The manufactured outrage over the California math recommendations keep getting posted on HN. Read the actual text of the plans here [1]. The FAQ is at [2] and directly responds to these characterizations. They are not banning gifted & talented programs or advanced students taking accelerated courses. They are not taking algebra out of the curriculum, although they are cutting geometry a bit, which doesn't make as much sense today as it did 100 years ago when far more people grew up to be farmers or ranchers. They are adding more statistics and probability, which I think are crucial in today's society.
What they are fundamentally doing is breaking up the classic U.S. staged path where you learn algebra for a year, then geometry for a year, then back to algebra / pre-calc for a year, then maybe take statistics or calculus as an elective, etc. Instead, all branches of math will be taught in an integrated approach focused around applied problems.
This is how a lot of European math courses are taught. In fact, I think HN would appreciate the shift from focusing on pure numbers and classic formulas to more applied uses of math, including algorithms, probability, data collected and analyzed in charts, etc. Students also forget a lot of algebra when they do a year of geometry by itself, then have to go back to algebra / pre-calc.
It also does mean that in the transition, it will be harder for students to "test out" of the classic algebra I/II, geometry, pre-calc sequence, because it will just be "year X integrated math." But the framework does not forbid gifted and talented programs or anything like that. There will just be a few awkward years while the curriculum shifts.
Now, there are some on the left who advocated for the elimination of gifted and talented programs altogether, for equity reasons. They did not get what they wanted in the new California framework. That hasn't stopped a lot of people from looking at what California is doing and imagining it is actually some kind of Harrison Bergeron dystopia, when that is absolutely not the case.
I had originally assumed the criticisms were exaggerated, but the more I read about the new curriculum the less comfortable I am.
It seems every defense is built around hedges like this one:
> although they are cutting geometry a bit, which doesn't make as much sense today as it did 100 years ago when far more people grew up to be farmers or ranchers
Which suggests to me that they really are trying to walk back the complexity of the education, perhaps as part of a goal to force the variance of educational progress into a narrower range within classes.
The language is so vague that it's hard to understand exactly what they're trying to do, which I think is their point. If they wanted to emphasize advanced education topics it would have been front and center in the plan. Instead, it seems like a footnote that we're supposed to assume will get taken care of in some future iteration of this integrative math program.
I teach math at a community college. It is all about removing complexity. The idea in education is that everyone is intellectually equal. Therefore the racial achievement gap in mathematics is due to racism. The solution is to change things. Too many POC students aren’t placing into college level math therefore get rid of placement test and get rid of remedial courses. Create new college algebra with just in time tutoring and voila, no more racial achievement gap. If you dumb things down enough everyone passes and we can pat ourselves on the back and claim to have solved the racial achievement gap.
My complaint about these reforms is that the root cause of the issue is not being addressed. This has long term negative effects. My own anecdotal experience is that what used to be a C is now an A or a B in my classes and I’m passing people who don’t know anything. I’m judged by the passing rate so I’m maximizing that metric. These reforms are just doing what I’m doing but in a less forthright way.
> My complaint about these reforms is that the root cause of the issue is not being addressed.
The root cause is well outside of the scope of schools to address. Perhaps they can help to a small extent through things like lunchtime meals. But curriculum reform itself will never narrow the gap more than a tiny amount.
Childhood nutrition, single parent households, health of mother during pregnancy, culture/respect towards education as a virtue in the community and household, education level of parents and the time they have to play and talk with their kids.
All these things are going to impact the capabilities of young school children and feed into outcome gaps between various groups (Black vs White, poor vs rich).
I believe most proponents of "math equity" actually know all this, and are just maliciously virtue signalling either because they're jealous that their own kids aren't doing well, or for social credit.
> Childhood nutrition, single parent households, health of mother during pregnancy, culture/respect towards education as a virtue in the community and household, education level of parents and the time they have to play and talk with their kids.
I'm not American, and I don't claim to know the environment and the issues people face there, or their root causes. I may not be fully understanding the extent of nutritional differences or family dynamics.
I am, however, absolutely certain that affluence feeds affluence and that misfortune feeds misfortune, on average. Even if you had all of the above equal except for the education levels and socio-economic status of the children's parents, you'd end up with statistically different outcomes.
I live in a fairly egalitarian country, and if I remember correctly, there's an average income gap of ~30 percent or so between people whose parents were in the highest quartile in income and those who were in the lowest quartile. While ethnicity may play some role in the statistical gap nowadays, I don't think it explains the statistical difference; ethnic minorities are disadvantaged here but they make up a small enough minority that I expect the bulk of the difference to be simply due to socio-economic differences within the same ethnic group.
Basically, if your parents and their social in-group got highly educated, I believe you perceive that as the norm. If they didn't, it's not as likely that you do.
Add in some practical stuff such as whether your parents can afford to finance or support your education, and the gap's already there. The rest just amplifies it.
Sure, physical health, nutrition etc. can have an effect, and they certainly do if the differences are great enough. I'm sure ethnicity or race has an effect, sometimes due to racism, and sometimes because people perceive their own opportunities or expectations differently depending on social roles, and for various other sociological dynamics. The latter is true even if you remove ethnicity or race from the equation. Racial stereotypes and images probably emphasize things but I don't think you can pin it all on that.
Considering how much worse off African Americans are socio-economically, on average, than white Americans, it's a no-brainer that their kids end up worse off on average as well. I'm not saying you should just shrug and accept that, and I'm sure actual racism exists as well, but the point is that some of it would happen even without racism, either overt or covert, or any "structural racism" that could include a whole spectrum of things.
That means any real solution is going to be hard and slow, unfortunately. Changing the subject matter in the name of equity really doesn't sound like one.
> I believe most proponents of "math equity" actually know all this, and are just maliciously virtue signalling either because they're jealous that their own kids aren't doing well, or for social credit.
It could also be that people take an easy non-solution in preference to working towards improvements and solutions that could take time, great patience, tolerance of morally and socially undesirable situations (one might have to accept that you can't achieve perfect equity, or at least not quickly, and be able to withstand social judgement for that), and are all around a lot harder to accomplish.
The poverty achievement gap is close to twice that of the racial achievement gap.
I don’t understand why we are so arrogant about everything that we don’t even try to teach 5th graders how to use spreadsheets and generate graphs. So much of math education is useless punishment.
> "to teach 5th graders how to use spreadsheets and generate graphs"
Given that we know how the sausage is made, pretty much the last thing on earth we as software professionals should want is to inculculate the public with an overreliance and blind trust of software.
>Considering how much worse off African Americans are socio-economically, on average, than white Americans, it's a no-brainer that their kids end up worse off on average as well.
It's worse than that. There's something about the American system which forces black families to be not just stagnant economically, but often to move backwards (at least in the transition from Boomer/Gen X to later generations). Both of my grandfathers provided a strikingly middle class life for their families, leaving the military after WWII for decent careers: one as a stable, unionized factory employee, the other as a nuclear physicist. All of their children went to college. Both of my parents hold advanced degrees. Even still, they face financial difficulties that their white peers don't seem to, and my generation of siblings and cousins, while along a spectrum of affluence, seems to have inherited a magnified version of their parents' diminished prospects relative to their achievement. On average, the families that were middle class mid-century are now working class, even with degrees.
And we're outliers, in terms of educational attainment in the black community heretofore. That's changing, but to what ends, when black professionals must have a more advanced degree to be considered for the same job as a white applicant with a less advanced degree? When our houses are worth $50k less, our access to credit is restricted, our tax burden relative to income tends to be higher, and we are actively sought out for discrimination by many bedrock institutions of American life? It's not a level playing field.
Interesting that you don't include genetics in your list, maybe it is a waste of time to try changing all those other things and instead we should focus on directing kids to aspire for their natural talents rather than trying to push them into something that doesn't suit them. To do this we will need to change the economy in a way that the market compensate other talents, not only the ones decided by the US coastal elites. We can do it by blocking illegal immigration and banning imports from countries that don't play by the same rules as western countries. Bringing back the power to the working class.
And the irony of course is that these anti-racism policies that are based on the assumption that minority students aren’t smart enough to pass the tests and therefore the tests need to dumbed down to achieve social justice, are fundamentally racist.
Well, that's not quite what they're saying - essentially what they're saying is that they're a different kind of smart. Not that I agree with the logic, but essentially what they're saying is that the tests - along with the whole curriculum - were designed and written by white people, so they're unintentionally biased in a way that non-white people (except, I guess, asians) can't understand them. The implication being, of course, that if black people had designed the entire curriculum and the tests, they would be similarly impenetrable to white people. Of course, I don't think that makes much sense either, but that is the essence of what they're trying to assert.
Mathematics is arguably (besides perhaps logic) one of the most pure, unbiased sciences one could imagine. Unless perhaps you take issue with the fact that notation borrows a lot of Greek symbols. It’s a difficult subject that requires struggle. Hand holding and dumbing it down is literally the worst thing you could do to make people better at mathematics. You must struggle or you will fail. Don’t think so? Let’s talk again when you hit real analysis.
> Mathematics is arguably (besides perhaps logic) one of the most pure, unbiased sciences one could imagine.
But teaching math absolutely is not. It is a very human process, helping students find handholds in what they know to make the next conceptual step. Absolutely breaking their minds with a new topic, then returning to it a month later and they find it obvious now. There are no platonic math lesson plans out there to tap into, and finding more effective ones has been one of humanity's jobs for at least as long as there has been written language.
(FWIW, real analysis is generally considered one of the easier courses in a typical math degree)
Real analysis courses vary a lot between schools. On YouTube I’ve seen 3rd year real analysis exam questions that were covered in my first year calculus course. All math students at my school had to deal with them.
On the other hand, in my real analysis course we worked with metric spaces, topological spaces, Hilbert spaces, the Baire Category Theorem, etc. I doubt most students in “a typical math degree” would be studying these topics outside of a pure mathematics specific degree program.
> (FWIW, real analysis is generally considered one of the easier courses in a typical math degree)
Quite a few colleges seem to use it as a filter class to determine who has the requisite aptitude and interest in pure math. At my college, the material wasn't particularly bad, but the evaluations were designed to be pretty challenging and grades weren't curved at all.
This is partly because the first course in real analysis (and usually the first upper division linear algebra course) is the first proof oriented course most students face. The material isn't necessarily the hardest, but the proof stuff is new to many people.
Chongli's experience is much more similar to mine, we covered basic real analysis topics in calculus classes, and the class titled real analysis was a third-year pure math course. It was designed for students who had taken multiple proof oriented classes already and were pursuing a pure math major. It's just one of those things that varies between colleges I guess.
you are correct, this is what they are saying. But i have yet to see anyone trying to give evidence that the test or curriculum contain thing that are inherently harder for black student to understand
I'm still waiting for the silence during which the insanity of this ideology finally clicks for those going along. We don't have to politely pretend that it isn't insane. We should pose direct questions to the lumpen commmissars trying to drag everyone into hell along with them.
What is a "white person"? A "black person"? Are these metaphysical categories? Biological categories? Cultural categories? Why would a person of one category be unable to understand curricula produced by people of another?
>The idea in education is that everyone is intellectually equal. Therefore the racial achievement gap in mathematics is due to racism. The solution is to change things.
If we're going to go there: I went from being a straight-A math student in Pre-Calculus to a C (verging on D) student in my AP Calculus course in high school. In college, I retook Calculus and aced it, receiving one of the highest final scores in the class. The first course was taught by a black woman. The second was taught by a white man. The last was taught by a black man. I am a black man.
People in this conversation are frequently quick to dismiss the value of anti-racist (and, for that matter, anti-sexist) policy and execution in STEM pedagogy. They lean on and extrapolate erroneously from the notion of many great mathematical thinkers' probable hereditary advantages to a general, in-born hierarchy of fitness for STEM thinking. Coincidentally, this shields them from tough conversations regarding their own fitness to teach, and especially to teach children whose backgrounds they cannot or will not find sympathy and empathy for. I will admit that the solution is not so simple as my anecdote might suggest, but the implied path shares character with the correct one, in recognizing the farcical nature of assuming that the status quo - especially in this country - is a product of actual potential playing out as it must necessarily so, and not of history overshadowing even the best of intentions (though they are usually less than that).
Definitely agree. There’s no reason for me to believe that I’m good at teaching. My students’ failings could be mostly a reflection of my own failing in teaching.
I don’t dismiss the value of anti-racist policy and attempts to rid myself of negative biases that affect my students. My compliant is when I’m told, and I have been told this by an educator, that the act of requiring knowledge of algebra is itself racist. That’s when I feel we’ve gone too far. I don’t necessarily think algebra should be required but the reasoning for getting rid of that requirement shouldn’t be because black students are not passing it at a high enough rate.
My belief is that far too many people are going to college. The degree therefore is being watered down. If we lived in a country where everyone had guaranteed access to food, shelter, and medical care then the emphasis on college wouldn’t be so pronounced and colleges could then concentrate on what’s needed.
I don’t believe your comment should have been downvoted. Thank you for sharing your experience and thoughts.
I disagree that "too many" people are going to college. That's a canard which defends the artificial exclusivity of education. The vast majority of people are capable of learning algebra, and geometry, and calculus, and in a timely manner, when empowered by conscientious and effective instruction. It is also true that many students - particularly black and Latino students - are place in the contradictory situation of urgently needing a credential that they were not trained correctly to earn. This has nothing to do with their capability, and everything to do with the dysfunctional system that their intellectual growth is beholden to.
So while I appreciate the sympathetic elements of your reply, I have to point out that the root of your argument is a baseless suspicion of the cognitive capabilities of students of color. Yes, requiring knowledge that has been systematically denied, effectively on the basis of race, in order to obtain a credential that is necessary to earn a dignified living, is a form of racism. And we will need to "change things" to fix that.
I made no assumptions, statements, or implications regarding the cognitive capabilities of students of color. You are incorrectly ascribing beliefs to me. I do believe too many people are going to college. I said people and not students of color.
Do you have any evidence that the vast majority of people can learn calculus in a timely manner? I have a lot of anecdotal evidence that this is simply not true. Please note that I’m making no reference to or claims about students of color. I’m speaking about all people. In my experience a lot of people simply can’t learn calculus to any reasonable definition of what that notion entails.
The requirement of a specific set of knowledge for a degree is not what is wrong. What is wrong is living in a society in which having a degree is increasingly necessary to live at a decent standard.
>The idea in education is that everyone is intellectually equal. Therefore the racial achievement gap in mathematics is due to racism. The solution is to change things.
I'm at a loss as to how you might construe these statements, which you presented as wrongheaded (i.e., that you believe the inverse of each), to not imply that you believe that the "cognitive capabilities of students of color" are lesser, considering the nature of the racial achievement gap (an aspect of the conversation which you broached). Either you simply do not remember what you stated earlier, or you're lying. This is clearly a reference to students of color, at the very least. I just want to establish the high probability that you are being disingenuous.
>Do you have any evidence that the vast majority of people can learn calculus in a timely manner?
Assuming that most people can learn at a 5th grade level, and that, as suggested several times in the comments, this lecture could be broken up into multiple days worth of dynamic, interactive instruction, rather than being presented as a blitzkrieg 20-minute lecture:
This is not conclusive, of course. But you asked for any evidence, and I think a reasonable person arguing in good faith would conclude that it suffices. You've shown evidence to be otherwise, so I don't expect you to agree, but I would be happy to be wrong for once in this conversation, on this matter.
The idea in education is that everyone is intellectually equal. Therefore the racial achievement gap in mathematics is due to racism. The solution is to change things.
This is a line of reasoning used by people to advocate for things like getting rid of remedial math. The problem with this line of reasoning to me is the premise that everyone is intellectually equal. Not all premises have to be wrong for an argument to be wrong. This comports with my later statement that too many people are going to college.
There is nothing of a racial nature in any of the statements I made in this regard. To reiterate, I believe that there is meaningful variation in the intellectual ability of humans. I believe too many people are going to college.
My problem with the California initiative is that it is based on the idea that everyone has the same intellectual ability and, furthermore, it does not meaningfully address the true cause of the problem of the racial achievement gap. It’s worthy to address biases amongst institutions and I agree with their efforts in this regard.
The racial achievement gap is a systemic wide problem caused by the structure of our society and nothing meaningful will improve until these things are addressed at a higher level. The effect of the California reforms, I fear, will cause more harm than good.
I understood what you said. This post is simply a reiteration of statements I've already addressed. If you did not mean to make racially-charged statements, you should reassess how you talk about your views in the future, because - and I am telling you this as someone who is taking your stated aim on your word, against my better judgment - what you said sounds racist. Full stop.
The problem is that our societies have made college a status symbol - everybody is supposed to strive for a degree even if what they're planning to do doesn't require it. This is particularly pronounced for white collar jobs, even though many of them are really more akin to tradecraft, and should be properly taught in trade school.
(I would argue that the majority of what we call "software engineering" is actually of this nature.)
And jumping past your comments about anti-racist and anti-sexist policy and execution in STEM pedagogy, your anecdotes point out an actually effective intervention -- supporting the development of a teaching workforce that reflects the communities of students in the classroom! There is a significant difference in approach when someone sees their students as "theirs", a resource to be developed and nurtured, instead of "someone else's", an unruly crowd to be disciplined, as you mention in a later comment. Is the teacher teaching, or babysitting/policing? Too much of US education is the second, for children of any color.
Must you have the same skin color to teach rather than babysit/police? No. In the American context, though, it takes effort rather than inertia to accurately see and develop the potential of your black students -- because inertia gives white teachers in particular a relentlessly negative media stream about "thugs" instead of "future Nobel winner". Our segregated society gives white teachers an incorrect set of Bayesian priors on the meaning of acting out or difficulties in class. They don't have black friends whose kids are going through a rough patch but are still the same sweet kid they were at age six. I mean, I just talked with a high school teacher in a rural Midwestern district who said 'at least she didn't have to worry about kids doing cocaine in the closet at school like at an inner city school', and as a graduate of such an inner city school, my response was "honey we couldn't afford cocaine, that's a rich kid drug". This is a lovely lady, dedicated teacher, and that's her prior on "inner city kids" as of Dec 3, 2021.
It was not the fact that they were black. It was the fact that, as a black student, I was not subject to the same warped expectations that I found common while taking higher-level courses under some of my white teachers. Not every white teacher was like this; however, I did notice, particularly in my AP courses, that many were less supportive and understanding of black students who hit periods of difficulty, and more disciplinarian in their regard. I'm unconvinced that American pedagogy in general has shaken off the inclination to view students of color as un-growing children to be trained and tamed, rather than growing thinkers to be taught and empowered.
This contributed to my later success, but it generally would not - and, to my recollection, doesn't - explain the massive jump in grade. The main difference was a more conscientious teacher and an environment that facilitated better study habits. The second time, unlike the first, I was not forced to fight my teacher's low expectations and lack of support in addition to learning the material.
I'm just trying to find a way to say how much it sucks that your comment is being downvoted.
Fuck it. It sucks so much that your comment is downvoted. Fuck that. This place is fucked up sometimes, where people downvote comments that might at a very long stretch be misconstrued as displaying some remote racial insensitivity if you squint really, reaaaaly hard, and then downvote a black guy who says what he's seen first-hand. It's like watching the BBC giving equal screen time to climate scientists and climate denials in service to some objectivity, long ago lost.
>My complaint about these reforms is that the root cause of the issue is not being addressed.
It becomes a question of how do we ensure every child has access to a dedicated adult willing to tutor them and push them in education matters. Once a child begins to fail in a class, unless someone is there who can help them back onto the route of succeeding, they risk developing learned helplessness around education. Maybe a single subject, maybe education in general. It takes a lot of time for someone to work with a kid, find out what the root cause of the problem is, help them overcome that, and then build up on the topics they have fallen behind on. It helps greatly when that person isn't just there for teaching/tutoring but also invested in the child in other ways so the child values their input.
When parents either don't have time, ability, or desire to do this, there is rarely a backup. Teachers try to fill the gap but they are spread too thin over too many students and rarely are with a student long enough to make a significant impact. Some teachers may even avoid it because it can quickly become an issue of favoring certain students over others. As for parents, while some parents will be able to fix the problem by having more time available, some parents lack enough education to keep helping their child past a certain point. Both finding how to give parents more time and how to educate parents enough to help their children are hard problems. As for the parents who don't have a desire to help, there might not be any solution at all.
In NYC, according NYC's mayor deBlasio and his racist former-DOE Chancellor, Asians are "white-adjacent" and are often bundled along with "rich white" when it's convenient for them to ignore Asians. Asians make up about 20% of NYC's public school, but they are the poorest ethnic group in NYC.
I'm curious how it's handled in California, considering that Asian's votes taken a bit more seriously.
There's a trivial explanation. If you're Chinese, you gotta be really smart, the top 1% smart, to immigrate into the US. This is also why Nigerian immigrants do so well here. The original European immigrants passed a similar test, as it takes a lot of courage and ambition to move across the ocean in a big wooden boat. But as you know the history, on one occasion, the admission process was violated, and since then America has been paying the price. The price has to be paid in full, for every cause has to be compensated with a result. Call it nation-scale karma, if you want.
From 1860 to 2016 the number of Asian Americans increased from 34,000 to over 20,000,000, according to U.S. census data [1]. The vast majority of that increase took place since 1950, which only recorded a population of 300,000.
Those long established Chinese families represent a tiny minority of Asian American university students. The vast majority are international students or first generation immigrants.
Moreover, Asian American immigrants encompass groups as diverse as Vietnamese and Hmong and Cambodian immigrants fleeing war and persecution, Chinese graduate students coming to study astrophysics and staying, and Filipino immigrants coming to work in healthcare. The educational outcomes of these groups are quite diverse; in fact if you are one of eight children living in poverty with illiterate parents you don't just magically do well in school because of your Asian heritage. If you want some vivid illustrations of divergent Asian American trajectories in the US, check out tensions around the Siskiyou fire...
> Those long established Chinese families represent a tiny minority of Asian American university students.
I’m sure it doesn’t help that admissions discriminate against them because they look similar to the international students and first generation immigrants.
> There are long established Chinese communities in the US who came over to be railroad laborers.
Descendants of those people are a tiny part of the Asian population (though probably formed an important part of the initial cultural support network for later immigrants, at least those settling in the area where those earlier groups were concentrated.)
This argument that populations only send their best to the US may be true today now that immigration is limited and there are large populations of well educated foreigners but its not true for large parts of American history. Most immigration is from the poorest regions- ie Irish during the potato famine, Sicilian Italians, Cantonese from China, Germans in the 19th C, to some extent the Scotch-Irish (well educated but poor) etc.
This is a worrying trend across the board. Everything has to be equal and politically correct, because if not then it has to be racism or something else evil.
The whole thing is a classic case of using averages to drive policy and action.
Your C student with an A doesn’t need your math class, they need an A.
The employer filters all non college graduates and then filters by GPA. With most employers, knowing what you are doing is not ranked 1st or 2nd. Price and qualification is up front.
i’m 100% agree with what you said. When i was in university the math teacher gave us access to previous year exam so we can (study/practice) with them.
I quickly found that we are now getting 40% on those math test which result in an (A+) because they grade in the curve but 20 years ago the real average for this teacher exams where around (75%) and those exam had question of similar difficulty.
TLDR: an A+ today is not the same as an A+ 20 years ago
Did you take geometry in a California public school? I did about 20 years ago, and my impression was that it's an extremely fluffy course that would absolutely benefit from being condensed, or at least rewritten.
California math education (again, at the time I took it) was already extremely oddly paced. The Algebra 2/Trig class I took was extremely aggressive, and then the year of pre-calc that followed it [1] had about 2 weeks of novel content spread over a year's worth of teaching. I was initially a year behind most of my classmates (starting in junior high), then skipped ahead to do Calculus BC alongside everyone who'd been a year ahead of me---and aced it. On the other hand, the people who were really advanced had already gone on to college courses at that point and basically hadn't bothered with anything in the system for many years.
In short, it's a mess and has been for decades. If they can clean it up a bit and make the pacing more even and integrated, I think that would be a net win.
[1]: "Introduction to Analysis", I think they called it.
I took geometry more than 50 years ago. From my perspective, it was useless then as well. As far as I can tell, its goal was to illustrate the importance of mathematical proofs. Perhaps they are important to mathematicians, and I suppose they would be important if lots of high-school and college mathematics were potentially incorrect, so we needed a proof to reassure ourselves, but for most of us, even those who actively use mathematics, proofs are a waste of time. It would be better for students to become more comfortable with abstractions beyond multiplication.
The geometry of computer graphics is differential geometry of curves and surfaces. As a topic it requires a strong background in linear algebra and multi variable calculus. Not something a typical high school student has any preparation for.
Seems like a disingenuous take. There's a very obvious path to understanding the basics of computer graphics by introducing the basic shapes of geometry, particularly triangles for obvious reasons.
My interpretation of "computer graphics" was based on modern 3D graphics: transformation, lighting, texture mapping, animation, etc. High school geometry will get you the basics but that's a long way from the state of the art. See the rendering equation [1] for an example.
Your original comment didn't say anything about introductory material. This whole discussion is about education to prepare students for university and beyond. No one is pursuing a career in computer graphics with only an introductory high school geometry background.
No, this whole discussion is about K-12 education, which includes the very first introductions to geometry, and if you look at the existing geometry content from 2013 [1] it's mostly about 2D geometry, shapes, angles, rotations, translations, etc. That fits squarely in with 2D computer graphics. I also did emphasize "basic geometry" and "basic computer graphics" in my first reply to you.
Finally, my first reply was disputing the claimed uselessness of geometry. It's very clear that it's far from useless these days, although some material is certainly less useful than it maybe used to be.
The entire point is not to emphasize the advanced education topics -- which are actually offered pretty universally in California schools -- but to increase the number of students actually _taking_ those classes through the entire pipeline, and to embed those concepts in a more consistent, structured way.
I'm not sure why how you get "walk back the complexity of education" when it's obvious that the current system is broken.
I believe you are mistaken. One of the goals is to deny that people have different intellectual abilities. They seek to get rid of tracking and advanced courses. These reforms are related to what is being advocated by www.equitablemath.org. From their website:
Students are tracked (into courses/pathways and within the classroom).
> Administrators should examine programs and policies and how white supremacy impacts student outcomes (e.g., tracking, course selection, intervention rosters).
> White supremacy culture shows up in math classrooms when... Students are tracked
I interpreted this to mean that tracking is (like course selection) a student outcome that can be impacted by "white supremacy culture", not that tracking is, inherently and unavoidably, a sign of white supremacy. If there's burglars around, unlocked doors are usually correlated with burglary; that doesn't mean you can't leave your doors unlocked, but you're going to want to be careful about it. Similarly, if you live in a society with pervasive racism (read: most societies), it's possible to track students in a way that doesn't reinforce those racist trends, but probably only if you're careful about it.
I think I probably agree with you that "white supremacy culture" is, as a term, perhaps more aggressive than it needs to be. Not being deeply embedded in this debate, I'd assume it's going to turn off more people who hear it, think "I'm not a klansman, so this isn't something I need to address" than it will engage people who think racism is bad but haven't considered how their own (probably unexamined) practices are leading to outcomes they don't want.
Somehow we’re supposed to believe that there’s no white supremacy, that mathematics simply lives in a platonic ideal world where it doesn’t matter that so few African America mathematics phds are awarded each year, for instance.
You are confusing racism in the world e.g. our education system, which exists and is quite impactful, with racism in mathematics, which is not at all a well defined concept.
If you told me that math education professionals were a fundamental cornerstone of an oppressive culture, I would sign on immediately. But you have to be aware that it is exactly that cadre of professionals that are offering up the recommended changes.
A central pillar of Equitable Math is that all children must always be at the same level up until their last year. This is what is in contention, and not whether the Common Core needs more revision in terms of depth or rearrangement of subjects.
Under the Common Core, children in middle school who are ready for Algebra may opt for Algebra, and children who benefit from a delay may opt for a delay — but this is viewed by Equitable Math as sustaining White Supremacy in math education.
Are the Equitable Math folks the entirety of the stakeholders involved? Will "all children be at the same level up until their last year"?
If no to both, it does seem an awful lot like invoking the motivations of some of the people involved as a boogeyman rather than making an argument about the final recommendations themselves.
Under current proposals, which have yet to be finalized, there are zero specifications for alternative tracks in math, including zero specification for Algebra in middle school. You seem to think that Equitable Math is an entirely separate proposal, and thus the authors of Equitable Math are just "some people". They are program architects. And the stakeholders? Why, all of California of course, including textbook publishers making decisions for 8th grade Algebra textbooks.
For schools under the Equitable Math proposals, the goal will be that for any given grade level, all children will be at the same level up until their last year. The explicitly stated reasoning by the program authors is that alternative tracks in math are a form of disparity which promotes White Supremacy. Will this in fact be the final final proposal? That is what is under debate right now.
Not all proponents of Jim Crow laws were hate filled but enough were that one can ascribe to the legislators of the Deep South that supported those laws as being hate filled. What you are being told are the intended consequences of the people writing the proposals and are now asking about the totality of the beliefs of the stakeholders. You are welcome to believe whatever you want about the motivations of the people writing the proposals as I am. But please don’t confuse their intentions with the intentions of all stakeholders. No one is doing this.
Same agenda from two different organizations. Effectively implementing the reforms will lead to a system where advanced math courses are taken by students in k-12 whose parents have money.
> The parent comment literally admitted that they were removing specific complex topics.
you quoted and responded to
> although they are cutting geometry a bit, which doesn't make as much sense today as it did 100 years ago when far more people grew up to be farmers or ranchers
so which specific and complex topics are you referring to in the OP?
they are cutting geometry a bit, which doesn't make as much sense today as it did 100 years ago when far more people grew up to be farmers or ranchers.
The point of high school Geometry was never to compute areas of fields. Trigonometry is far more useful for that anyway.
The point of high school Geometry is that it is the first introduction to rigorous mathematical proof -- and has been, ever since Euclid's Elements.
As someone who did a BA and PhD in math, went through high school geometry proofs, taught geometry proofs to math students and math education students:
Geometry proofs are a terrible way of introducing rigorous mathematical proofs to students. Seriously. I cannot overstate how misleading they are. I remember my first abstract algebra class in college, after the first HW I got called in by the TA because I tried to structure my proofs like I learned in geometry class - a sequence of symbols and references to hard-coded lists of axioms and prior deductions. I thought that's what proofs are, but they are not, at least not as humans do higher math. High school geometry tries to distill this process down to a symbol manipulation game that students can memorize and regurgitate, and in the process loses the essence of the thing it was meant to capture in the first place.
I would agree that proofs as introduced in high school Geometry have more in common with formal axiomatic logic than the vast majority of "real-world" mathematical proofs; but a large part of that is just clumsy notation.
The fundamental concepts
1. We have axioms which are things we accept without proof because we all agree that they're obvious;
2. Everything else should follow logically from things which come earlier;
3. Don't skip steps!
are extremely important and apply regardless of the field you're in.
But geometry is sort of badly suited to teaching this because it's very hard to justify. We're good at thinking geometrically so things look "obvious" unless you do bad things like explicitly mislabel images (I remember some geometric problems where clearly unequally drawn line segments were labeled as equivalent).
Like you end up having to reteach proof in university discrete math or stats classes anyway!
Using motivations that we know to be true (or can see empirically are true) but don't feel trivial because "duh those lines are the same length" is a lot more compelling. You actually feel like you've learned something, not just a dumb formalism for something you could already intuit (and I mean if that's all proof does, let you formalize things you already know, what's the point?)
You're of course not the audience of these changes, because I expect that my last statement made you gag a little bit. But that's the way a lot of people are, and we shouldn't restrict ourselves to teaching the way they did 2500 years ago[0] unless there's still good reason to do it that way.
[0]: I'll admit that I think "look they were able to prove these things in this way 2500 years ago prior to the conceptualization of zero" is a compelling way to teach this stuff, but we don't do it that way either.
I disagree: It's precisely when things are obvious that it's useful to teach formal proof. You can't teach the critical part of "don't skip steps" if nobody is even tempted to skip steps.
I think a large part of the problem is just that it's poorly integrated into the larger curricula[0]. By the time a typical student reaches geometry class, they have incorrectly learned that math consists of memorizing things, pattern matching onto things they've memorized, and making at most minor adjustments. The kind of logical inference and objective-based reasoning that is necessary for a rigorous proof is covered more in writing class than in math. Some of the kids I've seen adjust well to it have dabbled in software and pattern-matched proofs onto that (which has its own pitfalls, but better than nothing). The remainder had parents who taught this kind of thinking from a much younger age.
For those not so lucky, they need to spend probably about a semester un-learning what math is before they can really start.
[0]- In the arbitrary parts of the US that I know anything about
From Texas, and can absolutely confirm. I was one of my area’s top Number Sense (mental arithmetic) scorers in middle school and high school, and made it to the state MathCounts finals two years in middle school, and always got high A’s in my math classes. I squeaked by on the IB Math exam, which should have been a sign that something was off about my math education.
I did ok in college Cal I and II (I’d been warned by older friends that our high school calculus class was a joke) but hit the wall in Cal III and ended up dropping Diff Eq before I could actually fail it. I barely passed Discrete Math by memorizing a bunch of proofs.
Turns out, I’m really great at memorizing arithmetic tricks and wasn’t actually that good at math.
“The remainder had parents who taught this kind of thinking from a much younger age.”
Fortunately for our child, my husband was a success in Germany’s math education system, and will therefore have the lead on how our kid is taught to think about numbers - I’ll just give the English words for things.
Why? "Do as I say without clear motivation except that I'm telling you it's supposed to be done this way" is maybe the worst way to teach. Is that justification going to keep a group of 15 year olds engaged? It certainly didn't for me.
I think the point is to teach people that apparently obvious things are not always actually true. This is extremely important in math as you move on, as i'm sure you know. Many "obviously true" things are not actually true when you get really serious about formalization. Teaching kids that "seems true to me" isn't good enough is a critical step along that path.
I see this in theory, but I'm having a hard time thinking of geometric problems that violate intuition and that are appropriate to teach people who have no calculus and limited algebraic skills (admittedly this limits statistical problems too). I'm actually curious if you have any good examples, because I don't.
And I think that's where my objection comes in: if you spend the entire first year just developing that intuition but forcing a rote procedure, you'll have lost the majority of people already. Proof isn't arithmetic and we shouldn't teach it in the same way. Sure develop the process on the easy method first, but then show people why it's important to not skip steps.
One advantage of geometric proofs is that they seem to be more accessible to some kinds of learners (visual/spatial thinkers) than proofs of purely symbolic results.
It is interesting to me that you didn't encounter problems with the rote geometric method before abstract algebra. I went to a so-so public school in the American South, so I don't think I exactly had a stellar introduction to math or even school/academics in general, but beginning in trigonometry, we had to structure our proofs with more words and 'connective tissue,' and less explicit axiomatization/symbolization. Calculus continued this trend, and by the time I took linear algebra (at a local university while I was still in high school), the proofs were exactly like the proofs I would write throughout college. But there were several 'stepping stones' away from the original geometric proof.
Though admittedly I only got an SB in Math, I think geometric proofs were an okay introduction to the idea of the proof and of logic. Of course they are not representative of professional math. There are many things we learn as an introduction which don't turn out to bear that much resemblance to the more advanced form. I don't write 5-paragraph essays with clear thesis sentences anymore either. But it helped me to learn to write that way as a way of clarifying that I was stating my arguments effectively.
Sometimes, for my homework, I tried to state very explicitly in my proofs which axiomata I was using, both as an intellectual exercise and to see, e.g., where I might have gotten my logic backwards or where I used the axiom of choice (which constantly surprised me). I wouldn't turn these overexplicit proofs, but it helped to clarify that I was doing things correctly. If anything, when I was in college, the trend was away from 'informal' language. When I took, e.g., Discrete Math, for more complicated proofs, we were encouraged to write out a DAG for the dependencies of the proofs/lemmata so that it was exceedingly clear what depended on what and that we had in fact proven what we set out to prove.
What are those "geometric proofs"? I've never seen this term before. Geometry is really just numbers in disguise, e.g. a circle is really numbers that define its center and its radius, and sometimes those numbers are defined implicitly, e.g. when its a highly complex curve that's not reducible to simple circles and lines. In this sense, all proofs are about symbols and numbers, geometry is only there to guide our intuition.
High school students are frequently taught a highly routinized form of proof in Geometry class in the US: https://www.cuemath.com/geometry/geometrical-proofs/
That is what it seems the parent was referring to and what I was referring to.
Agreed. Personally I think we should swap our high school curriculum:
Geometry -> Proofy Linear Algebra
Trig -> Computational Linear Algebra
I think the heydey of Trig was in the age of navigation and the heydey of Geometry was in the age of machines. Meanwhile, today, linear algebra has supplanted both of them, runs the world besides, and it seems to only be getting started.
> I think the heydey of Trig was in the age of navigation and the heydey of Geometry was in the age of machines.
Sorry, but this is crazy. If you're in physics, electrical engineering, mechanical engineering, or civil engineering[1], then trigonometry appears in so many problems - including ones that have little to do with triangles and geometry.
Calc II is heavy on trigonometry for a good reason. So many integrals that show up in the "real world" are solvable if you know your trig identities. These show up in semiconductor theory, mechanics, electromagnetics, quantum mechanics, etc.
Trig is the one thing I'm glad I was taught well in high school. Used it all the time for over a decade.
That's a clever insight. Though the measurement of circles is done using triangles, so maybe there is an even cleverer more Germanic name? Circulotrigometry.
Linear algebra has geometry flat out beat in that arena, too. This isn't to say that Geometry doesn't help you learn about the world, but it is to say that Linear Algebra should be prioritized above Geometry if your goal is to understand the world.
I can't remember a physics class where LA didn't pay heavy dividends -- in particular, differential equations are the language of physics, and you'd be hard pressed to find either an analytical or computational diff eq technique that didn't have a core of linear algebra.
Meanwhile, the last time Power of a Point gave me dividends was on math contests.
But imagine that you never heard of concepts behind it.
It'd just become a more-or-less useful artefact. And in no time it would devolve into a useless ... thing so to say, a decoration, as you lose knowledge how to apply it.
Believe me, it pains me to suggest bumping it back. Introductory proofy linear algebra just hits a quadruple home run: it's astonishingly useful, it's getting moreso, it's simple enough to remain age appropriate, and it can serve as an intro to proofs. As much as I enjoy geometry puzzles, I just don't see how they compete with that.
For the true fans, of course, the answer today & in this hypothetical future is still to learn both.
> Geometry proofs are a terrible way of introducing rigorous mathematical proofs to students
You might be right, but they are the only high school math class that teaches proofs. If you take away geometry you are left with nothing.
Having said that - any math concept can be memorized and regurgitated. My kids are in CA elementary math right now and it seems to be better than when I was a kid. The emphasis is on derivation rather than memorization. It might just be that geometry is better now than when you were a kid.
For quite a while I thought I'd never be great at math because I struggled with geometry. Fortunately, I ignored that voice in my head and went on to do lots of advanced math (analysis, abstract algebra, computational methods), ranking in the top 10% of Polya, etc.
I still suck at geometry.
Geometry is a really poor representation of whether one can do proof based maths.
If you wrote everything like a high school essay, you’d be a pretty terrible writer. In real life you don’t need a topic sentence for every paragraph and sometimes an infinitive needs splitting. Nonetheless, high school essay writing is a pretty good way station to good writing. Perhaps high school geometry proofs are similar.
It's funny, I also think Euclidean geometry is a bad way to introduce proofs, but my reason is different from what you just said. I think what you just said is primarily about "writing proofs", which is certainly important, but I'm not sure it's the fundamental issue with Euclidean geoemtry (and I know that not everyone learns Euclidean geometry and comes away from it writing proofs as you did). It sounds like you came out of your highschool Euclidean geometry experience with good logic skills but poor communication skills (?).
The issue with Euclidean geometry as an entrance to proofs and logic is two-fold. First, the definitions and axioms of Euclidean geometry are incomplete in many ways. Many definitions, such as that of a line, cannot be understood from what is written in Euclid but require a significant amount of intution pumping to be able to know how to properly work with them. Thus, the fundamental definitions in Euclidean geometry are bad examples of what a definition in math should be, and we are already starting on very rocky footing. Moreover, the axioms, as they are presented in Euclid or common modern educational sources, are not sufficient to do what is claimed. For example, the proof of postulate 1 already has a logical gap because there is no axiom which guarantees the existence of a point lying at the intersection of the two circles one has drawn. Again, the argument relies crucially on a figure, which is the intuition pump used in all of Euclid, but the picture is not based on any of the axioms, so it is reinforcing a bad way of thinking about proofs that is intuitive and not at all focused on carefully using definitions and axioms. (Of course, one can fix Euclidean geometry to be rigorous by adding many extra axioms, but the resulting axiomatic system is much more complex and is not at all suitable for highschool students, except possibly the brightest.)
The second, somewhat more minor, issue I have with Euclidean geometry, related to the first, is that the way arguments are phrased, and the use of figures to illustrate, often hides many logical steps that are only implicit. In particular, I am thinking of the implicit use of qunatifiers in statements that are proven in Euclidean geometry. This is an issue because as soon as one moves on to proofs in any other context encountered by students, e.g. in first year undergrad, it becomes much more difficult to do things correctly while only thinking about quantifiers implicitly.
It would be much more beneficial, in my opinion, to have the first introduction to proofs be a topic that is much, much simpler (such as integers) where the focus can be purely on how statements are formed with quantifiers, how strategies of proof are determined based on the form of the statement and which quantifiers are involved, and how the (much shorter and simpler, and not requiring an intuition pump to use correctly) definitions and basic properties of that topic can be applied in a proof.
The root of all of this is the importance in proofs of properly using the definitions and axioms. Students in highschool, except the most talented, just are not careful thinkers and will revert to their preferred lazy way of thinking (such as pictures and vague ideas) as soon as you give them the opening. In my experience, the only way to force students to understand how to properly prove things is to pull out the rug of their intuition, even briefly, for just long enough so that they learn how to do things without it. Then later, once they have properly adopted the mindset of using the definitions, you can let the intuition back in.
For context, I don't know if any of what I just said reflects how Euclidean geometry is taught in, say, Caifornia. I only know this from the perspective of having tried to incorporate Euclidean geometry in an undergraduate proofs course (in Canada where Euclidean geometry hasn't been part of the grade school curriculum for some time).
While both are clearly important, if we only have so many hours in the day I'd rather a high school student have a grasp on basic stats than basic formal proofs.
As a data point of one (heh there's that stats again...) my two high school geometry classes 15 years ago never touched any proofs. I have no clue if they still teach that way.
Edit: just noticed that I'm replying to someone who is far more knowledgeable about math than me. I stand by my point though, people like Colin can seek that out in more advanced classes.
Proof-based high school geometry is an absolute joke and should be excised as soon as possible. There is no better way to ruin someone's enthusiasm for math while teaching them nothing useful... imo.
It is in geometry one can experience a spectrum of evidence from a picture (animated or not, interactive or not) to a line-to-line modus ponens proof. Not to mention the historical value that Euclid invented a literary genre that is now called "proofs". Good luck teaching kids "more useful" stuff like data science and quantum computing. High school teachers don't understand these topics and are more likely to teach them ineffectively. Now that's harmful and no one can blame geometry anymore.
A somewhat similar point is expressed in Underwood Dudley's article "What is Mathematics For?" from the May 2010 Notices of the AMS [1].
Briefly, he argues that we greatly exaggerate how much math you actually need in ordinary life and in most jobs that people usually think of as needing math (and what you do actually need can be learned on the job), but nevertheless learning math is worthwhile and important because of what it teaches you about how to think.
It's hard to imagine now, but back in the early days of the US similar debates played out over teaching arithmetic in schools. Most people didn't need more than counting and simple addition and subtraction, so why make everyone learn any more than that? Those few who meeded more could learn it outside of school.
I got nothing out of my high school geometry class but loved my foundations class in college. I would have been a lot better off just going straight to real proofs instead of those annoying pseudo-proofs. But I don't know, other people probably had different experiences and got a lot out of geometry.
At least at my school, there was a special geometry class that included proofs ("formal geometry"). Other than the handful of few people who bothered to take that class, there was very little way in the way of proofs in the geometry class that 98% of people took (ok, I tested out of geometry so I don't really know what was in the curriculum).
This makes me sad. High school Geometry without proofs is indeed not worth keeping. (Except maybe as a two week discussion of triangles and right angles so that students understand what they are when they hit trig.)
I have to agree wholeheartedly. The actual content in a classical geometry class is mostly related to logic; axiom, proof, theorem, inference, etc.
If you remove all of that, you can embed actual geometric content into other classes as you go, much like probability and statistics is currently integrated across multiple years.
> The FAQ is at [2] and directly responds to these characterizations.
I don't know whether it's intentional but the FAQ reads like it's intending to deceive me. They answer questions with "no we're not doing that", then follow up with how they do exactly that with different words. For example:
Q: "Does the draft Mathematics Framework eliminate middle school mathematics acceleration programs?"
A: "No. The draft Mathematics Framework does not eliminate middle school mathematics acceleration programs (including programs that offer Integrated Math 1 or Algebra 1 courses to grade eight students). The draft Mathematics Framework emphasizes the importance of following the sequenced progression of topics laid out in the Common Core State Standards for Mathematics (CCSSM) and considers the latest research on the impact of skipping grades or undermining the sequences progression."
They're not "eliminating", they're "emphasising" and "considering". Maybe what they're doing really isn't eliminating but it sure reads like it is. The tone reads like corporate damage control. 'We didn't "spill" the oil, we misplaced it.'
Yes, “for now we aren’t eliminating because we could never force that through, but we will definitely be eliminating at the right opportunity and this moves us toward that”.
Have you ever seen Terence Tao signing up for a manufactured outrage? Alan Kay? If you're the type to read technical papers you'll recognize a bunch more names on the list of signers. Furthermore the language in the post was calm and measured.
There is another comment in this thread that addresses this very well:
> I find it interesting with many of these criticisms that subject matter experts on maths, sciences, etc think that they are also subject matter experts on the pedagogy of maths, science, etc especially at a high school level.
The people you mentioned are my idols, same as the authors and hosts of this blog post. But there is a world of difference between being a great scientist and being a great K12 teacher.
> But there is a world of difference between being a great scientist and being a great K12 teacher.
Very good point. K12 teachers know a lot, but they may not know much about the path to becoming a world-renowned scientist. The signers of this letter know that path from their own experience and the experience of their colleagues. They may not be educators but they have intimate understanding of the education process of bright children.
Oh, this is a good point that did elude me. As long as some form of gifted programs continue existing (which, given my flawed reading of this document, they will continue existing, just by virtue of demand), I do not see it being a problem. You will raise the bottom significantly while not really changing the top.
Gifted programs are largely not a thing in Californian math. When we're talking about children who opt to take Algebra in middle school, or children who opt to take Calculus in high school, we aren't talking about gifted programs. We're talking about alternative pathways in math.
A central pillar of Equitable Math is that all children of any given grade ought to be in the same math class, and that there ought not be any standard specification for, say, taking Algebra "early" in middle school. The explicitly stated reasoning by the program authors is that this disparity sustains White Supremacy in math.
A child who is ready for Algebra would be best served by opting into a classroom where a teacher has been polishing a year-long discourse on Algebra, as opposed to creating an ad-hoc gifted program. A return to gifted programs would be a return to administrative opacity.
My comment left out this aspect only because the names aren't familiar to me:
> The signatories include ... educators with decades of experience teaching students at all levels ... people vested in mathematical high-school education, such as ...
That is a well-intentioned but simply wrong statement in the blog. One of the letter authors is what I would call a professional educator in some way (a non-profit). The rest are university professors and a few are industry scientists. They are certainly not "people with experience teaching at all levels" even if they believe that. Same with the signatories. The vast majority are university professors. These people are generally great at what they do and frequently terrible at teaching, *especially* when teaching K12 students. I have seen it first hand as I have been organizing K12 events (not for "gifted" kids) and have been tutoring gifted students competing in the international physics Olympics over the last 8 years while working at Yale, Harvard, and MIT (as a graduate student and postdoc). Teaching competitive physics, teaching college students, teaching K12 students, and doing research are 4 completely different things. The signatories are certainly amazing at the research, but I have seen first hand how that type of professionals are just terrible at teaching K12 students while thinking they are doing great. Even worse, we usually pat ourselves on the back for having a single-day event with cool math organized for the K12 students, but never bother with the year-long battle to actually lift all boats.
Obviously this is just my personal anecdote, but I do claim I have been very invested in exactly this type of education and have seen how well-meaning crazy-smart professors are failing to teach K12 students (in their once-a-year charity event) while patting themselves on the back for a job well done.
The letter isn't saying that all of them teach at all levels. It's true that I'm a lot more familiar with tech reputations than education reputations. OTOH education is an unusual field in that practically everyone has decade-plus full-time intimate first-hand experience with it; and more in the case of parents.
What do you think of the claim that the policy will increase inequality of preparation because better-off parents will bypass public education more? It sounds like you might have more light to shed on that.
I am hesitant of having an opinion. These are luminaries that I look up to, but I fundamentally disagree with their opinion on this topic. Probably partially because I have been very frustrated with snobbish and disconnected[1] attitude towards K12 education among scientists.
But to actually answer your question. Better-off parents already bypass public education, even if not completely. If this new program works (not a given), the problem will not be exacerbated, rather more students will be prepared to reach for these "gifted programs" (which in many cases, even if expensive, usually have good fee-waivers as this gives them more credibility).
[1] Obviously just a personal opinion. But in the interactions I have had in this context I feel I have seen a lot of inflated but unsubstantiated sense of competence.
Thanks. I guess I can see this working out if the classes end up being taught better on average (aiming for deeper understanding instead of faster advancement along a standard track to "advanced" math), and if the better-off parents generally appreciate this. If we did successfully get better teaching then it'd be natural for a greater proportion of the disadvantaged to discover they're interested in real math, too.
(I wouldn't bet on it, personally, and I don't think the infusion of wokeness is mainly about helping more people to understand math better. Hopefully I'm too cynical. The Common Core math stuff seems like progress, for instance.)
It is cited in the open letter's supporting document. It would take some very serious effort to read through these resources and try to disentangle the biases of the authors, but I guess this meltdown would not have happened if reading social/ed science papers was easy.
> Terence Tao signing up for a manufactured outrage? Alan Kay?
Or Scott Aaronson. Scott Aaronson is about as social-justice-y as you get. When even he thinks the equity types have gone too far, it's really time to step back and see if you're making sense, even to yourself.
Not sure I would describe Scott Aaronson as "social justice-y". He's had plenty of other quibbles with "equity types", for example, over the use of the term "quantum supremacy [1].
Just because Terence Tao is a genius at (and world-leading researcher in) mathematics, and Alan Kay is programming pioneer, doesn't mean that either of them understand the implications of the CMF, or are knowledgeable about children's education - they could merely be taking the word of someone else who is misinformed or not acting in good faith (perhaps through a telephone game mechanism).
It's not fair to talk about Alan Kay this way. Alan Kay actually did a ton of pioneering work in children's education, and in an applied (real-world) empirical way, not just in a theoretical sense.
He and some of his collaborators were among the earliest in applying Piaget and Bruner's learning models to programming education, mainly for learners under age 15.
I went looking at the names because "manufactured outrage" connotes politics or culture war. It's the sort of accusation you'd expect to see if the list was full of names like Jordan Peterson. Instead I see Tao who on his blog comes across as apolitical, mild-mannered, even humble. Not the kind of guy who's into culture fights. Or Kay whose book recommendations had a kind of 60s lefty flavor, as far as any political leaning came across to me.
There's a bigger argument here, but I'm just addressing this one unmerited accusation in this thread.
Talking about "testing out" and "gifted" programs is a complete distraction here, since very few students "test out", and taking Algebra in middle school is not considered a "gifted" program. With regards to math in California, gifted programs are largely not a story.
A pillar of Equitable Math is that all students should be at the same level up until the last year of high school.¹ The re-arrangement of subjects is not the hotspot of contention, and neither is the disagreement over "deepness".
The contention is over whether or not there ought to exist a faster track which, for example, permits students to take Algebra in middle school. This has been specifically derided as a sustainer of white supremacy under the Equitable Math discussion.
A return to gifted programs as the way to deal with students with differences in math preparation and ambition would be a return to administrative opacity. A failure to specify tracks which allow students to take Algebra in middle school would be a solid win for private schools and after-school programs like RSM.
Under Equitable Math, the last year in high school is the only year of differentiation.
> A return to gifted programs as the way to deal with students with differences in math preparation and ambition would be a return to administrative opacity.
I mean, if they're going to eliminate gifted programs for an advanced academic students, then they should eliminate sports teams for advanced athletic students by parity of reasoning. Isn't the star quarterback just as unfairly advantaged by family and genetics as the smart math geek?
Again, gifted programs are largely not a story in CA math. Students taking Algebra in middle school are not in a separate gifted and talented program, they are just in one of many pathways as specified by the Common Core. For example, in some nice school districts, about half of the students in middle school are on track for Algebra by 8th grade.
These don't apply to any special program, there is no lottery, and they aren't hand-picked by teachers or administrators.
"The manufactured outrage over the California math recommendations keep getting posted on HN. Read the actual text of the plans here [1]."
This is not manufactured outrage. I have read the framework (and many of the sources cited as support for the recommendations), and I am outraged.
If you follow the footnotes, you'll find instances where:
- the framework incorrectly states the conclusion/claim in the paper/study/web-page
- the framework relies on a claim in a paper/study/web-page, when the paper/study/web-page lacks sufficient evidence to support the claim due to poor experimental design, poor interpretation, or lack of evidence altogether
"The FAQ is at [2] and directly responds to these characterizations."
The FAQ does not accurately portray the implications of the recommendations. (I read both the framework and FAQ a few months ago.)
Interesting thing with the integrated approach is my high school had that approach. That was private school, and I entered high school in 1990. I wonder how long European countries have been using this approach. The curriculum at my high school very deliberately blended all the mathematical subjects across the first 3 years with Calculus becoming dominant by the end of the 3rd year.
However the entire goal of the integrated program was to maximize the amount of Calculus students could get through. I got not one year but two years of Calculus effectively by the end of HS and had no problem passing the AP calc exam. Probably only 10% of my HS class did that though, and that was already at a selective private school.
Integrated is great as long it gets students to the same place.. it's still really important to get as many talented students into Calculus before HS graduation.
Ironically, California is so mismanaged and corrupted that many counties simple do not have gifted programs. Yeah, the 6th wealthiest state in the world couldn't afford a god damn gifted program, all the in name of so-called equity and inclusiveness. It's not the well-made families that get hurt. It is the families who try to make ends meet get hurt. Their kids are simply deprived the opportunity to continuously learn and get challenged. And for that, I won't forgive California's politicians and bureaucrats.
It's also funny you mentioned that California will emphasize more on "applied math". I mean really? We're talking about high school maths. They are so simple and so fundamental that there shouldn't be a distinction between the applied and the theoretical. Teaching "applied maths" is simply a coded word for watering down the standard.
> the framework does not forbid gifted and talented programs
How do I square this with their claim that the CMF is "placing obstacles (such as doubling-up, compressed courses, or outside-of-school private courses) in the way of those who want to take advanced math in higher grades."?
To get around the obstacles most kids will need a very motivated parent who can advocate for them with admins, and that basically will just harm kids who's parents don't have the time/resources/charisma to make it happen for their kid.
I’ve read most of the text. It’s pretty misleading to say the guidelines don’t ban accelerated courses, because they don’t really have a concept of “banning” things in general; they’re a vision of what the curriculum should look like, not a list of rules. The guidelines do make it pretty clear that accelerated classes are not part of the vision.
Thanks. The new emphasis on stats and probability is so important and is something I wish I’d had before taking my first university stats courses. There’s probably no branch of math more important to everyday life and maintaining an educated discourse in society.
Ironically, geometry literally means "the measuring of land" because it's a field derived from the bronze age super powers, who needed to resurvey the farming plots after each river flood. A farmer might actually have some benefit knowing it really well.
Also, it helps to have some intuition of geometry when you're actually building something (whether that be construction, mechanical engineering, woodcutting, papercrafting, you name it...)
Geometry is one of those things that you can teach in the utmost horrible way though (make students memorize theorems verbatim), I understand why students can perceive it as incredibly boring and useless.
Does it really help though? I mean parents with resources will always put their kids through private math courses which can be more rigorous and give their children an advantage in AP Math/Calc/etc. I don't think the disparity in math learning is from school.
Thanks very much for adding this context! I have not read the full docs and based on what I've read so far I don't feel like I'm thoroughly qualified to answer "is California removing Algebra from middle school?"
Which, if they did, would I think be a mistake.
What I can see is:
(1) Chapter 7 of the first field review draft says that they intend to de-recommend "Algebra I" for people in grade, in favor of something called "CA CCSSM" which incorporates concepts of algebra. They seem to say that CA CCSSM is much more thorough and comprehensive than Algebra I and is a better choice for students who are showing particularly strong math skills.
"In grade eight, the CA CCSSM are significantly more rigorous than those from previous grade-eight content standards. They address the foundations of algebra by including content that was previously part of the Algebra I course—such as more in-depth study of linear relationships and equations, a more formal treatment of functions, and the exploration of irrational numbers. … The rigor of the CA CCSSM for grade eight means the course sequencing needs to be calibrated to ensure students are able to productively engage with the additional content. Specifically, students who previously may have been able to succeed in an Algebra I course in eighth grade may find the new CA CCSSM for grade-eight content significantly more difficult. The CA CCSSM provides for strengthened conceptual understanding by encouraging students—even strong mathematics students—to take the grade eight CA CCSSM course instead of skipping ahead to Algebra I or Mathematics I in grade eight."
(2) The FAQ and accompanying diagram say that they intend to recommend "Algebra I" as one of three options for a 9th grade curriculum -- with the other standard options being "Integrated I" and "MIC I". I think the idea this diagram presents is that 9th/10th grade carries Algebra I/Geometry or Integrated 1/Integrated 2 or MIC 1/MIC 2, and then you can spend 11th/12th grade studying other concepts in detail like statistics (great choice IMHO) or calculus.
(3) Critics of this proposal (writing at https://bit.ly/cmfanalysis cited in the guest blog post linked here) argue that postponing Algebra I from 8th grade to 9th grade reduces the opportunity for students to study calculus in detail in high school.
I happen to agree that calculus concepts might not be the most important -- maybe it's more important to get a good grounding in statistical thinking as opposed to integral calculus? Maybe it's better to learn really strong proof skills and approach calculus directly via real analysis? I dunno.
I guess what would bug me would be if kids didn't get abstract thinking early. The core concept of algebraic thinking to me as a nonexpert is treating things as variables rather than concrete numbers, and being able to reason about changing a function or a family of functions rather than a specific line or curve.
But what confuses me overall here is -- why does the CA Math Framework still include Algebra I as a 9th grade program? If the new 8th grade CA CCSSM is indeed so rigorous that stronger math students should take it, and if it includes the essentials of Algebra I, then why waste another year on the concepts again? I don't understand.
It's quite reminiscent of the Common Core fight. No one read the standards. I mean, you ask someone to sit in front of you and read "Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data." and they just don't get that worked up. Instead it was a cultural fight over power, control, and who gets to set the agenda, that ignored the fact that Republicans participated in creating the Common Core. Nothing gets people to the polls like "schools brainwashing children" -- see Glenn Youngkin.
We have the shittiest math education in the developed world, and it comes down to teacher training, teacher support, professional development, and ensuring that children are fed and in safe situations where they can do laundry and wear non-smelly clothes to school [1]. In Finland that is understood, and lo and behold, good scores overall. In the US we think that curriculum is a magic bullet. Like changing the textbook will change what kids learn. As a former math professor, this is bullshit. I can take whatever curriculum you want in math and transform it to meet students where they're at -- because I f*(&ing know math. Too many of our teachers don't, and it's our fault as a society. I left education because of the crap wages and that creeping feeling that my individual efforts to better things just couldn't match the magnitude of the problems.
America keeps being a magic-bullet country. The vaccine will fix COVID, so we don't need societal support for public health measures. Right or left, I don't care; the right thinks "individual responsibility" is the magic bullet in the face of infrastructure problems, funding problems, everything, while the left thinks technocratic solutions or "being correct" will be the fix.
I strongly support the shift to more applications of math, more stats and probability, more analysis of real-world systems. There is plenty of room to challenge gifted students in this context and I have done so myself -- you do need the time and support to build scaffolded projects so when "that kid" is done you can say, "Well, what about this?" and when that other kid is still struggling you can break it down. The factory grind of education in American and the fact that many math teachers don't even have a degree in math means that is quite difficult to put in place.
>They are not taking algebra out of the curriculum, although they are cutting geometry a bit, which doesn't make as much sense today as it did 100 years ago when far more people grew up to be farmers or ranchers.
this blurb alone invalidates everything else you have to say. you have absolutely no idea what are you talking about.
Regardless of how wrong someone else is or you feel they are, it's not ok to break the site guidelines like this, so I've banned the account. Could you please not create accounts to break HN's rules with?
I don't understand how you can remove algebra from middle-school curricula without exacerbating inequality.
Supplementary math education in our area costs about $1500-$2500/year (looking at Russian School of Math list prices). The exemplary private schools in the area I grew up charge $30k-$35k annual tuition (with financial aid available for some families). And you can DIY home instruction -- I've been working through the Moebius Noodles play with our 4yo, and I guess you could try to see if there's a Math Circle to sign up for.
But not every household can afford the time or money to coordinate extracurricular instruction. The kids whose parents are hyper-prepared and able to spend the time and money will end up with better math background, maybe a better shot at the AHSME/AIME/USAMO, and I guess maybe better career outcomes, versus their peers. Is that a fair outcome? Is it a good thing to do?
I'm very willing to be wrong here … I just don't understand how this plan promotes equity.
p.s. saw this in the news and tried introducing algebra to the 4yo. We're not quite ready yet.
"Hey kid -- if I have four of something but I want to have six of them, how many do I need to add?"
He holds up a fist, empty. "Four." Then he starts counting out fingers. One finger: "Five!". Two fingers: "Six!". He says, "Two!"
"That's right, kid. Sometimes we say 4+x=6, so x=2."
He gives a sly grin. "But I know my numbers so well that I don't need to use x!"
Related, I also have a hunch that the UC system dropping the SAT is going to promote inequality. I don't want to defend standardized tests as flawless, but the SAT has been around forever, you can go to basically any public library and get a prep book, one of the librarians can probably help explain it to you, most teachers are familiar with the strategies to improve score on it, resources exist on the internet, etc. So there exists a multitude of paths toward showing proficiency on it.
Now that we're not doing standardized tests and turning admission into high school transcript plus additional material it's really going to help the kids whose parents can organize and pay for the most extra circulars.
>"Related, I also have a hunch that the UC system dropping the SAT is going to promote inequality."
My guess is that it will reduce racial inequality, but increase inequality based on parental income (class). Eliminating SAT scores will result in greater affirmative action, and the richest people of each race will be able to sculpt a compelling resume for their child; there will be no way for those with poorer parents to compete on the holistic measures.
You guessed it, poor whites and asians. The kids who couldn't afford extra curricular but who did great on the tests. Who is it going to help the most? Children of wealthy East-African and Caribbean immigrants.
This focus on extra-curricular also makes it really easy to sneak-in affirmative action (despite voters repeatedly saying no). Because, let's be honest, you can't objectively compare these things to one another.
> I don't want to defend standardized tests as flawless, but the SAT has been around forever, you can go to basically any public library and get a prep book
That's great unless there are a few other kids in the same area that also need to the book and also think to get it from the library.
Most people have smart phones and getting free resources online are easy enough.
The larger overall point is that acquiring SAT prep resources is easier to do than acquiring resources for volunteering or extra curricular activities. While the former may be difficult in some situations, in those same situations the latter has even greater difficulty.
What about the kids who can afford to pay for top tier college consultants and tutors to maximize their standardized test scores? Doesn’t that also exacerbate inequity?
The question is which system exacerbates inequality the least: On the one hand we have a well-known system with objective answers and a widely available study catalog, and on the other hand we have a system that largely involves administrators applying their subjective discretion to which extra-curriculars or essay is "best".
I am not from the US but I did appear for the SAT. The books are more than enough to get a very good score on the SAT. In my opinion, SAT is not difficult enough for coaching to make a very big difference.
For those interested in understanding what it looks like on the flip side - from the generally underserved side of things - here's an interesting article.
Middle-school students embrace endless summer ... of linear equations
This should be the foundation for all teacher training: spend most of your time sitting with small groups of kids at various ages and try to teach them concepts that are obviously beyond their current knowledge. Take copious notes. Patterns will emerge, and you’ll develop an intuition about what sticks and what doesn’t.
> For many teaching is just a steady paycheck and generous time off.
A tiny paycheck and... I'm sorry, I have no idea how to read "generous" time off; are you referring to summers when they don't get paid, or something else? My impression is that most teachers are working significantly over 40h/wk and either don't know that they're victims of wage theft or somehow don't care.
My mom taught high school for 35 years, and said that was the biggest misconception: “Oh, you teach? Summers off must be nice.” She’d reply “not when you don’t get paid over the summer.”
Also, teachers doing things like chaperoning the dance and stuff are probably not getting paid for that time.
There is no “generous” time off if talking about public primary education in the US. Curriculum development and continuing education most frequently happen outside the “day job hours”.
I don't have kids but I keep seeing https://www.kiwico.com/ recommended all over the internet and it seems like a great way to get projects and learning infused into early childhood play and exploration.
> I just don't understand how this plan promotes equity.
Well, it can turn every one into a bad pupil :-)
I wish people would take a look at what happened in other countries which followed a somehow similar path of dumbing down courses and lowering requirements.
Here is what 25 years of dumbing down achieved in France:
It is about maths (calculus) but we have somewhat similar drops in other matters, notably in French language.
You can easily see on the graph how the above average pupils from now perform as bas as the below average pupils from 30 years ago. Only a small part of pupils perform as the average pupil used to perform. You can also note that the 'excellent' pupils have basically disappeared: there is no bump (and no long tail) on the right of the curve any more.
Not a single category got something positive about it. The lower social classes for which this dumbing down was intended actually suffer badly from it; the upper classes didn't find ways to escape it either.
It is estimated that when they reach the end of high school, pupils' level is late by 1 or 2 years (depending on the matter) compared to what it was in the last two decades of the XXth century (when high school access was already expanded massively, we're not talking about the 50s-60s-70s). And yet the high-school pupils are basically automatically all given the degree: 95% success rate compared to 75% in the 90s (and in those days that was after many had repeated 1 or more years, which they don't any more, they almost all pass all classes automatically, even though they didn't assimilate the necessary knowledge and understanding to follow next classes ).
Another troublesome consequence is that it propagates. Very recently, universities, which for a long time tried to keep the same level as before, started to dumb down their courses an lower their requirements for passing years too, because the first years of university had become a slaughterhouse for a mass of students who were coming with a completely insufficient level (the high-school graduation serves as an automatic entry ticket for universities, there is no entrance exam). So the same effect as in primary and secondary education is about to happen, and selection is pushed to the Master level, but that last barrier will probably very soon break too (we already hear complaints about it).
I actually remember worksheets in first grade (around age 7) where we had problems exactly like that, but with an empty box instead of a letter and we wrote the answer in the box.
Father of five, and husband of teacher here. Math is a problem for middle school teachers because they often don't understand algebra, trigonometry, calculus or geometry well enough to teach it. When you add to that common core style arithmetic where parents and family can't help (because they do not understand how to do common core-style math), teachers are struggling to even teach math at all.
Additionally, many professions pay better than being a teacher, and unfortunately, that includes package handling for FedEx and UPS (just drove by a sign promising $24/hour starting) in some areas.
> Math is a problem for middle school teachers because they often don't understand algebra,
Thank you for saying this. I am/was a high school math teacher and this was always the biggest problem when we got students in. The teachers at lower levels just don't understand it well enough to teach it. And, sadly, the same can even be said to be true for some of my coworkers. Our calculus teacher hasn't retired yet because there's nobody she trusts enough in the math department to understand pre-cal/calculus well enough to teach it (I'm on a leave of absence and have switched to the science department, though I've been asked by her and admin to teach those if I return).
To me, common core math makes perfect sense. It's how I do math in my head. But it's also because I feel like I understand math. If I'm subtracting 26 from something, I'm going to subtract 30 and add back 4. It's just quicker and simpler. That's what I've seen parents struggling with, and even teachers struggle with it too! Because they don't get how numbers work. It's really frustrating and harms the kids. I wish I could overhaul how elementary school teachers are trained as in my state they're not even required to do well in math, or take any upper level math courses, before teaching math.
This is a huge problem. I have friends who are teachers and have never taken anything past trig at a high school level, and certainly have no understanding of calculus. I think this results in a fundamental understanding gap, since the main application for algebra is really cemented in higher math (calculus).
I sadly don't know how to fix it without reworking the entire teacher education system, sadly, but I do believe it's the problem affecting primary schools especially. How many times are you taught to read and the 'importance' of reading by a teacher who doesn't like to read themselves? Or 'science' by a teacher who has no grasp of what science is and just reads the slides (I distinctly remember having to correct my 5th grade teacher becasue the notes she used were so old it said Saturn was the only planet with rings...I was that kid, but at least it was after class!).
We need teachers who have trained in those areas, and then wanted to become teachers. And it needs to go all the way up through middle and high schools, but I truly think the focus should be on primary first. It's why we get so many kids who don't understand multiplication when they get to high school, let alone division -- their teachers don't either and they just give them calculators at a young age! And it all boils down to how teachers themselves are trained.
Back to math at the school I taught at, there are two there who understand it. Funnily enough, they both came out of retirement to teach again (one has been doing it for 15 years, and the other just retired from her VP job a few years ago), and they're related. The older one married the younger one's uncle. It's funny how it stays in the family. The younger one's dad was also a math/chem/physics teacher, and was an amazing teacher until he just got too old. They were the only teachers I know or had at that school when I was there who truly knew math, and it showed in how they taught and the general outcomes of their students -- A "C" student in the accelerated algebra II class made an easy "A" on college algebra when they got there two years later, simply because it had been imparted to them that well.
I'd argue it is the reason. I know parents who've had no problem helping their kids with the "right way/new math". But it's because the parents knew numbers, and realized that taking away 20 and adding 3 is the same as taking away 17. The number of teachers I've met who "know" it but don't truly grok it is way too high.
"Additionally, many professions pay better than being a teacher, and unfortunately, that includes package handling for FedEx and UPS (just drove by a sign promising $24/hour starting) in some areas."
In California, teachers' retirement benefits include defined-benefit pensions, with some inflation-protection. They also don't work the same hours as package handlers. Total pay+benefits for teachers in SF is about 50% higher than base salary.[0]
I'm never heard of a middle school offering trigonometry or calculus. The rare kid who is ready for those topics by age 13 can be accommodated by allowing him to attend that class at the local high school.
A middle school algebra teacher should of course understand middle school algebra. This is not an unreasonable expectation for a job that requires a college education. If a teacher lacks the ability to master middle-school algebra, how on earth did he get into college?
It's not that the students need to be taught high school or college math in Junior high.
It's that a teacher which did not master high school and college math is not necessarily a good candidate to teach high school or advanced middle school math, and it absolutely occurs when the primary focus of the teacher's college career was teaching and not Math or another STEM field.
The model in the US seems to have become that the Teaching degree is the most important degree for a public school teacher regardless of the subject that is going to be taught. At some point that breaks down in a big way in the STEM fields in the range of middle or high school. Certainly you are not going to be taught Math at the College level by someone who does not have a Math degree. But in public school they've decided at some point that a math teacher doesn't need to have a math degree.
> But in public school they've decided at some point that a math teacher doesn't need to have a math degree.
For anything pre-high school that would seem sort of overkill. A "good" teacher in the earlier grades is more of a function of how well they work with children.
Honest question from someone from the Netherlands: when are kids in the states old enough for these topics?
Me and all of my friends were thaught the fundamentals of algebra & trigonomatry (admittedly not calculus) at 13 years old. I had no idea the wasn't the case in the US and it honestly kind of blows my mind.
In some US public schools, the "advanced math" curriculum puts 7th graders in algebra. In more, though, algebra isn't available until 8th grade (and that is still treated as accelerated). "Normal" math progression has standardized on algebra as the first high school course, followed by geometry, then trig, then precalculus/analysis.
The first level of math acceleration moves that high school progression up a year and has seniors taking calc 1 (limits/derivates & single variable integrals. The second level of acceleration has calc 1 in 11th grade and calc 2 (multi-variable) in 12th grade.
There are a handful of schools, mostly private, that move faster or have more diverse math curriculum offerings, but this is the most common.
The norm for exposure to basic algebra is 5th (10-11 years old) grade in most US states. Not sure what the standards are exactly, but each grade after that does progressively more, with 14 year olds expected to complete a full year course.
My school was rural and that is way more advanced than mine was.
8: Algebra I
9: Algebra II
10: Geometry
11: Trigonometry
12: Pre-calculus
Advanced class was -1 year. This was Upstate New York 90s/00s. Though I guess to be more specific these courses were actually combination. So it was 3 years of mixed algebra/geometry/trigonometry. Math A, B I think New York called it. Until Pre-calculus Which was actually year and a half courses of mixed topics.
I should've added that I was on the advanced track and was a year ahead of most of my peers, though we had full class of > 20 students (in a graduating class of, I wanna say, ~100-ish) who were in this track. IIRC, it was a toss up what most students did for Math in the 11th and 12th grade. I do believe that the school offered a dedicated Trigonometry and Pre-Calculus course that many students took in the 11th and 12th grades, and there was also an Algebra-based Physics class that students could take, but I want to say that they were not necessary for graduation.
Very roughly, subtract 6 from age to get grade. For example, barring being held back, jumping a grade, or unusual things around birthday timing, you'd usually finish 12th grade at age 18.
> A middle school algebra teacher should of course understand middle school algebra.
Yes. Exactly.
> If a teacher lacks the ability to master middle-school algebra, how on earth did he get into college?
Knowing a subject well enough to pass a class or pass a test is not the same as knowing it well enough to teach. STEM in schools is a real problem because, well, non-education jobs pay 3-5x what teaching jobs do for math, CS, and robotic.
Maybe we need a reformed "Teach for America" style program, where the government gives scholarships to students getting double undergrad major in Mathematics and Education, if they agree to teach in inner city schools for X years after graduation.
> Math is a problem for middle school teachers because they often don't understand algebra, trigonometry, calculus or geometry well enough to teach it.
The other problem you alluded to is that if they do understand well enough to teach it and teach it well, there’s a good chance there’s an engineering position they can get instead.
Eh, watching all this makes me only more willing to properly research homeschooling ( it is not yet apparent whether we will be able to afford private school.. so I am assuming we won't be ).
“We basically decided, no, race is still a social construction, it’s not a biological thing,” Ken Miller, an author of the widely used Prentice Hall biology textbook, told the science magazine Undark of the decision to omit mention of race.
I guess what I am saying is not new to anyone. Public schools will continue to degrade. There is no benefit to any of the groups other than the parents to ensure kids learn things ( administrators, their lawyers, your congressman, my congressman, teachers, teacher's unions, book publishers ). Sure, they pay lip service and some individual teachers care, but each of those groups have goals beyond kid's education.
edit: I was gonna add Apple and Microsoft in that list, but I removed them, because, as flawed as their reasoning is, at least they pretend they want to teach kids basic coding, which is not horrible.
Race as biological concept exists but there are no human races in the biological sense. Humans are able to interbreed and were not selected by their environments for long enough to develop significantly different cognitive abilities. If we use the word race for human being it can only mean cultural or other such societal concepts meaning it is a social construction. I hope that helped.
Seems like a weird false dichotomy - even in the olden days of pseudoscience on race, obviously people didn't believe that races couldn't interbreed, as they observed such themselves.
The fact remains that if you run PCA and clustering on genetic data as in
https://en.wikipedia.org/wiki/Human_genetic_clustering#/medi...
you will get groups that generally correspond with Caucasian/SS African/East Asian/Amerindian. You can call those "races" or something else, but they are not just artifacts of society/culture.
> even in the olden days of pseudoscience on race, obviously people didn't believe that races couldn't interbreed, as they observed such themselves.
They did however believe that there were "purebreeds" of races; that you could objectively categorize people into various races. Mixing races wouldn't create new races, it would only create a mixture of races. As an analogy, you can create metallic alloys from different metallic elements. That won't create new metallic elements though, it will just create new mixtures of the pure elements.
The strongest example of this view is Polygenism. Before Darwin, people were arguing about whether there was a single origin for people or multiple origins corresponding to the assumed races. This
The person you're responding to is trying to say that humans are a single species, and thus we can't be different races (species). But that is obvious in the modern context and isn't really what people are saying when they talk about race. Today, the argument is over: what are racial categories if they aren't species, and given a definition of race what does it actually tell us?
> If we use the word race for human being it can only mean cultural or other such societal concepts meaning it is a social construction.
> The fact remains that if you run PCA and clustering on genetic data ... you will get groups that generally correspond with Caucasian/SS African/East Asian/Amerindian
The person you're responding to is being very imprecise. There is no one definition of race. It a squishy class of "categorizations I can define which separate europeans, amerindians, africans, and asians". When we create a racial categorization, we are flattening these various categorizations into a single categorization. It is a social construction to choose the most important categories as "europeans, amerindians, africans, and asians" regardless of the categorization you're using.
As an example of the limitations of defining race from genetic clusters, Think of Obama in the U.S. He has a White mother and a Black father, but can you honestly say he is treated as equally White and Black in the U.S.? No, he is treated as predominately Black, even though the genetic view disagrees. You could say that the social definition is wrong and the genetic definition is correct, but you could equally say that your genetic definition fails to describe the social racial categorization.
>and were not selected by their environments for long enough to develop significantly different cognitive abilities
This is patently false. There are hundreds of known genes which are strongly correlated/anticorrelated with above average and exceptional intelligence and are absent or underrepresented among various ethnic groups. Humans left africa some 200k years ago and even if you think thousands of generations of adaptation to drastically different environments before agriculture wouldn't have been enough time for populations to evolve cognitive adaptations, the fact that geographically isolated interbreeding with other homonids occured further suggests a genetic basis for differences in cognition.
The modern scientific establishment's denial of race based differences in cognition (not just intelligence, see e.g. warrior gene) is nothing but politically motivated science denialism, and does immense harm to the institution's credibility.
No, there is just history to the word you might not know, some extra meaning. Race fundamentally refers to the idea that there are different kinds of people. Which is why 'interbreeding' comes up, because some people used to believe that a black person and a white person having a child was more like crossing a horse and a donkey than say a person with light hair and a person with dark hair.
That's not really a good argument for the thesis that "there are no human races in the biological sense". Even if there were misconceptions embedded into the definition of the word "race", that doesn't mean there's no underlying biological reality to the differences between human populations that are identified by categories of race.
Nobody has lost sight of genetic differences across populations. I don't know why you are bringing that up.
But, there are no human 'races' in the biological sense. At best it makes you sound like you're discussing the politics in your Tolkien fanfiction. It is purely a social construct.
> Nobody has lost sight of genetic differences across populations. I don't know why you are bringing that up.
Listen, I'm not saying self-identified race and genetic or ancestral population are the same thing, but there are strong correlations. Perhaps you can clarify how the claim "there is no biological basis for race" makes sense in light of this fact?
> It is purely a social construct.
Something being a "social construct" does not mean it is purely arbitrary.
Even if there wasn't enough time for selection to act on cognitive abilities (citation needed), the fact of the matter is that patterns of population genetics do correlate highly with self-identified race.
>> whether we will be able to afford private school
Private school is not necessarily better than public school, especially for high school. If you are in a good public school district then it is unlikely that a private school will give your children a better education.
Because, and I don't think that is questioned, race as a biological concept exists and, as Prentice Hall quote demonstrates, the publisher unilaterally decided on a lie of omission, while attempting to teach. It is not a good look if the goal is teach kids basic biology.
Unless, naturally, it is not the goal; or even a goal.
You're really referring to genetic ancestry, which is regularly used in biology without any issue. The term "race" is really not used anymore, except in a social/historical/statistical (population) context for humans. It's only informally used in human biology.
> Because, and I don't think that is questioned, race as a biological concept exists
This is questioned constantly, and is far from the standard or consensus opinion for human biology. In reality, most scientists and biologists don't use the term "race" often or at all precisely because of it's historical connotations and social uses. Removing the term "race" from a science textbook does not change anything really, beside clarify that race in the context of racial essentialism in biology is a useless concept. Understanding how the concept of race was used to abuse science, and in turn abuse large swathes of the population, is more important, and likely has a role in learning about the ethics and uses of biology.
Race is better replaced by populations. Populations are groups of people who grew up in a region back when travel between regions was restricted enough that genetic differences appears. As our world become more connected, populations were grouped based on similar phenotype (not similar genotype) into races. Races do exist in that they are phenotypically similar groupings of population, but they have little value in comparison to populations at the biology level. Sociology level race has more importance because of how society reacted once those races were created (which also means it has an importance in the fields dealing with the history of science). And as the world becomes more globalized, the effects of populations decrease. It isn't gone and has a long way to go before it is gone, but as long as the world stays globalized it will happen. Far into the future, assume humanity achieves long distance space travel, it will likely result in new populations emerging and potentially even different species evolving. But that's so far away that it is best left to science fiction.
Hmm. I like the explanation and I appreciate some of the concern.
I would personally argue its absence says more than its presence given race is used in other contexts you listed. You simply can't get away from it when discussing demographics, so I question a little your statement that the term is not used in biology or other sciences.
Could you share an example of a paper that follows that 'no race' ( "at all" ) approach? I may very well be wrong. I am pretty ancient.
<< This is questioned constantly, and is far from the standard or consensus opinion for human biology.
You clearly are more immersed in it than me. Could you elaborate a little bit and link to two recent opposing papers? Sorry for all the questions. I am genuinely curious now.
To be clear, the term is used and has been used. But the idea that it's a concept that everyone agrees on, or that everyone agrees must be used, is not at all true. The debate is alive and well in philosophy and in the sciences. Personally, I don't really see any use for the term in science, beyond referring to a social/informally named group.
> Even though there is a broad scientific agreement that essentialist and typological conceptions of race are untenable,[12][13][14][15][16][17] scientists around the world continue to conceptualize race in widely differing ways.[18] While some researchers continue to use the concept of race to make distinctions among fuzzy sets of traits or observable differences in behavior, others in the scientific community suggest that the idea of race is inherently naive[7] or simplistic.[19] Still others argue that, among humans, race has no taxonomic significance because all living humans belong to the same subspecies, Homo sapiens sapiens.[20][21]
You can clearly see a number of competing views, including constructivist, essentialist, and anti-essentialist, the idea that the concept of race is irrelevant to the study of biology.
I assure you that it is questioned. How do you define race, biologically? How would you test, say, former president Obama to determine his biological race?
EDIT: To be more precise: of course there is no question that the biological concept “exists”. The biological concept of Lamarckian genetics exists, too. The question is whether race is meaningful, useful, and whether it should be taught in the textbook.
So different people look different. Why is that an important principle of biology that needs to be developed in a textbook? How does it help us to understand anything?
And I persist: if you can’t measure it, and tell me what someone’s “race” is in a way that biologists in general would agree with, the concept is too wobbly to be of any scientific interest. Finding definitions merely shows that the word exists. It doesn’t support the idea that it’s a meaningful or useful categorization.
> So different people look different. Why is that an important principle of biology that needs to be developed in a textbook? How does it help us to understand anything?
Race strongly correlates with other things; for instance, per https://www.cdc.gov/heartdisease/facts.htm "White (Non-Hispanic)" men are most at risk of heart disease, and "American Indian or Alaska Native" are winning by several percentage points. That is deeply of scientific interest.
In order to apply these supposed correlations, we would need to be able to determine the patient’s race. How do we do that?
(It seems to me that there is at least a hint of tautology in your comment. How can we talk about these correlations with race unless we're assuming that racial categorizations are meaningful in the first place?)
Because, and I do not think I can stress that enough, science is not a religion. It is not a movement or a cause. And I am concerned that you are worried more about the 'good' derived from uhomitting a bad word might cause than about exploring and describing reality for what it is.
That's super easy, in fact. Measure all significant physical traits, such as eye color or height, group the resulting vectors using PCA, notice that the vectors form a few distinct clusters.
I can help. You can measure various traits of the dog, such as ear length or nose shape, and compare the results with a table that says that such and such breed has ears of such and such shape.
I cannot tell you that this has never happened to you, but I can inform you that the person you are responding to did not say a single word about either black people or intelligence.
From the post: “The report states that while 80% of all students have access to Algebra I in middle school, only 24% enroll.”
A solution is to enroll all students in schools that offer the course by default, but let some opt out if they have a very good reason to do so (ie, nudging in behavioral economics term.) A potential problem is the pressure to water down the course for unwilling students but many countries have already solved that by having different streams/versions of the course.
Another objection is that it could be too hard for some students. I’d say it should be possible for a majority of students to understand Algebra I if they are taught properly, as in the case of many countries with high PISA Math score. In these countries/regions, to my knowledge, much of Algebra I is taught in math courses compulsory for ALL middle school students.
I grew up in Asia, taught math there for several years, and have run a tutoring school specializing in math tutoring there for over a decade. I was quite surprised when I saw how easy the American math curriculum/textbook is for a given grade. (I’d say 1-3 grades easier than Asian counterparts) Others in Quora have expressed the same sentiment.
Math is a skill that requires a great deal of time to master. Those who start properly sooner tend to have an advantage. US schools should offer more advanced math courses to all students at a younger age, rather than the reverse.
We all know what initiatives like California's leads to. Parents from middle to upper class families will send their kids to private schools or invest in extracurricular math programs. This will be especially true in immigrant and tech-worker parents who know the value of a strong STEM education. Only people who suffer will be kids from families without the means or the desire to go beyond public education - most likely the same people that these initiatives purport to help.
> This will be especially true in immigrant and tech-worker parents who know the value of a strong STEM education. Only people who suffer will be kids from families without the means or the desire to go beyond public education - most likely the same people that these initiatives purport to help.
Short term schools like Lowell are switching from using test score to a lottery based admission. And so are UC schools! So the smart kid interested in learning but who doesn't have parents in tech to send him to private tutoring better be lucky at the lottery or have the correct "holistic" attributes his target school will admit on!
"We all know what initiatives like California's leads to. Parents from middle to upper class families will send their kids to private schools or invest in extracurricular math programs."
A lot of high-earning parents in California send their children to public schools, and they are willing to pay extra money to buy homes in the best school districts in order to do so.
School district quality has a significant impact on home values in California, and that wouldn't be the case if the majority of high earners sent their kids to private schools.
Whether or not it's happening now, doesn't preclude opposition to policy choices that actively accelerate the process.
People with money and wherewithal are always going to have alternative options available to them, such as private education or moving to expensive neighborhoods with strong schools. The problem is when public school policy results in actual degradation of education for everyone else.
What value is there in a strong STEM education? A weak one might be fine too.
Just because tiger moms think there is one doesn't mean there is. You'd have to believe students actually remember or use everything they learn in class, vs it being signalling you're conscientious enough to do the homework.
Here's a little paper on just this:
- STEM education is associated with better problem-solving capability
- better problem-solving capability leads to higher earnings
- higher earnings (to a point) lead to greater happiness
https://files.eric.ed.gov/fulltext/ED531752.pdf
I'm confused, what is the proposed framework supposed to fix, or how is it better? Is the goal really to reduce achievement gaps by limiting the advancement of top students? Surely, that can't be the goal...that's crazy. Furthermore, that has the possibility to exacerbate the problem by forcing advanced students to augment their math education in the private sector, something only available to wealthier families.
Also, the shifted emphasis on data science stuff is a joke. The very courses they're talking about minimizing are the building blocks of data science and there's no shortcut.
Not sure, from other comments I gather the goal is to de-emphasize the idea that you need to be gifted to be good at math, which studies apparently have shown that this idea tend to discourage other students, often girls or racially disadvantaged boys, which do have the ability to succeed at math, to pursue math or be interested in it.
I don't think anything is changing for truly gifted students, they should still have the ability to be fast-tracked or options to take more advanced topics. It seems more that it's about focusing on students who don't see themselves as gifted or who aren't yet showing signs of it.
This is incorrect. Their explicit goal is to remove fast tracking and options to take more advanced topics for gifted students. The vision is for uniformly paced classes for all same-aged students.
> Does the draft Mathematics Framework eliminate middle school mathematics acceleration programs?
No. The draft Mathematics Framework does not eliminate middle school mathematics acceleration programs (including programs that offer Integrated Math 1 or Algebra 1 courses to grade eight students). The draft Mathematics Framework emphasizes the importance of following the sequenced progression of topics laid out in the Common Core State Standards for Mathematics (CCSSM) and considers the latest research on the impact of skipping grades or undermining the sequences progression. Additionally, the CA CCSSM are significantly more rigorous than those from previous grade eight content standards. They address the foundations of algebra and geometry by including content that was previously part of the Algebra I course, including but not limited to a more in-depth study of linear relationships and equations, a more formal treatment of functions, and the exploration of irrational numbers.
>I'm confused, what is the proposed framework supposed to fix, or how is it better? Is the goal really to reduce achievement gaps by limiting the advancement of top students?
Yes, that is the explicitly stated goal. Unfortunately a large number of ideologues believe that all people have the same inherent intelligence, and that disparities in outcome among children are due solely to racism and other forms of discrimination. That's the whole thrust of "equity". "Equity" means equal outcomes. It's proven too difficult for these people to bring up the performance of low achieving students, so they are left to bring down the performance of high achieving students and eliminate all objective metrics (like standardized testing) that can be used to assess student learning.
I find it interesting with many of these criticisms that subject matter experts on maths, sciences, etc think that they are also subject matter experts on the pedagogy of maths, science, etc especially at a high school level.
Many advanced practitioners don’t even have a good grasp of college level/post-grad pedagogy which they’d use more in their day to day work.
Using a skill isn’t the same as teaching it, and just like anything else there are plenty of fallacies to be had. I’d be more persuaded by angry hot takes from High School teachers worried that their students aren’t going to hit the grades they deserve / learn the things they need than anything else.
Even then, single high school teachers experiences are closer to anecdotes than actual pedagogical research, with which the original proposal is backed.
You are missing the key point: these experts on maths, sciences, etc are not arguing HOW to teach maths, sciences, etc.
They are only arguing WHAT is important to teach.
High school math teachers do not have the perspective to understand what kind of math is needed for jobs in engineering, data science, etc (The fact is that a background in algebra and calculus is necessary for almost all of these jobs).
"I’d be more persuaded by angry hot takes from High School teachers worried that their students aren’t going to hit the grades they deserve / learn the things they need than anything else."
> I find it interesting with many of these criticisms that subject matter experts on maths, sciences, etc think that they are also subject matter experts on the pedagogy of maths, science, etc especially at a high school level.
Public education in the US has a long history of fads, manias, and ill-conceived attempts at reform. There's little evidence of improvement over time or competitive performance.
The most recent PISA results, from 2015, placed the U.S. an unimpressive 38th out of 71 countries in math and 24th in science. Among the 35 members of the Organization for Economic Cooperation and Development, which sponsors the PISA initiative, the U.S. ranked 30th in math and 19th in science.
Given these results I'll trust subject matter experts over educators any day.
I didn't see anyone claiming to be a subject matter expert in math/science education in the article. So a second possibility remains open: they believe that it's possible to raise reasonable objections to this proposal without being an expert in education specifically.
Whenever public discourse turns to topics within my domain I realize that even one degree of separation from a subject means you're basically just making stuff up.
How many people on the planet are worth listening to when it comes to teaching math?
If I were a billionaire I would fund Asia-style 'cram' academies in disadvantaged neighborhoods and make them free. Provide a safe place where students can get extra-school training in music, writing, math, etc. Create communities of students who, yes, compete against each other and become motivated to succeed.
From my experience, the students who are truly gifted only needs a good environment they can study in (without worrying about money/work/bullying/parental abuse) but they definitely do not need 'cram schools'. The talented ones often have enough motivation to study what they like, and they can do self-study well with just light attention/mentoring from teachers.
People who are blindly praising Asian-style cram education really haven't actually experienced one in their youth at all; it is a fucking disaster at raising actual talent, and it robs you so much of your adolescence.
"The talented ones often have enough motivation to study what they like, and they can do self-study well with just light attention/mentoring from teachers."
There are many people who do not fit this category, but could still benefit immensely from good teaching.
I live in one of those neighborhoods and you would find that literally no one would enroll.
Cram schools succeed in Asian countries because there's an enormous amount of pressure to pass entrance exams, in disadvantaged neighborhoods kids often aren't even pressured to the point of graduating high school at all.
Do you ever wonder why American schools finish at 2-3pm rather than run the entire day as Western Europe? So that teachers could get that extra 3-4+ hours of doing the administration side of classroom work (grading, report writing, planning, etc). Even when parents request it there never appears to be enough money for afterschool programs, school districts create and withdraw them all the time depending on budget that you can't actually make plans for them.
Most American schools finish then because they start an hour or more before schools in most European countries, typical primary school (4-13 years) hours in the UK are 8:30 to 3:30 with an hour for lunch, France is 8:30 to 4:30 but with two hours for lunch and Spain is 9:00 to 5:00 with a two hour lunch as well. In Germany schools start between 7:30 and 8:30, but finish anywhere between 11:30 and 1:30.
The number of hours of class per week in the US matches a lot of European countries, but most countries in Europe have schools start and finish later on in the day, and some have extended lunch breaks that also push the end of day forwards.
> I would fund Asia-style 'cram' academies in disadvantaged neighborhoods and make them free
Cram schools are laughably useless. Works well at a national level with a large enough population but they are really a side effect of the intense competition and pressure for the few decent university spots available in Asian countries (per capita).
It's basically optimized to pass a test, not learn, and heavily rewards rote memorization.
I suppose this is a new trend, but there's constant pressure to lower the standards here in California. We genuinely graduate some students who can't multiply as-is.
I went to Sonoma State, which at the time had at least 3 semesters of remedial math you could take, plus a tutoring program, trying to fill in the knowledge a high school graduate was supposed to have. The state got mad about all those classes because the high schools were supposed to cover the material.
I started reading the California Math Framework but stopped partway through the intro, when I got to the part that says:
> we reject ideas of natural gifts and talents
It must be nice to think about a world in which every child is an equally-capable blank slate. But we do not live in that world. We live in a world where some people are tall, and somewhat more likely to be successful basketball players. And some people find math easy, and are somewhat more likely to succeed in math.
When you start out with flawed assumptions, it's not surprising when your prescriptions (no advanced math for anyone!) are foolish and counterproductive.
It seems like tabula rasa idealism has made a serious resurgence in leftist and liberal circles and the scary thing is that nobody (other than extremists saying nonsense) is really talking about this explicitly. Somehow we went from a bunch of stuff being cultural constructs to literally everything is a cultural construct and then this somehow became extremely widespread in no time at all. We need to have this conversation out-loud.
Every single one of us has things we support in-public but don't sincerely support in-private. Most of the time this isn't a problem because the endorsements we make don't end up affecting our own personal lives.
I have not met a single parent who didn't want to try and give their own children an advantage over the others. It is one thing to support "equity in education", but when parents sense that these activists are trying to dumb-down the curriculum, I expect significant pushback. Especially because this is quite literally a "won't somebody please think of the children" issue.
Why would there be pushback if they can just send their kids to private schools and not bear the negative consequences? Virtue signalling is actually advantageous to them. If they handicap all the public school kids then their own kids will be more likely to get into the top schools that manufacture scarcity.
I suspect plenty of parents will begin the process of trying to get their kinds into a private school, but it still requires a lot of resources and effort. I sense that most parents would try to fight this while simultaneously trying to find a way out while the process goes on.
As for the competitive advantage, I think that only works for the children who are already in the private school system.
Sending your kids to a private school is already considered suspect these days in some circles. And, conversely, some people specifically send their children to public schools for ideological reasons.
This seems inconsistent on the surface, but I think it is reasonable to want both. You can push for a more equitable world while recognizing that we currently live in a society that's pretty economically savage to some of its members, and it's understandable to want yourself and loved ones to not be the ones on the losing end of our society.
It's not just the assumption of a blank slate -- it's the assumption that because everyone is a blank slate, differences between people must be the result of oppression or racism of some kind, and that the primary purpose of education is not to teach, but rather to fight that oppression.
Even mathematics education is now being twisted by this -- it's now seen as more important for math classes to pursue equality/equity than it is to teach math.
One outcome of this is a levelling effect -- an equal outcome for all students, in which they all possess average mathematical skills, is preferred to a situation in which some students perform above average.
> Somehow we went from a bunch of stuff being cultural constructs to literally everything is a cultural construct and then this somehow became extremely widespread in no time at all.
The people who were critical of the first moves in this direction and explicitly said it would be a slippery slope were dismissed at the time. We're still moving in that direction. Hopefully the pendulum will swing back to something more reasonbale.
> tabula rasa idealism has made a serious resurgence in leftist and liberal circles
Maybe from liberals, but from what I've seen not the left. Marx's mantra is literally "From each according to his ability, to each according to his needs", it has nothing to do with liberal conceptions of tabula rasa idealism. I've never seen a leftist who asserts that people start from a blank state and can be "anyone" depending on the circumstances, that statement will get you accused of having bourgeois sensibilities who ignore the material forces of the world.
Here is a noted leftist writer who is not necessarily arguing for the strongest case of "blank slatism" but is definitely pushing in that direction here, claiming that inherent differences are overemphasized.
Well, I can't say the same as that's the majority of where I see it from right now. I don't follow MLs on twitter but most of who I follow are anarchists and democratic socialists.
> and somewhat more likely to be successful basketball players. And some people find math easy, and are somewhat more likely to succeed in math.
I wholeheartedly agree with your point, but there is no "somewhat" about it. The differences can be and often are stark, and we shouldn't shy away from saying that if we want an honest and productive conversation. It does not exclude the also-true fact that good education, practice, and other controllable environmental factors play an important role.
Absolutely. Some people are gifted. Not everybody is, otherwise it wouldn't be called that. They are better than other people at certain things. It may be math, it may be athletic ability, it may be music or another artistic talent. We should be nurturing and developing individuals in what they are naturally best at, as that tends to also be what they like to do and probably leads to happier and more successful lives.
> we shouldn't shy away from saying that if we want an honest and productive conversation
What makes you think anybody wants an honest and productive conversation? One half is just trying to get the other half to slip up and say something - anything - they can cancel them for saying. The other half is just keeping their heads down and trying not to lose their job for heresy.
Context is important, no? I'm not sure how you got to read that bit, without reading the preceding rationale:
> Research is also clear that all students are capable of becoming powerful mathematics learners and users (Boaler, 2019a, c). This notion runs counter to many students’ ideas about school mathematics. Most adults can recall times when they received messages during their school or college years that they were not cut out for mathematics-based fields. The race-, class-, and gender-based differences in those who pursue more advanced mathematics make it clear that messages students receive about who belongs in mathematics are biased along racial, socioeconomic status, language, and gender lines, a fact that has led to considerable inequities in mathematics.
>In 2015, Sarah-Jane Leslie, Andrei Cimpian, and colleagues interviewed university professors in different subject areas to gauge student perceptions of educational “gifts”—the concept that people need a special ability to be successful in a particular field. The results were staggering; the more prevalent the idea, in any academic field, the fewer women and people of color participating in that field. This outcome held across all thirty subjects in the study. More mathematics professors believed that students needed a gift than any other professor of STEAM content. The study highlights the subtle ways that students are dissuaded from continuing in mathematics and underscores the important role mathematics teachers play in communicating messages that mathematics success is only achievable for select students. This pervasive belief more often influences women and people of color to conclude they will not find success in classes or studies that rely on knowledge of mathematics.
>Negative messages, either explicit (“I think you’d be happier if you didn’t take that hard mathematics class”) or implicit (“I’m just not a math person”), both imply that only some people can succeed. Perceptions can also be personal (“Math just doesn’t seem to be your strength”) or general (“This test isn’t showing me that these students have what it takes in math.” My other class aced this test.”). And they can also be linked to labels (“low kids,” “bubble kids,” “slow kids”) that lead to a differentiated and unjust mathematics education for students.
That leads to the principals:
> ● All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015).
> ● The belief that “I treat everyone the same” is insufficient: Active efforts in mathematics teaching are required in order to counter the cultural forces that have led to and continue to perpetuate current inequities (Langer-Osuna, 2011).
FYI the first cited research is to the work of the primary author of the CMF. Her work appears to be very ideologically-motivated, and her colleagues have raised serious questions about her research. She also routinely misrepresents the work of others. Based on what I have read [1, 2 of many], I no longer trust anything she says without checking the actual source.
Based on coverage I've read, the CMF does not cite, acknowledge, or discuss any of the critiques of Boaler's work. If they had good responses to these critiques, they probably would have spent some of their 800 pages addressing these serious challenges.
> "The results were staggering; the more prevalent the idea, in any academic field, the fewer women and people of color participating in that field. This outcome held across all thirty subjects in the study. More mathematics professors believed that students needed a gift than any other professor of STEAM content."
Wait, the finest minds and educators in their respective fields are providing observational data that gifts are a real phenomenon, literally contradicting "reject ideas of natural gifts and talents". This is tremendous news that should have been a clarion call to seek out and elevate the gifted and invest every possible effort to nurture their gifts.
Yet the conclusion is somehow the exact opposite: that "gifts" are a falsehood used to malignly, even if unconsciously and unintentionally, dissuade people. How is this possible?
> The results were staggering; the more prevalent the idea, in any academic field, the fewer women and people of color participating in that field. This outcome held across all thirty subjects in the study.
This is not evidence that natural talent is not needed, it is at best some evidence that minorities and women maybe don't think they have the requisite natural talent.
> Negative messages, either explicit (“I think you’d be happier if you didn’t take that hard mathematics class”) or implicit (“I’m just not a math person”), both imply that only some people can succeed.
To say the evidence for stereotype threat is "weak" is charitable at best [1], and multiple replication attempts have failed entirely.
Overall, the evidence that was cited is simply not sufficient to justify the principles you list.
None of that actually shows that natural gifts and talents do not exist or are not necessary. Their results could be equally well explained by mathematics success requiring both gifts and early encouragement and support to develop those gifts, with children from less well off groups receiving less of the latter.
Thanks for this. It's important to highlight that if students had problems with one area of math but are talented in another that they might never experience that they are good at when math is taught area by area and not in an integrated way.
Math is not scalar is skill! When I am working with Boolean value function i almost always need to draw a table of all options while in Linear Algebra or numerics of differential equations I have a quiet good intuition.
It's actually a lot better if they reject ideas of natural gifts and talents but at the same time admit that a lot of those "gifts" are given post-birth by childhood education. In that case we might miss a few natural gifted children but could raise alertness to family education (that schools simply cannot substitute).
"It must be nice to think about a world in which every boy and girl is an equally-capable blank slate. But we do not live in that world. We live in a world where some people are tall, and somewhat more likely to be successful basketball players. And boys find math easy, and are somewhat more likely to succeed in math.
When you start out with flawed assumptions, it's not surprising when your prescriptions (no advanced math for anyone!) are foolish and counterproductive."
This is what society used to believe. How was that productive and wise?
I must have missed the part where girls were not expected to do just as well as the boys if they wanted to advance, and if they didn't perform as well, then we just changed the criteria for what constitutes success so the gender outcomes were equal. Women proved they were just as capable, arguably even more capable in many subjects, so we obviously do live in that world where the genders are equal in this sense.
This is not a flawed assumption with respect to baseline high school learning.
People can be taught much more mathematics and science than they normally learn.
This is not limited to STEM--people can be taught to write much better than they normally learn, as well.
The trick with the students is getting to the students before the "I'm not a <X> person/<X> isn't for me" kicks in. That means you have to get them in the 5th-8th grades--5th is a bit early/8th is a bit late.
Really frustrating that these sorts of arguments usually devolve into making no distinction between "basically everyone can pass a high school math curriculum with the right resources and support" and "not everyone can be a world class mathematician". Those are both true!
People talk about "holding back advanced students", but, in the real world, this never happens.
My father (a high school teacher for almost 4 decades) used to say: "I can't stop an advanced student even if I wanted to--sheer boredom will propel them to do something." For him, dealing with an advanced student was the easiest thing in the world and took practically no effort--a little extra work with a slight bit of focus and they're off and running. At that point, he could practically forget about them until they raised an interrupt.
My own personal experiences in school also reflect this. Most of my teachers forced me to turn in "normal" homework, pointed me at something more advanced, and let me at it while occasionally checking in on me or offering advice. Sure, they did this so that they could get me off their plate to focus on someone else. But, to be fair, what they had me doing is also the essence of learning--self-directed engagement with an unfamiliar knowledge base via intrinsic motivation.
And, to be fair, if your "advanced" student can't operate in that regime, are they really that "advanced" after all? Far too many parents think their children are "advanced" when they are merely a touch above average and really do fit inside the "standard" curriculum.
The real problem in high school is motivating average to below-average students who want to be anywhere but in class. Video games, hanging with friends/dates, vaping/CBD, etc. is way more compelling than anything having to do with school. Getting through to those students is difficult and has very little to do with the curriculum.
The biggest irony is that the same people who preach that there are intrinsic differences always seem to forget that concept when it comes time to hire and pay teachers. Funny that.
It comes from a real place of privilege to claim schools holding advanced students back never happens. To name one specific example with the most capable, Miraca Gross ran a longitudinal study with children scoring above 180 on IQ tests and found stark differences in motivation, satisfaction, and accomplishment depending on their level of academic acceleration[1]. (Terence Tao was “Adrian” in this study and was one of the models of successfully educating an advanced student). Kids might do something more with math out of sheer boredom, or they might just devote their energy to Pokemon instead—believe me, it’s not just the below average students who feel the urge towards everything else you mention.
Every student, no matter how capable, benefits dramatically from instruction tuned to their level and ability. Claiming advanced students will take care of themselves is an absolute failure in an instructor’s duty of care towards them, an excuse to make the teacher feel better about not having the time, interest, or knowledge to provide proper instruction. There is no merit to the notion.
You are talking about a 4 sigma deviation. Really? Your objection to a curriculum is that it doesn't cater to the 1 in 50,000 child? A child that 90%+ of school districts will never see.
Sorry. That's not even close to being a valid argument.
> Every student, no matter how capable, benefits dramatically from instruction tuned to their level and ability.
Oh, I agree. And the research supports it. However, when you tally up the bill for 2 teachers per every 10 or fewer students to make that happen, suddenly everybody starts screaming and objecting.
Really, you’re objecting to rarity after the emphasis you presented? I went with 4 sigma because you claimed truly gifted kids would take care of themselves. As you note, you can’t get much more extreme than that. My point was to directly refute that specific claim of yours. The same principles absolutely apply for the one in a thousand, or one in a hundred, or one in twenty; they’re just proportionately less extreme for each.
>However, when you tally up the bill for 2 teachers per every 10 or fewer students to make that happen, suddenly everybody starts screaming and objecting.
If you want to hear screaming and objecting, try to suggest that teachers need to be competent and tested in the areas in which they teach. Yes, if we had an entirely different educational system with an intelligent, competent teacher for every 5 students instead of a semi-literate, incompetent teacher with 30 kids in every classroom, some of these "reforms" might make more sense. But that isn't what we are seeing. Advanced math and gifted programs are being eliminated with the same semi-literate, incompetent teacher still responsible for 30 kids. Only now the few bright kids and the few kids who work very hard to excel will have no opportunity to do so. They will sit at the back of the class and scroll on their phones while the barely competent teacher struggles to crawl through a remedial lesson that the dumbest 10 kids in class cannot master. But we'll have equity when all of them are handed the same worthless diploma after 12 years.
> The real problem in high school is motivating average to below-average students who want to be anywhere but in class.
And that is the real problem for parents looking for an "accelerated" track at school.
All they really want is a program that will challenge their kids and surround them with an equally motivated peer group that has a goal of getting into a selective university.
That is what drives private school enrollment, selecting public schools in areas with high property tax revenues, and accelerated tracks within public schools with lower socio-economic status.
> All they really want is a program that will challenge their kids and surround them with an equally motivated peer group that has a goal of getting into a selective university.
You have part of that right. What most parents want is a magic piece of paper that says "Good for one admission to Prestigious University." The achievement of their child and whether it brings down other students is irrelevant to them. The credential is everything.
We see this with AP (Advanced Placement) programs. Parents will sue the district to get their child put into the AP class (who almost always also has an ADHD exemption for extra time on all tests due to "anxiety")--who is completely unequipped for the class and then doesn't succeed in the class and scores a 1 on the AP exam afterward. This is practically a tautology because if the parents were actually engaged in their child's education, the child would already be in the AP class by credential.
This, of course, brings down the children who do belong in the AP class. But the parents don't care because now their child is punching above their weight in terms of credential.
This is the standard "Something ceases to be a good metric once it becomes known to be a metric."
Here is the full context. Our current media environment includes a lot of cherry-picking to provoke outrage. Better to judge from a more complete text:
Learning Mathematics: for All
Introduction
Students learn best when they are actively engaged in questioning, struggling, problem solving, reasoning, communicating, making connections, and explaining. The research is overwhelmingly clear that powerful mathematics classrooms thrive when students feel a sense of agency (a willingness to engage in the discipline, based in a belief in progress through engagement) and an understanding that the intellectual authority in mathematics rests in mathematical reasoning itself (in other words, that mathematics makes sense) (Boaler, 2019 a, b; Boaler, Cordero & Dieckmann, 2019; Anderson, Boaler & Dieckmann, 2018; Schoenfeld, 2014). These factors support students as they develop their own identities as powerful mathematics learners and users. Further, active-learning experiences enable students to engage in a full range of mathematical activities—exploring, noticing, questioning, solving, justifying, explaining, representing and analyzing—making clear that mathematics represents far more than calculating.
Research is also clear that all students are capable of becoming powerful mathematics learners and users (Boaler, 2019a, c). This notion runs counter to many students’ ideas about school mathematics. Most adults can recall times when they received messages during their school or college years that they were not cut out for mathematics-based fields. The race-, class-, and gender-based differences in those who pursue more advanced mathematics make it clear that messages students receive about who belongs in mathematics are biased along racial, socioeconomic status, language, and gender lines, a fact that has led to considerable inequities in mathematics.
In 2015, Sarah-Jane Leslie, Andrei Cimpian, and colleagues interviewed university professors in different subject areas to gauge student perceptions of educational “gifts”—the concept that people need a special ability to be successful in a particular field. The results were staggering; the more prevalent the idea, in any academic field, the fewer women and people of color participating in that field. This outcome held across all thirty subjects in the study. More mathematics professors believed that students needed a gift than any other professor of STEAM content. The study highlights the subtle ways that students are dissuaded from continuing in mathematics and underscores the important role mathematics teachers play in communicating messages that mathematics success is only achievable for select students. This pervasive belief more often influences women and people of color to conclude they will not find success in classes or studies that rely on knowledge of mathematics.
Negative messages, either explicit (“I think you’d be happier if you didn’t take that hard mathematics class”) or implicit (“I’m just not a math person”), both imply that only some people can succeed. Perceptions can also be personal (“Math just doesn’t seem to be your strength”) or general (“This test isn’t showing me that these students have what it takes in math.” My other class aced this test.”). And they can also be linked to labels (“low kids,” “bubble kids,” “slow kids”) that lead to a differentiated and unjust mathematics education for students.
A fundamental aim of this framework is to respond issues of inequity in mathematics learning; equity influences all aspects of this document. Some overarching principles that guide work towards equity in mathematics include the following:
⦁ Access to an engaging and humanizing education—a socio-cultural, human endeavor—is a universal right, central among civil rights.
⦁ All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015).
⦁ The belief that “I treat everyone the same” is insufficient: Active efforts in mathematics teaching are required in order to counter the cultural forces that have led to and continue to perpetuate current inequities (Langer-Osuna, 2011).
⦁ Student engagement must be a design goal of mathematics curriculum design, co-equal with content goals.
⦁ Mathematics pathways must open mathematics to all students, eliminating option-limiting tracking.
⦁ Students’ cultural backgrounds, experiences, and language are resources for learning mathematics (González, Moll, & Amanti, 2006; Turner & Celedón-Pattichis, 2011; Moschkovich, 2013).
⦁ All students, regardless of background, language of origin, differences, or foundational knowledge are capable and deserving of depth of understanding and engagement in rich mathematics tasks.
> All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015).
could be replaced with:
> All students deserve powerful mathematics.
and still make the same pedagogical point, that all students should be taught with the expectation they will succeed at learning mathematical concepts.
Putting the emphasis on believing people do not differ in natural ability, is obviously false and therefor detracts from the overall goal.
The point they are making is that the belief that one must be "gifted" to learn math is a damaging and destructive belief: it leads students who could otherwise be successful to not try and not learn, and this affects most to students who are marginalized in other ways.
The rejection of "ideas of natural gifts" is rejecting that success in math is tied to natural gifts (as opposed to say hard work or careful study.)
It is not rejecting the idea that some students will have an easier or harder time learning!
If we were to abandon a policy after the first objection we can raise over some disagreement we have with the policy, then all policies would be rejected. This is not an intelligent way to evaluate it.
It's not whether gifted students exist - it's the extent they should be catered to. Society benefits more when you raise the average than when you foster the top 0.1%. Even Soviet mathematicians who moved to and taught in the US after the fall of the Soviet Union said something to the effect of "sucks for talented folks, but better for society" when they compared it to Soviet education.
With that context, whether they exist or not is really a rounding error. Most gifted students will do well eventually whether we have special programs for them or not. And it's challenging to show strong net positives for society if you did have those programs. As in, actual data that supports having them, vs mere anecdotes.
Not catering to the gifted is a dangerous game for society as an disproportionate amount of progress is made by gifted which are properly nurtured.
> Gifted will do well regardless whether we have special programs for them or not.
This is very much not true. Only gifted with rich or caring parents will do well. Others might suffer a lot. Being in a program for gifted for me made the difference between being thrown out of a school because I never did the homework and being invited and having my flights paid to a conference in Japan where I gave a presentation while in the last grade of school.
> Being in a program for gifted for me made the difference between being thrown out of a school because I never did the homework and being invited and having my flights paid to a conference in Japan where I gave a presentation while in the last grade of school.
The state can provide this without believing you have a naturally innate ability in mathematics. They can still construct programs for people who are performing better in math.
The discussion is about innate talent, not whether we treat people who do well in math differently.
The discussion of innate vs learned talent is a distraction. When new students arrive in a teacher's classroom on the first day of classes the teacher must accept each student at face value. It doesn't matter how they reached their present level of math ability. It only matters where their new teacher takes them from that point on. Leaving the advanced students to fend for themselves is a dereliction of their duties as an educator.
I have direct experience with this problem. I was labeled as a gifted student in elementary school but offered no opportunity to take enriched or accelerated classes. Out of boredom I quit trying and my grades collapsed. I dropped out of high school at age 16. Now I am an undergraduate student in mathematics, age 37, trying to put the pieces of my life back together. I have been forced to make friends with classmates half my age. All but 2 of my friends from elementary school have moved on.
> The state can provide this without believing you have a naturally innate ability in mathematics.
True. However the state can not provide this "regardless whether we have special programs for them or not". You migh not have intended to but
>>> Gifted will do well regardless whether we have special programs for them or not.
is a claim which has policy implications orthogonal to any discussion about the innateness of talent. It is in this component that i disagree with you. I couldn't care less whether people being good at something is being caused by something innate or taught as far as that is not relevant for pushing the being good at further.
Have there been any studies separating "natural talents and gifts" from a privileged upbringing where education was prioritized from the moment of birth? I don't think enough attention is paid to what happens during the critical period of early child development (0-3 years of age).
If it turns out that "natural talents and gifts" are really just due to a better critical period for the child, then the liberals here are really shooting themselves in the foot with this argument.
Are you aware of Twin studies that also control for pregnancy?
Meaning two quiet identical children are born and raised by mothers of different social class?
Possibly but they're not perfect either. If the hypothesis is that discrimination post-birth is tied to innate characteristics, then presumably both twins will face similar discrimination and this will correlated their environment, even though they've never met and were raised by different people.
That said, twin studies do provide substantial evidence that giftedness is highly heritable and probably significantly genetic.
I mean either you are aware of such studies or you aren't. What do you mean with you are possibly aware of such studies?
I am well aware of how twin studies but any claim about the genetic component kinda falls apart for me based on them as the children were in the same pregnant mother at the same time.
I meant they've possibly been done, just that I don't know either way.
> any claim about the genetic component kinda falls apart for me based on them as the children were in the same pregnant mother at the same time.
They do somewhat control for pregnancy by comparing identical vs fraternal twins, and finding a higher correlation in intelligence between the former, as well as a far more similar brain structure in regions known to be related to intelligence (frontal cortex).
Anyway, it's impossible to get rid of all confounds via twin studies. But this doesn't mean that twin studies provide zero evidence. It just means the evidence can't be fully conclusive. It just strongly points in the direction of genetics.
While Twin studies can explain like 50% of the observed variance with heritability of IQ, genome wide association studies using Polygenic scores are only able to predict 5% of the variance from the genome itself when n=O(10^6). The truth is most likely somewhere between those two.
Predicting IQ from genetic information alone should remove all the of compounding factors (except those introduced by IQ measurement itself) but can only serve as a lower bound unless predictor overfitted the study data.
Where did you get 50%? Wikipedia says "Early twin studies [show] 57% and 73%, with the most recent studies [showing] 80%."[1]
> The truth is most likely somewhere between those two.
> but can only serve as a lower bound unless predictor overfitted the study data.
Yes, but the truth is likely somewhere much closer to the upper bound (twin studies) than the lower bound (genome studies).
Genome studies are only good for lower bounds. They're a new methodology that isn't good with complex traits. For example, they can only explain 20-30% of the variability in hair color even though we know that hair color is almost 100% genetic due to the observation that identical twins always have the same hair color. Intelligence is much more complex than hair color, so it's no surprise that this method has failed to explain more than 5%. Further, these studies often rely on weak proxies like educational attainment because of the difficulty of IQ testing at scale, and the studies that do try to IQ test at scale suffer from small sample sizes which impacts the ability to find results due to being underpowered.
Also, IQ becomes more correlated with parents as you age, suggesting childhood environment plays a less important role.
In addition, the jump in correlation from fraternal to identical suggests more role for genetics than merely a few %.
Perhaps not, but the purpose of the public school system is not to turn out a couple of geniuses every year. It’s to maintain a well-educated populace. Most resources should be going towards making the average student better. I can’t tell you how many people have told me that I must be very smart for going into computer science, and that they could never do it because they’re just not math/stem people. That negative self-talk certainly has a huge amount to do with whether they’re capable of going into STEM.
To me, it seems these changes are oriented towards helping everyone succeed in STEM, even those who don’t think they’re math people. Which, again, is less to do with their actual abilities and much more to do with their mental dialogue.
This makes a ton of sense. Basically any skill or habit you might want to develop can be easily thwarted if you’re struggling mentally with discipline, focus, self-image, etc. In my opinion, the “mental game” is crucial to nearly everything and doesn’t get enough focus. (Think of how in sports, a bad mental game can easily loose you the physical game even if you’re an incredible athlete.)
I doubt these educational changes would ever have much of an impact on bonafide geniuses, because they are operating in an entirely different context.
> Perhaps not, but the purpose of the public school system is not to turn out a couple of geniuses every year. It’s to maintain a well-educated populace.
Even if it can't be both, a few geniuses could very well outweigh the benefits of a slightly more well-educated populace. Einstein arguably gave us GPS and space flight. I'm not sure any amount of average-person level mathematics could make some advances like that.
Yes ? Ramanujan's introduction to math was when he stumbled upon a book by Hardy. If that book hadn't showed up in his life, his gift might never have been discovered
The wider discussion is about how to structure public math education. If we're not going to connect it to the details of said education, then it is a moot point to discuss.
Of all the things to evaluate the policy on, this is a real poor proxy as whether there are gifted people or not usually has little bearing on the overall health of math education across a very highly populated state.
I never disagreed with whether they exist or not. I just don't see why this is such a sore point for people. I can virtually guarantee that the existing education system in CA didn't really benefit the gifted folks either. If I were setting up the program for a whole state, whether it will be good for a Jacobi/Euler/Gauss is totally irrelevant. We're not going to make people who show up once every 50-100 years be a major factor in educating millions of people.
This is a straw man. My original point (root level comment) was that the authors of this plan do not believe there are any innate differences in math ability, full stop. A reply to my comment supported my position by showing that obviously there are examples of people who are extreme outliers in terms of math ability. This proves the point that there are differences in innate math ability.
Your reply is that we shouldn't design a state-wide math program for extreme outliers. But no one said we should! We only said that we should design a math program that acknowledges a diversity in innate math ability (as proven by the existence of extreme outliers, and the many, many less extreme outliers).
The wealthy are going to send their kids to private schools, and homeschool coops.
People might talk a lot of woke on twitter, but nobody is going to willingly handicap their own children in the name of some nebulous greater good.
It's exactly the same as liberal NIMBYs. Preach tolerance and acceptance until somebody who doesn't look, talk, and think exactly like you, wants to live in your neighborhood and alter your precious neighborhood aesthetic.
You think private schools aren’t teaching woke ideologye? You are wrong. The future rules are are getting schooled in proper wokeness so they can run hr department and navigate proper corporate norms.
The difference is that private schools teach math/reading/writing at high levels. Otherwise parents would not put up with the political stuff that also gets packaged in.
Exactly. Every time it's the same thing. They come up with stupid rules for the sake of equity, just to realize they made things worse cause everyone who could afford it moved to another town, or private school, etc. My town one day decided to cancel so many school traditions like the halloween parade for the sake of equity. Then they didn't allow in-person learning during the entire year. Then they did many other stupid things like that. Everyone I know who could afford it moved. They just have no clue what they are doing, they are just trying to look good, but in practice are doing more harm than good.
The irony is that this same logic is twisted beyond recognition to justify these “alternative” curricula: just because these math classes don’t look like yours (algebra is “white” math, I guess) doesn’t mean they aren’t just as valuable.
What is worrying though is that universities preach the same wokeism and seem to apply it to their recruitment. Whatever value they add or not, the top universities form a very effective cartel and gatekeeper to the most prestigious and/or lucrative careers. This can efficiently cancel the benefits of taking your kids out of public schools.
I think long term, wokeism will kill those universities. A not insignificant part of the population isn’t impressed with slogans like “decolonise maths”, and the perception that they are handing over diplomas in the name of social justice, rather than skills, inflates away the value of those diploma. My own modest contribution to their demise is to give equal consideration to CVs of candidates from less prestigious universities. And I have seen enough idiots graduating from top universities to think that this credentials system was broken even before wokeism.
At the end of the day what makes a top university is its reputation, its brand. Any other measurable metric (SAT scores, quality of research, size of endowment fund, etc) is a consequence of that. There is no better way to hurt their brand than what they are doing now. And by "kill" I don't mean "close", I mean kill their reputation.
And I think it's a good thing. I much prefer the German system which, as I understand it, doesn't rely on a small number of elite universities, and where you have to evaluate the candidate rather than its credentials.
I took an informal poll of foreign students at the US university I went to. Regardless of major, they all took Algebra in 6th grade. This was quite some time ago.
I was interested as I was ready for Algebra in 6th grade, but was unable to take it until 8th grade. If you don't get into Algebra before high school, there is no chance of taking a reasonable calculus class before college, which puts you way behind the curve if you get into an engineering program.
I went to a state university that had a strong engineering program. The students that I knew who were having difficulty and eventually dropped all had first seen calculus at the university. These were smart, talented people, but they were not given the chance to succeed.
Public education in the US sits at a difficult nexus of political will, cultural ideology, public opinion, and educational 'theory'. It rarely goes well, because everyone vehemently believes they know the 'purpose' of public education.
And so, we get posts like this: public ed as a 'pipeline to STEM careers'.
The reductionist view of public education-as-career-training is one of those contentious topics. I myself find it absurd. An ed system driven by vocations and political/ideological nation-state goals has been so genuinely harmful to people it's hard to know where to begin.
> Public education in the US sits at a difficult nexus of political will, cultural ideology, public opinion, and educational 'theory'.
And that doesn't even list the people with remunerative interests, teachers unions, textbook publishers the testing/test-prep industry, the for-profit outrage machine., etc.
My armchair take of the situation is that the administrators of K-12 education are too focused on the potential value of kids actually using these math frameworks instead of how they sort of rewire how to logically reason about things.
I'm having trouble finding the right words to describe myself, but I vividly remember how many moments of epiphany I had when I took Calculus and Linear Algebra. I don't directly use either of them at all in my day job, but I feel like they were foundational in developing reasoning skills.
This is, I believe, the fundamental problem. Administrators, and, to some degree, math teachers themselves, don’t like or understand math. They constantly talk about what it’s “for”, as if math class serves a purpose similar to car repair shop class. They seem to understand that you can have an English class treating poetry, or a history class, without needing to justify them with practical applications. I think most of this bunch have no concept of studying math for its own sake, and the idea that you might do so for enjoyment would probably seem incomprehensibly bizarre. During my brief stints teaching math in high schools, my attitude was that I was guiding students along the path to becoming people—members of their civilization.
At some point they'll cut out all the foundational mathematics needed for hard science and engineering. Then only foreign students will be qualified for bachelor's programs. Complex numbers will be first at the chopping block.
There's a map showing percent of schools with 8th grade algebra by district. There's another map farther down shown percent of 8th graders who took it by school district. (The maps can be slow to load).
Overall 80% of students have access to algebra I in 8th grade. Breaking that down by type of school it is 88% in magnet schools, 81% in traditional schools, 60% in charter schools.
It is 86% in suburban schools, 75% in urban schools, 75% in rural schools, and 76% in town schools.
That is access. Enrollment is another matter. 24% of 8th graders actually take it. By gender that is 25% of the females and 22% of the males. By race 34% of the Asians, 24% of the Whites, 23% of the two-or-more race students, 14% of Pacific Islanders, 13% of the Hispanics, 13% of the Natives, and 12% of the Blacks.
I think many of the commenters posting that this step will necessarily lower mathematical achievement are unlikely to have taught math to small children (or at least to a large number of them). The change has tradeoffs, but I think we'll likely end up a more numerate state for the change.
It's important to remember that children are not tiny adults. At an early enough developmental stage, a child may be physically unable to learn algebra. The number of such children is much higher in middle school than freshman year of high school. Note that developing later doesn't mean you're not very smart nor that you have aptitude. A student I had many years with this issue now has his PhD in mathematics.
By delaying algebra, you give a large chunk of students time to move forward developmentally so they can engage in the material. The current system ill suits them for a few reasons. One is that curriculum (somewhat necessarily) assumes high mastery of pre-requisite concepts, when it turns out this isn't the case students tend to not understand the material and get very frustrated. That frustration and anger often causes lasting damage that may never be undone.
My mother was a math educator during the years when Algebra first moved into middle school fought heavily against it. According to her the push came mainly from professors of Mathematics (with no educational training) who wanted better trained students. I think this has worked out for some of the top schools. If you're smart and a little precocious algebra in 8th grade is good, but I think net we lose out on a lot of talent.
Under the Common Core as specifically implemented in California, children who are ready for Algebra in middle school may take it, and children who benefit from a delay may opt for delay.
A central pillar of Equitable Math is that this disparity sustains White Supremacy in math, and thus all children should always be in the same class, up until the last year of high school.¹
This is the central point of contention, and not whether some children benefit from a delay of Algebra past middle school, and nor whether all children ought to learn Calculus.
> A central pillar of Equitable Math is that this disparity sustains White Supremacy in math, and thus all children should always be in the same class, up until the last year of high school.
Could you cite a more direct source for this? It's in direct contradiction with the materials the site you linked provided me [0]. If you go to page 17 "September Who are my students?" they do not discourage different classes or tracks existing, they discourage placing students in different tracks without input from the student or their parents. As a former educator that seems sensible to me. Sometimes a student isn't quite ready to enter the more advanced mathematical track but could be made so with if provided some guidance on how to self study. I've seen many high school freshman apply themselves more readily when I laid out the long term consequences of different math tracks.
Everybody hates it to different degrees, but grinding Algebra I & II problem sets hard for a few years was a dramatic advantage in college calc & physics. Some classmates were still struggling with special right triangles where it was completely intuitive to me at that point.
The applications of math that everyone clamors for in high school eduction became far more apparent once I got to college.
While very much different in terms of the number and financial size of directly-applicable job prospects, American pre-collegiate math and musical training share a very important thing in common -- there is a step-function proficiency gain to be had from trained parents living in the same house as the child.
Yes, primary and secondary curriculum matters, but in the same way a church musician parent will politely nod approval at the elementary school musical show knowing full well that real musical development for children usually happens in the home with parental involvement -- a mechanical engineer or e.g. actuary parent living in a small or under-schooled town will also politely acknowledge the child's remedial math homework assignments, yet know enough to be able to seek out quality instruction for the child, even if it means utilizing community college or other nearby resources.
Given the same family and upbringing, something tells me that Scott would still excel in math as a HS student in today's California, were he there and that age now.
Why do educators always fail to effectively communicate with a non-captive audience?
The author needs to re-work this so that the first paragraph tells me everything that I need to know, and the rest of the essay/letter/memo can elaborate on things that I should or might want to know.
If they aren't willing to do that then they are going to continue to remain out of touch to most people.
I don't understand why there is so much effort put onto cramming math into high school. I took calculus in high school and then repeated it in college. There is plenty of time in college (especially if some of the less useful elective requirements were taken away) to catch up on your math requirements, so whether you are ready for Algebra in 8th grade or not should have no barring on whether you are able to pursue a STEM major in college, let alone be successful in your career.
I think we lane people out of STEM way too early, which is what I believe some of these curriculum changes are trying to redress.
Math is one of the pure foundations for liberal arts so getting it done early is better. We should be focusing on getting high schools teaching it so well that colleges don't feel the need to rerun it not saying you can do it later. High school grads should be able to pass the AP Calc and AP Stats exams to the level colleges feel they can totally ditch the 100 level courses for those subjects.
If you don't have students repeating basic math (and chemistry) in college, they can do deeper on an elective track involving a STEM because because their STEM credit hours aren't spent getting a rerun of Calc I.
Yes, because mastering Calc wasn’t what I was capable of in high school.
It would have been a huge shame if I was slightly worse at math, didn’t even take Calc and thus wasn’t accepted into a CS program upon graduation.
So much stress and consternation is spent on saving one calculus corse in college (and it’s used as gate keeping to get into an elite college stem program).
The US unfortunately has lost its direction. Everything is so political, including education. They don't try to improve equity, just to look good from the outside.
I'm as red blooded American as they come but I believe we are on a downward slide with little to no hope for recovery. Outside sources have so successfully utilized technology to drive a wedge between two sides the country that I don't see how it can ever be brought back together. The wedge pushes further every single day it seems like.
It's almost as if this is all going according to some plan and we are crafting the next generation of "working class" Americans with intent.
It's a lot easier to become oppressed when you don't possess these most fundamental tools for understanding the nature of that reality. Maybe that's what we need to keep this shit show moving along for another generation.
To my reading the posted article makes only passing reference to the California recommendations, and gives positive emphasis to a number of focussed initiatives or programs.
I assume because it's easier to extrapolate an "alarming trend" from a curated subset of small initiatives and programs than it is from a bunch of recommendations for improving maths education. Seems to have worked, there's more comments here about a single program than the recommendations themselves.
The biggest problem I see with this article is not the obvious intended political sizzle but an assumption early in the article along the lines of the only purpose of public education is the eventual production of STEM college graduates and everyone else can and should go directly to hell and absolutely no resources or encouragement should be provided for any other educational outcome. It makes you wonder how the public school system is not in a continuous state of civil rights lawsuits over the equal protection clause.
“every child must master algebra, preferably by eighth grade, for algebra is the gateway to the college-prep curriculum, which in turn is the path to higher education.” But that's not the life path for perhaps 90%+ of the population. I don't think we can justify burning tax dollars to exclusively and solely support a tiny minority of kids at the expense of nearly all the other kids.
I would not be bothered by mindless STEM boosterism if it were not for pages like this:
It offends me as a EE type person that the top job title for graduating engineers is software dev, where they'd have been better off with a CS degree, or no degree. Meanwhile I'm told by the other side that we have a terrifying massive shortage of engineering grads, despite that clearly not being the case and it being VERY difficult for new kids to get a job in the field. I'm led to believe by "shortage" they actually mean a "shortage of people willing to work 80 hrs/wk for minimum wage and no bennies" or "shortage of experts with decades years of masterful experience willing to accept apprentice level pay scales"
We simply seem to have too many STEM grads for our economy to support. I don't see any realistic reason for future improvement in that situation. Meanwhile public education policy, meant to serve EVERYONE, is telling most of the kids to go to hell. And those are the kids running the rest of the economy and we're relying on them to grow the economy enough to support the 5% of STEM workers whom are the only important people to educate according to "public" education, which is now really only college prep STEM education and F every other kid.
This path cannot possibly end well.
The best way to handle algebra education as applied to the entire student body, is to acknowledge that for 95% of the population, learning how to change the oil in a car or how to identify when someone is using statistics as propaganda, would be a more valuable life skill. Yes I acknowledge STEM is and will remain important for a tiny subset of both kids and future jobs, but...
> But that's not the life path for perhaps 90%+ of the population. I don't think we can justify burning tax dollars to exclusively and solely support a tiny minority of kids at the expense of nearly all the other kids.
Sure, but that's not what they're objecting to. They're objecting specifically to cutting off avenues to those advanced paths, and in ways that harm underprivileged students more. Quote:
> the bottom line is that rather than trying to elevate under-served students, such “reforms” reduce access and options for all students. In particular, the CMF encourages schools to stop offering Algebra I in middle school, while placing obstacles (such as doubling-up, compressed courses, or outside-of-school private courses) in the way of those who want to take advanced math in higher grades. When similar reforms were implemented in San Francisco, they resulted in an “inequitable patchwork scheme” of workarounds that affluent students could access but that their less privileged counterparts could not.
> We simply seem to have too many STEM grads for our economy to support.
No, we don't. STEM grads makes way more money than most other grads, hence there is no glut of them if it were then STEM grads salaries would fall until they make the same as business grads or even literature grads or other fields where there is a glut of people to do the jobs. Engineers go to software since it pays more than their main field, but their main field still pays way more than a typical grad job.
Why are they integrating and layering the religion of social justice and gender ideology onto math? I would be just as alarmed if Christianity or any other religion or dogma or ideology was embedded with math and how it's taught. This document is pushing evangelical-level indoctrination and is certainly less about teaching math than our current system. At the very least it's orthogonal to learning how to add and subtract.
"Teach Toward Social Justice"
"Teachers can take a justice-oriented perspective at any grade level, K–12"
"teachers need to work consciously to counter racialized or gendered ideas"
"Students are able to take what they noticed and named – in this case, how gender played out in the problem"
"Learning is not just a matter of gaining new knowledge—it is also about a change in identity. As teachers introduce mathematics to students, they are helping them shape their identity as people"
>"Learning is not just a matter of gaining new knowledge—it is also about a change in identity. As teachers introduce mathematics to students, they are helping them shape their identity as people"
I don't get it... what about this is so scary to you? Is it the word 'identity'? Because as a standalone statement, I actually think this is a healthy approach to education.
I get that "social justice" and apparently now "justice" are loaded terms in our modern political discourse, but countering racialized ideas and framing education as a part of our identity as people/citizens... I mean, that hardly seems like objectionable to me.
Culture and identity have always been present in math. Starting words problems with "Bob makes $50,000 a year" or "Alice needs 10 onions from the store" helps frame men as workers and women as home-makers. Taken by themselves they're fairly innocuous. Combined with every other social signal children hear every day, they can perpetuate out of date and harmful stereotypes.
"Starting words problems with "Bob makes $50,000 a year" or "Alice needs 10 onions from the store" helps frame men as workers and women as home-makers."
This is one of those statements where part of your brain goes "well, I guess there might be atom-sized kernel of truth to this". But in reality, I doubt anyone is tangibly affected by the congruent use of Male/Female names in word problems that map to traditional Male/Female gender roles. I believe this is a result of a hypersensitive social-justice filter which results in an astonishingly large false-positive rate.
Quite frankly, I just fail to see how gendered language in word problems not only 1) reflects math being inherently cultured and identity-based, 2) harmfully reinforces malicious stereotypes (people can just as easily write Alice makes $50,000 a year, Bob needs 10 onions from the store), and 3) are odious enough to justify a substantial, near fundamental, change in math education.
Lord jesus what a strawman. You have any good evidence that math word problems in elementary ed are systematically biased in this way - and the plural of anecdote is not data, so don't waste our time.
They were working overtime not to allow any of this into the curriculum even when I was in elementary school back in the 80's. Usually it was worthy of an eyeroll from all of us: "John and his friends Jamal, Carlos and Akira are on the bus..."
Yet being able to map real world problems into math problems and solve them is an essential skill. In my class in Europe story driven problems were read aloud.
I guess it's just I think that the pursuit of knowledge shall have nothing to do with any one 'identity' or 'ideology'. It is orthogonal to that, or it just doesn't work and then why teach something that does not work.
I think your interpretation of the word identity in this case is wrapped up in political discourse. Encouraging students to identify as an educated people for whom pursuing knowledge is both important and desirable seems like a net positive goal. Understanding that there are cultural and psychological hurdles that can stand in the way of this when people don't see themselves as math people is part of solving the problem.
I can also agree that it is very difficult to do and learn Calculus when your understanding of Algebra is limited or out of practice as someone who went back to get an undergraduate degree after almost 2 decades of not doing math. Is Calculus actually essential for critical thinking ? No and it does serve as a stand-in for this in many STEM degrees and if someone is lacking in understanding of the basic principles of algebra then it is going to feel like torture to solve calculus problems even if you can understand the concepts.
It’s this metastasized concept of identity that scares me. The traditional response to “I’m not a math person” was to reassure students that, hey, you don’t have to be a math person to learn and get value from math. (This is where culturally responsive education was understood to come in - it helps students realize that math is useful for them no matter who they are and where they come from.)
Now the conventional wisdom seems to be that you do have to be a math person, and teachers had better work hard on cultivating a “math person” identity, because otherwise there’s no way their students can learn math. I think this is a false belief that will make education quite a bit worse if acted on. I would never have learned to write well if teachers told me I needed to identify as a writer first!
I don't think the person you're replying to is saying that the pursuit of knowledge has anything to do with any one identity, they're simply saying that the pursuit of knowledge inherently changes the way we conceive of ourselves, which seems pretty universal.
So surely you're on board with fighting any racism or sexism in the classroom, right? Specifically that any "racialized or gendered ideas" have no place in a math class, and that "teachers need to work consciously to counter" them if they do come up? In other words, exactly what the the original report said to do...
It's meaningless pablum taking away class time from actually teaching mathematics to promote political ideology.
What does it mean that learning mathematics changes your "identity"? You are still the same person you were before, but now you know some math and can do and can understand some things you couldn't before.
>
As a visual indicator, we italicize the terms used to identify white supremacy characteristics as defined by Jones and Okun (2001). They are as follows:
• Perfectionism
• Sense of Urgency
• Defensiveness
• Quantity Over Quality
• Worship of the Written Word • Paternalism
• Either/Or Thinking
• Power Hoarding
• Fear of Open Conflict
• Individualism
• Only One Right Way
• Progress is Bigger, More
• Objectivity
• Right to Comfort
If you look at the source of these terms they aren't as inflammatory and include a number of antidotes to how these can manifest in organizations - https://www.thc.texas.gov/public/upload/preserve/
museums/files/White_Supremacy_Culture.pdf
I would personally say that this is sort of a manifestation of hierarchicalism which can be predominantly connected to white people in the United States but really transcends the racial dynamics and instead focus on accepting and promoting social structures that make those who have power over others feel like their power is justified and that those who question it or don't accept it are wrong.
For instance here is how they define paternalism:
decision-making is clear to those with power and unclear to those without it
• those with power think they are capable of making decisions for and in the interests of those without power
• those with power often don't think it is important or necessary to understand
the viewpoint or experience of those for whom they are making decisions
• those without power understand they do not have it and understand who does
• those without power do not really know how decisions get made and who makes what decisions, and yet they are completely familiar with the impact of those decisions on them
Here they present some antidotes:
make sure that everyone knows and understands who makes what
decisions in the organization;
make sure everyone knows and understands their level of responsibility and authority in the organization; include people who are affected by decisions in the decision-making
Is this directly related math, not necessarily and should it be tied exclusively to white supremacy culture, I would argue no but it can certainly be the case that the corporate culture of our hierarchical society has a lot of these problems. I just wouldn't lump it under a racial lens because I feel like that misses the mark.
I also agree that the short list included is sort of a disservice/reductionist as it doesn't explain how these are problems or how they can be overcame whereas the source document at least provides context and explanation.
> I would personally say that this is sort of a manifestation of hierarchicalism which can be predominantly connected to white people in the United States
I find this an absurd and utterly indefensible statement.
You cannot find any examples of "hierarchicalism" outside of white people in the United States? Seriously?
You put the weasel word "predominantly" in there, but I think most human civilizations through out history have featured these kinds of dynamics.
Come on, this is such a willfully ignorant reading of this text. Check the FAQs, interviews with the authors, or simply the rest of this very document. Sure, it could have been written better in order to not trigger and scare people, but the meaning is pretty trivial if you read it without being primed, especially in the context of all the other words around it.
First, they are listing words cited in an academic study, to set up the language used for the rest of the document. Claiming they are saying "objectivity in math is white surpremacy" is like saying "critical race theory is taught in high school".
Second, the overall message is that "roteness" is a bad way to teach. Sure, they link it to how "my way or the high way" authoritarianism is linked to how the downtrodden have been treated in America and make a parallel between that and rote memorization style of teaching. How is that unreasonable in a document talking about the experience of black people in highschool?
> Come on, this is such a willfully ignorant reading of this text.
Maybe you are the willfully ignorant one here?
I understand roteness is bad. But please explain:
1. How roteness is linked to white supremacy.
2. How objectivity is linked to roteness. They are not related at all. You can be objective and creative. E.g., Ramanujan.
3. Asians are well known for rote learning. I am Indian. I know how rote it can get and I agree it is bad. But stop conflating that with objectivity.
4. > Claiming they are saying "objectivity in math is white surpremacy" is like saying "critical race theory is taught in high school".
Did you read the document? That is exactly what they say and imply in multiple places. Roteness is different from objectivity. You are defending a straw man. Words have meanings. If they mean't roteness, use that.
Do not pick one word out of context, especially when the (obtuse and academic) definition of that word is important for the understanding of the text (as explained by the sibling comment). Again, this document does not at any place say anything that can reasonably be interpreted as "objectivity in math is white supremacy".
Here is an example of what this document is talking about (in unnecessarily obtuse language, but the authors probably did not expect readers primed to read it with a negative interpretation): A *very* common wasted opportunity is the following. A student is given a problem to solve. They solve it by method A. The teacher wanted method B and grades the student poorly because method A is objectively different from method B. An opportunity to learn was wasted because the teacher used something they would consider "objective" or call "expecting perfectionism". "Objective" is a weasel word in this context that just absolves the instructor from considering the particular situation of the student and teaching to them.
It seems you would be incredulous that this is my reading of the document. On the other hand, until six months ago, I was absolutely incredulous that anyone would read anything different in this document. It sounded crazy to me that people would read it the way you do. But I guess I have to concede that the document was written poorly and it triggers a lot of people.
For context, if you care, to me the reading I presented seems obvious because I have read other pedagogical research literature that gives the same advice without discussing race. So the (tangential) mention along the lines of "ideologies of supremacy use the same language as inflexible teachers incapable of adjusting to the needs of their students" seemed like a curiosity, not like something over which to grab pitchforks.
It's not that identity defines math from a correctness point-of-view, it's that math can become a part of and enrich your identity. Countered with the perspective that math is a chore or 'useless', this instead posits that you can make education a part of your identity.
And what is academic passion if not a combination of identity, desire, and education? I think it's a nice framing, one that engage students more than 'you will learn math because we say you must learn math.' One that ensures teachers are aware of their role in shaping the identity of students.
If you trace back the history of math, it's not uncommon to make math a passion, a part of your identity (think of the Pythagoreans, for a historical example). When you become a mathematician, is math not then a part of your identity? That's what I interpret from:
>As teachers introduce mathematics to students, they are helping them shape their identity as people.
So the idea is to have teachers be aware of the impact of math and education on people's identity. It is a consciousness thing.
Everything we do is part of our "identity". That doesn't really bring anything new to the conversation.
Math deal with concepts, forms and quantities and their relationships and their abstractions, not personal identity. There are more proper academic fields for this (such as language and art), although it doesn't remove the fact that DIE is a discredited field and should be done away with anyway.
Why is making math a part of your "identity" preferable to seeing math as a tool you can apply to accomplish your goals, or something you can do for fun?
The vast majority of high school math students will not become mathematicians.
>So the idea is to have teachers be aware of the impact of math and education on people's identity. It is a consciousness thing.
It's not a question of preferability (one view is not mutually exclusive of the other), and I didn't claim high schoolers should all become mathematicians (where did that come from?). In either case, I fail to see how training instructors to be aware of their teachings' effect on identity can be harmful. I'm not particularly scared nor threatened by the idea of it, and the idea that there's no connection between education and identity doesn't make sense to me.
Why is it a bad thing? It's a personal choice, so let them be. That used to be the popular identity. It's only because now STEM is associated with money and power that people are butthurt.
When I searched for the definition of indoctrination I get this:
"The process of teaching a person or group to accept a set of beliefs uncritically."
What I see in your examples does sound like teaching a set of beliefs, but there is nothing that I see where it is done uncritically. For example, there are stereotypes in our society about what genders and races are good at STEM and which are not. If a word problem reverses those stereotypes, do you think that encourages or discourages the reader to think critically about their own biases?
I would suggest this not be done in math class, lest you go down this path [1]:
"Before the Great Proletarian Cultural Revolution there were 48 students in class one in Qunli Elementary: During the six years of obliteration by revisionism on the educational system, 13 students dropped out. All 13 students were from the worker or poor peasant families. Compute how many students from the worker or poor peasant families dropped out and how many were retained due to the obliteration by revisionism?"
> "The process of teaching a person or group to accept a set of beliefs uncritically."
> there is nothing that I see where it is done uncritically.
I mean, how is it going for those criticizing CRT-ification of education? It doesn't seem like its advocates are actually interested in criticism of the dogma.
> how is it going for those criticizing CRT-ification of education?
From what I can tell in our local area it seems to be going about as well as they hoped.
First they rail against about some weird graduate-level field most people have never heard of that isn't related to anything taught in our elementary schools. Then they interpret the eyerolls from the other parents and patient administrators attempting to keep the conversation focused on relevant topics as attacks on their freedom and they get to play the martyr.
It's hard to say whether the teaching is uncritical without actually being present in the classroom. If to "counter racialized or gendered ideas" is implemented by insisting anything other than 50/50 representation across all occupations is evidence of discrimination and that any suggestion to the contrary is sexism, then yeah that's definitely uncritical. I'm not sure how prevalent those kind of simplistic teachings are, but they do exist.
> but there is nothing that I see where it is done uncritically
And you yet you immediately say:
> there are stereotypes in our society about what genders and races are good at STEM and which are not
Your post is a good example for why it is very difficult to make any critique of the DIE "teachings" in a public / classroom setting. DIE only makes sense if front of a mob.
If you disagree, you are against the DIE (diversity, inclusion and equity) virtuous teachings. Unlike other theoretical fields, to understand is to agree with DIE and its apparent virtues.
That's also about not calling attention to its cult-like characteristics. DIE is a little too on the nose for a group that demands conformity and unpersons those that dissent.
There's a critical distinction to your complaint - the linked doc addresses how one teaches math, not the math one teaches. It's not unreasonable to suggest that curricula authors maybe choose not to make all the $PREDOMINATELY_MALE_OCCUPATION characters in their word problems males etc. etc. Using the 'defaults' in construction of narrative problems and lessons is itself a choice, so why not take the one that tends toward equity, equality, and inclusion?
The subsequent exercise suggesting a close reading of the gender roles in said word problems ... doesn't seem to have a lot to do with learning math, I'll grant.
They could handle that by providing a simple solution: Randomize names.
This isn't about avoiding stereotypes though. This is about pushing a belief system and an agenda. A dangerously misguided one at that. Equity is about equal outcomes. Which you can only get through force because people have different preferences, different abilities and make different choices. Choices necessarily lead to different outcomes.
Equality and equality of opportunity, yes, please. Equity, absolutely not.
You can argue the best technique to accomplish the goal, but `social justice` just means that you believe every person deserves an equal opportunity to thrive. That is not a religion, that is the American dream.
Social Justice is simply the idea that we actually need to work towards providing the American Dream to everyone. That shouldn't be controversial.
a. That isn't "simply" what Social Justice is. Not by a long shot, not in practice.
b. It sounds like you are arguing for Equality based on merit, allowing each person a chance to thrive. I agree, that would be great. But what is actually happening is different: equity, where in practice most implementations stunt growth and paper over achievement gaps.
c. I want a equal opportunity to thrive. But "social justice" is also extra-judicial justice. It sounds nice, but isn't waht I want.
>`social justice` just means that you believe every person deserves an equal opportunity to thrive. That is not a religion, that is the American dream
No. That is the surface level definition which insidiously hides the conflation between opportunity and equity that underlies the politicized restructuring of our institutions. Equality of outcome is only possible by hindering high achievers.
In part it is the purely faith based belief in the tenet of tabula rasa that makes this movement resemble a religion. There is no quality science which suggests that all people are equally capable given identical environments; in fact such an assertion would completely deny the realities of genetics and culture.
From my perspective, the term "Social Justice" is more of a rhetorical tool than a cohesive ideology. Yes, I know I can google "define social justice" but if you look at the results there is no agreed definition. You will instead see dozens of different think-thanks, universities, and NGOs 'define' social justice use very flowery feel-good language that is almost impossible to disagree with. And yet, the details about how to achieve such positive things are what people would actually disagree with.
Your statement "That shouldn't be controversial" encapsulates this perfectly.
> ...the National Society of Black Engineers (NSBE), which set in 2015 a goal to double the number of African American students taking calculus by 2025.
Which would be a step towards improving educational opportunities for everyone.
The new California standards are arguably going in the opposite direction.
I find this to be a trend, that many pushes for "equity" in education seeks to achieve this by reducing the success of high achieving groups to match that of the low achieving groups, instead of figuring out how to get the low achieving groups to the level of the high achievers.
We've been playing games with education in the US for a while now. This identity stuff is the newest, but you can go back every decade or so for some 60 years and find some fad that was really big at the time.
Now look at the test scores over time. Up? Down? Flat? Break it out into race, socioeconomic class, religion, however you want. Check again. Up? Down? Flat?
We pretty well know how to teach things like math. It's a lot of drills. It's a lot of homework. It's word problems. It's all the things that both teachers and students hate, because it's annoying to do and annoying to check. But math is more or less like learning a language. You have to immerse yourself in it and do a lot of practice.
And, in the end, you have to accept that some people are just not going to cut it. They will top out at about 8th grade basic Algebra. And that's okay! Cramming some kid who can't cut Calculus into a Calculus class just because you need to count a certain number of different colored noses is daft and unproductive. School should educate people to their maximum ability, and everybody's maximum ability is different.
It doesn't matter if it makes you feel better to attribute somebody's poor performance to some vaporous societal ill. That's not helping. That's trying to shoehorn your preferred reality into actual reality. The hell of it is that it completely shafts those who really did earn their way into the top ranks. There is always the spectre that they're there because some administrator needed enough $IDENTITY to make their Powerpoint presentation look good.
FWIW, a few years ago I read an article with short discussions of "100 Good Ideas in Education." The article was written by a well-qualified educational journalist. Again, FWIW, I'd estimate that at least 10% of the discussions essentially concluded with: But we can't do this because it would increase disparities.
> hell of it is that it completely shafts those who really did earn their way into the top ranks
But ... again do we know this based on data, or it's patting our own back for finding a logical consequence that seems to nuke the whole affirmative action system?
> math
I think the real problem is that we should not teach math, nor most of the abstract arts. We should teach learning, acquiring skills, and ... picking and sticking to strategies.
And then it makes sense to help them learn whatever they want.
Because social justice and gender ideology are universal, important concepts that apply in mathematics and science as well?
I fail to see how it is "clearly" indoctrination as it is taught critically (as is well evidenced in the link) unless you are some sort of "anti-SJW warrior" against any sort of modernization of our curriculum.
> Because social justice and gender ideology are universal, important concepts that apply in mathematics and science as well?
Then you are doing mathematics and science wrong.
The whole point of those disciplines is to eliminate human bias in favor of objectivity in order to accurately understand the world, or to make correct conclusions or predictions based on axioms, observations, and data.
If you introduce biases like gender ideology into those subjects, you are defeating the purpose.
The whole point is to remove biases -- did you even read any of the source material?
Right now there is tremendous societal pressure and varying outcomes depending on _who_ you are (race/gender/other socioeconomic factors) and the entire point is to remove that from the equation to lead to better outcomes overall.
To do that, you need to be aware of those factors and control for them. That is very basic science.
You seem to be advocating putting ones head in the sand and saying that those factors don't matter and should be removed.
> "teachers need to work consciously to counter racialized or gendered ideas"
Is this wrong? Is it indoctrination?
> "Are there word problems that challenge gender stereotypes?"
I don't see the issue here. Should all word problems reflect 1920s America and ask about the challenges with the dust bowl harvest and how many bathroom stalls you need to serve a particular crowd, accounting for segregation? No that's silly. We want word problems to reflect the world we live in today, which means sometimes having physician Alice and nurse Bob.
> "Learning is not just a matter of gaining new knowledge—it is also about a change in identity. As teachers introduce mathematics to students, they are helping them shape their identity as people"
There's lots of discussion about how women especially, but also lots of minorities, seem to leave STEM after primary school. To me, this seems to be reminding educators that they should make an effort to keep these classes engaging and inviting for people who leave, in case the cause has historically been something in how we do math education.
> "Students are able to take what they noticed and named – in this case, how gender played out in the problem"
This is talking about teaching critical analysis (in the "how do I analyze a text" sense, not the "race theory" sense), where the teacher uses a math word problem as one of a number of places to do this. There's nothing wrong with this, in fact its actually really good to read critically in all contexts!
Given the underlying ideological current, I don't expect a letter like this to move very many people. You want to entice them with the future possibility of career opportunities? Not very rousing or compelling in this environment. And indeed this career-centric view of education and learning I claim is what produced the conditions for further decadence in the first place. Classical education places truth and understanding at the top of its list. Modern education shifts to "know how", manipulation, and production. Truth takes a back seat. Once that happens, myth and gnosis re-enter the picture, and that's what we've been witnessing for some time. What we're seeing now is just the latest development.
So in a way, the letter is arguing for a regression to an earlier status quo which itself contributed to the very conditions we're seeing now. Societies don't really rewind like that.
Math at school started losing me some time around multiplying and dividing fractions, and I haven't seen anything uses of math in any of my jobs. I, for one, am glad that schools are finally removing the unnecessary pressure to Take More Math Than Necessary. Maybe they can now focus on more practical subjects like CS or shop, or even just reduce the number of hours students spend cooped up in those kid prisons with tyrannical teachers.
I learned the conversion factors approach in chemistry but it's really just a basic math process of starting with something in one unit set, having a target unit and applying conversions until you get to your goal. It's probably the single most powerful technique I took from public school.
If you think we can teach CS at any sort of non-trivial level without an understanding of math beyond grade 7/8 you don't really know what computer science is. Even if you mean "programming", kids want to primarily build games which involves tonnes of HS math. Even shop courses often involve questions like "find the center of an object".
I think units are brilliant, and use them extensively in math and programming. However I often get sloppy and conflate conversion factors (60 minutes per hour) and quantities (44100 samples per second). This usually isn't a problem, as long as I use different units for sampling rates (samples per second) and waveform frequencies (cycles per second) instead of calling them both hertz. But things get messy when you're converting between multiple different sampling rates, polyphase resamplers ("64 subsamples per sample" etc.), overlap-add convolution (which has like 3 different quantities all labeled "samples"), and such.
> I haven't seen anything uses of math in any of my jobs
Math didn't "click" with me until well after college, when I eventually caught up on a lot of calculus, discrete math, probability and stats, to the point where I ended up doing math most of the day as a data scientist.
Before I learned math I used to feel like you did, and would argue that math wasn't necessary to be a good programmer.
Funny thing is that only once I learned a lot of math did I realize how insanely applicable it was to a wide, wide range of problems I was working on. Because I had to learn it late in life I learned math more enthusiastically than most of my data science peers and so find that even in that domain people don't realize how often they can use math to solve problems better and faster.
I wish I had had better teachers in HS that were able to make me realize just how important math is to so many interesting and fun problems.
It's sort of shocking to me, looking back at HS, how many math teachers didn't have a good answer to "when are we going to use stuff?". I wish I could take some of my friends making high six figure salaries with a penchant for late night partying to explain to HS students exactly how math is useful because it lets you get a job where nobody cares how much weed you smoke, how late you sleep, and pay your more than many doctors all because you can do some basic calculus tricks. Plus you get to work on really fun problems.
> Maybe they can now focus on more practical subjects like CS or shop, or even just reduce the number of hours students spend cooped up in those kid prisons with tyrannical teachers.
Well that is a strong argument for separate tracks. Advanced math courses for those intending to study STEM in university, CS and shop for those intending to get a job directly out of high school.
(And yes, CS as "programming" and not an academic discipline is something you could learn well enough to get a job right out of high school, or maybe with a couple more years technical education, at most.)
they are screaming Fire!!..no one is listening. The only solution is to split public schools into two streams STEM and liberal arts studies(I don’t know what it’s called).+ more vocational/trade schools. We can’t cater to the lowest common denominator in math.
This makes no sense - stem and liberal arts aren’t mutually exclusive things you can just separate. In fact math itself is generally thought to be part of the “liberal arts”, along with logic, which could be said to be the precursor to computer science.
We don't need more trade schools though. Over here on hacker news many of us have day jobs eliminating those jobs. While we won't succeed (and trades are still a better job than many artistic degrees) there are a lot of kids going into them. Most trades are also taught on the job. Want to be a carpenter - you can start tomorrow morning at 7am in any large city. From there you can branch out if you want.
The majority of programming jobs, DevOps jobs, etc. could be learned in a trade school. Only a minority of programming jobs really require a four year CS degree.
Also, is that true that most trades can be learned on the job without prior training? I thought you needed a decent amount of training to be a plumber, electrician, etc.
liberal arts may include parts of stem, but stem and humanities are pretty much disjoint, which is probably a better way to have this discussion. I think there's an argument for not forcing people who are interested/capable in stem to suffer through perfunctory humanities courses (and vice versa).
is something lost when someone learns about propositional logic and set theory without learning about the vienna circle and logical positivism? yes. does it matter very much practically? probably not, and stem people who are interested in that kind of thing can probably pick it up on their own.
> not forcing people who are interested/capable in stem to suffer through perfunctory humanities courses
I hated my humanities courses all through middle and high school and college. I took as many advanced math/science courses as my high school had. I graduated from a well-regarded technical university.
My humanities courses have probably had more positive impact on my career earnings than my tech courses. I feel like I should find my old English teachers and apologize to them.
They're not disjoint. At an advanced level, subjects like linguistics and psychology heavily cross displines with mathematics, logic, and neuroscience at least.
Students probably shouldn't be falling hard on one side or the other any earlier than they already do lest even more of them believe they are completely unrelated.
If you read the whole "Modern usage" section rather than just the first line, you will see that mathematics is listed prominently there (and also logic, CS, physics, etc...).
I had two different Physics teachers/classes in high school.
One was almost entirely conceptual and provided a fantastic base with which to reason about the world. Everything was explained completely without math and then a little bit of math (usually no higher than basic algebra) was used to describe what we had just developed to fulfill basic requirements of the curriculum. People had wonderful conversations about how things worked and understanding was developed from observation and intuition.
The other was almost completely the opposite direction and calculus based. I often found errors in the application of math and reasoning about the subject. There was a moment where the teacher couldn't be convinced that something he said was wrong because of the math he was looking at. Years later, in a college Physics course, a similar core concept was covered and I was internally vindicated.
Einstein/Feynman were known to be highly conceptual and the math was often worked out after a thought experiment. A famous quote by Einstein, "Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater."
It all depends on how it is taught.
All of that being said, Mathematics is an excellent tool to sharpen ones ability to reason.
Effectively most high and even middle schools are already split in the sense that students can take more or less math based on interest and skill. At my daughters' middle school there were three tracks: low, medium and high. My kids were in medium and high level and the curriculum was different for each. By the time they were in 11 or 12 grade they had maxxed out math (including calculus) and could have taken college math (but chose not to).
I think the complaint from the left is that minorities don't end up in the higher math offerings because they are either not offered at certain schools or, for whatever reason, unattractive to those students. That's the problem that needs to be fixed. Whether any public school can do that is questionable.
Not exactly, it sounds to me that the idea is to push out Algebra I and offer the data-sciency, more "equitable" option earlier. Nerdy kids would still go through the Algebra-Calc-AP track but on a slightly different schedule.
In my local school district there is a dedicated Arts School (Art, Music, Dance, etc.) for grades 6-12 and a dedicated STEM school for grades 6-12. Kids within the district have to apply to get accepted to either of them otherwise they just go to the traditional middle/high schools.
A neighboring district has a similar school geared towards Healthcare.
These schools obviously teach all necessary subjects but have more advanced classes geared towards those subjects than your average school would have.
What they are fundamentally doing is breaking up the classic U.S. staged path where you learn algebra for a year, then geometry for a year, then back to algebra / pre-calc for a year, then maybe take statistics or calculus as an elective, etc. Instead, all branches of math will be taught in an integrated approach focused around applied problems.
This is how a lot of European math courses are taught. In fact, I think HN would appreciate the shift from focusing on pure numbers and classic formulas to more applied uses of math, including algorithms, probability, data collected and analyzed in charts, etc. Students also forget a lot of algebra when they do a year of geometry by itself, then have to go back to algebra / pre-calc.
It also does mean that in the transition, it will be harder for students to "test out" of the classic algebra I/II, geometry, pre-calc sequence, because it will just be "year X integrated math." But the framework does not forbid gifted and talented programs or anything like that. There will just be a few awkward years while the curriculum shifts.
Now, there are some on the left who advocated for the elimination of gifted and talented programs altogether, for equity reasons. They did not get what they wanted in the new California framework. That hasn't stopped a lot of people from looking at what California is doing and imagining it is actually some kind of Harrison Bergeron dystopia, when that is absolutely not the case.
[1] https://www.cde.ca.gov/ci/ma/cf/
[2] https://www.cde.ca.gov/ci/ma/cf/mathfwfaqs.asp