it is this that makes paying attention to the views of a university math professor a good idea in this case.

There’s commentary about this appearing elsewhere, including a Wall Street Journal article, and a blog entry by my Columbia colleague Andrew Gelman.

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9 Responses to Brian Conrad on the California Mathematics Framework

  1. just different says:

    I haven’t been following this closely and I certainly don’t know whether the CMF is on balance a good idea, but my general impression is that the viewpoint of Conrad and other signatories of the “open letter” is fundamentally elitist. There seem to be a lot of predictions that CMF will delay or discourage the “better” students–the only students who matter, apparently–from pursuing STEM in college, but not a lot of concern about the students who have been failed for decades by the conventional mathematics sequence.

    It would be easier to take these critics seriously if they paid attention to the goals of the CMF and offered constructive alternatives instead of dismissing as inconsequential the abysmal track record of the status quo for the great majority of students.

  2. Brian Conrad says:

    @just different:

    Please clarify what “open letter” refers to. I never signed the one from the Independent Institute (despite being asked to do so multiple times, as were many other STEM faculty who did not sign it), nor did I sign the K-12 letter (though in that case I agree with what it says).

    The statement I actually did sign was the more recent . What is elitist about alerting parents and students to the reality of what college degrees in STEM fields require? Or about being concerned that the Introduction to Data Science course explicitly advocates to women and minorities that they forgo learning Algebra II in high school and that the CMF also advocates data science as an alternative to Algebra II without clearly indicating the downstream effects on access to 4-year STEM degrees, including in data science?

    Please explain where in what I have written on my website or in the more recent statement that I actually did sign you see something that is “fundamentally elitist”. And why do you think my views on this are only focused on the “better” students, or that I ever thought they are the only students who matter? Did you know that within my own institution I was involved in creating a summer bridge program

    to help students from under-resourced schools to be better-prepared on the core high school math needed for intro-level courses across all STEM fields? (Stanford has some incoming students who struggle with fractions and basic algebra facts too.) And that I spear-headed two curricular overhauls of core service-level math courses in my institution (involving input from experts across many STEM fields — in contrast with the CMF process that did not solicit input from real experts in data science without a financial stake) to modernize motivation in the learning of core math topics without sacrificing the substantive content? Where have you seen me “dismiss as inconsequential the abysmal track record of the status quo for the great majority of students”? (I never have, and I am perfectly well-aware of that issue; to express concern about one facet of a multi-part problem doesn’t necessitate fixing everything at once.) How do you know I haven’t offered some constructive alternatives? (I have offered constructive suggestions on improving the CMF in past months to people involved in the process; I simply don’t post about that on social media.)

    And when a document is produced that has many vague half-baked proposals and falsifications of evidence (even if it has other parts which are fine), how much of a burden should there be on those who object to tell the people responsible how to fix the mess? The fact that a document claims to have certain goals doesn’t mean it actually contains a realistic or sustainable approach toward those goals (one reason I read the entire CMF was so that I would not be an armchair critic).

    You insinuate that I have not paid attention to the goals of the CMF, yet right here on the desk as I type this is a print-out of the entire thing full of comments in the margins from reading the whole thing. I have not internalized the CMF to the level I did with EGA (for multiple reasons), but I’m well aware of what the CMF claims its goals to be and how it falls very short. Please state clearly what you think the CMF’s goals are at the high school level (which is the focus of what I have written on this matter) and where the evidence is that the CMF provides a realistic path toward such goals.

    SFUSD implemented a version of the CMF’s earlier proposals at the high school level, and it was later exposed as such a fiasco that all mention of SFUSD has been scrubbed from the 2nd draft. The data science advocacy now in the CMF has been done for years in LAUSD, and has been described to me as a “disaster” in terms of how it has off-ramped kids at the most under-resourced LA schools (those who rely fully on public education, without access to tutors or other work-arounds) from learning the math they need to be prepared for a 4-year STEM degrees in college.

    To be clear: I have never said that all students must learn Algebra II (the UC & CSU systems have chosen to have a single math prerequisite across all fields, so please criticize that if you wish — it is orthogonal to the reality of the math one has to learn to earn a data science degree at those places), nor have I ever said that the public math education system doesn’t need significant improvements.

    My point is about the necessity for transparency about downstream consequences of public policy guidance on the content of math options in the high schools, and the unacceptability of the CMF peddling fantasies about what math in high school is actually preparatory for 4-year college STEM degrees.

    I read the entire CMF (both drafts) to fully inform myself on what the CMF does and does not actually do (lofty goals are easy — I look for details), and have spent many hours speaking with the leadership of the National Society of Black Engineers (which shares the same concerns as I do), leaders of the DEI efforts in the Berkeley School of Engineering (who share the same concerns), people with track records of real success in URM outreach such as Adrian Mims (founder of the Calculus Project; he also shares the same concerns) and college faculty at many other institutions many levels who have put in years of effort on improving access to math classes, and many other thoughtful people with years of experience on these matters.

    You say you “haven’t been following this closely” (a contrast with me, to put it mildly) and end with a paragraph that lumps me in with “these critics” (whomever they are) and suggests my concerns don’t need to be taken seriously because of two reasons that don’t apply to me at all. Please clarify on what basis should your comments be taken seriously.

  3. just different says:

    @Brian Conrad

    Here’s the thing: the past two years have made it blindingly obvious that a very large fraction of Americans are too innumerate to respond appropriately to a global pandemic or correctly interpret election results at a basic level. This bothers me a lot more than the possibility that Stanford freshmen will be less than optimally prepared for STEM majors.

    The failure of K-12 mathematics instruction is particularly acute in California, and racial and gender disparities have been static for decades. Some people have identified algebra as the bottleneck where so many American students stall, and most of the ones who pass don’t seem to be acquiring any real-world understanding anyway. So on the face of it, it is not unreasonable to ask whether some other curriculum might better serve the educational goal of creating a functionally numerate and mathematically prepared citizenry. I have no idea whether the CMF does a better job of this, but this line of discussion has been shunted to the margins.

    Instead, the CMF debate has been largely hijacked by right-wing culture warriors, who as always are arguing in bad faith: their true dispute is with the underlying premise that there are persistent disparities which we have an obligation to recognize and address. So no, I don’t think criticism about “woke math” or whatever deserves to be taken seriously. The more substantive objection that delaying or replacing Algebra has knock-on effects for potential STEM majors is fair enough (if a bit privileged), but this seems to me to be a much more academic question that can be resolved without the overheated rhetoric and multiple editorials and open letters.

    As I said above, I am only a casual observer with general impressions obtained from nonspecialist media, and I am not directing my remarks at you (or anyone) personally. But since your name gets dropped by people saying some pretty repugnant things, it might make sense to make the sound-bite version of your own position clearer.

  4. More Anonymous says:

    @Brian Conrad

    It’s nice of you to address this personally. I suspect what’s happening is in society is people are unfortunately looking at everything from a particular lens. And now anyone who wants to do anything his/her actions will be used as a tool for some political ideologue and to score some points. It’s tragic from the Information Age we have regressed to what I dub as the “Data Age.”

  5. Mark Hillery says:

    I have read parts of the California Mathematics Framework, and I admire the patience of anyone who was able to read the whole thing. It is very hard to read because of all the verbiage that conveys no information. While I don’t teach in California, what starts there often spreads to the rest of the country, and people like Boaz Barak, Jelani Nelson, and especially Brian Conrad have done us all a huge favor in pointing out its flaws. There are already problems with the mathematical preparation of college students, and the current CMF, if implemented, would make them worse. If someone hasn’t looked at the document, I would suggest their opinion is not worth considering. This is doubly so if they are not aware of what happened when parts of the CMF were implemented (as noted by Brian Conrad) in the SFUSD. Check out Scott Aaronson’s blog for comments by some San Francisco math teachers.

    It was interesting to hear that there are incoming Stanford students who have problems with fractions (What is it about fractions? They really cause a lot of students trouble.) and basic algebra. At Hunter College, where I teach physics, we have, I am sure, far more. I have often taught our algebra-based introductory physics courses, and a large portion of the class struggles with the math. If you are trying to learn some physics and fighting with the math as well, the course becomes twice as hard. The last thing we need is something that would make the mathematics preparation of college students worse, and I am afraid the CMF would do just that.

    I am no expert on high school education; I just know what I would like the students who take our courses to be able to do. Why so many cannot, I don’t know, but I expect under-resourced elementary and high schools have a lot to do with it. At Hunter we know about under-resourced schools. See, for example, the recent article in New York Magazine entitled “Hunter College is Falling Down”, and I was once in a classroom at Hunter when a rat fell from the ceiling. Our students would benefit from more individual attention, but we don’t have the resources to give it to them.

    While resources matter, so does curriculum. In the 1990’s we had a contingent of students who were recent immigrants from what had been the Soviet Union. I don’t know anything about Soviet schools or their resources, but the facility of these students with high school mathematics was greater than that of our native born students (this is an impression, I never did a systematic study). Is there something to be learned here?

  6. just different: As someone who was also involved in the campaign to defend serious math education in California, let me give you my personal perspective. I care enormously about instilling broad mathematical and statistical literacy in the population. Societally, that’s an even bigger issue than training the next generation of mathematicians and scientists, which of course I care about also. But crucially, anyone who has sneering contempt for the top STEM students and their needs, is not someone who I trust to design a curriculum for the average students either.

    Have you seen the emails that were disclosed just yesterday, where Jo Boaler (the mastermind of the CMF) is asking someone whether the concept of inequalities (yes, like x+2y≤5) is actually needed for college-level data science, or whether, presumably, that topic can be omitted? Is this someone who you trust to be in charge? If so, why?

    Compare the many people a few generations ago who said: “It’s elitist to care about a few persecuted geniuses like Sakharov and Solzhenitsyn. The Soviet Union is trying to improve conditions for the great mass of people!” The fallacy, we now understand, is that any government that would persecute Sakharov and Solzhenitsyn, that would regard them as existential threats, is not a government that you want in charge of the great mass of people either.

  7. Brian Conrad says:

    @just different:

    Let me add some points not already in the comments of Mark Hillery and Scott Aaronson. Firstly, due to this communication being in writing rather than in person (so tone of voice is missing), I can’t quite tell if you’re being sarcastic in seeming to say that I don’t recognize innumeracy among the wider population is a more important concern than the STEM-preparedness of students admitted to places like Stanford. I considered pointing out in my original response that I am aware of such type of things (with the example of what I did to assist incoming freshmen here just being an illustration), but I didn’t since it seemed clear enough not to need such comment. So I hope you were being sarcastic.

    There are two completely different topics (among many others): (i) math education for general citizenship (to give it a name), and (ii) math education for STEM careers. You are focusing on the former, and I and many at universities in industry have been focused on the latter. I wouldn’t criticize someone for preferring to focus their concern on (i), and for the same reason I am mystified by your apparent objection that others choose to focus attention on (ii) (or some other aspect of this multi-faceted puzzle, such as teacher training, the grip of publishing companies with dreadfully boring material, etc.). If the goal is to make an impact, rather than just talk about it, we have to choose our focus where we think it can actually make a difference.

    The two issues (i) and (ii) interact insofar as students’ interests can evolve during middle and high school, and even college (many kids who develop interest in CS in college are surprises to realize they should have paid more attention during math class in earlier years). STEM degrees and college-level STEM coursework are an important factor of the social mobility that college makes possible (it’s not the majority of degrees, but it is a sizable fraction and will keep growing as the workforce becomes more automated), so referring to concern about preparedness for such degrees as “a bit privileged” sounds like objecting to government funding of scientific research on the grounds that poverty is still a big problem.

    On your concern (i), let me just say that the CMF does not have anything genuinely new to contribute towards it, beyond the hype of renaming things related to statistical topics as “data” or “data science” (for reasons I leave to your imagination). That is why you don’t hear anything in the media about the CMF’s K-6 components (the parts related to basic numeracy skills); to first-order approximation it is not changing things in any significant way. One can quibble locally, and more globally object to the verbose writing style and poor organizational structure that permeates the document (in contrast with CMF’s of the past), but this is not fodder for news media and I am certain that any “public comments” I post about that will be met with a big yawn.

    There are many nuances to these matters, so a position fitting into a sound-bite is inevitably going to be too superficial to be meaningful. I’m not aware of repugnant things people are saying while dropping my name (it reminds me why I am not on social media; ignorance is bliss), but it would be a fool’s errand to imagine that when speaking out on something then some people will twist one’s words out of context to justify things with which one disagrees. Also, I have seen many examples (going beyond my post on misrepresentation of citations within the CMF) of people on the “left” side of this topic misrepresenting written things in deeply deceptive ways too.

    But what I’d really like to address is the impression you have of the CMF issue being largely high-jacked by right-wing culture warriors. You are correct that nearly all media attention comes from the right (to the extent the “left” media says things, they have usually ignored the concerns from STEM experts), but you are misdiagnosing it. This is not a hijacking. It is more like leaving one’s car unlocked with the engine running and and being surprised that someone drives off with the car.

    The story of coverage of the CMF concerns is an illustration of the huge difficulties confronting traditional journalism. The almost total failure by national-level non-right-wing media to pay attention to concerns about the CMF at the high school level is not for lack of trying by those who are eager to share a lot of information with their fellow citizens. When the K-12 letter came out, first the WSJ wrote something and then only media further and further to the right (Daily Caller, Epoch Times, Russia Today,…) wrote anything. It was astounding.

    Why did NYT, Washington Post, LA Times, etc. say nothing at the time in December? Why does the LA Times publish CMF propaganda pieces timed with the release of the new version but never report on the reality that actual STEM experts in industry and academia are pretty much uniformly alarmed by the CMF’s high school proposals (I am not referring much to acceleration aspects, which have been toned down for the 2nd draft)? Why does the NYT not publish an Op-Ed written by two deans at UC Berkeley cogently explaining how the CMF will be damaging to efforts at STEM career access and pipeline diversification? Why do education writers who are provided with compelling information laying out the basis for concerns with the CMF not follow up?

    One explanation I heard from someone who spoke with a NYT reporter is that the NYT thought the concerns about the CMF at the high school level is just a local story to California. If so then they have made a huge mistake, and not only for the reason Scott Aaronson points out (“as goes California, so goes the nation”). The “disease” of promoting data science in place of other math in the high schools with false promises and very inadequate guidance about downstream effects on preparedness for a wide range of college degrees is already spreading around the country, and is popping up in other countries such as Australia and Germany (and perhaps others).

    Someone else told me that this is an expensive story to write (to track down the necessary evidence and organize it). It may seem so, but that isn’t really the case because through the individual actions of many concerned private citizens acting on their own since last summer there is a treasure trove of information already assembled (the recent posting of emails that Scott mentioned is but one such example; that one had nothing to do with me).

    I have spoken with a couple of journalists for some non-national venues (and will be speaking with another), and it has led me to the conclusion that the root of the problem is that the story of CMF concerns is very difficult for journalists to write because it involves how the content of high school math connects to other things. That is doubly challenging: most education journalists don’t have a math background, and explaining the concerns to a general audience in an engaging way is difficult too (though the emails may provide a hook that finally draws in some journalists not focused on culture wars).
    The falsehoods being spread about data science in relation to math for 21st-century jobs are a kind of truthiness: they sound very plausible to people who are not well-educated enough in technical matters to realize it’s nonsense. (I heard of a prominent expert on quantum computing saying that if he were an ordinary educated person but not in matters related to STEM then he’d believe the propaganda too.) That can make it hard to convince many journalists away from culture wars that there’s something objectionable enough to be newsworthy. So if you’re looking for reporting from a source that is not focused on culture war topics then you’re not going to find many options.

    The fact that math-types are often reluctant to speak up too visibly without being fully informed and the CMF is a nightmare of poor writing (making it hard to reach a state of feeling fully informed about it) is further discouragement. The pro-CMF side also proclaims themselves (falsely) to the champions of equity, which scares many people into not speaking up, due to fear of being “cancelled”.

    Here is an ironic aspect you may wish to consider. The way your initial comment expressed a dismissive view of the STEM-related content-based concerns I and others have spelled out in detail is exactly the type of reaction that many people with such concerns and a reluctance to speak up (such as due to not having a full command of the details and nuances) are concerned with having to confront. I have no such concerns because (i) I am not on social media, and (ii) I know enough about it to be self-confident. So when you next wonder why you only see reporting on CMF concerns from sources which don’t care what people in the center and left think, in a sense your way of discussing it represents part of the problem. Dishonesty spread from the left on these matters (I am not referring to you, just to be clear) — which is now starting to become more widely known (e.g., I’m told that 70,000 people have now seen those email posts on Twitter since they appeared around 18 hours ago; maybe it’ll reach Hagoromo-level virality) — doesn’t help things either. To paraphrase TFG: there are very dishonest people on both sides.

    I suspect that if we were to discuss these matters in a cafe and thereby had an opportunity for genuine back-and-forth based on nuance and details then we’d probably agree on most things related to this matter apart from perhaps where to focus personal attention on it. And I think you’d be astounded at the layers of complexity in this CMF topic (that was my own experience as I spoke with people coming to it from many different angles). The analogy I made somewhere on my “public comments” website to an iceberg seen from the surface is more accurate than you realize.

    You should take some inspiration from the efforts by Bob Moses, a math teacher turned civil rights activist in the 1960’s who recognized in the mid-1980’s that learning algebra is the key to economic mobility for those from less-resourced backgrounds. (Read his book Radical Equations for more on this if you haven’t read it already.) Had he not passed away last summer, I’m sure he would have been alarmed at what the CMF is proposing in opposition to what he pushed for in the last 35 years of his life. There are others continuing Moses’ legacy, showing the way to continue broaden engagement with algebra and other math that leads to actual STEM readiness, not the content-changing approach that is preferred in the CMF. I am optimistic that at the high school level, a responsible balance between access to math for real STEM-readiness and other options in high school math will be achieved. Failure is not an option.

  8. Peter Woit says:

    I’m reverting to usual blog policy and deleting all further comments that try to engage in the culture wars. Comments not specifically about what is in the CMF are highly discouraged, and it may get to the point where I’ll have to insist that commenters prove they have read the thing (although then I suspect we’d just be left with Brian Conrad debating himself…).

  9. comment says:

    Politics and education are of course not cleanly separable, but it’s dismaying to see many (on ‘both sides’) seeming to not even try to distinguish (1) their political/cultural beliefs (2) their expert knowledge (3) their understanding of education research. Although I strongly agree with the majority of what ‘just different’ said above, I think they are a bit off in their targeting. It is very good and clarifying for me to see Brian Conrad explicitly say above that he is focused on “math education for STEM careers”. Similarly the “Math in Data Science” open letter (unlike some others) is very good for its focus and its avoidance of surrounding political debates. What I have read from BC’s new website is (unlike many other similarly-minded websites/blogs) likewise very good. As someone with deep sympathies and frustrations with ‘both sides’ of the underlying debate, I find it very useful and clarifying to have material explicitly presented with such clear framing and purpose. (It probably also makes it a little harder for the anti-diversity extremists to hijack the cause.)

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