"One of the ideas underpinning the California Math Framework is the notion that math needs to be “detracked”—instead of allowing some students to take Algebra I in 8th grade, it would require all students to enroll in the same math curriculum until the 9th grade."
This is the single most utterly moronic proposal I have ever seen in all the annals of education reform.
I went to a small, fairly traditional K-8 private school. No fancy technology or trend-chasing pedagogy, but relentlessly back-to-basics, serious education. Our entire reading education was phonics for instance, and this was in the early-mid 2000s when I am under the impression that the war on phonics had made significant gains. Each grade had two math tracks, with the upper track one year ahead of the lower track. From Kindergarten on, I and a couple other kids were tracked *two* levels ahead, meaning I took the math classes of the upper track in the grade above. What this meant was that I took Algebra 1 in 7th grade. In 8th grade I arrived at school 40 minutes early to take Geometry one-on-one with one of the 8th grade math teachers (the other few 2-track-up kids had dropped down to regular upper-track by then).
This was an immense benefit to me, and meant I was able to take Calc BC in 11th grade, allowing room for one more STEM elective in 12th grade. The idea of having to stick 2 grade levels below what I did is just horrifying. Not only in terms of boredom and lack of challenge, but also the impact on the other kids. I was already hyperactive enough in the classroom as is. Me in 8th grade in a pre-algebra class would have been a total shitshow.
I know this is a bit long-winded and ranty, but there are few things that make me seethe with incandescent rage as much as this new trend of forcing everyone to operate at the very lowest level for the sake of "equity". Let's be real about what "equity" is: kneecapping the best and brightest so that the worst and least competent can feel better about themselves and useless bureaucrats can pat themselves on the back. It's this absolutely poisonous idea that because some people are incapable of achieving something, nobody at all should allowed to achieve it for themselves. Literal kindergarten playground mentality. Frankly, even in the counterfactual world where detracking *did* reduce racial gaps, I wouldn't care.
Keep the law of Jante over in Scandinavia please. I don't want it here.
And ed school PhD programs frankly seem more like a massive grift the more I read about them. Is there any evidence to the contrary? If so, I'd love to see it. My impression is basically they're a giant factory of breaking things that ain't broke. The war on phonics being the most obvious example.
I don't understand how people can see the purpose of education as anything other than ensuring each student goes as fast and as far as they personally are capable of going. If students who are coming from disadvantaged backgrounds need more assistance to do that, I'm all for giving it to them. But denying _any_ student access to material that they are ready to learn, in the name of "equity" or anything else, is just anathema.
My county's public school system had an advanced math program available that bussed high-achieving students together for an after-school program that got us through all of Algebra, Geometry, and Algebra II, by the end of 8th grade. So we entered high school with Trigonometry and Analytic Geometry, then Calc I in sophomore and Calc II in junior. (I took a _lot_ of AP tests, entered college as a second-semester sophomore, and then did two majors and a minor.)
I'm a big fan of independent study for that reason.
To some extent, equity is really about resource constraints. Your teachers only have so much time in the day. So from their perspective, it's not really "denial" so much as "is teacher time better spent on keeping your lowest performers from failing or helping your highest performers achieve more?"
One case for the former from a teacher's perspective: If a kid fails, you get the joy of dealing with a difficult student for an extra year.
Anyhoo, I think you can argue either position in good faith. But in the cases where kids are just skipping three grades of math or whatever, just have the kids teach themselves and avoid the trade off altogether.
I took Calc AB in 9th grade. I took a lot of AP courses. I had good teachers but after a certain point, I didn't really need them. I just read the books myself and figured it out. And the school wasn't exactly super eager to set up a Calc BC or AP European History or whatever course just for me and a handful of other overachievers, but it also cost them almost nothing to just let us have a free study period and then administer a test.
Obviously not for everyone. But AFAIK, the CME doesn't prohibit self study, so maybe we'll see more of that.
"is teacher time better spent on keeping your lowest performers from failing or helping your highest performers achieve more?"
There are a lot of moral issues around that question, it's hard to say what the ethical answer is. Certainly "No Child Left Behind" assumed the former. But from a utilitarian point of view of what is going to be most important for the scientific, economic and technological progress of society, the answer is clearly the latter.
When I started Kindergarten I was already reading at a second grade level and got extra tutoring after school. In first grade I was put in a 1st/2nd combined classroom and did both classes work and then skipped second grade. I was small, late developing boy and I think this was a big mistake. If I had perhaps stayed with the same set of kids it might have been okay, but we moved every year or two so I was always the new kid, smallest in my class and nerdy. I read lots of books. In high school, we didn't move so I made a group of friends via drama, band and D&D that made it a good experience.
I ended up graduating right after turning 17 and going to a top university and having a good career in tech, so from some sense of "success" it was a success. I went from being very poor to wealthy in one generation. But it was a difficult time from 7 to 14. I didn't need to be put up a grade and would have been better off just teaching myself. I was constantly reading when I was young and was taking community college classes from the time I was 13, so I didn't need to be advanced in grade. I was going to learn no matter what.
Yeah I was reading YA novels by the time I was in third grade. I was lucky that my county's public school system, at the time, had a very extensively multi-tracked system, with four different levels for each subject (remedial, standard, honors, and "gifted and talented"), in _every school_, and then a significant number of opportunities for really advanced students to pick a subject where they'd advance even one level higher, in an after school program. They'd bus all the students for that to one school a couple times a week, and then the maybe 2-3 students who were in the program, at a given school, would work in kind of an independent-study manner sitting in a small study room off the G&T class, so they'd have some access to the G&T teacher from time to time if they needed it.
We really should fund education to the point that heavily individualized study programs can work for every student. If we need higher taxes, including hitting the middle class, so be it. Collectively we'd be way better off with the Scandinavian deal, where private goods (like larger houses or restaurant meals) are a little less available, and in exchange you get better education, healthcare, and general social insurance against a string of bad luck throwing you out of the middle class entirely. One of my favorite stats is that Norway produces more startups per capita per annum than the US. It turns out that when _failing_ in business doesn't mean seeing you family starve in the streets, it's a lot easier to take a flyer on an interesting idea: https://www.inc.com/magazine/20110201/in-norway-start-ups-say-ja-to-socialism.html
This is an interesting thought but I do want to say that there are benefits to keeping people in classes and working on things in groups. I was someone who was in the two above track for math for all of my schooling years starting from 6th Grade. (Note this was actually fairly common in my district/school and we were easily able to get multiple full classes of tracked ahead students.) Throughout my experience some of my best learning came from interacting with my peers where we either discussed a problem or tried to explain our thought process. This helps bring peers who might be slightly confused up to speed while also helping the peer who teaches in refine his understanding (Protege effect/Feynman Technique). With the hyper individualized style of learning I fear you lose this incredibly important network effect.
Additionally, I would argue that most kids are not self motivated and that the self motivated are often the anomaly rather than the standard. I hated math for a decent chunk of High School because compared to my peers in the higher level classes I kind of sucked at it. Yet, social pressure around performance made me study and succeed. If I didn’t have the outside forces I’m positive that I would have performed below my potential. And I wager most kids are like that, they do things due to outside pressure and not intrinsic motivation. For a lot of people intrinsic motivation comes in much later in life.
To the best of my knowledge, the advanced programs I'm talking about did ensure that at each individual school, there would be two or more top students who would be in that super-advanced track. Which meant as long as you got along well with the other folks at your school who were tracked with you, it was a collaborative, peer-motivated system. You'd go have actual class after school 1-2 days a week, and the other days you'd be doing "small group" exercises with your maybe 1-3 peers, with your school's math teacher available as a resource if the group got stuck.
And I did, in fact, get along well with my fellow math nerd. (There were just two of us, at my particular school.) He was one of my best friends through middle and high school. We kinda drifted apart after that, but I actually ran into him at a reunion a few years back and we had a great time catching up. (He was doing research on experimental advanced PV materials. I work for Tesla Energy.)
“society simply refuses to address equity later on in the lives of your citizenry“ in reality taxes and transfers greatly reduce inequality in the U.S. and public spending targets low income people. CMS, Social Security and welfare comprise 60% of federal spending (and of course much state and local spending also targets low income residents). We directly spend trillions of dollars a year addressing equity later on in the lives of people.
Massive, unrelenting inequality can and in fact does go on indefinitely. Egyptian society was astonishingly stable while some people at the top had pyramids built in their honor and others had to do the building. Greg Clark recently has been doing research showing inherited social status to be robust even in the face of Maoism.
Let's not misconstrue Clark's research here -- the important takeaway from the pre-to-post Mao inequality study was that any serious attempt to completely treat inequality as derived from social status was a fool's game. Even when the playing field was completely leveled, the families (genes) which succeeded under prior conditions also tended to succeed after a generation of brutal impoverishment in the name of equity.
I’m a California high school physics teacher and this just freaks me out. My district recently moved physics from 3rd to 2nd year and I already have a majority of students incapable of handling the simplified math we are allowed to include according to the Next Gen Science Standards. Math skills took the biggest hit in the pandemic, and I’ve been holding my breath for a return to normalcy that I do not see happening. I agree that this new framework is mostly just giving up on math.
Physics was 2nd year in my high school, 1st year in my daughter's. I hadn't even thought about the fact that there's a certain level of math required for it, unlike basic HS biology. Huh.
Saying these policies were mere mistakes and had nothing to do with "woke" is misleading. They weren't mistakes, they were conclusions that are natural outcomes of embracing the "woke" world view
Meh. It depends what you mean by "woke". If you mean the very broad recognition of how past choices haunt the present, as described in Matt Yglesias' old piece on "the Great Awokening", then that by itself doesn't lead to choosing to ignore evidence. A lot of good has come from people finally reckoning with the fact that _some_ people's grandparents got gifted a few hundred thousand dollars in housing wealth, and others' didn't, because we had government programs that were, explicitly or implicitly, tied to race. That subsidy still gives descendants a leg up today. If you claim to support "equality of opportunity", you're going to have to consider this stuff.
This doesn't necessarily mean you have to use explicitly racial approaches to deal with the issue. Redlining and zoning and so on were generally race-neutral, and we could use similarly race-neutral programs to make things more economically-equitable, and that would probably, as a happy side-effect, make things more racially-equitable as well.
But in any case, if just thinking that history matters makes me woke, I guess I'm woke. If we played a game of Monopoly, and for the first thirty turns, I randomly sent you to jail now and then, and made you pay twice as much for properties, and then on the thirtieth turn I said, "OK, from now on we're playing by equal rules. Just ignore the fact that I already own half the board!" ... you would not think that constituted making the game fair!
OTOH, if "woke" means _specifically_ the rather weird definition of anti-racism pushed by Ibram X. Kendi ( https://www.slowboring.com/p/racism-kendi ), or the actively-counter-productive stuff pushed by Tema Okun ( https://www.slowboring.com/p/tema-okun ), then sure, the way people like that structure their worldview leads to this kind of pedagogy.
But I think most of the time, "woke" just serves to lump together "vaguely lefty stuff I don't like". It conceals more than it reveals.
The Monopoly example is interesting because, of course, Monopoly was not designed to be a fun game. It was designed to be a teaching game illustrating that owning land in San Francisco was unfair and we needed a land value tax.
If this was the purpose of monopoly, it completely failed in my circles. What it actually taught us kids is the drive to attempt to own everything instead of enough, and made blatant greed a desirable trait.
Oh I'm all for increasing oportunity for people regardless of background. The "woke" aspect I'm referring to is the instinct to flatten everything if it produces unequal outcomes. Like, why in the world would you delay math education for people when learning it earlier clearly works for some?
The woke approach imo is the instinct that unequal outcomes are inherently due to discrimination, and the desire to fix disparities by merely advancing people even though they haven't shown sufficient skill, or stunting the advancement of those who have.
If there are unequal outcomes due to past discrimination, the only valid approach is to help people catch up by actually helping them learn so that they could be equals with more privilaged people. This is hard of course, so "woke" activists just try to either pretend the people who are not doing as well are actually doing well (affirmative action) or stunt the development of the people better off (this system in California). Either way the appearance of equality they can produce are illusory imo.
People have been talking about that "cut down the tall poppies" issue since _way_ before the word "woke" was in use in its modern form. I remember reading "Harrison Bergeron" for an English class in grade school.
I think you're correct to say that _assuming_ differences in outcome have to be the result of unfair treatment is a problem -- that's precisely what Matt Yglesias criticizes in Ibram Kendi's work. I just think it's a mistake to say that's all "wokeness" is. It's one counter-productive strand, within a larger collection of "woke progressive" ideas, as Noah has explored in a series of posts about different ways to view the "wokeness" phenomenon.
Plenty of manifestations of wokeness explicitly focus on the idea of "leveling up" (i.e. helping those at a disadvantage to rise to the level of others), rather than tearing down. For instance, the classic meme of people trying to see over a fence.
In my view, the functional strain of these ideas is just regular progressivism as it should be. I don't think we'd need a new term, "woke" for them if that's all they were. What I call woke are basically the dysfunctional directions these ideas get taken into, in the modern context
Yeah I mean I think there is an important argument to be had within the lefty / progressive / liberal / Democratic coalition about this stuff. That's a big part of why I subscribe to moderate-left writers like Noah and MattY.
But I think "woke", for better or worse, has a much squishier definition than you're allowing, in terms of how it is getting used across various communities, and in particular, the Right has been _very_ successful at applying it in a broad-brush manner to basically, as I said earlier, "anything vaguely lefty that we don't like". So, Target deciding to sell stuff for Pride month that makes queer people feel like folks at least like them enough to want them as customers is "woke capitalism". As is a more substantive corporate policy for attracting talent from the queer community, e.g. offering domestic partner benefits even when not compelled to by law.
If you just say you're against wokeness, without being very specific about how you're defining it, a lot of people are going to hear, "I agree with Ron DeSantis." Maybe that's not fair, but it is what it is.
When the Spanish Inquisition or Nazis started to systematically murder Jews, they didn't consult a rabbinic council to determine who was a Jew. They knew who the Jews were. You might turn out to be Jewish even if you great-grandparents converted to Christianity a century ago. Golly, what a surprise when they put you on the rack or the cyanide gas starts to flow.
If you want to understand "woke", look at what Florida has been doing. Saying that being a slave wasn't all fun and games is woke. Pointing out that God created gay people too is woke. Immigrants, except for Cubans, are woke. Putting the life of the mother above the life of a fetus is woke. Fighting infectious disease is woke. Teaching that the world is older than 5000-something years old is woke. Industrial policy is woke.
You can learn a lot about a group by the enemies it chooses, real or imaginary. (For those interested in some historical perspective on how this works, check out Norman Cohn's "Europe's Inner Demons". It's about witches, Satan and witchcraft, and it's an excellent piece of scholarly work.)
To be honest I sort of blame the "woke" movement for the recent excesses of DeSantis and tribe. What goes unstated when we talk about the backlash about target, budweiser and various appeals to queer culture is the way symbols that appeal to conservatives have more or less been censored out of much visible culture. The "woke" left is very organized in campaigning against anything that doesn't fall in line with their world view (I don't think I need to provide evidence, we all know what major brands and banks are comfortable advertising and which side of the spectrum feels they can't speak their mind freely in most offices). Tbh the backlash against target and budweiser surprised me, because it felt like every other brand had already been doing stuff like that for a while now, but I guess since they felt an ownership over these lower class brands, they got extra animated in their anger. In any case, the excesses of the woke movement I think made it inevitable that the rabble would eventually organize against it, and the pushback wasn't going to be of a high minded sort because the higher minded critics just kept their mouth shut the whole time.
If you want to understand why we have a word "woke", you should understand why people invented it. They used it as a term for people who had "woken up" to all of the ways that society is unequal, and the many forms of un-earned privilege that exist in the world. It was originally specifically about awareness of the historic mistreatment of Black people over the decades and centuries, but came to be used more broadly. It's not the same as Progressivism (which has some parts that are race-blind), but it's also not the same as saying everything should be leveled down. Some of the dysfunctional stuff evolved out of this specific context, but that's not all there is.
Interesting write up. I quite like the prospect of taking race neutral approaches to address racially divergent outcomes. I think if these methods can lift everybody up, and as a consequence, also massively benefit less fortunate people of comparatively less affluent racial backgrounds, then that would be great.
One: End exclusionary zoning. This is just straight-up taking a "race-neutral" policy that served racist ends, and turning it on its head. Make sure that smaller, naturally-affordable homes are available in "high-resource" neighborhoods, so we have more economically diverse communities, and poorer families can send their kids to schools that benefit from the influence of educated, wealthy parents.
On the numbers, the program that Booker proposed would do more to close the wealth gap between White and Black families than basically any idea that's been seriously proposed. _Functionally_, it provides a realistic form of reparations for the harms of slavery and redlining. Yet it doesn't have to explicitly use race to get the job done.
See these race neutral approach is the right call imo, but not favored by "woke" (I don't like the term, but using it since it was called out in the article) because
1. It's possible that racial gaps won't be closed, or won't be closed quickly enough even if this is done perfectly
2. Like George Orwell described in his critique of a specific type of socialist, they seem to be more animated by a hatred of the privilaged people rather than a love of unprivileged people. The fact that these policies might actually help some poor person from an unsympathetic background (white, male, straight, etc) I think is super unappealing to them
Oh you're _definitely_ correct about (2). It's quite clear that there's a strain of urban progressive for whom the goal of housing policy is not to house people, but to make sure that eeeeevil developers can never make a profit from providing housing. It's nuts. They would much rather see 10 affordable units get built, than 50 affordable units and 50 market rate units.
Meanwhile, it's not like anyone's saying that some random independent restaurant owner shouldn't be able to sell food at a profit. But the politics of housing is cursed.
That's called projection. Most liberals have been fighting for programs that make it possible for developers to provide affordable housing. They've generally been stymied by right wing push back defending property values. Liberal cities are where most of those contingent affordable units have been built, not right wing suburban enclaves. The housing advocates in the cities want to get as many affordable units built as they can. The developers want to build zero and whine like stuck pigs when the deal is for 10%.
Where the hell do you come up with this stuff? Is it drugs? Fox News?
Being a Torontonian, I very strongly agree. I had to move, it got so bad.
It completely boggled my mind that these people are trying to tax the very people who are supposed to bring more supply of housing. If you want more of something, you might wanna subsidize it, but you definitely wouldn't tax it even harder. But the existing taxes on new developments (the insane "growth pays for growth" dogma) mixed with the "affordable" unit requirements all tantamount to a a prohibitive tax on new developments at a time we need them most, and it's the new home buyers who have to pay it in the end.. Developers aren't charities after all. Why a young home buyer, who doesn't find the options affordable and has not benefited from the astronomical housing price growth should also be saddled with subsidizing someone else's "affordable" (if you can even call 10-20% price reduction affordable) housing is beyond me. But I suppose if you already own a home, putting in affordable housing policies that don't cost you a cent but let you pretend you're a fairness advocate, it's pretty appealing. That is, if you're extremely delusional, or just a super callused person.
Looking at the effect of sudden shifts in adulthood is a _terrible_ way to test for the effects of a gradual thumb on the scale over time. There is a TON of evidence of how cumulative advantages have an effect. Also a ton of evidence around how being at perpetual _disadvantage_ in youth alters the brain in ways that makes people more impulsive, short-termist, and pessimistic about their options.
I hate to tell you this, dude, but this has nothing to do with "woke." Instead, it's reflective of educational fads that have been swinging back and forth since the mid-nineteeth century, if not for longer. Wake up and get away from ideology.
Signed, a third generation teacher (now retired) who spent a lot of time talking about trends in education with her mother long before she became a teacher.
"woke" is just a name for a modern configuration of ideas that are animated by an impulse that is age old in humans. We wouldn't call the people who advocated for these fads "woke" back then, but they are the same types of people
"Woke" is a right wing term for everything right wingers don't like. It was briefly a left wing term with a narrow meaning, but now it's just an umbrella term for every right wing discontent. Women voting - woke. Counting the ballots and letting the candidate with the most votes win - woke.
Hmm... there may be some truth to this, but I think on practical grounds it is good for critics of the CMF to avoid this particular word. As soon as it get mentioned, people stop arguing about maths and start arguing about this nebulous culture-war concept that nobody can even quite agree on exactly what it is.
I hate to tell you this, but many people who are just as ideologically progressive as the CMF architects are extensively criticising its shoddy implementation and complete lack of evidence for the methods employed. See the above article.
So claiming that this is somehow an outcome of a progressive or left wing worldview is just flat out wrong.
I think there is a functional strain of progressive, left wing, but sadly they seem to have been losing to the dysfunctional, "woke" coalition. Seems the tide might be turning somewhat now that some of their policies having been implemented have proven to have very poor outcomes, but we'll see how far that gets us.
Yep. Many of us were saying this from the very beginning. It's better than nothing that people like the author have realized their mistakes, but preferably they wouldn't have been in a position to make those mistakes in the first place.
Its really regretful that many on the left doesn't have the courage to state it clearly that woke is a thing(even if hard to define) and is harmful to society in some ways. Bcoz dancing around it and just talking about the issue directly is not really an effective startegy.
Read this and then had my husband read this who has a masters in engineering (aka very good at math. His eyes nearly fell out of his head when he read that you couldn’t take algebra until 9th grade. I mean talk about a way to not encourage kids to live up to their full potential. In fact you’re penalizing them for doing so. Sorry but some people are good at math and they should be rewarded with classes that meet them where they are just like people who are average at math (like me) have classes that meet them where they are. Why we are penalizing kids for being smart in the name of fairness is beyond me!
I’m a SFUSD high schooler and I completely agree with the point of meeting everyone where they are. I’ve heard other students say that having advanced courses leads to bullying/shaming dealt out to people not in the higher level courses. I feel like there’s way too much of a stigma around “achievement”— people put too much stock in these higher level course, like it’s great for you if you’re in one, but it obviously doesn’t mean you’re better than those who aren’t. If we could find a way to prevent that poor treatment and devaluation, then just simply putting everyone in the class that suits their level would be guiltless and beneficial to everyone. The whole problem (not just with math, but with our school system in general) is that no one pauses to consider the individuals, they try to treat everyone the same way whether that’s disregarding the needs of disadvantaged kids or whether it’s forcing kids who are excelling to sit through classes for which they already know the material. Teachers who just go by the textbook and don’t engage with each student’s needs perpetuate this, I’ve experienced it personally. This is not to disregard the care and commitment many teachers show their students, but it definitely happens more frequently than it should.
Former middle school special education teacher who absolutely agrees with you about the heavy emphasis put on higher level courses.
There needs to be a greater awareness amongst those who would wax opinionated about education that readiness, strengths, and weaknesses ARE NOT THE SAME FOR ALL STUDENTS. But those who tend to make those errors (not you, obviously, you see the need for individualized education) frequently haven't been in a classroom other than as a student. A bunch of 'em need to try teaching math to first grade students, or remedial math to discouraged middle school students who are already mad about being placed in Resource Math because they get called stupid.
Education should be individualized, and if there's one damn thing these LLM/Chat GPT models ought to be good for, is writing Individual Education Plans for EVERY student. Not just special ed. Not just talented and gifted. EVERYONE.
Yeah agree with AV: IEPs are a huge regulatory burden and the benefit for the students who have them is more about legal protections than actual instruction. Agree in principle that education needs to be more individualized, but in practice IEPs are a money pit for the school and a time suck for the sped teachers, who become compliance officers rather than specialized teachers.
We do a terrible job at this as a country frankly on both ends. We fail to meet really gifted kids where they are at because it’s not fair to other students or frankly it’s inconvenient for the school to do so. “Achievement” has a different meaning for everyone but we’ve put far too much emphasis on one type of achievement which is ridiculous.
Kids who struggle or are in special education have it equally as bad because we provide them with terrible resources because good resources are generally expensive. Special ed also sadly has become a game of politics. Some districts want to keep kids they really shouldn’t because they get more money from the state if they are enrolled but it’s truly not what’s best for the kid. And that’s sad.
Tailoring education to each kid is nearly impossible but if we at least started with more tailoring to high achieving students I actually think it would help. I think some of the reason there is bullying is because those kids find the higher level courses boring. I think it would actually help the kids “in the middle” a lot because their peers may actually have a class that’s challenging them.
CA is probably the worst state in the union to be poor or working class. Schools are horrific, gangs run rampant in many areas, cost of food and gasoline is exorbitant and housing expenses are ridiculous.
My local school district was majority Latino but the town wasn’t gang infested and most parents worked (I interfaced with some of them through an after-work ESL program). The kids (who I also got to volunteer with) were generally sweet and obedient through about 4th or 5th grade. These kids seemed very teachable to me for reading and basic arithmetic K-4, yet the standardized test scores were abysmal. Practically a crime. Breaks my heart. The teachers aren’t bad people - most merely see their mission as showing up every day and delivering the lesson plan. Getting every kid up to grade level is not the objective, and it shows.
I was denied 8th grade algebra and also denied calculus in high school. No problem because all the kids who already had calculus in HS were retaking it with me freshman year in college. I took an accelerated version that did differential, integral, multivariate and series during Freshman year. So DiffEQs would be a firsr semester sophomore year course. Not really behind at all (unless I wanted to be a math major). Some of the kids who had already had calculus in HS were taking the slower version of the calc program, hoping to get easy A’s (especially the pre-meds). Didn’t always work out as they hoped, because HS calculus is BS in many districts.
I didn’t like the math program when my kids went to grammar school so we paid up for Kumon math. All of them had progressed through Algebra to Geometry by end of 6th grade, doing simple worksheets for 15 minutes a day. Most of school is a joke- more like babysitting and playtime. If you want to teach a subject it doesn’t actually take a lot of time.
I mean I’m glad it worked out for you and HS Calculus certainly isn’t for everyone so I’m not surprised many of them had to retake, but I took diffeq first semester freshman year thanks to the opportunities I had in high school and I definitely think having a stronger math background helped me with the science classes I was taking in college. No, it wouldn’t have been the end of the world if I didn’t have those opportunities, but it’s still bad to deny them to students who are ready for them. Just like it’s bad to push students to take classes they aren’t ready for (this article seems to suggest that prior to banning 8th grade algebra, SF required it for all students, an equally dumb policy. Is it really so hard to let 8th grade algebra be optional?)
Honestly have no recollection- Same thing kids in SF are doing as they aren’t taking algebra.
Didn’t really hurt me at all- caught up quickly at university. Algebra is important for life - bigger issue is the teaching is likely crap rather than whether most kids learn it in junior high or 9th grade. However, kids that are ready for it should get it as soon as possible. I didn’t, but it didn’t matter.
There's an overarching cultural problem here. The folks who go on to be authors and screenwriters and other creative types mostly grew up hating maths, because it was seen as "not creative". (Honestly a fair assessment.) Their hatred for maths then percolates into "maths is hard" or "maths isn't for everyone" tropes which are everywhere in popular culture. And then kids grow up in that culture and absorb the idea that they can't do maths either.
If math is a building, the foundation is arithmetic. There is no way around it. Every student should be pushed as hard as possible to master the foundation. From what I've noticed, the jaded "reformers" have pretty much destroyed the teaching of arithmetic by vastly overcomplicating it.
I have an issue with 8th grade algebra, a HUGE issue.
I don't think every student is ready for algebra in 8th grade. I'm speaking as a former middle school special education teacher, and as someone who graduated from high school in the '70s. Back in that era, the norm was Algebra I by 10th grade (in a junior high/senior high system, 3 years of junior high, 3 years of senior high). The typical sequence was 10th grade Algebra I, 11th grade Geometry, 12th grade Algebra II. I'm also the parent of a student who graduated in the mid '00s and took Algebra I in 9th grade.
In my teaching experience, in a high-poverty exurban (not Californian) k-8 school with, teaching from 2004-2014, most of our students were not ready to start Algebra I in 8th grade. Some of the issues were purely developmental. There are three elements to math ability--calculation (which is best served by memorization), math reasoning, and math fluency (how fast can you run those single-digit calculations?). Too many people, including non-educators, think that calculation and fluency skills make up for lags in math reasoning. Not really, not when it comes to algebra.
I've seen too much pushing down of higher concepts happening especially since the adoption of Common Core methodology. I keep hearing the justifications for introducing higher-level reasoning at younger ages, but you know what gets sacrificed when you do that? Yep, the other two foundational concepts, calculation and fluency. There is only so much time in the school day, and you can only push so much foundational work down to younger grades before you start running foul of developmental limitations (cough cough fractions cough cough really suffer under this notion).
Better to create that firm foundation of calculation and fluency BEFORE getting all hyper about teaching higher-level math reasoning concepts. As it is now, we have lost the necessary parts of kindergarten--learning how to behave in school, how to function socially in school, fine motor activity, and so on--to academics. Students now are expected to arrive in kindergarten ready to read (which means understanding letter-sound correspondences and some phonemic awareness) and learn calculation (which means they already have a grasp of numeracy).
You get into ridiculous situations such as I encountered when substituting in a first grade classroom in early October, where I'm supposed to teach these kids (who barely have a grasp of calculation) the distributive and associative properties of addition.
1st grade. Early October. Can we say tears, agony, and a lot of misery? Plus, talking to the classroom aide, *I* was the one introducing the concept, not the classroom teacher.
The next day I drew on special ed experience and pulled out manipulatives. That helped. But those kids barely understood 2 + 2 = 4.
I'm not aware that anyone is advocating for all 8th graders to be forced to take algebra. It's that it needs to be an option, and tracking is good and necessary. Plenty of kids are perfectly ready for algebra in 8th grade. And some are ready in 7th grade - I was one of them. Thus I did geometry in 8th, algebra II in 9th, precalc in 10th, and calculus BC in 11th. That gave me room for an extra science AP in 12th grade.
Oh, that's a common feature of Common Core ideology and education reform--algebra by 8th grade. And not everyone has reached the developmental level where it's appropriate.
Just because many students are ready doesn't mean no students should get the opportunity. Everyone should proceed at their own pace to topics only when they have mastered the prerequisites.
If administrators and voters would provide sufficient funding, then this could happen. The problem is that there isn't sufficient funding to ensure everyone has appropriate fundamentals.
It’s not (yet) possible to provide individualized instruction for every student, but it’s not hard to provide two classes for 8th graders, on that teaches algebra and one that reinforces arithmetic and prealgebra.
We had it decades ago and it was dead simple. You divide the year's math objectives into 12 2-week segments. At the start of fourth grade, you take a post test on third grade math segments to check for summer learning loss. Any third grade topics not passed at 90%, that student must repeat them. When you finish third grade, you then take a pre-test on all fourth grade topics, with a 90% criteria. When a student masters all of the fourth grade topic, they get to take the pre-test for all of the 5th grade topics.
Every two weeks, you group the students by the lowest level topic they need to master across the grade level. We had about 5 classes, so there were usually a few main groups of students that could fill an entire classroom, and then a classroom with a mix of topics for the various students that were further behind and generally taking something for the second time, and one with the students that were further ahead that were often autodidacts. Sometimes you could end up in the room with students a grade below or above you. I remember missing just one topic on the grade's pretests, the teacher explained to me how it was done in a couple of minutes, I took the post-test and moved on. I was able to complete 3 years of math in one year, with minimal teacher involvement.
At the end of the year, if you haven't mastered the grade you are in, you have to go to summer school to keep working on it, or you don't advance.
It didn't require any additional teachers or funding, except printing out a bunch of worksheets.
The essential characteristic of math classes is that they are lergely sequential - they build upon one another and if your mastery of a lower level concept is problematic, that is likely to cause significant problems later. But some students progress much faster than others and should not be held back by their peer's limitations. My daughter did take calculus in 10th grade, but when she went to the University the next year, she retook in at the University Honors level. She knew enough to handle the calculus requirements of her physics and engineering classes, and the Honors class was much more thorough and demanding - but not so much as the Departmental Honors Math classes that are intended for students planning on being mathematicians.
But bright students who want to cut their college costs in half via the Running Start type approach need to be ready for college level calculus no later than the start 11th grade. Work backwards from there. There is actually very little flexibility. At the minimum, that puts pre-calculus in 10th grade, Algebra 2 in 9th grade, Geometry in 8th grade, and Algebra 1 in 7th grade - unless you are willing to double up on math. I went to Baltimore Polytechnic more than 50 years ago, and there was one year where we did double up on math. In fact, I would recommend doubling up on math (optionally) for at least a year or two to add statistics and an introduction to data analysis.
Fine. Then you support sufficient funding for public schools to provide individualized instruction that will allow this.
Funny how all these math prodigies show up whenever math education gets discussed; but when you take a look at the typical school, they're...not as common as anecdotes have it.
You also don't allow for differences in cognitive development by such lack of flexibility.
It doesn't require individualized instruction. Most cases can be handled by ability / advancement grouping. It would be more efficient to have schools have lab areas where students can go to small partitioned desks to allow them to do remote attendance in specialized classes. Then the school district would be able to offer classes efficiently because they are drawing from all the students in the district. Now, you can't offer a class unless you have a classroom full. This incidentally is the reason for magnet schools, as you can group advanced students together so that you have the necessary numbers to offer the advanced classes.
I would not call my daughter a prodigy, I have met them and she is not. But the high school she went to had an active IB program that was heavily enrolled.
Allowing ability / advancement grouping provides more flexibility for differences in cognitive development than trying to keep everybody in the same class.
We have been talking math. How are the schools dealing with the differences in reading levels? By 5th grade you are going to have students with 12 grade plus reading levels and 3d grade - reading levels. I am not convinced that you can really do literature or history reasonably in a class with such a diversity in reading level.
It is not hard to get kids to such reading levels - no TV or screens, extended bedtimes for reading, and regular library visits. I got my son a kindle so that he could read under the covers when his mother thought he was sleeping.
And your actual classroom experience is--? Or *do* you have experience beyond your own time in the classroom and as a parent?
Lovely theory, but we had such remote classes as you describe at the school where I taught explicitly for 8th grade algebra. Is not very effective in practice. You need to have aides present in the lab who understand and can help students. You also need to have reliable technology that isn't breaking down, suffering from transmission issues, and...you need to have a lab that doesn't need to be scheduled for high-stakes academic assessment and that doesn't need to be accessed by other classes during that period.
ETA: You also need supervision to ensure that the students are studying and not playing video games. Yes, we had to deal with that, and it can be a greater problem with the higher-performing students, especially in the middle school years.
Note: I also taught in a blended learning program at the high school level for a couple of years. Canned curriculum. I was remote, some of the students were remote, the others were going to a computer lab. There were issues.
And there *are* issues with ability grouping. I'm not going to get into all of the details, except that it leads to greater bullying and scorn for the lower-performing levels.
Reading levels in subject matter courses such as literature, general science, and history? Much, much easier to handle and differentiate amongst ability levels than in math. I've done that. I taught one year of US History as part of a humanities team--higher level students--and brought in some of my higher level special ed students so they wouldn't be buried in the lower level humanities course. They were actually better students than a couple of the alleged talented and gifted students in that class, who explicitly asked me to tell them where the answer to a question was in the textbook. My sped kids flinched, because the first thing they learned when they came onto my caseload was that I would help them *find* the answer, but I would not *tell* them the answer.
In fact, one of the best remedial reading programs, REWARDS, uses science and history subject matter as part of their reading remediation at the secondary level. It's much easier to remediate reading when the reading matter is interesting, and if it matches what the students are learning in their subject matter courses....
I dispute your assertion that it is not hard to get kids to such reading levels, especially with the solutions you offer. That does not address students with language processing issues (a much greater problem than most realise), decoding issues, or comprehension issues. Additionally, these solutions you suggest require a certain family income and stability that is often lacking in families with struggling readers.
My teaching experience is as a teaching assistant at senior and graduate students in physics and engineering, - more grading and explanation. I have talked a lot and provided guidance to #1 daughter about her kids, who are also capable. She is in Atlanta where they are pulling the college prep classes - so the grandkids are off to private school. I went to Washington DC schools in the early 60's and we moved out of the city when the school board cancelled the college prep classes. My grandfather was a chemistry teacher in high school who was in trouble with the school board for his high standards - until Sputnik went up, at which point he became the teacher of the year for Kansas.
The fight over equality and excellence has been going on for a long time. To do excellence economically pretty much requires tracking or some form of online study - and my daughter did ~ 50% of her 7th grade online, rather than go to the classes. Online works very well for auto-didacts - and the middle school material that was in her online classes was not particularly demanding - she burned her way through it, and we would return the books and they would send her the next set.
Her high school experience was better - she was in the honors track of a school filled with the children of highly educated south and east Asian parents who were driving their kids hard - rather like my peers in my high school, who were the children of survivors of the Holocaust who were driving their kids hard. The science, engineering, and honors classes at the university was better than high school, it is more where she belonged.
There is a world of difference between k-12 classroom teaching and the college experience you cite, especially at the k-8 grade levels. Excellence does not demand tracking. It simply demands a commitment to staffing and the flexibility to differentiate and innovate.
Additionally, the experiences you describe firmly place you in the upper middle class, which is not the case for the overwhelming majority of students in the US educational system. Alas, this is the situation for most wannabe education reformers. Very few have the experience or knowledge of high-poverty schools as a teacher or as a student. Their solutions then become "drill and kill" pounding of facts with little opportunity to cultivate the love of learning and desire to be creative.
It is a very different world in a high-poverty school (and not exactly like the "culture of poverty" sorts would describe it). When your students are having problems focusing because they can't get a good night's sleep due to not having reliable housing, or they can't use a computer because the family doesn't have the $$$ for paying that month's electricity bill, much less internet or even a basic computer...well, online study is not an option, and a brilliant kid stuck in a high-poverty school is unlikely to receive the opportunity for online study, even at the school itself.
Joyce, you are a joy to read. And yes, I am a very long-term teacher who has taught math and economics in 6 countries (mostly IB). Not the US though. But I really don't think that matters. Children are children. And reading articles like the one above that, though well meaning and not without excellent points, miss completely developmental progress of children. And budget constraints of schools. And the workload of teachers in budget constrainted schools who are constantly trying to implement initiatives. I too also hope that technology will help with more individualised learning programs to cater for student needs. But until children can move from a concrete understanding to abstract understanding then algebra is a mystery to them. I have listened to well meaning pundits raging against teaching for nearly 40 years now but have never heard them include a commitment to paying higher levels of tax to fund schools to provide what they want. Of course separate math classes would be great. So would smaller class sizes as would more specialist teachers rather than generalist teachers. But it needs to be paid for. Which means individuals accepting higher levels of tax.
Perry, thank you! Your feedback--especially from an IB background and from teaching in other countries--is really useful.
One of the things that infuriates me about the whole Common Core fiasco is the absolute lack of understanding and concern about developmental progression and how it differs from student to student. I was part of a group of teachers devising Common Core standards for middle school social studies students, and the degree to which we were passing down prerequisite requirements for middle school to the elementary levels was--worrisome.
The lack of funding support for schools cancels out many reforms. A lot could be done simply by fully funding special education in the US, for one thing (special education has never received the full funding from the Federal Government that it is supposed to receive, for one). Funding for more specialist teachers, smaller class sizes, and so on would make a huge difference. When I was able to rove from class to class, work one-on-one with students, push into classrooms to work with students, I was much more effective as a special education teacher than when I was pressed into filling in for a general education teacher in social studies, for one. Or required to teach classes to a mix of general and special education students every period that I was on campus, without the ability to respond to specific emergencies or problems. It was a darn good thing during that time that we did not have the students with complex emotional problems that I managed earlier in my career.
“ The primary reason girls, for example, diverge from boys in math performance is because society teaches them that math is not for girls.”
That is a stretch. The male sex may have better innate ability to reason mathematically. And that is OK, because the sexes are not identical in traits.
To bely that cause is to turn a blind eye to reality in the name of equity or other nonsense.
And how many women have been president? Are women also not charismatic? If you suppose, for the sake of argument, that society is to blame instead of people’s innate ability, then this is a pretty mean-spirited thing to say.
Two. And this is arguably symptomatic of the cited research. Since whilst girls tend to just as well as (and in many cases better than) boys in secondary level science and mathematics, they are less likely to go into STEM careers at a university level.
And after all, every Fields Medal recipient has a PhD in either Mathematics or Physics, so one would expect to find that they end up overwhelmingly male.
Also, without examining the underlying systems of education in various countries around the world, and the methodologies of research in the area, it could be something as simple as:
1. There has been a broad push worldwide to include girls in STEM education.
2. More resources are directed towards educating girls in this regard.
3. That is reflected in the data.
Visit the math department in any research university, or engineering or computer science. Overwhelmingly dominated by men. Now visit the schools of education or social work, overwhelmingly dominated by women.
The push to achieve equality of outcome results in lowering standards so the equal outcome is achieved. See California's push for equity.
The paper you cited does not support the claim that women entering STEM at a university and career level are a lower rate is primarily due to biological differences between men and women, rather they attribute it to a complex range of factors.
To quote from the paper you cited:
“Experience alters brain structures and functioning, so causal statements about brain differences and success in math and science are circular. A wide range of sociocultural forces contribute to sex differences in mathematics and science achievement and ability—including the effects of family, neighborhood, peer, and school influences; training and experience; and cultural practices. We conclude that early experience, biological factors, educational policy, and cultural context affect the number of women and men who pursue advanced study in science and math and that these effects add and interact in complex ways. There are no single or simple answers to the complex questions about sex differences in science and mathematics.”
Secondly, whilst the “broad push worldwide to include girls in STEM education” sounds plausible, unfortunately it doesn’t explain the data very well. Since as observed in the UNESCO report data, girls exceeding boys in high school mathematics results also occurred in countries where there is not a broad progressive push to include girls in STEM education.
The other reason why this hypothesis does not explain the data is because if it were the case that girls were biologically worse at mathematics yet being progressively pushed to go into STEM, then we would expect to see them being less proficient in secondary school yet going into STEM degrees at increased rates anyway. Yet as shown by the data, what we see is the complete opposite. After grade 4, girls are consistently just as if not more proficient than boys in mathematics scores, yet enter STEM related fields at comparatively lower rates.
If you are suggesting that the “progressive push to include girls in STEM” is causing them to perform well at secondary level mathematics, then this is merely a reinforcement of Armand’s initial argument in the article.
A better argument for your position would be pointing out that perhaps the entrance examinations for colleges and careers are more problem-solving focused and the typical male brain structure is better suited to this. And whilst this would be more plausible, it would still be limited as an explanation of the data since many universities don’t have specific entrance examinations, and this wouldn’t really account for the real discrepancy - which lies in the number of applicants themselves.
In summary, whilst yes there absolutely are biological differences between male and female cerebral and brain structures, these differences are not sufficient to explain the data at hand. Which is why the research you cited does not claim that it does.
The future of math instruction is likely individualized instruction based on student's abilities and their own tablets. The tablet senses the current state of the child's knowledge and generates challenges and interactions that engage them up a ladder of learning tailored to their capacities. Arguing over what age algebra should be introduced is nonsense. Introducing equity into the strategy is deranged.
Even if you took the ideals being expressed at face value, that raising the kids at the bottom is more important than raising the kids at the top, detracking would not accomplish that. I took Algebra in 7th grade. Before I had the opportunity to split onto a higher track, I spent math class either being a distraction or a jackass by making other kids feel dumb. Getting me out of that class was good for learning.
If you really truly cared about raising the bottom, you would give them a dedicated class that had good resources and good teachers. One policy goal you could have would be to ensure that the best teachers weren't disproportionately going to the top level classes for a grade, which they tend to do because they naturally want to teach the most engaged students. Allow students to track but have some sort of incentive, either carrot or stick, to keep resources and attention equal among tracks.
"We have a chance to do exactly that with the release of a new California Math Framework "
"We" (as in Californians) do not have this opportunity. "We" live in a one-party state, and one party states tend to migrate toward the extreme ends. As a result, on this issue and almost every other, the fix is already in and "we" are going to be saddled with an new "inclusive-math" where 2+2 might equal 5 for black kids and where word problems will be something like...
"Sam needs puberty blockers, but their state (Utah) discriminates against them for their non-binary identity. Sam knows that in CA is a sanctuary state and would give them the medical care they need to not commit suicide, so they run away from their parents house in South Lake City on an all-electric bus that averages 50 mph. Salt Lake City is 650 miles from the California border. How long will it take before Sam is safe from transphobia as a ward of the state in CA?"
It would be funnier if it wasn't actually plausible.
It’s also worth noting that California’s Community Colleges have taken a similar approach to math as part of its remediation reform. If a student enters community college without a proficient understanding of algebra (which is many students due to our poor K-12 math outcomes, as the article points out) there are not any pre-transfer or standalone support courses available to them any longer. They are pushed directly into transfer level math and forced to complete in one year.
Many such examples - whole language reading, denial of physiological sex differences, blank slatism in general. If anything, this one is thankfully dying a faster death than many others.
"Math, out of all subjects, seems to hold a special terror for Americans, who often seem to view the subject as a test of innate intelligence rather than a skill that can be acquired and honed through hard work."
you seem to disagree with this view, which is part of the problem. You just aren't going to be able to have at the same time high level of math ability AND no child left behind. The fantasy that everyone can get to a truly competent level of math with reasonable effort (which "hard work" in previous sentence implies, rather than Korean/Chinese kid level of effort) is just that.
The only way to have peak excellence in anything is to nurture with focused intensity the segment of the population with predispositions, and there is a wide range of abilities among kids even at HS math level. If you want equity of course the outcome has to be some kind of lowest common denominator strategy. Until the politics in California change the direction of travel of the educational establishment will continue as is.
“You just aren't going to be able to have at the same time high level of math ability AND no child left behind.” I believe you can have this. Instead of trying to get every student to conform to a single curriculum and level of math, why not provide multiple opportunities? higher level math for those who want/are ready for it and algebra in 9th grade or whatever for those who need that? Maybe this is naive but I personally don’t believe that either of the other solutions really solves more than one of the many problems with the curriculum.
Tell it to the administrators who don't want to spend the money to differentiate to accommodate the wide range of student math ability by middle school. That would require spending more $$ on teachers. Yes, it can be done, but a.) you need more teachers, b.) you need more classroom aides, and c.) fund all levels equally instead of concentrating on the highest performers.
Completely agree. You can do both we are just unwilling to. No child left behind was not designed to hold smart kids back, it was implemented that way because it was easier to do so.
it depends on what one means by no child left behind. Giving every child a chance to succeed (as in reaching their personal "full potential" in maths) would be possible with enough resources and some goodwill from parents. Having every child (or at least every race, gender, family income segment and sexual orientation) achieve similar outcomes which are the current equity goals is only possible by dumbing down the better students, because the opposite is just going to be too hard.
YES. You cannot have both high levels of ability AND no child left behind. That ignores the realities that not every student is as strong in math reasoning as they may be in calculation, and a lack of fluency in calculation is going to handicap a student's ability to learn math reasoning.
Interesting post, a bit of rant. I guess the crux of it to "stick" with what "works." My sense is that the students of California could do a lot better unburdened by the shackles of the conventional school system. So..what's so special about the 8th grade ? What is the value of "repeating ?" Is there some sort of race we need to forcibly participate? The public school system is a brain-dead which does NOT have student progression at its heart. Math in particular is a subject with wildly different absorption rates. Thank God there are much better alternatives coming out of the non-public world ...Kahn Academy as just one example. There is a lot of innovation in this space.. just not in the traditional public school system.
"One of the ideas underpinning the California Math Framework is the notion that math needs to be “detracked”—instead of allowing some students to take Algebra I in 8th grade, it would require all students to enroll in the same math curriculum until the 9th grade."
This is the single most utterly moronic proposal I have ever seen in all the annals of education reform.
I went to a small, fairly traditional K-8 private school. No fancy technology or trend-chasing pedagogy, but relentlessly back-to-basics, serious education. Our entire reading education was phonics for instance, and this was in the early-mid 2000s when I am under the impression that the war on phonics had made significant gains. Each grade had two math tracks, with the upper track one year ahead of the lower track. From Kindergarten on, I and a couple other kids were tracked *two* levels ahead, meaning I took the math classes of the upper track in the grade above. What this meant was that I took Algebra 1 in 7th grade. In 8th grade I arrived at school 40 minutes early to take Geometry one-on-one with one of the 8th grade math teachers (the other few 2-track-up kids had dropped down to regular upper-track by then).
This was an immense benefit to me, and meant I was able to take Calc BC in 11th grade, allowing room for one more STEM elective in 12th grade. The idea of having to stick 2 grade levels below what I did is just horrifying. Not only in terms of boredom and lack of challenge, but also the impact on the other kids. I was already hyperactive enough in the classroom as is. Me in 8th grade in a pre-algebra class would have been a total shitshow.
I know this is a bit long-winded and ranty, but there are few things that make me seethe with incandescent rage as much as this new trend of forcing everyone to operate at the very lowest level for the sake of "equity". Let's be real about what "equity" is: kneecapping the best and brightest so that the worst and least competent can feel better about themselves and useless bureaucrats can pat themselves on the back. It's this absolutely poisonous idea that because some people are incapable of achieving something, nobody at all should allowed to achieve it for themselves. Literal kindergarten playground mentality. Frankly, even in the counterfactual world where detracking *did* reduce racial gaps, I wouldn't care.
Keep the law of Jante over in Scandinavia please. I don't want it here.
And ed school PhD programs frankly seem more like a massive grift the more I read about them. Is there any evidence to the contrary? If so, I'd love to see it. My impression is basically they're a giant factory of breaking things that ain't broke. The war on phonics being the most obvious example.
I don't understand how people can see the purpose of education as anything other than ensuring each student goes as fast and as far as they personally are capable of going. If students who are coming from disadvantaged backgrounds need more assistance to do that, I'm all for giving it to them. But denying _any_ student access to material that they are ready to learn, in the name of "equity" or anything else, is just anathema.
My county's public school system had an advanced math program available that bussed high-achieving students together for an after-school program that got us through all of Algebra, Geometry, and Algebra II, by the end of 8th grade. So we entered high school with Trigonometry and Analytic Geometry, then Calc I in sophomore and Calc II in junior. (I took a _lot_ of AP tests, entered college as a second-semester sophomore, and then did two majors and a minor.)
I'm a big fan of independent study for that reason.
To some extent, equity is really about resource constraints. Your teachers only have so much time in the day. So from their perspective, it's not really "denial" so much as "is teacher time better spent on keeping your lowest performers from failing or helping your highest performers achieve more?"
One case for the former from a teacher's perspective: If a kid fails, you get the joy of dealing with a difficult student for an extra year.
Anyhoo, I think you can argue either position in good faith. But in the cases where kids are just skipping three grades of math or whatever, just have the kids teach themselves and avoid the trade off altogether.
I took Calc AB in 9th grade. I took a lot of AP courses. I had good teachers but after a certain point, I didn't really need them. I just read the books myself and figured it out. And the school wasn't exactly super eager to set up a Calc BC or AP European History or whatever course just for me and a handful of other overachievers, but it also cost them almost nothing to just let us have a free study period and then administer a test.
Obviously not for everyone. But AFAIK, the CME doesn't prohibit self study, so maybe we'll see more of that.
"is teacher time better spent on keeping your lowest performers from failing or helping your highest performers achieve more?"
There are a lot of moral issues around that question, it's hard to say what the ethical answer is. Certainly "No Child Left Behind" assumed the former. But from a utilitarian point of view of what is going to be most important for the scientific, economic and technological progress of society, the answer is clearly the latter.
When I started Kindergarten I was already reading at a second grade level and got extra tutoring after school. In first grade I was put in a 1st/2nd combined classroom and did both classes work and then skipped second grade. I was small, late developing boy and I think this was a big mistake. If I had perhaps stayed with the same set of kids it might have been okay, but we moved every year or two so I was always the new kid, smallest in my class and nerdy. I read lots of books. In high school, we didn't move so I made a group of friends via drama, band and D&D that made it a good experience.
I ended up graduating right after turning 17 and going to a top university and having a good career in tech, so from some sense of "success" it was a success. I went from being very poor to wealthy in one generation. But it was a difficult time from 7 to 14. I didn't need to be put up a grade and would have been better off just teaching myself. I was constantly reading when I was young and was taking community college classes from the time I was 13, so I didn't need to be advanced in grade. I was going to learn no matter what.
Yeah I was reading YA novels by the time I was in third grade. I was lucky that my county's public school system, at the time, had a very extensively multi-tracked system, with four different levels for each subject (remedial, standard, honors, and "gifted and talented"), in _every school_, and then a significant number of opportunities for really advanced students to pick a subject where they'd advance even one level higher, in an after school program. They'd bus all the students for that to one school a couple times a week, and then the maybe 2-3 students who were in the program, at a given school, would work in kind of an independent-study manner sitting in a small study room off the G&T class, so they'd have some access to the G&T teacher from time to time if they needed it.
We really should fund education to the point that heavily individualized study programs can work for every student. If we need higher taxes, including hitting the middle class, so be it. Collectively we'd be way better off with the Scandinavian deal, where private goods (like larger houses or restaurant meals) are a little less available, and in exchange you get better education, healthcare, and general social insurance against a string of bad luck throwing you out of the middle class entirely. One of my favorite stats is that Norway produces more startups per capita per annum than the US. It turns out that when _failing_ in business doesn't mean seeing you family starve in the streets, it's a lot easier to take a flyer on an interesting idea: https://www.inc.com/magazine/20110201/in-norway-start-ups-say-ja-to-socialism.html
This is an interesting thought but I do want to say that there are benefits to keeping people in classes and working on things in groups. I was someone who was in the two above track for math for all of my schooling years starting from 6th Grade. (Note this was actually fairly common in my district/school and we were easily able to get multiple full classes of tracked ahead students.) Throughout my experience some of my best learning came from interacting with my peers where we either discussed a problem or tried to explain our thought process. This helps bring peers who might be slightly confused up to speed while also helping the peer who teaches in refine his understanding (Protege effect/Feynman Technique). With the hyper individualized style of learning I fear you lose this incredibly important network effect.
Additionally, I would argue that most kids are not self motivated and that the self motivated are often the anomaly rather than the standard. I hated math for a decent chunk of High School because compared to my peers in the higher level classes I kind of sucked at it. Yet, social pressure around performance made me study and succeed. If I didn’t have the outside forces I’m positive that I would have performed below my potential. And I wager most kids are like that, they do things due to outside pressure and not intrinsic motivation. For a lot of people intrinsic motivation comes in much later in life.
To the best of my knowledge, the advanced programs I'm talking about did ensure that at each individual school, there would be two or more top students who would be in that super-advanced track. Which meant as long as you got along well with the other folks at your school who were tracked with you, it was a collaborative, peer-motivated system. You'd go have actual class after school 1-2 days a week, and the other days you'd be doing "small group" exercises with your maybe 1-3 peers, with your school's math teacher available as a resource if the group got stuck.
And I did, in fact, get along well with my fellow math nerd. (There were just two of us, at my particular school.) He was one of my best friends through middle and high school. We kinda drifted apart after that, but I actually ran into him at a reunion a few years back and we had a great time catching up. (He was doing research on experimental advanced PV materials. I work for Tesla Energy.)
Ah got you, I had interpreted “highly individualized” as a system that was student specific and not group oriented but your explanation makes sense
💯 to your long winded rant, especially “And ed school PhD programs frankly seem more like a massive grift “
“society simply refuses to address equity later on in the lives of your citizenry“ in reality taxes and transfers greatly reduce inequality in the U.S. and public spending targets low income people. CMS, Social Security and welfare comprise 60% of federal spending (and of course much state and local spending also targets low income residents). We directly spend trillions of dollars a year addressing equity later on in the lives of people.
Massive, unrelenting inequality can and in fact does go on indefinitely. Egyptian society was astonishingly stable while some people at the top had pyramids built in their honor and others had to do the building. Greg Clark recently has been doing research showing inherited social status to be robust even in the face of Maoism.
Let's not misconstrue Clark's research here -- the important takeaway from the pre-to-post Mao inequality study was that any serious attempt to completely treat inequality as derived from social status was a fool's game. Even when the playing field was completely leveled, the families (genes) which succeeded under prior conditions also tended to succeed after a generation of brutal impoverishment in the name of equity.
I’m a California high school physics teacher and this just freaks me out. My district recently moved physics from 3rd to 2nd year and I already have a majority of students incapable of handling the simplified math we are allowed to include according to the Next Gen Science Standards. Math skills took the biggest hit in the pandemic, and I’ve been holding my breath for a return to normalcy that I do not see happening. I agree that this new framework is mostly just giving up on math.
Physics was 2nd year in my high school, 1st year in my daughter's. I hadn't even thought about the fact that there's a certain level of math required for it, unlike basic HS biology. Huh.
Saying these policies were mere mistakes and had nothing to do with "woke" is misleading. They weren't mistakes, they were conclusions that are natural outcomes of embracing the "woke" world view
Meh. It depends what you mean by "woke". If you mean the very broad recognition of how past choices haunt the present, as described in Matt Yglesias' old piece on "the Great Awokening", then that by itself doesn't lead to choosing to ignore evidence. A lot of good has come from people finally reckoning with the fact that _some_ people's grandparents got gifted a few hundred thousand dollars in housing wealth, and others' didn't, because we had government programs that were, explicitly or implicitly, tied to race. That subsidy still gives descendants a leg up today. If you claim to support "equality of opportunity", you're going to have to consider this stuff.
This doesn't necessarily mean you have to use explicitly racial approaches to deal with the issue. Redlining and zoning and so on were generally race-neutral, and we could use similarly race-neutral programs to make things more economically-equitable, and that would probably, as a happy side-effect, make things more racially-equitable as well.
But in any case, if just thinking that history matters makes me woke, I guess I'm woke. If we played a game of Monopoly, and for the first thirty turns, I randomly sent you to jail now and then, and made you pay twice as much for properties, and then on the thirtieth turn I said, "OK, from now on we're playing by equal rules. Just ignore the fact that I already own half the board!" ... you would not think that constituted making the game fair!
OTOH, if "woke" means _specifically_ the rather weird definition of anti-racism pushed by Ibram X. Kendi ( https://www.slowboring.com/p/racism-kendi ), or the actively-counter-productive stuff pushed by Tema Okun ( https://www.slowboring.com/p/tema-okun ), then sure, the way people like that structure their worldview leads to this kind of pedagogy.
But I think most of the time, "woke" just serves to lump together "vaguely lefty stuff I don't like". It conceals more than it reveals.
The Monopoly example is interesting because, of course, Monopoly was not designed to be a fun game. It was designed to be a teaching game illustrating that owning land in San Francisco was unfair and we needed a land value tax.
If this was the purpose of monopoly, it completely failed in my circles. What it actually taught us kids is the drive to attempt to own everything instead of enough, and made blatant greed a desirable trait.
A lot of people don't actually follow the rules because they make it not fun. (Without the tax anyway.)
Oh I'm all for increasing oportunity for people regardless of background. The "woke" aspect I'm referring to is the instinct to flatten everything if it produces unequal outcomes. Like, why in the world would you delay math education for people when learning it earlier clearly works for some?
The woke approach imo is the instinct that unequal outcomes are inherently due to discrimination, and the desire to fix disparities by merely advancing people even though they haven't shown sufficient skill, or stunting the advancement of those who have.
If there are unequal outcomes due to past discrimination, the only valid approach is to help people catch up by actually helping them learn so that they could be equals with more privilaged people. This is hard of course, so "woke" activists just try to either pretend the people who are not doing as well are actually doing well (affirmative action) or stunt the development of the people better off (this system in California). Either way the appearance of equality they can produce are illusory imo.
People have been talking about that "cut down the tall poppies" issue since _way_ before the word "woke" was in use in its modern form. I remember reading "Harrison Bergeron" for an English class in grade school.
https://www.tnellen.com/cybereng/harrison.html
I think you're correct to say that _assuming_ differences in outcome have to be the result of unfair treatment is a problem -- that's precisely what Matt Yglesias criticizes in Ibram Kendi's work. I just think it's a mistake to say that's all "wokeness" is. It's one counter-productive strand, within a larger collection of "woke progressive" ideas, as Noah has explored in a series of posts about different ways to view the "wokeness" phenomenon.
https://www.noahpinion.blog/p/wokeness-as-old-time-american-religion
https://www.noahpinion.blog/p/wokeness-as-prairie-fire
Plenty of manifestations of wokeness explicitly focus on the idea of "leveling up" (i.e. helping those at a disadvantage to rise to the level of others), rather than tearing down. For instance, the classic meme of people trying to see over a fence.
https://interactioninstitute.org/illustrating-equality-vs-equity/
See also: https://twitter.com/krisstraub/status/751163631300063232?lang=en
In my view, the functional strain of these ideas is just regular progressivism as it should be. I don't think we'd need a new term, "woke" for them if that's all they were. What I call woke are basically the dysfunctional directions these ideas get taken into, in the modern context
Yeah I mean I think there is an important argument to be had within the lefty / progressive / liberal / Democratic coalition about this stuff. That's a big part of why I subscribe to moderate-left writers like Noah and MattY.
But I think "woke", for better or worse, has a much squishier definition than you're allowing, in terms of how it is getting used across various communities, and in particular, the Right has been _very_ successful at applying it in a broad-brush manner to basically, as I said earlier, "anything vaguely lefty that we don't like". So, Target deciding to sell stuff for Pride month that makes queer people feel like folks at least like them enough to want them as customers is "woke capitalism". As is a more substantive corporate policy for attracting talent from the queer community, e.g. offering domestic partner benefits even when not compelled to by law.
If you just say you're against wokeness, without being very specific about how you're defining it, a lot of people are going to hear, "I agree with Ron DeSantis." Maybe that's not fair, but it is what it is.
When the Spanish Inquisition or Nazis started to systematically murder Jews, they didn't consult a rabbinic council to determine who was a Jew. They knew who the Jews were. You might turn out to be Jewish even if you great-grandparents converted to Christianity a century ago. Golly, what a surprise when they put you on the rack or the cyanide gas starts to flow.
If you want to understand "woke", look at what Florida has been doing. Saying that being a slave wasn't all fun and games is woke. Pointing out that God created gay people too is woke. Immigrants, except for Cubans, are woke. Putting the life of the mother above the life of a fetus is woke. Fighting infectious disease is woke. Teaching that the world is older than 5000-something years old is woke. Industrial policy is woke.
You can learn a lot about a group by the enemies it chooses, real or imaginary. (For those interested in some historical perspective on how this works, check out Norman Cohn's "Europe's Inner Demons". It's about witches, Satan and witchcraft, and it's an excellent piece of scholarly work.)
To be honest I sort of blame the "woke" movement for the recent excesses of DeSantis and tribe. What goes unstated when we talk about the backlash about target, budweiser and various appeals to queer culture is the way symbols that appeal to conservatives have more or less been censored out of much visible culture. The "woke" left is very organized in campaigning against anything that doesn't fall in line with their world view (I don't think I need to provide evidence, we all know what major brands and banks are comfortable advertising and which side of the spectrum feels they can't speak their mind freely in most offices). Tbh the backlash against target and budweiser surprised me, because it felt like every other brand had already been doing stuff like that for a while now, but I guess since they felt an ownership over these lower class brands, they got extra animated in their anger. In any case, the excesses of the woke movement I think made it inevitable that the rabble would eventually organize against it, and the pushback wasn't going to be of a high minded sort because the higher minded critics just kept their mouth shut the whole time.
If you want to understand why we have a word "woke", you should understand why people invented it. They used it as a term for people who had "woken up" to all of the ways that society is unequal, and the many forms of un-earned privilege that exist in the world. It was originally specifically about awareness of the historic mistreatment of Black people over the decades and centuries, but came to be used more broadly. It's not the same as Progressivism (which has some parts that are race-blind), but it's also not the same as saying everything should be leveled down. Some of the dysfunctional stuff evolved out of this specific context, but that's not all there is.
Interesting write up. I quite like the prospect of taking race neutral approaches to address racially divergent outcomes. I think if these methods can lift everybody up, and as a consequence, also massively benefit less fortunate people of comparatively less affluent racial backgrounds, then that would be great.
Two good examples of the idea:
One: End exclusionary zoning. This is just straight-up taking a "race-neutral" policy that served racist ends, and turning it on its head. Make sure that smaller, naturally-affordable homes are available in "high-resource" neighborhoods, so we have more economically diverse communities, and poorer families can send their kids to schools that benefit from the influence of educated, wealthy parents.
Two: Baby bonds. https://www.vox.com/policy-and-politics/2018/10/22/17999558/cory-booker-baby-bonds
On the numbers, the program that Booker proposed would do more to close the wealth gap between White and Black families than basically any idea that's been seriously proposed. _Functionally_, it provides a realistic form of reparations for the harms of slavery and redlining. Yet it doesn't have to explicitly use race to get the job done.
See these race neutral approach is the right call imo, but not favored by "woke" (I don't like the term, but using it since it was called out in the article) because
1. It's possible that racial gaps won't be closed, or won't be closed quickly enough even if this is done perfectly
2. Like George Orwell described in his critique of a specific type of socialist, they seem to be more animated by a hatred of the privilaged people rather than a love of unprivileged people. The fact that these policies might actually help some poor person from an unsympathetic background (white, male, straight, etc) I think is super unappealing to them
Oh you're _definitely_ correct about (2). It's quite clear that there's a strain of urban progressive for whom the goal of housing policy is not to house people, but to make sure that eeeeevil developers can never make a profit from providing housing. It's nuts. They would much rather see 10 affordable units get built, than 50 affordable units and 50 market rate units.
Meanwhile, it's not like anyone's saying that some random independent restaurant owner shouldn't be able to sell food at a profit. But the politics of housing is cursed.
That's called projection. Most liberals have been fighting for programs that make it possible for developers to provide affordable housing. They've generally been stymied by right wing push back defending property values. Liberal cities are where most of those contingent affordable units have been built, not right wing suburban enclaves. The housing advocates in the cities want to get as many affordable units built as they can. The developers want to build zero and whine like stuck pigs when the deal is for 10%.
Where the hell do you come up with this stuff? Is it drugs? Fox News?
Being a Torontonian, I very strongly agree. I had to move, it got so bad.
It completely boggled my mind that these people are trying to tax the very people who are supposed to bring more supply of housing. If you want more of something, you might wanna subsidize it, but you definitely wouldn't tax it even harder. But the existing taxes on new developments (the insane "growth pays for growth" dogma) mixed with the "affordable" unit requirements all tantamount to a a prohibitive tax on new developments at a time we need them most, and it's the new home buyers who have to pay it in the end.. Developers aren't charities after all. Why a young home buyer, who doesn't find the options affordable and has not benefited from the astronomical housing price growth should also be saddled with subsidizing someone else's "affordable" (if you can even call 10-20% price reduction affordable) housing is beyond me. But I suppose if you already own a home, putting in affordable housing policies that don't cost you a cent but let you pretend you're a fairness advocate, it's pretty appealing. That is, if you're extremely delusional, or just a super callused person.
A lot of those things have been favored by liberals for decades now. They've caught a lot of flak for it, too.
The Georgia land lottery shows the results of "the subsidy of history".
https://westhunt.wordpress.com/2015/04/22/the-lottery/
https://westhunt.wordpress.com/2014/03/23/the-son-also-rises/
Looking at the effect of sudden shifts in adulthood is a _terrible_ way to test for the effects of a gradual thumb on the scale over time. There is a TON of evidence of how cumulative advantages have an effect. Also a ton of evidence around how being at perpetual _disadvantage_ in youth alters the brain in ways that makes people more impulsive, short-termist, and pessimistic about their options.
https://www.nytimes.com/2021/08/24/podcasts/transcript-ezra-klein-interviews-bessel-van-der-kolk.html
You didn't read the linked posts, which discuss later generations instead of just people who were already adults.
I hate to tell you this, dude, but this has nothing to do with "woke." Instead, it's reflective of educational fads that have been swinging back and forth since the mid-nineteeth century, if not for longer. Wake up and get away from ideology.
Signed, a third generation teacher (now retired) who spent a lot of time talking about trends in education with her mother long before she became a teacher.
"woke" is just a name for a modern configuration of ideas that are animated by an impulse that is age old in humans. We wouldn't call the people who advocated for these fads "woke" back then, but they are the same types of people
And...you reveal your ideology by doubling down on this notion.
You mean I've revealed what I think about it? Good, I guess I've communicated effectively
"Woke" is a right wing term for everything right wingers don't like. It was briefly a left wing term with a narrow meaning, but now it's just an umbrella term for every right wing discontent. Women voting - woke. Counting the ballots and letting the candidate with the most votes win - woke.
Hmm... there may be some truth to this, but I think on practical grounds it is good for critics of the CMF to avoid this particular word. As soon as it get mentioned, people stop arguing about maths and start arguing about this nebulous culture-war concept that nobody can even quite agree on exactly what it is.
I hate to tell you this, but many people who are just as ideologically progressive as the CMF architects are extensively criticising its shoddy implementation and complete lack of evidence for the methods employed. See the above article.
So claiming that this is somehow an outcome of a progressive or left wing worldview is just flat out wrong.
I think there is a functional strain of progressive, left wing, but sadly they seem to have been losing to the dysfunctional, "woke" coalition. Seems the tide might be turning somewhat now that some of their policies having been implemented have proven to have very poor outcomes, but we'll see how far that gets us.
Yep. Many of us were saying this from the very beginning. It's better than nothing that people like the author have realized their mistakes, but preferably they wouldn't have been in a position to make those mistakes in the first place.
Its really regretful that many on the left doesn't have the courage to state it clearly that woke is a thing(even if hard to define) and is harmful to society in some ways. Bcoz dancing around it and just talking about the issue directly is not really an effective startegy.
Read this and then had my husband read this who has a masters in engineering (aka very good at math. His eyes nearly fell out of his head when he read that you couldn’t take algebra until 9th grade. I mean talk about a way to not encourage kids to live up to their full potential. In fact you’re penalizing them for doing so. Sorry but some people are good at math and they should be rewarded with classes that meet them where they are just like people who are average at math (like me) have classes that meet them where they are. Why we are penalizing kids for being smart in the name of fairness is beyond me!
I’m a SFUSD high schooler and I completely agree with the point of meeting everyone where they are. I’ve heard other students say that having advanced courses leads to bullying/shaming dealt out to people not in the higher level courses. I feel like there’s way too much of a stigma around “achievement”— people put too much stock in these higher level course, like it’s great for you if you’re in one, but it obviously doesn’t mean you’re better than those who aren’t. If we could find a way to prevent that poor treatment and devaluation, then just simply putting everyone in the class that suits their level would be guiltless and beneficial to everyone. The whole problem (not just with math, but with our school system in general) is that no one pauses to consider the individuals, they try to treat everyone the same way whether that’s disregarding the needs of disadvantaged kids or whether it’s forcing kids who are excelling to sit through classes for which they already know the material. Teachers who just go by the textbook and don’t engage with each student’s needs perpetuate this, I’ve experienced it personally. This is not to disregard the care and commitment many teachers show their students, but it definitely happens more frequently than it should.
Former middle school special education teacher who absolutely agrees with you about the heavy emphasis put on higher level courses.
There needs to be a greater awareness amongst those who would wax opinionated about education that readiness, strengths, and weaknesses ARE NOT THE SAME FOR ALL STUDENTS. But those who tend to make those errors (not you, obviously, you see the need for individualized education) frequently haven't been in a classroom other than as a student. A bunch of 'em need to try teaching math to first grade students, or remedial math to discouraged middle school students who are already mad about being placed in Resource Math because they get called stupid.
Education should be individualized, and if there's one damn thing these LLM/Chat GPT models ought to be good for, is writing Individual Education Plans for EVERY student. Not just special ed. Not just talented and gifted. EVERYONE.
Yeah agree with AV: IEPs are a huge regulatory burden and the benefit for the students who have them is more about legal protections than actual instruction. Agree in principle that education needs to be more individualized, but in practice IEPs are a money pit for the school and a time suck for the sped teachers, who become compliance officers rather than specialized teachers.
And you know that IEPs are a money pit because...???
Because my wife and I work at schools and know what our sped budgets are?
And you're a special ed teacher who drafts those IEPs and works with them?
If you want the best of education, that's what it takes.
While Rob Lowe is an ass, his sound-bite from the West Wing was a great description of what our nation should aspire to.
https://www.facebook.com/watch/?v=779714802205600
We do a terrible job at this as a country frankly on both ends. We fail to meet really gifted kids where they are at because it’s not fair to other students or frankly it’s inconvenient for the school to do so. “Achievement” has a different meaning for everyone but we’ve put far too much emphasis on one type of achievement which is ridiculous.
Kids who struggle or are in special education have it equally as bad because we provide them with terrible resources because good resources are generally expensive. Special ed also sadly has become a game of politics. Some districts want to keep kids they really shouldn’t because they get more money from the state if they are enrolled but it’s truly not what’s best for the kid. And that’s sad.
Tailoring education to each kid is nearly impossible but if we at least started with more tailoring to high achieving students I actually think it would help. I think some of the reason there is bullying is because those kids find the higher level courses boring. I think it would actually help the kids “in the middle” a lot because their peers may actually have a class that’s challenging them.
That is where custom AI tutors comes into play.
No.
CA is probably the worst state in the union to be poor or working class. Schools are horrific, gangs run rampant in many areas, cost of food and gasoline is exorbitant and housing expenses are ridiculous.
My local school district was majority Latino but the town wasn’t gang infested and most parents worked (I interfaced with some of them through an after-work ESL program). The kids (who I also got to volunteer with) were generally sweet and obedient through about 4th or 5th grade. These kids seemed very teachable to me for reading and basic arithmetic K-4, yet the standardized test scores were abysmal. Practically a crime. Breaks my heart. The teachers aren’t bad people - most merely see their mission as showing up every day and delivering the lesson plan. Getting every kid up to grade level is not the objective, and it shows.
My only regret is not going hard enough on the math in college, and I majored in ChemE. I would die I had been denied seventh grade algebra.
I was denied 8th grade algebra and also denied calculus in high school. No problem because all the kids who already had calculus in HS were retaking it with me freshman year in college. I took an accelerated version that did differential, integral, multivariate and series during Freshman year. So DiffEQs would be a firsr semester sophomore year course. Not really behind at all (unless I wanted to be a math major). Some of the kids who had already had calculus in HS were taking the slower version of the calc program, hoping to get easy A’s (especially the pre-meds). Didn’t always work out as they hoped, because HS calculus is BS in many districts.
I didn’t like the math program when my kids went to grammar school so we paid up for Kumon math. All of them had progressed through Algebra to Geometry by end of 6th grade, doing simple worksheets for 15 minutes a day. Most of school is a joke- more like babysitting and playtime. If you want to teach a subject it doesn’t actually take a lot of time.
I mean I’m glad it worked out for you and HS Calculus certainly isn’t for everyone so I’m not surprised many of them had to retake, but I took diffeq first semester freshman year thanks to the opportunities I had in high school and I definitely think having a stronger math background helped me with the science classes I was taking in college. No, it wouldn’t have been the end of the world if I didn’t have those opportunities, but it’s still bad to deny them to students who are ready for them. Just like it’s bad to push students to take classes they aren’t ready for (this article seems to suggest that prior to banning 8th grade algebra, SF required it for all students, an equally dumb policy. Is it really so hard to let 8th grade algebra be optional?)
Agreed- kids should have the opportunities to progress at an accelerated pace if they so desire (and are capable) in all subjects.
I mean I guess but like what were you doing on seventh grade? Eating jello???
Honestly have no recollection- Same thing kids in SF are doing as they aren’t taking algebra.
Didn’t really hurt me at all- caught up quickly at university. Algebra is important for life - bigger issue is the teaching is likely crap rather than whether most kids learn it in junior high or 9th grade. However, kids that are ready for it should get it as soon as possible. I didn’t, but it didn’t matter.
There's an overarching cultural problem here. The folks who go on to be authors and screenwriters and other creative types mostly grew up hating maths, because it was seen as "not creative". (Honestly a fair assessment.) Their hatred for maths then percolates into "maths is hard" or "maths isn't for everyone" tropes which are everywhere in popular culture. And then kids grow up in that culture and absorb the idea that they can't do maths either.
If math is a building, the foundation is arithmetic. There is no way around it. Every student should be pushed as hard as possible to master the foundation. From what I've noticed, the jaded "reformers" have pretty much destroyed the teaching of arithmetic by vastly overcomplicating it.
There can also be processing issues, especially if fluency or calculation ability is impaired.
I have an issue with 8th grade algebra, a HUGE issue.
I don't think every student is ready for algebra in 8th grade. I'm speaking as a former middle school special education teacher, and as someone who graduated from high school in the '70s. Back in that era, the norm was Algebra I by 10th grade (in a junior high/senior high system, 3 years of junior high, 3 years of senior high). The typical sequence was 10th grade Algebra I, 11th grade Geometry, 12th grade Algebra II. I'm also the parent of a student who graduated in the mid '00s and took Algebra I in 9th grade.
In my teaching experience, in a high-poverty exurban (not Californian) k-8 school with, teaching from 2004-2014, most of our students were not ready to start Algebra I in 8th grade. Some of the issues were purely developmental. There are three elements to math ability--calculation (which is best served by memorization), math reasoning, and math fluency (how fast can you run those single-digit calculations?). Too many people, including non-educators, think that calculation and fluency skills make up for lags in math reasoning. Not really, not when it comes to algebra.
I've seen too much pushing down of higher concepts happening especially since the adoption of Common Core methodology. I keep hearing the justifications for introducing higher-level reasoning at younger ages, but you know what gets sacrificed when you do that? Yep, the other two foundational concepts, calculation and fluency. There is only so much time in the school day, and you can only push so much foundational work down to younger grades before you start running foul of developmental limitations (cough cough fractions cough cough really suffer under this notion).
Better to create that firm foundation of calculation and fluency BEFORE getting all hyper about teaching higher-level math reasoning concepts. As it is now, we have lost the necessary parts of kindergarten--learning how to behave in school, how to function socially in school, fine motor activity, and so on--to academics. Students now are expected to arrive in kindergarten ready to read (which means understanding letter-sound correspondences and some phonemic awareness) and learn calculation (which means they already have a grasp of numeracy).
You get into ridiculous situations such as I encountered when substituting in a first grade classroom in early October, where I'm supposed to teach these kids (who barely have a grasp of calculation) the distributive and associative properties of addition.
1st grade. Early October. Can we say tears, agony, and a lot of misery? Plus, talking to the classroom aide, *I* was the one introducing the concept, not the classroom teacher.
The next day I drew on special ed experience and pulled out manipulatives. That helped. But those kids barely understood 2 + 2 = 4.
I'm not aware that anyone is advocating for all 8th graders to be forced to take algebra. It's that it needs to be an option, and tracking is good and necessary. Plenty of kids are perfectly ready for algebra in 8th grade. And some are ready in 7th grade - I was one of them. Thus I did geometry in 8th, algebra II in 9th, precalc in 10th, and calculus BC in 11th. That gave me room for an extra science AP in 12th grade.
Oh, that's a common feature of Common Core ideology and education reform--algebra by 8th grade. And not everyone has reached the developmental level where it's appropriate.
Just because many students are ready doesn't mean no students should get the opportunity. Everyone should proceed at their own pace to topics only when they have mastered the prerequisites.
If administrators and voters would provide sufficient funding, then this could happen. The problem is that there isn't sufficient funding to ensure everyone has appropriate fundamentals.
It’s not (yet) possible to provide individualized instruction for every student, but it’s not hard to provide two classes for 8th graders, on that teaches algebra and one that reinforces arithmetic and prealgebra.
You clearly haven't taught in a building with budget cuts that reduce staff-to-student ratios.
We had it decades ago and it was dead simple. You divide the year's math objectives into 12 2-week segments. At the start of fourth grade, you take a post test on third grade math segments to check for summer learning loss. Any third grade topics not passed at 90%, that student must repeat them. When you finish third grade, you then take a pre-test on all fourth grade topics, with a 90% criteria. When a student masters all of the fourth grade topic, they get to take the pre-test for all of the 5th grade topics.
Every two weeks, you group the students by the lowest level topic they need to master across the grade level. We had about 5 classes, so there were usually a few main groups of students that could fill an entire classroom, and then a classroom with a mix of topics for the various students that were further behind and generally taking something for the second time, and one with the students that were further ahead that were often autodidacts. Sometimes you could end up in the room with students a grade below or above you. I remember missing just one topic on the grade's pretests, the teacher explained to me how it was done in a couple of minutes, I took the post-test and moved on. I was able to complete 3 years of math in one year, with minimal teacher involvement.
At the end of the year, if you haven't mastered the grade you are in, you have to go to summer school to keep working on it, or you don't advance.
It didn't require any additional teachers or funding, except printing out a bunch of worksheets.
The essential characteristic of math classes is that they are lergely sequential - they build upon one another and if your mastery of a lower level concept is problematic, that is likely to cause significant problems later. But some students progress much faster than others and should not be held back by their peer's limitations. My daughter did take calculus in 10th grade, but when she went to the University the next year, she retook in at the University Honors level. She knew enough to handle the calculus requirements of her physics and engineering classes, and the Honors class was much more thorough and demanding - but not so much as the Departmental Honors Math classes that are intended for students planning on being mathematicians.
But bright students who want to cut their college costs in half via the Running Start type approach need to be ready for college level calculus no later than the start 11th grade. Work backwards from there. There is actually very little flexibility. At the minimum, that puts pre-calculus in 10th grade, Algebra 2 in 9th grade, Geometry in 8th grade, and Algebra 1 in 7th grade - unless you are willing to double up on math. I went to Baltimore Polytechnic more than 50 years ago, and there was one year where we did double up on math. In fact, I would recommend doubling up on math (optionally) for at least a year or two to add statistics and an introduction to data analysis.
Fine. Then you support sufficient funding for public schools to provide individualized instruction that will allow this.
Funny how all these math prodigies show up whenever math education gets discussed; but when you take a look at the typical school, they're...not as common as anecdotes have it.
You also don't allow for differences in cognitive development by such lack of flexibility.
It doesn't require individualized instruction. Most cases can be handled by ability / advancement grouping. It would be more efficient to have schools have lab areas where students can go to small partitioned desks to allow them to do remote attendance in specialized classes. Then the school district would be able to offer classes efficiently because they are drawing from all the students in the district. Now, you can't offer a class unless you have a classroom full. This incidentally is the reason for magnet schools, as you can group advanced students together so that you have the necessary numbers to offer the advanced classes.
I would not call my daughter a prodigy, I have met them and she is not. But the high school she went to had an active IB program that was heavily enrolled.
Allowing ability / advancement grouping provides more flexibility for differences in cognitive development than trying to keep everybody in the same class.
We have been talking math. How are the schools dealing with the differences in reading levels? By 5th grade you are going to have students with 12 grade plus reading levels and 3d grade - reading levels. I am not convinced that you can really do literature or history reasonably in a class with such a diversity in reading level.
It is not hard to get kids to such reading levels - no TV or screens, extended bedtimes for reading, and regular library visits. I got my son a kindle so that he could read under the covers when his mother thought he was sleeping.
And your actual classroom experience is--? Or *do* you have experience beyond your own time in the classroom and as a parent?
Lovely theory, but we had such remote classes as you describe at the school where I taught explicitly for 8th grade algebra. Is not very effective in practice. You need to have aides present in the lab who understand and can help students. You also need to have reliable technology that isn't breaking down, suffering from transmission issues, and...you need to have a lab that doesn't need to be scheduled for high-stakes academic assessment and that doesn't need to be accessed by other classes during that period.
ETA: You also need supervision to ensure that the students are studying and not playing video games. Yes, we had to deal with that, and it can be a greater problem with the higher-performing students, especially in the middle school years.
Note: I also taught in a blended learning program at the high school level for a couple of years. Canned curriculum. I was remote, some of the students were remote, the others were going to a computer lab. There were issues.
And there *are* issues with ability grouping. I'm not going to get into all of the details, except that it leads to greater bullying and scorn for the lower-performing levels.
Reading levels in subject matter courses such as literature, general science, and history? Much, much easier to handle and differentiate amongst ability levels than in math. I've done that. I taught one year of US History as part of a humanities team--higher level students--and brought in some of my higher level special ed students so they wouldn't be buried in the lower level humanities course. They were actually better students than a couple of the alleged talented and gifted students in that class, who explicitly asked me to tell them where the answer to a question was in the textbook. My sped kids flinched, because the first thing they learned when they came onto my caseload was that I would help them *find* the answer, but I would not *tell* them the answer.
In fact, one of the best remedial reading programs, REWARDS, uses science and history subject matter as part of their reading remediation at the secondary level. It's much easier to remediate reading when the reading matter is interesting, and if it matches what the students are learning in their subject matter courses....
I dispute your assertion that it is not hard to get kids to such reading levels, especially with the solutions you offer. That does not address students with language processing issues (a much greater problem than most realise), decoding issues, or comprehension issues. Additionally, these solutions you suggest require a certain family income and stability that is often lacking in families with struggling readers.
My teaching experience is as a teaching assistant at senior and graduate students in physics and engineering, - more grading and explanation. I have talked a lot and provided guidance to #1 daughter about her kids, who are also capable. She is in Atlanta where they are pulling the college prep classes - so the grandkids are off to private school. I went to Washington DC schools in the early 60's and we moved out of the city when the school board cancelled the college prep classes. My grandfather was a chemistry teacher in high school who was in trouble with the school board for his high standards - until Sputnik went up, at which point he became the teacher of the year for Kansas.
The fight over equality and excellence has been going on for a long time. To do excellence economically pretty much requires tracking or some form of online study - and my daughter did ~ 50% of her 7th grade online, rather than go to the classes. Online works very well for auto-didacts - and the middle school material that was in her online classes was not particularly demanding - she burned her way through it, and we would return the books and they would send her the next set.
Her high school experience was better - she was in the honors track of a school filled with the children of highly educated south and east Asian parents who were driving their kids hard - rather like my peers in my high school, who were the children of survivors of the Holocaust who were driving their kids hard. The science, engineering, and honors classes at the university was better than high school, it is more where she belonged.
There is a world of difference between k-12 classroom teaching and the college experience you cite, especially at the k-8 grade levels. Excellence does not demand tracking. It simply demands a commitment to staffing and the flexibility to differentiate and innovate.
Additionally, the experiences you describe firmly place you in the upper middle class, which is not the case for the overwhelming majority of students in the US educational system. Alas, this is the situation for most wannabe education reformers. Very few have the experience or knowledge of high-poverty schools as a teacher or as a student. Their solutions then become "drill and kill" pounding of facts with little opportunity to cultivate the love of learning and desire to be creative.
It is a very different world in a high-poverty school (and not exactly like the "culture of poverty" sorts would describe it). When your students are having problems focusing because they can't get a good night's sleep due to not having reliable housing, or they can't use a computer because the family doesn't have the $$$ for paying that month's electricity bill, much less internet or even a basic computer...well, online study is not an option, and a brilliant kid stuck in a high-poverty school is unlikely to receive the opportunity for online study, even at the school itself.
Joyce, you are a joy to read. And yes, I am a very long-term teacher who has taught math and economics in 6 countries (mostly IB). Not the US though. But I really don't think that matters. Children are children. And reading articles like the one above that, though well meaning and not without excellent points, miss completely developmental progress of children. And budget constraints of schools. And the workload of teachers in budget constrainted schools who are constantly trying to implement initiatives. I too also hope that technology will help with more individualised learning programs to cater for student needs. But until children can move from a concrete understanding to abstract understanding then algebra is a mystery to them. I have listened to well meaning pundits raging against teaching for nearly 40 years now but have never heard them include a commitment to paying higher levels of tax to fund schools to provide what they want. Of course separate math classes would be great. So would smaller class sizes as would more specialist teachers rather than generalist teachers. But it needs to be paid for. Which means individuals accepting higher levels of tax.
Perry, thank you! Your feedback--especially from an IB background and from teaching in other countries--is really useful.
One of the things that infuriates me about the whole Common Core fiasco is the absolute lack of understanding and concern about developmental progression and how it differs from student to student. I was part of a group of teachers devising Common Core standards for middle school social studies students, and the degree to which we were passing down prerequisite requirements for middle school to the elementary levels was--worrisome.
The lack of funding support for schools cancels out many reforms. A lot could be done simply by fully funding special education in the US, for one thing (special education has never received the full funding from the Federal Government that it is supposed to receive, for one). Funding for more specialist teachers, smaller class sizes, and so on would make a huge difference. When I was able to rove from class to class, work one-on-one with students, push into classrooms to work with students, I was much more effective as a special education teacher than when I was pressed into filling in for a general education teacher in social studies, for one. Or required to teach classes to a mix of general and special education students every period that I was on campus, without the ability to respond to specific emergencies or problems. It was a darn good thing during that time that we did not have the students with complex emotional problems that I managed earlier in my career.
“ The primary reason girls, for example, diverge from boys in math performance is because society teaches them that math is not for girls.”
That is a stretch. The male sex may have better innate ability to reason mathematically. And that is OK, because the sexes are not identical in traits.
To bely that cause is to turn a blind eye to reality in the name of equity or other nonsense.
The “innate mathematical reasoning” argument is possible but it is not supported by the wealth of evidence from other countries, which show boys doing better up to grade 4, but past that, girls tending to score better in higher education yet still being less likely to opt for STEM careers. https://world-education-blog.org/2022/04/27/girls-are-now-performing-the-same-as-boys-in-mathematics/
How many women have won the Fields Medal?
And how many women have been president? Are women also not charismatic? If you suppose, for the sake of argument, that society is to blame instead of people’s innate ability, then this is a pretty mean-spirited thing to say.
Two. And this is arguably symptomatic of the cited research. Since whilst girls tend to just as well as (and in many cases better than) boys in secondary level science and mathematics, they are less likely to go into STEM careers at a university level.
And after all, every Fields Medal recipient has a PhD in either Mathematics or Physics, so one would expect to find that they end up overwhelmingly male.
You didn't cite research, you cited a blog post. Here is some research:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4270278/
Also, without examining the underlying systems of education in various countries around the world, and the methodologies of research in the area, it could be something as simple as:
1. There has been a broad push worldwide to include girls in STEM education.
2. More resources are directed towards educating girls in this regard.
3. That is reflected in the data.
Visit the math department in any research university, or engineering or computer science. Overwhelmingly dominated by men. Now visit the schools of education or social work, overwhelmingly dominated by women.
The push to achieve equality of outcome results in lowering standards so the equal outcome is achieved. See California's push for equity.
The blog that I linked was a summary of the 2022 UNESCO Global Education Monitoring Report:
https://unesdoc.unesco.org/ark:/48223/pf0000381329/PDF/381329eng.pdf.multi
The paper you cited does not support the claim that women entering STEM at a university and career level are a lower rate is primarily due to biological differences between men and women, rather they attribute it to a complex range of factors.
To quote from the paper you cited:
“Experience alters brain structures and functioning, so causal statements about brain differences and success in math and science are circular. A wide range of sociocultural forces contribute to sex differences in mathematics and science achievement and ability—including the effects of family, neighborhood, peer, and school influences; training and experience; and cultural practices. We conclude that early experience, biological factors, educational policy, and cultural context affect the number of women and men who pursue advanced study in science and math and that these effects add and interact in complex ways. There are no single or simple answers to the complex questions about sex differences in science and mathematics.”
Secondly, whilst the “broad push worldwide to include girls in STEM education” sounds plausible, unfortunately it doesn’t explain the data very well. Since as observed in the UNESCO report data, girls exceeding boys in high school mathematics results also occurred in countries where there is not a broad progressive push to include girls in STEM education.
The other reason why this hypothesis does not explain the data is because if it were the case that girls were biologically worse at mathematics yet being progressively pushed to go into STEM, then we would expect to see them being less proficient in secondary school yet going into STEM degrees at increased rates anyway. Yet as shown by the data, what we see is the complete opposite. After grade 4, girls are consistently just as if not more proficient than boys in mathematics scores, yet enter STEM related fields at comparatively lower rates.
If you are suggesting that the “progressive push to include girls in STEM” is causing them to perform well at secondary level mathematics, then this is merely a reinforcement of Armand’s initial argument in the article.
A better argument for your position would be pointing out that perhaps the entrance examinations for colleges and careers are more problem-solving focused and the typical male brain structure is better suited to this. And whilst this would be more plausible, it would still be limited as an explanation of the data since many universities don’t have specific entrance examinations, and this wouldn’t really account for the real discrepancy - which lies in the number of applicants themselves.
In summary, whilst yes there absolutely are biological differences between male and female cerebral and brain structures, these differences are not sufficient to explain the data at hand. Which is why the research you cited does not claim that it does.
The future of math instruction is likely individualized instruction based on student's abilities and their own tablets. The tablet senses the current state of the child's knowledge and generates challenges and interactions that engage them up a ladder of learning tailored to their capacities. Arguing over what age algebra should be introduced is nonsense. Introducing equity into the strategy is deranged.
Even if you took the ideals being expressed at face value, that raising the kids at the bottom is more important than raising the kids at the top, detracking would not accomplish that. I took Algebra in 7th grade. Before I had the opportunity to split onto a higher track, I spent math class either being a distraction or a jackass by making other kids feel dumb. Getting me out of that class was good for learning.
If you really truly cared about raising the bottom, you would give them a dedicated class that had good resources and good teachers. One policy goal you could have would be to ensure that the best teachers weren't disproportionately going to the top level classes for a grade, which they tend to do because they naturally want to teach the most engaged students. Allow students to track but have some sort of incentive, either carrot or stick, to keep resources and attention equal among tracks.
"We have a chance to do exactly that with the release of a new California Math Framework "
"We" (as in Californians) do not have this opportunity. "We" live in a one-party state, and one party states tend to migrate toward the extreme ends. As a result, on this issue and almost every other, the fix is already in and "we" are going to be saddled with an new "inclusive-math" where 2+2 might equal 5 for black kids and where word problems will be something like...
"Sam needs puberty blockers, but their state (Utah) discriminates against them for their non-binary identity. Sam knows that in CA is a sanctuary state and would give them the medical care they need to not commit suicide, so they run away from their parents house in South Lake City on an all-electric bus that averages 50 mph. Salt Lake City is 650 miles from the California border. How long will it take before Sam is safe from transphobia as a ward of the state in CA?"
It would be funnier if it wasn't actually plausible.
It’s also worth noting that California’s Community Colleges have taken a similar approach to math as part of its remediation reform. If a student enters community college without a proficient understanding of algebra (which is many students due to our poor K-12 math outcomes, as the article points out) there are not any pre-transfer or standalone support courses available to them any longer. They are pushed directly into transfer level math and forced to complete in one year.
This is the new Lysenko-ism.
Many such examples - whole language reading, denial of physiological sex differences, blank slatism in general. If anything, this one is thankfully dying a faster death than many others.
"Math, out of all subjects, seems to hold a special terror for Americans, who often seem to view the subject as a test of innate intelligence rather than a skill that can be acquired and honed through hard work."
you seem to disagree with this view, which is part of the problem. You just aren't going to be able to have at the same time high level of math ability AND no child left behind. The fantasy that everyone can get to a truly competent level of math with reasonable effort (which "hard work" in previous sentence implies, rather than Korean/Chinese kid level of effort) is just that.
The only way to have peak excellence in anything is to nurture with focused intensity the segment of the population with predispositions, and there is a wide range of abilities among kids even at HS math level. If you want equity of course the outcome has to be some kind of lowest common denominator strategy. Until the politics in California change the direction of travel of the educational establishment will continue as is.
“You just aren't going to be able to have at the same time high level of math ability AND no child left behind.” I believe you can have this. Instead of trying to get every student to conform to a single curriculum and level of math, why not provide multiple opportunities? higher level math for those who want/are ready for it and algebra in 9th grade or whatever for those who need that? Maybe this is naive but I personally don’t believe that either of the other solutions really solves more than one of the many problems with the curriculum.
Tell it to the administrators who don't want to spend the money to differentiate to accommodate the wide range of student math ability by middle school. That would require spending more $$ on teachers. Yes, it can be done, but a.) you need more teachers, b.) you need more classroom aides, and c.) fund all levels equally instead of concentrating on the highest performers.
Completely agree. You can do both we are just unwilling to. No child left behind was not designed to hold smart kids back, it was implemented that way because it was easier to do so.
it depends on what one means by no child left behind. Giving every child a chance to succeed (as in reaching their personal "full potential" in maths) would be possible with enough resources and some goodwill from parents. Having every child (or at least every race, gender, family income segment and sexual orientation) achieve similar outcomes which are the current equity goals is only possible by dumbing down the better students, because the opposite is just going to be too hard.
YES. You cannot have both high levels of ability AND no child left behind. That ignores the realities that not every student is as strong in math reasoning as they may be in calculation, and a lack of fluency in calculation is going to handicap a student's ability to learn math reasoning.
lol have you been hacked?
Interesting post, a bit of rant. I guess the crux of it to "stick" with what "works." My sense is that the students of California could do a lot better unburdened by the shackles of the conventional school system. So..what's so special about the 8th grade ? What is the value of "repeating ?" Is there some sort of race we need to forcibly participate? The public school system is a brain-dead which does NOT have student progression at its heart. Math in particular is a subject with wildly different absorption rates. Thank God there are much better alternatives coming out of the non-public world ...Kahn Academy as just one example. There is a lot of innovation in this space.. just not in the traditional public school system.
For those who are interested..... here is ted talk with my deeper thoughts: https://www.ted.com/talks/dr_rahul_razdan_sir_ken_robinson_was_right_about_the_symptom_now_let_s_talk