An alarming trend in K-12 math education: a guest post and an open letter
scottaaronson.blog
scottaaronson.blog
What they are fundamentally doing is breaking up the classic U.S. staged path where you learn algebra for a year, then geometry for a year, then back to algebra / pre-calc for a year, then maybe take statistics or calculus as an elective, etc. Instead, all branches of math will be taught in an integrated approach focused around applied problems.
This is how a lot of European math courses are taught. In fact, I think HN would appreciate the shift from focusing on pure numbers and classic formulas to more applied uses of math, including algorithms, probability, data collected and analyzed in charts, etc. Students also forget a lot of algebra when they do a year of geometry by itself, then have to go back to algebra / pre-calc.
It also does mean that in the transition, it will be harder for students to "test out" of the classic algebra I/II, geometry, pre-calc sequence, because it will just be "year X integrated math." But the framework does not forbid gifted and talented programs or anything like that. There will just be a few awkward years while the curriculum shifts.
Now, there are some on the left who advocated for the elimination of gifted and talented programs altogether, for equity reasons. They did not get what they wanted in the new California framework. That hasn't stopped a lot of people from looking at what California is doing and imagining it is actually some kind of Harrison Bergeron dystopia, when that is absolutely not the case.
The point of high school Geometry was never to compute areas of fields. Trigonometry is far more useful for that anyway.
The point of high school Geometry is that it is the first introduction to rigorous mathematical proof -- and has been, ever since Euclid's Elements.
As a data point of one (heh there's that stats again...) my two high school geometry classes 15 years ago never touched any proofs. I have no clue if they still teach that way.
Edit: just noticed that I'm replying to someone who is far more knowledgeable about math than me. I stand by my point though, people like Colin can seek that out in more advanced classes.
Geometry proofs are a terrible way of introducing rigorous mathematical proofs to students. Seriously. I cannot overstate how misleading they are. I remember my first abstract algebra class in college, after the first HW I got called in by the TA because I tried to structure my proofs like I learned in geometry class - a sequence of symbols and references to hard-coded lists of axioms and prior deductions. I thought that's what proofs are, but they are not, at least not as humans do higher math. High school geometry tries to distill this process down to a symbol manipulation game that students can memorize and regurgitate, and in the process loses the essence of the thing it was meant to capture in the first place.
The fundamental concepts
1. We have axioms which are things we accept without proof because we all agree that they're obvious;
2. Everything else should follow logically from things which come earlier;
3. Don't skip steps!
are extremely important and apply regardless of the field you're in.
Like you end up having to reteach proof in university discrete math or stats classes anyway!
Using motivations that we know to be true (or can see empirically are true) but don't feel trivial because "duh those lines are the same length" is a lot more compelling. You actually feel like you've learned something, not just a dumb formalism for something you could already intuit (and I mean if that's all proof does, let you formalize things you already know, what's the point?)
You're of course not the audience of these changes, because I expect that my last statement made you gag a little bit. But that's the way a lot of people are, and we shouldn't restrict ourselves to teaching the way they did 2500 years ago[0] unless there's still good reason to do it that way.
[0]: I'll admit that I think "look they were able to prove these things in this way 2500 years ago prior to the conceptualization of zero" is a compelling way to teach this stuff, but we don't do it that way either.
And I think that's where my objection comes in: if you spend the entire first year just developing that intuition but forcing a rote procedure, you'll have lost the majority of people already. Proof isn't arithmetic and we shouldn't teach it in the same way. Sure develop the process on the easy method first, but then show people why it's important to not skip steps.
For those not so lucky, they need to spend probably about a semester un-learning what math is before they can really start.
[0]- In the arbitrary parts of the US that I know anything about
I did ok in college Cal I and II (I’d been warned by older friends that our high school calculus class was a joke) but hit the wall in Cal III and ended up dropping Diff Eq before I could actually fail it. I barely passed Discrete Math by memorizing a bunch of proofs.
Turns out, I’m really great at memorizing arithmetic tricks and wasn’t actually that good at math.
“The remainder had parents who taught this kind of thinking from a much younger age.”
Fortunately for our child, my husband was a success in Germany’s math education system, and will therefore have the lead on how our kid is taught to think about numbers - I’ll just give the English words for things.
Geometry -> Proofy Linear Algebra
Trig -> Computational Linear Algebra
Math, and specifically Geometry aren't about useful skills, they are about understanding the world.
I can't remember a physics class where LA didn't pay heavy dividends -- in particular, differential equations are the language of physics, and you'd be hard pressed to find either an analytical or computational diff eq technique that didn't have a core of linear algebra.
Meanwhile, the last time Power of a Point gave me dividends was on math contests.
But imagine that you never heard of concepts behind it.
It'd just become a more-or-less useful artefact. And in no time it would devolve into a useless ... thing so to say, a decoration, as you lose knowledge how to apply it.
Believe me, it pains me to suggest bumping it back. Introductory proofy linear algebra just hits a quadruple home run: it's astonishingly useful, it's getting moreso, it's simple enough to remain age appropriate, and it can serve as an intro to proofs. As much as I enjoy geometry puzzles, I just don't see how they compete with that.
For the true fans, of course, the answer today & in this hypothetical future is still to learn both.
Sorry, but this is crazy. If you're in physics, electrical engineering, mechanical engineering, or civil engineering[1], then trigonometry appears in so many problems - including ones that have little to do with triangles and geometry.
Calc II is heavy on trigonometry for a good reason. So many integrals that show up in the "real world" are solvable if you know your trig identities. These show up in semiconductor theory, mechanics, electromagnetics, quantum mechanics, etc.
Trig is the one thing I'm glad I was taught well in high school. Used it all the time for over a decade.
[1] And probably many other disciplines.
Though admittedly I only got an SB in Math, I think geometric proofs were an okay introduction to the idea of the proof and of logic. Of course they are not representative of professional math. There are many things we learn as an introduction which don't turn out to bear that much resemblance to the more advanced form. I don't write 5-paragraph essays with clear thesis sentences anymore either. But it helped me to learn to write that way as a way of clarifying that I was stating my arguments effectively.
Sometimes, for my homework, I tried to state very explicitly in my proofs which axiomata I was using, both as an intellectual exercise and to see, e.g., where I might have gotten my logic backwards or where I used the axiom of choice (which constantly surprised me). I wouldn't turn these overexplicit proofs, but it helped to clarify that I was doing things correctly. If anything, when I was in college, the trend was away from 'informal' language. When I took, e.g., Discrete Math, for more complicated proofs, we were encouraged to write out a DAG for the dependencies of the proofs/lemmata so that it was exceedingly clear what depended on what and that we had in fact proven what we set out to prove.
You might be right, but they are the only high school math class that teaches proofs. If you take away geometry you are left with nothing.
Having said that - any math concept can be memorized and regurgitated. My kids are in CA elementary math right now and it seems to be better than when I was a kid. The emphasis is on derivation rather than memorization. It might just be that geometry is better now than when you were a kid.
I still suck at geometry.
Geometry is a really poor representation of whether one can do proof based maths.
The issue with Euclidean geometry as an entrance to proofs and logic is two-fold. First, the definitions and axioms of Euclidean geometry are incomplete in many ways. Many definitions, such as that of a line, cannot be understood from what is written in Euclid but require a significant amount of intution pumping to be able to know how to properly work with them. Thus, the fundamental definitions in Euclidean geometry are bad examples of what a definition in math should be, and we are already starting on very rocky footing. Moreover, the axioms, as they are presented in Euclid or common modern educational sources, are not sufficient to do what is claimed. For example, the proof of postulate 1 already has a logical gap because there is no axiom which guarantees the existence of a point lying at the intersection of the two circles one has drawn. Again, the argument relies crucially on a figure, which is the intuition pump used in all of Euclid, but the picture is not based on any of the axioms, so it is reinforcing a bad way of thinking about proofs that is intuitive and not at all focused on carefully using definitions and axioms. (Of course, one can fix Euclidean geometry to be rigorous by adding many extra axioms, but the resulting axiomatic system is much more complex and is not at all suitable for highschool students, except possibly the brightest.)
The second, somewhat more minor, issue I have with Euclidean geometry, related to the first, is that the way arguments are phrased, and the use of figures to illustrate, often hides many logical steps that are only implicit. In particular, I am thinking of the implicit use of qunatifiers in statements that are proven in Euclidean geometry. This is an issue because as soon as one moves on to proofs in any other context encountered by students, e.g. in first year undergrad, it becomes much more difficult to do things correctly while only thinking about quantifiers implicitly.
It would be much more beneficial, in my opinion, to have the first introduction to proofs be a topic that is much, much simpler (such as integers) where the focus can be purely on how statements are formed with quantifiers, how strategies of proof are determined based on the form of the statement and which quantifiers are involved, and how the (much shorter and simpler, and not requiring an intuition pump to use correctly) definitions and basic properties of that topic can be applied in a proof.
The root of all of this is the importance in proofs of properly using the definitions and axioms. Students in highschool, except the most talented, just are not careful thinkers and will revert to their preferred lazy way of thinking (such as pictures and vague ideas) as soon as you give them the opening. In my experience, the only way to force students to understand how to properly prove things is to pull out the rug of their intuition, even briefly, for just long enough so that they learn how to do things without it. Then later, once they have properly adopted the mindset of using the definitions, you can let the intuition back in.
For context, I don't know if any of what I just said reflects how Euclidean geometry is taught in, say, Caifornia. I only know this from the perspective of having tried to incorporate Euclidean geometry in an undergraduate proofs course (in Canada where Euclidean geometry hasn't been part of the grade school curriculum for some time).
If you remove all of that, you can embed actual geometric content into other classes as you go, much like probability and statistics is currently integrated across multiple years.
https://www.maa.org/external_archive/devlin/LockhartsLament.... makes the best case for this.
Briefly, he argues that we greatly exaggerate how much math you actually need in ordinary life and in most jobs that people usually think of as needing math (and what you do actually need can be learned on the job), but nevertheless learning math is worthwhile and important because of what it teaches you about how to think.
It's hard to imagine now, but back in the early days of the US similar debates played out over teaching arithmetic in schools. Most people didn't need more than counting and simple addition and subtraction, so why make everyone learn any more than that? Those few who meeded more could learn it outside of school.
It seems every defense is built around hedges like this one:
> although they are cutting geometry a bit, which doesn't make as much sense today as it did 100 years ago when far more people grew up to be farmers or ranchers
Which suggests to me that they really are trying to walk back the complexity of the education, perhaps as part of a goal to force the variance of educational progress into a narrower range within classes.
The language is so vague that it's hard to understand exactly what they're trying to do, which I think is their point. If they wanted to emphasize advanced education topics it would have been front and center in the plan. Instead, it seems like a footnote that we're supposed to assume will get taken care of in some future iteration of this integrative math program.
I'm not sure why how you get "walk back the complexity of education" when it's obvious that the current system is broken.
Students are tracked (into courses/pathways and within the classroom).
This is a sign of white supremacy in their view.
See this PDF:
https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
Under the Common Core, children in middle school who are ready for Algebra may opt for Algebra, and children who benefit from a delay may opt for a delay — but this is viewed by Equitable Math as sustaining White Supremacy in math education.
But that's not what's happening, so, again, what does that have to do with the actual changes being made?
If no to both, it does seem an awful lot like invoking the motivations of some of the people involved as a boogeyman rather than making an argument about the final recommendations themselves.
For schools under the Equitable Math proposals, the goal will be that for any given grade level, all children will be at the same level up until their last year. The explicitly stated reasoning by the program authors is that alternative tracks in math are a form of disparity which promotes White Supremacy. Will this in fact be the final final proposal? That is what is under debate right now.
> Administrators should examine programs and policies and how white supremacy impacts student outcomes (e.g., tracking, course selection, intervention rosters).
> White supremacy culture shows up in math classrooms when... Students are tracked
I interpreted this to mean that tracking is (like course selection) a student outcome that can be impacted by "white supremacy culture", not that tracking is, inherently and unavoidably, a sign of white supremacy. If there's burglars around, unlocked doors are usually correlated with burglary; that doesn't mean you can't leave your doors unlocked, but you're going to want to be careful about it. Similarly, if you live in a society with pervasive racism (read: most societies), it's possible to track students in a way that doesn't reinforce those racist trends, but probably only if you're careful about it.
I think I probably agree with you that "white supremacy culture" is, as a term, perhaps more aggressive than it needs to be. Not being deeply embedded in this debate, I'd assume it's going to turn off more people who hear it, think "I'm not a klansman, so this isn't something I need to address" than it will engage people who think racism is bad but haven't considered how their own (probably unexamined) practices are leading to outcomes they don't want.
If you told me that math education professionals were a fundamental cornerstone of an oppressive culture, I would sign on immediately. But you have to be aware that it is exactly that cadre of professionals that are offering up the recommended changes.
The parent comment literally admitted that they were removing specific complex topics.
That is what I was responding to.
you quoted and responded to
> although they are cutting geometry a bit, which doesn't make as much sense today as it did 100 years ago when far more people grew up to be farmers or ranchers
so which specific and complex topics are you referring to in the OP?
My complaint about these reforms is that the root cause of the issue is not being addressed. This has long term negative effects. My own anecdotal experience is that what used to be a C is now an A or a B in my classes and I’m passing people who don’t know anything. I’m judged by the passing rate so I’m maximizing that metric. These reforms are just doing what I’m doing but in a less forthright way.
The root cause is well outside of the scope of schools to address. Perhaps they can help to a small extent through things like lunchtime meals. But curriculum reform itself will never narrow the gap more than a tiny amount.
Childhood nutrition, single parent households, health of mother during pregnancy, culture/respect towards education as a virtue in the community and household, education level of parents and the time they have to play and talk with their kids.
All these things are going to impact the capabilities of young school children and feed into outcome gaps between various groups (Black vs White, poor vs rich).
I believe most proponents of "math equity" actually know all this, and are just maliciously virtue signalling either because they're jealous that their own kids aren't doing well, or for social credit.
I'm not American, and I don't claim to know the environment and the issues people face there, or their root causes. I may not be fully understanding the extent of nutritional differences or family dynamics.
I am, however, absolutely certain that affluence feeds affluence and that misfortune feeds misfortune, on average. Even if you had all of the above equal except for the education levels and socio-economic status of the children's parents, you'd end up with statistically different outcomes.
I live in a fairly egalitarian country, and if I remember correctly, there's an average income gap of ~30 percent or so between people whose parents were in the highest quartile in income and those who were in the lowest quartile. While ethnicity may play some role in the statistical gap nowadays, I don't think it explains the statistical difference; ethnic minorities are disadvantaged here but they make up a small enough minority that I expect the bulk of the difference to be simply due to socio-economic differences within the same ethnic group.
Basically, if your parents and their social in-group got highly educated, I believe you perceive that as the norm. If they didn't, it's not as likely that you do.
Add in some practical stuff such as whether your parents can afford to finance or support your education, and the gap's already there. The rest just amplifies it.
Sure, physical health, nutrition etc. can have an effect, and they certainly do if the differences are great enough. I'm sure ethnicity or race has an effect, sometimes due to racism, and sometimes because people perceive their own opportunities or expectations differently depending on social roles, and for various other sociological dynamics. The latter is true even if you remove ethnicity or race from the equation. Racial stereotypes and images probably emphasize things but I don't think you can pin it all on that.
Considering how much worse off African Americans are socio-economically, on average, than white Americans, it's a no-brainer that their kids end up worse off on average as well. I'm not saying you should just shrug and accept that, and I'm sure actual racism exists as well, but the point is that some of it would happen even without racism, either overt or covert, or any "structural racism" that could include a whole spectrum of things.
That means any real solution is going to be hard and slow, unfortunately. Changing the subject matter in the name of equity really doesn't sound like one.
> I believe most proponents of "math equity" actually know all this, and are just maliciously virtue signalling either because they're jealous that their own kids aren't doing well, or for social credit.
It could also be that people take an easy non-solution in preference to working towards improvements and solutions that could take time, great patience, tolerance of morally and socially undesirable situations (one might have to accept that you can't achieve perfect equity, or at least not quickly, and be able to withstand social judgement for that), and are all around a lot harder to accomplish.
I don’t understand why we are so arrogant about everything that we don’t even try to teach 5th graders how to use spreadsheets and generate graphs. So much of math education is useless punishment.
Given that we know how the sausage is made, pretty much the last thing on earth we as software professionals should want is to inculculate the public with an overreliance and blind trust of software.
It's worse than that. There's something about the American system which forces black families to be not just stagnant economically, but often to move backwards (at least in the transition from Boomer/Gen X to later generations). Both of my grandfathers provided a strikingly middle class life for their families, leaving the military after WWII for decent careers: one as a stable, unionized factory employee, the other as a nuclear physicist. All of their children went to college. Both of my parents hold advanced degrees. Even still, they face financial difficulties that their white peers don't seem to, and my generation of siblings and cousins, while along a spectrum of affluence, seems to have inherited a magnified version of their parents' diminished prospects relative to their achievement. On average, the families that were middle class mid-century are now working class, even with degrees.
And we're outliers, in terms of educational attainment in the black community heretofore. That's changing, but to what ends, when black professionals must have a more advanced degree to be considered for the same job as a white applicant with a less advanced degree? When our houses are worth $50k less, our access to credit is restricted, our tax burden relative to income tends to be higher, and we are actively sought out for discrimination by many bedrock institutions of American life? It's not a level playing field.
Well, that's not quite what they're saying - essentially what they're saying is that they're a different kind of smart. Not that I agree with the logic, but essentially what they're saying is that the tests - along with the whole curriculum - were designed and written by white people, so they're unintentionally biased in a way that non-white people (except, I guess, asians) can't understand them. The implication being, of course, that if black people had designed the entire curriculum and the tests, they would be similarly impenetrable to white people. Of course, I don't think that makes much sense either, but that is the essence of what they're trying to assert.
But teaching math absolutely is not. It is a very human process, helping students find handholds in what they know to make the next conceptual step. Absolutely breaking their minds with a new topic, then returning to it a month later and they find it obvious now. There are no platonic math lesson plans out there to tap into, and finding more effective ones has been one of humanity's jobs for at least as long as there has been written language.
(FWIW, real analysis is generally considered one of the easier courses in a typical math degree)
Quite a few colleges seem to use it as a filter class to determine who has the requisite aptitude and interest in pure math. At my college, the material wasn't particularly bad, but the evaluations were designed to be pretty challenging and grades weren't curved at all.
On the other hand, in my real analysis course we worked with metric spaces, topological spaces, Hilbert spaces, the Baire Category Theorem, etc. I doubt most students in “a typical math degree” would be studying these topics outside of a pure mathematics specific degree program.
I'm pretty sure that is exactly what they are saying. The 2021 version of it anyway
What is a "white person"? A "black person"? Are these metaphysical categories? Biological categories? Cultural categories? Why would a person of one category be unable to understand curricula produced by people of another?
Some have suggested racism is cause for inequality, yet Asians do well in America where they’re a small minority.
Some have suggested culture: certain parents promote education more.
Some have suggested examining IQ more closely (though thinking along these lines is a doubleplusungood thought crime)
Ridiculous.
There are long established Chinese communities in the US who came over to be railroad laborers. Why would they somehow be in the top 1% smart?
Those long established Chinese families represent a tiny minority of Asian American university students. The vast majority are international students or first generation immigrants.
[1] https://en.wikipedia.org/wiki/Demographics_of_Asian_American...
I’m sure it doesn’t help that admissions discriminate against them because they look similar to the international students and first generation immigrants.
Descendants of those people are a tiny part of the Asian population (though probably formed an important part of the initial cultural support network for later immigrants, at least those settling in the area where those earlier groups were concentrated.)
or that the kid inherit good DNA so probably also have high IQ like their parent ?
I'm curious how it's handled in California, considering that Asian's votes taken a bit more seriously.
If we're going to go there: I went from being a straight-A math student in Pre-Calculus to a C (verging on D) student in my AP Calculus course in high school. In college, I retook Calculus and aced it, receiving one of the highest final scores in the class. The first course was taught by a black woman. The second was taught by a white man. The last was taught by a black man. I am a black man.
People in this conversation are frequently quick to dismiss the value of anti-racist (and, for that matter, anti-sexist) policy and execution in STEM pedagogy. They lean on and extrapolate erroneously from the notion of many great mathematical thinkers' probable hereditary advantages to a general, in-born hierarchy of fitness for STEM thinking. Coincidentally, this shields them from tough conversations regarding their own fitness to teach, and especially to teach children whose backgrounds they cannot or will not find sympathy and empathy for. I will admit that the solution is not so simple as my anecdote might suggest, but the implied path shares character with the correct one, in recognizing the farcical nature of assuming that the status quo - especially in this country - is a product of actual potential playing out as it must necessarily so, and not of history overshadowing even the best of intentions (though they are usually less than that).
I don’t dismiss the value of anti-racist policy and attempts to rid myself of negative biases that affect my students. My compliant is when I’m told, and I have been told this by an educator, that the act of requiring knowledge of algebra is itself racist. That’s when I feel we’ve gone too far. I don’t necessarily think algebra should be required but the reasoning for getting rid of that requirement shouldn’t be because black students are not passing it at a high enough rate.
My belief is that far too many people are going to college. The degree therefore is being watered down. If we lived in a country where everyone had guaranteed access to food, shelter, and medical care then the emphasis on college wouldn’t be so pronounced and colleges could then concentrate on what’s needed.
I don’t believe your comment should have been downvoted. Thank you for sharing your experience and thoughts.
(I would argue that the majority of what we call "software engineering" is actually of this nature.)
So while I appreciate the sympathetic elements of your reply, I have to point out that the root of your argument is a baseless suspicion of the cognitive capabilities of students of color. Yes, requiring knowledge that has been systematically denied, effectively on the basis of race, in order to obtain a credential that is necessary to earn a dignified living, is a form of racism. And we will need to "change things" to fix that.
Do you have any evidence that the vast majority of people can learn calculus in a timely manner? I have a lot of anecdotal evidence that this is simply not true. Please note that I’m making no reference to or claims about students of color. I’m speaking about all people. In my experience a lot of people simply can’t learn calculus to any reasonable definition of what that notion entails.
The requirement of a specific set of knowledge for a degree is not what is wrong. What is wrong is living in a society in which having a degree is increasingly necessary to live at a decent standard.
https://matheducators.stackexchange.com/questions/11396/what...
I'm at a loss as to how you might construe these statements, which you presented as wrongheaded (i.e., that you believe the inverse of each), to not imply that you believe that the "cognitive capabilities of students of color" are lesser, considering the nature of the racial achievement gap (an aspect of the conversation which you broached). Either you simply do not remember what you stated earlier, or you're lying. This is clearly a reference to students of color, at the very least. I just want to establish the high probability that you are being disingenuous.
>Do you have any evidence that the vast majority of people can learn calculus in a timely manner?
Assuming that most people can learn at a 5th grade level, and that, as suggested several times in the comments, this lecture could be broken up into multiple days worth of dynamic, interactive instruction, rather than being presented as a blitzkrieg 20-minute lecture:
This is not conclusive, of course. But you asked for any evidence, and I think a reasonable person arguing in good faith would conclude that it suffices. You've shown evidence to be otherwise, so I don't expect you to agree, but I would be happy to be wrong for once in this conversation, on this matter.
The idea in education is that everyone is intellectually equal. Therefore the racial achievement gap in mathematics is due to racism. The solution is to change things.
This is a line of reasoning used by people to advocate for things like getting rid of remedial math. The problem with this line of reasoning to me is the premise that everyone is intellectually equal. Not all premises have to be wrong for an argument to be wrong. This comports with my later statement that too many people are going to college.
There is nothing of a racial nature in any of the statements I made in this regard. To reiterate, I believe that there is meaningful variation in the intellectual ability of humans. I believe too many people are going to college.
My problem with the California initiative is that it is based on the idea that everyone has the same intellectual ability and, furthermore, it does not meaningfully address the true cause of the problem of the racial achievement gap. It’s worthy to address biases amongst institutions and I agree with their efforts in this regard.
The racial achievement gap is a systemic wide problem caused by the structure of our society and nothing meaningful will improve until these things are addressed at a higher level. The effect of the California reforms, I fear, will cause more harm than good.
So, no. Please read carefully and avoid kneejerk responses.
Fuck it. It sucks so much that your comment is downvoted. Fuck that. This place is fucked up sometimes, where people downvote comments that might at a very long stretch be misconstrued as displaying some remote racial insensitivity if you squint really, reaaaaly hard, and then downvote a black guy who says what he's seen first-hand. It's like watching the BBC giving equal screen time to climate scientists and climate denials in service to some objectivity, long ago lost.
Must you have the same skin color to teach rather than babysit/police? No. In the American context, though, it takes effort rather than inertia to accurately see and develop the potential of your black students -- because inertia gives white teachers in particular a relentlessly negative media stream about "thugs" instead of "future Nobel winner". Our segregated society gives white teachers an incorrect set of Bayesian priors on the meaning of acting out or difficulties in class. They don't have black friends whose kids are going through a rough patch but are still the same sweet kid they were at age six. I mean, I just talked with a high school teacher in a rural Midwestern district who said 'at least she didn't have to worry about kids doing cocaine in the closet at school like at an inner city school', and as a graduate of such an inner city school, my response was "honey we couldn't afford cocaine, that's a rich kid drug". This is a lovely lady, dedicated teacher, and that's her prior on "inner city kids" as of Dec 3, 2021.
We really need to divorce the teaching and accreditation functions bundled in the modern university. There is a clear conflict of interest.
It becomes a question of how do we ensure every child has access to a dedicated adult willing to tutor them and push them in education matters. Once a child begins to fail in a class, unless someone is there who can help them back onto the route of succeeding, they risk developing learned helplessness around education. Maybe a single subject, maybe education in general. It takes a lot of time for someone to work with a kid, find out what the root cause of the problem is, help them overcome that, and then build up on the topics they have fallen behind on. It helps greatly when that person isn't just there for teaching/tutoring but also invested in the child in other ways so the child values their input.
When parents either don't have time, ability, or desire to do this, there is rarely a backup. Teachers try to fill the gap but they are spread too thin over too many students and rarely are with a student long enough to make a significant impact. Some teachers may even avoid it because it can quickly become an issue of favoring certain students over others. As for parents, while some parents will be able to fix the problem by having more time available, some parents lack enough education to keep helping their child past a certain point. Both finding how to give parents more time and how to educate parents enough to help their children are hard problems. As for the parents who don't have a desire to help, there might not be any solution at all.
Your C student with an A doesn’t need your math class, they need an A.
The employer filters all non college graduates and then filters by GPA. With most employers, knowing what you are doing is not ranked 1st or 2nd. Price and qualification is up front.
I quickly found that we are now getting 40% on those math test which result in an (A+) because they grade in the curve but 20 years ago the real average for this teacher exams where around (75%) and those exam had question of similar difficulty.
TLDR: an A+ today is not the same as an A+ 20 years ago
California math education (again, at the time I took it) was already extremely oddly paced. The Algebra 2/Trig class I took was extremely aggressive, and then the year of pre-calc that followed it [1] had about 2 weeks of novel content spread over a year's worth of teaching. I was initially a year behind most of my classmates (starting in junior high), then skipped ahead to do Calculus BC alongside everyone who'd been a year ahead of me---and aced it. On the other hand, the people who were really advanced had already gone on to college courses at that point and basically hadn't bothered with anything in the system for many years.
In short, it's a mess and has been for decades. If they can clean it up a bit and make the pacing more even and integrated, I think that would be a net win.
[1]: "Introduction to Analysis", I think they called it.
Finally, my first reply was disputing the claimed uselessness of geometry. It's very clear that it's far from useless these days, although some material is certainly less useful than it maybe used to be.
[1] https://www.cde.ca.gov/ci/ma/cf/documents/mathfwgeometryjl.p...
Geometry is one of those things that you can teach in the utmost horrible way though (make students memorize theorems verbatim), I understand why students can perceive it as incredibly boring and useless.
this blurb alone invalidates everything else you have to say. you have absolutely no idea what are you talking about.
However the entire goal of the integrated program was to maximize the amount of Calculus students could get through. I got not one year but two years of Calculus effectively by the end of HS and had no problem passing the AP calc exam. Probably only 10% of my HS class did that though, and that was already at a selective private school.
Integrated is great as long it gets students to the same place.. it's still really important to get as many talented students into Calculus before HS graduation.
Have you ever seen Terence Tao signing up for a manufactured outrage? Alan Kay? If you're the type to read technical papers you'll recognize a bunch more names on the list of signers. Furthermore the language in the post was calm and measured.
> I find it interesting with many of these criticisms that subject matter experts on maths, sciences, etc think that they are also subject matter experts on the pedagogy of maths, science, etc especially at a high school level.
The people you mentioned are my idols, same as the authors and hosts of this blog post. But there is a world of difference between being a great scientist and being a great K12 teacher.
> The signatories include ... educators with decades of experience teaching students at all levels ... people vested in mathematical high-school education, such as ...
Obviously this is just my personal anecdote, but I do claim I have been very invested in exactly this type of education and have seen how well-meaning crazy-smart professors are failing to teach K12 students (in their once-a-year charity event) while patting themselves on the back for a job well done.
What do you think of the claim that the policy will increase inequality of preparation because better-off parents will bypass public education more? It sounds like you might have more light to shed on that.
But to actually answer your question. Better-off parents already bypass public education, even if not completely. If this new program works (not a given), the problem will not be exacerbated, rather more students will be prepared to reach for these "gifted programs" (which in many cases, even if expensive, usually have good fee-waivers as this gives them more credibility).
[1] Obviously just a personal opinion. But in the interactions I have had in this context I feel I have seen a lot of inflated but unsubstantiated sense of competence.
(I wouldn't bet on it, personally, and I don't think the infusion of wokeness is mainly about helping more people to understand math better. Hopefully I'm too cynical. The Common Core math stuff seems like progress, for instance.)
It is cited in the open letter's supporting document. It would take some very serious effort to read through these resources and try to disentangle the biases of the authors, but I guess this meltdown would not have happened if reading social/ed science papers was easy.
Very good point. K12 teachers know a lot, but they may not know much about the path to becoming a world-renowned scientist. The signers of this letter know that path from their own experience and the experience of their colleagues. They may not be educators but they have intimate understanding of the education process of bright children.
A central pillar of Equitable Math is that all children of any given grade ought to be in the same math class, and that there ought not be any standard specification for, say, taking Algebra "early" in middle school. The explicitly stated reasoning by the program authors is that this disparity sustains White Supremacy in math.
A child who is ready for Algebra would be best served by opting into a classroom where a teacher has been polishing a year-long discourse on Algebra, as opposed to creating an ad-hoc gifted program. A return to gifted programs would be a return to administrative opacity.
Or Scott Aaronson. Scott Aaronson is about as social-justice-y as you get. When even he thinks the equity types have gone too far, it's really time to step back and see if you're making sense, even to yourself.
There's a bigger argument here, but I'm just addressing this one unmerited accusation in this thread.
He and some of his collaborators were among the earliest in applying Piaget and Bruner's learning models to programming education, mainly for learners under age 15.
A pillar of Equitable Math is that all students should be at the same level up until the last year of high school.¹ The re-arrangement of subjects is not the hotspot of contention, and neither is the disagreement over "deepness".
The contention is over whether or not there ought to exist a faster track which, for example, permits students to take Algebra in middle school. This has been specifically derided as a sustainer of white supremacy under the Equitable Math discussion.
A return to gifted programs as the way to deal with students with differences in math preparation and ambition would be a return to administrative opacity. A failure to specify tracks which allow students to take Algebra in middle school would be a solid win for private schools and after-school programs like RSM.
Under Equitable Math, the last year in high school is the only year of differentiation.
I mean, if they're going to eliminate gifted programs for an advanced academic students, then they should eliminate sports teams for advanced athletic students by parity of reasoning. Isn't the star quarterback just as unfairly advantaged by family and genetics as the smart math geek?
These don't apply to any special program, there is no lottery, and they aren't hand-picked by teachers or administrators.
How do I square this with their claim that the CMF is "placing obstacles (such as doubling-up, compressed courses, or outside-of-school private courses) in the way of those who want to take advanced math in higher grades."?
When I read "they're not forbidden", I take that to also mean that there's few new obstacles.
I don't know whether it's intentional but the FAQ reads like it's intending to deceive me. They answer questions with "no we're not doing that", then follow up with how they do exactly that with different words. For example:
Q: "Does the draft Mathematics Framework eliminate middle school mathematics acceleration programs?"
A: "No. The draft Mathematics Framework does not eliminate middle school mathematics acceleration programs (including programs that offer Integrated Math 1 or Algebra 1 courses to grade eight students). The draft Mathematics Framework emphasizes the importance of following the sequenced progression of topics laid out in the Common Core State Standards for Mathematics (CCSSM) and considers the latest research on the impact of skipping grades or undermining the sequences progression."
They're not "eliminating", they're "emphasising" and "considering". Maybe what they're doing really isn't eliminating but it sure reads like it is. The tone reads like corporate damage control. 'We didn't "spill" the oil, we misplaced it.'
It is almost as if words have actual meanings ...
This is not manufactured outrage. I have read the framework (and many of the sources cited as support for the recommendations), and I am outraged.
If you follow the footnotes, you'll find instances where:
- the framework incorrectly states the conclusion/claim in the paper/study/web-page
- the framework relies on a claim in a paper/study/web-page, when the paper/study/web-page lacks sufficient evidence to support the claim due to poor experimental design, poor interpretation, or lack of evidence altogether
"The FAQ is at [2] and directly responds to these characterizations."
The FAQ does not accurately portray the implications of the recommendations. (I read both the framework and FAQ a few months ago.)
It's also funny you mentioned that California will emphasize more on "applied math". I mean really? We're talking about high school maths. They are so simple and so fundamental that there shouldn't be a distinction between the applied and the theoretical. Teaching "applied maths" is simply a coded word for watering down the standard.
Which, if they did, would I think be a mistake.
What I can see is:
(1) Chapter 7 of the first field review draft says that they intend to de-recommend "Algebra I" for people in grade, in favor of something called "CA CCSSM" which incorporates concepts of algebra. They seem to say that CA CCSSM is much more thorough and comprehensive than Algebra I and is a better choice for students who are showing particularly strong math skills.
"In grade eight, the CA CCSSM are significantly more rigorous than those from previous grade-eight content standards. They address the foundations of algebra by including content that was previously part of the Algebra I course—such as more in-depth study of linear relationships and equations, a more formal treatment of functions, and the exploration of irrational numbers. … The rigor of the CA CCSSM for grade eight means the course sequencing needs to be calibrated to ensure students are able to productively engage with the additional content. Specifically, students who previously may have been able to succeed in an Algebra I course in eighth grade may find the new CA CCSSM for grade-eight content significantly more difficult. The CA CCSSM provides for strengthened conceptual understanding by encouraging students—even strong mathematics students—to take the grade eight CA CCSSM course instead of skipping ahead to Algebra I or Mathematics I in grade eight."
(2) The FAQ and accompanying diagram say that they intend to recommend "Algebra I" as one of three options for a 9th grade curriculum -- with the other standard options being "Integrated I" and "MIC I". I think the idea this diagram presents is that 9th/10th grade carries Algebra I/Geometry or Integrated 1/Integrated 2 or MIC 1/MIC 2, and then you can spend 11th/12th grade studying other concepts in detail like statistics (great choice IMHO) or calculus.
That's the diagram here: https://www.cde.ca.gov/ci/ma/cf/images/mathfwfaqs.png
(3) Critics of this proposal (writing at https://bit.ly/cmfanalysis cited in the guest blog post linked here) argue that postponing Algebra I from 8th grade to 9th grade reduces the opportunity for students to study calculus in detail in high school.
I happen to agree that calculus concepts might not be the most important -- maybe it's more important to get a good grounding in statistical thinking as opposed to integral calculus? Maybe it's better to learn really strong proof skills and approach calculus directly via real analysis? I dunno.
I guess what would bug me would be if kids didn't get abstract thinking early. The core concept of algebraic thinking to me as a nonexpert is treating things as variables rather than concrete numbers, and being able to reason about changing a function or a family of functions rather than a specific line or curve.
But what confuses me overall here is -- why does the CA Math Framework still include Algebra I as a 9th grade program? If the new 8th grade CA CCSSM is indeed so rigorous that stronger math students should take it, and if it includes the essentials of Algebra I, then why waste another year on the concepts again? I don't understand.
We have the shittiest math education in the developed world, and it comes down to teacher training, teacher support, professional development, and ensuring that children are fed and in safe situations where they can do laundry and wear non-smelly clothes to school [1]. In Finland that is understood, and lo and behold, good scores overall. In the US we think that curriculum is a magic bullet. Like changing the textbook will change what kids learn. As a former math professor, this is bullshit. I can take whatever curriculum you want in math and transform it to meet students where they're at -- because I f*(&ing know math. Too many of our teachers don't, and it's our fault as a society. I left education because of the crap wages and that creeping feeling that my individual efforts to better things just couldn't match the magnitude of the problems.
America keeps being a magic-bullet country. The vaccine will fix COVID, so we don't need societal support for public health measures. Right or left, I don't care; the right thinks "individual responsibility" is the magic bullet in the face of infrastructure problems, funding problems, everything, while the left thinks technocratic solutions or "being correct" will be the fix.
I strongly support the shift to more applications of math, more stats and probability, more analysis of real-world systems. There is plenty of room to challenge gifted students in this context and I have done so myself -- you do need the time and support to build scaffolded projects so when "that kid" is done you can say, "Well, what about this?" and when that other kid is still struggling you can break it down. The factory grind of education in American and the fact that many math teachers don't even have a degree in math means that is quite difficult to put in place.
[1] https://www.nytimes.com/2019/03/13/us/schools-laundry-rooms....
Supplementary math education in our area costs about $1500-$2500/year (looking at Russian School of Math list prices). The exemplary private schools in the area I grew up charge $30k-$35k annual tuition (with financial aid available for some families). And you can DIY home instruction -- I've been working through the Moebius Noodles play with our 4yo, and I guess you could try to see if there's a Math Circle to sign up for.
But not every household can afford the time or money to coordinate extracurricular instruction. The kids whose parents are hyper-prepared and able to spend the time and money will end up with better math background, maybe a better shot at the AHSME/AIME/USAMO, and I guess maybe better career outcomes, versus their peers. Is that a fair outcome? Is it a good thing to do?
I'm very willing to be wrong here … I just don't understand how this plan promotes equity.
p.s. saw this in the news and tried introducing algebra to the 4yo. We're not quite ready yet.
"Hey kid -- if I have four of something but I want to have six of them, how many do I need to add?"
He holds up a fist, empty. "Four." Then he starts counting out fingers. One finger: "Five!". Two fingers: "Six!". He says, "Two!"
"That's right, kid. Sometimes we say 4+x=6, so x=2."
He gives a sly grin. "But I know my numbers so well that I don't need to use x!"
A tiny paycheck and... I'm sorry, I have no idea how to read "generous" time off; are you referring to summers when they don't get paid, or something else? My impression is that most teachers are working significantly over 40h/wk and either don't know that they're victims of wage theft or somehow don't care.
Also, teachers doing things like chaperoning the dance and stuff are probably not getting paid for that time.
Now that we're not doing standardized tests and turning admission into high school transcript plus additional material it's really going to help the kids whose parents can organize and pay for the most extra circulars.
These tests are notorious for having all the prep material in a few inexpensive books.
My guess is that it will reduce racial inequality, but increase inequality based on parental income (class). Eliminating SAT scores will result in greater affirmative action, and the richest people of each race will be able to sculpt a compelling resume for their child; there will be no way for those with poorer parents to compete on the holistic measures.
That's great unless there are a few other kids in the same area that also need to the book and also think to get it from the library.
The larger overall point is that acquiring SAT prep resources is easier to do than acquiring resources for volunteering or extra curricular activities. While the former may be difficult in some situations, in those same situations the latter has even greater difficulty.
You guessed it, poor whites and asians. The kids who couldn't afford extra curricular but who did great on the tests. Who is it going to help the most? Children of wealthy East-African and Caribbean immigrants.
This focus on extra-curricular also makes it really easy to sneak-in affirmative action (despite voters repeatedly saying no). Because, let's be honest, you can't objectively compare these things to one another.
Middle-school students embrace endless summer ... of linear equations
https://edsource.org/2017/middle-school-students-embrace-end...
The Effects of the Elevate Math Summer Program on Math Achievement and Algebra Readiness
https://www.wested.org/resources/effects-of-elevate-math-sum...
Khan Academy in 7th Grade Math Classes: A Case Study
https://www.wested.org/resources/khan-academy-7th-grade-math...
Well, it can turn every one into a bad pupil :-)
I wish people would take a look at what happened in other countries which followed a somehow similar path of dumbing down courses and lowering requirements.
Here is what 25 years of dumbing down achieved in France:
https://3.bp.blogspot.com/-xHQ532qyiek/XJ8kH-PnVTI/AAAAAAAAH...
This extremely telling graph about the level in the end of primary school is taken from an official note from the Ministry of Education itself: https://www.education.gouv.fr/media/22373/download
It is about maths (calculus) but we have somewhat similar drops in other matters, notably in French language.
You can easily see on the graph how the above average pupils from now perform as bas as the below average pupils from 30 years ago. Only a small part of pupils perform as the average pupil used to perform. You can also note that the 'excellent' pupils have basically disappeared: there is no bump (and no long tail) on the right of the curve any more.
Furthermore, every social category performs much worse: http://centre-alain-savary.ens-lyon.fr/CAS/documents/documen...
Not a single category got something positive about it. The lower social classes for which this dumbing down was intended actually suffer badly from it; the upper classes didn't find ways to escape it either.
It is estimated that when they reach the end of high school, pupils' level is late by 1 or 2 years (depending on the matter) compared to what it was in the last two decades of the XXth century (when high school access was already expanded massively, we're not talking about the 50s-60s-70s). And yet the high-school pupils are basically automatically all given the degree: 95% success rate compared to 75% in the 90s (and in those days that was after many had repeated 1 or more years, which they don't any more, they almost all pass all classes automatically, even though they didn't assimilate the necessary knowledge and understanding to follow next classes ).
Another troublesome consequence is that it propagates. Very recently, universities, which for a long time tried to keep the same level as before, started to dumb down their courses an lower their requirements for passing years too, because the first years of university had become a slaughterhouse for a mass of students who were coming with a completely insufficient level (the high-school graduation serves as an automatic entry ticket for universities, there is no entrance exam). So the same effect as in primary and secondary education is about to happen, and selection is pushed to the Master level, but that last barrier will probably very soon break too (we already hear complaints about it).
Additionally, many professions pay better than being a teacher, and unfortunately, that includes package handling for FedEx and UPS (just drove by a sign promising $24/hour starting) in some areas.
A middle school algebra teacher should of course understand middle school algebra. This is not an unreasonable expectation for a job that requires a college education. If a teacher lacks the ability to master middle-school algebra, how on earth did he get into college?
Me and all of my friends were thaught the fundamentals of algebra & trigonomatry (admittedly not calculus) at 13 years old. I had no idea the wasn't the case in the US and it honestly kind of blows my mind.
7: Algebra I
8: Algebra II
9: Geometry
10: Trigonometry/Pre-Calculus
11: Calculus
12: Calculus-based Physics
8: Algebra I 9: Algebra II 10: Geometry 11: Trigonometry 12: Pre-calculus
Advanced class was -1 year. This was Upstate New York 90s/00s. Though I guess to be more specific these courses were actually combination. So it was 3 years of mixed algebra/geometry/trigonometry. Math A, B I think New York called it. Until Pre-calculus Which was actually year and a half courses of mixed topics.
The first level of math acceleration moves that high school progression up a year and has seniors taking calc 1 (limits/derivates & single variable integrals. The second level of acceleration has calc 1 in 11th grade and calc 2 (multi-variable) in 12th grade.
There are a handful of schools, mostly private, that move faster or have more diverse math curriculum offerings, but this is the most common.
So, when do American kids his algebra?
Standard curriculum: 9th grade, ~14yo
It's that a teacher which did not master high school and college math is not necessarily a good candidate to teach high school or advanced middle school math, and it absolutely occurs when the primary focus of the teacher's college career was teaching and not Math or another STEM field.
The model in the US seems to have become that the Teaching degree is the most important degree for a public school teacher regardless of the subject that is going to be taught. At some point that breaks down in a big way in the STEM fields in the range of middle or high school. Certainly you are not going to be taught Math at the College level by someone who does not have a Math degree. But in public school they've decided at some point that a math teacher doesn't need to have a math degree.
For anything pre-high school that would seem sort of overkill. A "good" teacher in the earlier grades is more of a function of how well they work with children.
Yes. Exactly.
> If a teacher lacks the ability to master middle-school algebra, how on earth did he get into college?
Knowing a subject well enough to pass a class or pass a test is not the same as knowing it well enough to teach. STEM in schools is a real problem because, well, non-education jobs pay 3-5x what teaching jobs do for math, CS, and robotic.
By eliminating all testing and objective standards.
Thank you for saying this. I am/was a high school math teacher and this was always the biggest problem when we got students in. The teachers at lower levels just don't understand it well enough to teach it. And, sadly, the same can even be said to be true for some of my coworkers. Our calculus teacher hasn't retired yet because there's nobody she trusts enough in the math department to understand pre-cal/calculus well enough to teach it (I'm on a leave of absence and have switched to the science department, though I've been asked by her and admin to teach those if I return).
To me, common core math makes perfect sense. It's how I do math in my head. But it's also because I feel like I understand math. If I'm subtracting 26 from something, I'm going to subtract 30 and add back 4. It's just quicker and simpler. That's what I've seen parents struggling with, and even teachers struggle with it too! Because they don't get how numbers work. It's really frustrating and harms the kids. I wish I could overhaul how elementary school teachers are trained as in my state they're not even required to do well in math, or take any upper level math courses, before teaching math.
We need teachers who have trained in those areas, and then wanted to become teachers. And it needs to go all the way up through middle and high schools, but I truly think the focus should be on primary first. It's why we get so many kids who don't understand multiplication when they get to high school, let alone division -- their teachers don't either and they just give them calculators at a young age! And it all boils down to how teachers themselves are trained.
Back to math at the school I taught at, there are two there who understand it. Funnily enough, they both came out of retirement to teach again (one has been doing it for 15 years, and the other just retired from her VP job a few years ago), and they're related. The older one married the younger one's uncle. It's funny how it stays in the family. The younger one's dad was also a math/chem/physics teacher, and was an amazing teacher until he just got too old. They were the only teachers I know or had at that school when I was there who truly knew math, and it showed in how they taught and the general outcomes of their students -- A "C" student in the accelerated algebra II class made an easy "A" on college algebra when they got there two years later, simply because it had been imparted to them that well.
Is that the reason? Or because they've been told to "do it the right way"?
In California, teachers' retirement benefits include defined-benefit pensions, with some inflation-protection. They also don't work the same hours as package handlers. Total pay+benefits for teachers in SF is about 50% higher than base salary.[0]
[0] https://transparentcalifornia.com/download/salaries/school-d...
The other problem you alluded to is that if they do understand well enough to teach it and teach it well, there’s a good chance there’s an engineering position they can get instead.
Still, the pattern is hard to miss. I think my current favorite is biology and its treatment of race ( https://www.nytimes.com/2019/12/07/us/race-biology-genetics.... ).
Quote directly from the article:
“We basically decided, no, race is still a social construction, it’s not a biological thing,” Ken Miller, an author of the widely used Prentice Hall biology textbook, told the science magazine Undark of the decision to omit mention of race.
I guess what I am saying is not new to anyone. Public schools will continue to degrade. There is no benefit to any of the groups other than the parents to ensure kids learn things ( administrators, their lawyers, your congressman, my congressman, teachers, teacher's unions, book publishers ). Sure, they pay lip service and some individual teachers care, but each of those groups have goals beyond kid's education.
edit: I was gonna add Apple and Microsoft in that list, but I removed them, because, as flawed as their reasoning is, at least they pretend they want to teach kids basic coding, which is not horrible.
I am not confusing race and species.
There is some real ugly history here.
But, there are no human 'races' in the biological sense. At best it makes you sound like you're discussing the politics in your Tolkien fanfiction. It is purely a social construct.
Listen, I'm not saying self-identified race and genetic or ancestral population are the same thing, but there are strong correlations. Perhaps you can clarify how the claim "there is no biological basis for race" makes sense in light of this fact?
> It is purely a social construct.
Something being a "social construct" does not mean it is purely arbitrary.
Which then result in patterns of race related medical diseases and similar topics. Sickle cell anemia, etc.
The fact remains that if you run PCA and clustering on genetic data as in https://en.wikipedia.org/wiki/Human_genetic_clustering#/medi... you will get groups that generally correspond with Caucasian/SS African/East Asian/Amerindian. You can call those "races" or something else, but they are not just artifacts of society/culture.
They did however believe that there were "purebreeds" of races; that you could objectively categorize people into various races. Mixing races wouldn't create new races, it would only create a mixture of races. As an analogy, you can create metallic alloys from different metallic elements. That won't create new metallic elements though, it will just create new mixtures of the pure elements.
The strongest example of this view is Polygenism. Before Darwin, people were arguing about whether there was a single origin for people or multiple origins corresponding to the assumed races. This
https://en.wikipedia.org/wiki/Polygenism#Scientific_polygeni...
The person you're responding to is trying to say that humans are a single species, and thus we can't be different races (species). But that is obvious in the modern context and isn't really what people are saying when they talk about race. Today, the argument is over: what are racial categories if they aren't species, and given a definition of race what does it actually tell us?
> If we use the word race for human being it can only mean cultural or other such societal concepts meaning it is a social construction.
> The fact remains that if you run PCA and clustering on genetic data ... you will get groups that generally correspond with Caucasian/SS African/East Asian/Amerindian
The person you're responding to is being very imprecise. There is no one definition of race. It a squishy class of "categorizations I can define which separate europeans, amerindians, africans, and asians". When we create a racial categorization, we are flattening these various categorizations into a single categorization. It is a social construction to choose the most important categories as "europeans, amerindians, africans, and asians" regardless of the categorization you're using.
As an example of the limitations of defining race from genetic clusters, Think of Obama in the U.S. He has a White mother and a Black father, but can you honestly say he is treated as equally White and Black in the U.S.? No, he is treated as predominately Black, even though the genetic view disagrees. You could say that the social definition is wrong and the genetic definition is correct, but you could equally say that your genetic definition fails to describe the social racial categorization.
This is patently false. There are hundreds of known genes which are strongly correlated/anticorrelated with above average and exceptional intelligence and are absent or underrepresented among various ethnic groups. Humans left africa some 200k years ago and even if you think thousands of generations of adaptation to drastically different environments before agriculture wouldn't have been enough time for populations to evolve cognitive adaptations, the fact that geographically isolated interbreeding with other homonids occured further suggests a genetic basis for differences in cognition.
The modern scientific establishment's denial of race based differences in cognition (not just intelligence, see e.g. warrior gene) is nothing but politically motivated science denialism, and does immense harm to the institution's credibility.
Unless, naturally, it is not the goal; or even a goal.
EDIT: To be more precise: of course there is no question that the biological concept “exists”. The biological concept of Lamarckian genetics exists, too. The question is whether race is meaningful, useful, and whether it should be taught in the textbook.
Does God exists? Does wind? We look for effects.
No. I am not going to go that route, because helpfully Webster dictionary defines race as:
"any one of the groups that humans are often divided into based on physical traits regarded as common among people of shared ancestry"
But that is not biological race definition. Fair enough. From biologyonline ( https://www.biologyonline.com/ ):
"(1) A group or population of humans categorized on the basis of various sets of heritable characteristics (such as color of skin, eyes, and hair)."
Now, I get that it is a touchy topic in US, but what heritable characteristics does Obama possess that are visible to the naked eye?
And I persist: if you can’t measure it, and tell me what someone’s “race” is in a way that biologists in general would agree with, the concept is too wobbly to be of any scientific interest. Finding definitions merely shows that the word exists. It doesn’t support the idea that it’s a meaningful or useful categorization.
Race strongly correlates with other things; for instance, per https://www.cdc.gov/heartdisease/facts.htm "White (Non-Hispanic)" men are most at risk of heart disease, and "American Indian or Alaska Native" are winning by several percentage points. That is deeply of scientific interest.
(It seems to me that there is at least a hint of tautology in your comment. How can we talk about these correlations with race unless we're assuming that racial categorizations are meaningful in the first place?)
> Because, and I don't think that is questioned, race as a biological concept exists
This is questioned constantly, and is far from the standard or consensus opinion for human biology. In reality, most scientists and biologists don't use the term "race" often or at all precisely because of it's historical connotations and social uses. Removing the term "race" from a science textbook does not change anything really, beside clarify that race in the context of racial essentialism in biology is a useless concept. Understanding how the concept of race was used to abuse science, and in turn abuse large swathes of the population, is more important, and likely has a role in learning about the ethics and uses of biology.
I would personally argue its absence says more than its presence given race is used in other contexts you listed. You simply can't get away from it when discussing demographics, so I question a little your statement that the term is not used in biology or other sciences.
Could you share an example of a paper that follows that 'no race' ( "at all" ) approach? I may very well be wrong. I am pretty ancient.
<< This is questioned constantly, and is far from the standard or consensus opinion for human biology.
You clearly are more immersed in it than me. Could you elaborate a little bit and link to two recent opposing papers? Sorry for all the questions. I am genuinely curious now.
For a philosophical discussion see a good summary here: https://ndpr.nd.edu/reviews/what-is-race-four-philosophical-...
And for a very extensive summary of relevant scientific and genetic findings, see the wikipedia page on Race as a system of human categorization: https://en.wikipedia.org/wiki/Race_(human_categorization)#Bi...
The key quote from that article is:
> Even though there is a broad scientific agreement that essentialist and typological conceptions of race are untenable,[12][13][14][15][16][17] scientists around the world continue to conceptualize race in widely differing ways.[18] While some researchers continue to use the concept of race to make distinctions among fuzzy sets of traits or observable differences in behavior, others in the scientific community suggest that the idea of race is inherently naive[7] or simplistic.[19] Still others argue that, among humans, race has no taxonomic significance because all living humans belong to the same subspecies, Homo sapiens sapiens.[20][21]
You can clearly see a number of competing views, including constructivist, essentialist, and anti-essentialist, the idea that the concept of race is irrelevant to the study of biology.
Private school is not necessarily better than public school, especially for high school. If you are in a good public school district then it is unlikely that a private school will give your children a better education.
A solution is to enroll all students in schools that offer the course by default, but let some opt out if they have a very good reason to do so (ie, nudging in behavioral economics term.) A potential problem is the pressure to water down the course for unwilling students but many countries have already solved that by having different streams/versions of the course.
Another objection is that it could be too hard for some students. I’d say it should be possible for a majority of students to understand Algebra I if they are taught properly, as in the case of many countries with high PISA Math score. In these countries/regions, to my knowledge, much of Algebra I is taught in math courses compulsory for ALL middle school students.
PISA 2018 results: https://www.oecd.org/pisa/PISA-results_ENGLISH.png
I grew up in Asia, taught math there for several years, and have run a tutoring school specializing in math tutoring there for over a decade. I was quite surprised when I saw how easy the American math curriculum/textbook is for a given grade. (I’d say 1-3 grades easier than Asian counterparts) Others in Quora have expressed the same sentiment.
Math is a skill that requires a great deal of time to master. Those who start properly sooner tend to have an advantage. US schools should offer more advanced math courses to all students at a younger age, rather than the reverse.
Are you saying it's not happening now?
People with money and wherewithal are always going to have alternative options available to them, such as private education or moving to expensive neighborhoods with strong schools. The problem is when public school policy results in actual degradation of education for everyone else.
School district quality has a significant impact on home values in California, and that wouldn't be the case if the majority of high earners sent their kids to private schools.
Short term schools like Lowell are switching from using test score to a lottery based admission. And so are UC schools! So the smart kid interested in learning but who doesn't have parents in tech to send him to private tutoring better be lucky at the lottery or have the correct "holistic" attributes his target school will admit on!
Just because tiger moms think there is one doesn't mean there is. You'd have to believe students actually remember or use everything they learn in class, vs it being signalling you're conscientious enough to do the homework.
Also, the shifted emphasis on data science stuff is a joke. The very courses they're talking about minimizing are the building blocks of data science and there's no shortcut.
I don't think anything is changing for truly gifted students, they should still have the ability to be fast-tracked or options to take more advanced topics. It seems more that it's about focusing on students who don't see themselves as gifted or who aren't yet showing signs of it.
> Does the draft Mathematics Framework eliminate middle school mathematics acceleration programs? No. The draft Mathematics Framework does not eliminate middle school mathematics acceleration programs (including programs that offer Integrated Math 1 or Algebra 1 courses to grade eight students). The draft Mathematics Framework emphasizes the importance of following the sequenced progression of topics laid out in the Common Core State Standards for Mathematics (CCSSM) and considers the latest research on the impact of skipping grades or undermining the sequences progression. Additionally, the CA CCSSM are significantly more rigorous than those from previous grade eight content standards. They address the foundations of algebra and geometry by including content that was previously part of the Algebra I course, including but not limited to a more in-depth study of linear relationships and equations, a more formal treatment of functions, and the exploration of irrational numbers.
Yes, that is the explicitly stated goal. Unfortunately a large number of ideologues believe that all people have the same inherent intelligence, and that disparities in outcome among children are due solely to racism and other forms of discrimination. That's the whole thrust of "equity". "Equity" means equal outcomes. It's proven too difficult for these people to bring up the performance of low achieving students, so they are left to bring down the performance of high achieving students and eliminate all objective metrics (like standardized testing) that can be used to assess student learning.
Many advanced practitioners don’t even have a good grasp of college level/post-grad pedagogy which they’d use more in their day to day work.
Using a skill isn’t the same as teaching it, and just like anything else there are plenty of fallacies to be had. I’d be more persuaded by angry hot takes from High School teachers worried that their students aren’t going to hit the grades they deserve / learn the things they need than anything else.
Even then, single high school teachers experiences are closer to anecdotes than actual pedagogical research, with which the original proposal is backed.
They are only arguing WHAT is important to teach.
High school math teachers do not have the perspective to understand what kind of math is needed for jobs in engineering, data science, etc (The fact is that a background in algebra and calculus is necessary for almost all of these jobs).
How many people on the planet are worth listening to when it comes to teaching math?
How about this teacher, who teaches math at San Francisco's top public school: https://cheesemonkeysf.blogspot.com/
Public education in the US has a long history of fads, manias, and ill-conceived attempts at reform. There's little evidence of improvement over time or competitive performance.
The following is an excerpt from (https://www.pewresearch.org/fact-tank/2017/02/15/u-s-student...).
The most recent PISA results, from 2015, placed the U.S. an unimpressive 38th out of 71 countries in math and 24th in science. Among the 35 members of the Organization for Economic Cooperation and Development, which sponsors the PISA initiative, the U.S. ranked 30th in math and 19th in science.
Given these results I'll trust subject matter experts over educators any day.
Bloomberg giving $750 million to charter schools is a great start: https://www.wsj.com/articles/michael-bloomberg-why-im-backin...
People who are blindly praising Asian-style cram education really haven't actually experienced one in their youth at all; it is a fucking disaster at raising actual talent, and it robs you so much of your adolescence.
There are many people who do not fit this category, but could still benefit immensely from good teaching.
I know, because I was one of them.
Do you ever wonder why American schools finish at 2-3pm rather than run the entire day as Western Europe? So that teachers could get that extra 3-4+ hours of doing the administration side of classroom work (grading, report writing, planning, etc). Even when parents request it there never appears to be enough money for afterschool programs, school districts create and withdraw them all the time depending on budget that you can't actually make plans for them.
The number of hours of class per week in the US matches a lot of European countries, but most countries in Europe have schools start and finish later on in the day, and some have extended lunch breaks that also push the end of day forwards.
Cram schools succeed in Asian countries because there's an enormous amount of pressure to pass entrance exams, in disadvantaged neighborhoods kids often aren't even pressured to the point of graduating high school at all.
Cram schools are laughably useless. Works well at a national level with a large enough population but they are really a side effect of the intense competition and pressure for the few decent university spots available in Asian countries (per capita).
It's basically optimized to pass a test, not learn, and heavily rewards rote memorization.
I went to Sonoma State, which at the time had at least 3 semesters of remedial math you could take, plus a tutoring program, trying to fill in the knowledge a high school graduate was supposed to have. The state got mad about all those classes because the high schools were supposed to cover the material.
> we reject ideas of natural gifts and talents
It must be nice to think about a world in which every child is an equally-capable blank slate. But we do not live in that world. We live in a world where some people are tall, and somewhat more likely to be successful basketball players. And some people find math easy, and are somewhat more likely to succeed in math.
When you start out with flawed assumptions, it's not surprising when your prescriptions (no advanced math for anyone!) are foolish and counterproductive.
It seems like tabula rasa idealism has made a serious resurgence in leftist and liberal circles and the scary thing is that nobody (other than extremists saying nonsense) is really talking about this explicitly. Somehow we went from a bunch of stuff being cultural constructs to literally everything is a cultural construct and then this somehow became extremely widespread in no time at all. We need to have this conversation out-loud.
I have not met a single parent who didn't want to try and give their own children an advantage over the others. It is one thing to support "equity in education", but when parents sense that these activists are trying to dumb-down the curriculum, I expect significant pushback. Especially because this is quite literally a "won't somebody please think of the children" issue.
As for the competitive advantage, I think that only works for the children who are already in the private school system.
So the "social disease" of virtue signaling will follow the higher socioeconomic crowd where ever they go.
Maybe from liberals, but from what I've seen not the left. Marx's mantra is literally "From each according to his ability, to each according to his needs", it has nothing to do with liberal conceptions of tabula rasa idealism. I've never seen a leftist who asserts that people start from a blank state and can be "anyone" depending on the circumstances, that statement will get you accused of having bourgeois sensibilities who ignore the material forces of the world.
https://www.currentaffairs.org/2020/09/we-dont-know-our-pote...
Even mathematics education is now being twisted by this -- it's now seen as more important for math classes to pursue equality/equity than it is to teach math.
One outcome of this is a levelling effect -- an equal outcome for all students, in which they all possess average mathematical skills, is preferred to a situation in which some students perform above average.
The people who were critical of the first moves in this direction and explicitly said it would be a slippery slope were dismissed at the time. We're still moving in that direction. Hopefully the pendulum will swing back to something more reasonbale.
I wholeheartedly agree with your point, but there is no "somewhat" about it. The differences can be and often are stark, and we shouldn't shy away from saying that if we want an honest and productive conversation. It does not exclude the also-true fact that good education, practice, and other controllable environmental factors play an important role.
What makes you think anybody wants an honest and productive conversation? One half is just trying to get the other half to slip up and say something - anything - they can cancel them for saying. The other half is just keeping their heads down and trying not to lose their job for heresy.
> Research is also clear that all students are capable of becoming powerful mathematics learners and users (Boaler, 2019a, c). This notion runs counter to many students’ ideas about school mathematics. Most adults can recall times when they received messages during their school or college years that they were not cut out for mathematics-based fields. The race-, class-, and gender-based differences in those who pursue more advanced mathematics make it clear that messages students receive about who belongs in mathematics are biased along racial, socioeconomic status, language, and gender lines, a fact that has led to considerable inequities in mathematics.
>In 2015, Sarah-Jane Leslie, Andrei Cimpian, and colleagues interviewed university professors in different subject areas to gauge student perceptions of educational “gifts”—the concept that people need a special ability to be successful in a particular field. The results were staggering; the more prevalent the idea, in any academic field, the fewer women and people of color participating in that field. This outcome held across all thirty subjects in the study. More mathematics professors believed that students needed a gift than any other professor of STEAM content. The study highlights the subtle ways that students are dissuaded from continuing in mathematics and underscores the important role mathematics teachers play in communicating messages that mathematics success is only achievable for select students. This pervasive belief more often influences women and people of color to conclude they will not find success in classes or studies that rely on knowledge of mathematics.
>Negative messages, either explicit (“I think you’d be happier if you didn’t take that hard mathematics class”) or implicit (“I’m just not a math person”), both imply that only some people can succeed. Perceptions can also be personal (“Math just doesn’t seem to be your strength”) or general (“This test isn’t showing me that these students have what it takes in math.” My other class aced this test.”). And they can also be linked to labels (“low kids,” “bubble kids,” “slow kids”) that lead to a differentiated and unjust mathematics education for students.
That leads to the principals:
> ● All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015).
> ● The belief that “I treat everyone the same” is insufficient: Active efforts in mathematics teaching are required in order to counter the cultural forces that have led to and continue to perpetuate current inequities (Langer-Osuna, 2011).
Based on coverage I've read, the CMF does not cite, acknowledge, or discuss any of the critiques of Boaler's work. If they had good responses to these critiques, they probably would have spent some of their 800 pages addressing these serious challenges.
1: http://www.danielwillingham.com/daniel-willingham-science-an...
2: https://gregashman.wordpress.com/2019/03/03/jo-boaler-cites-...
Math is not scalar is skill! When I am working with Boolean value function i almost always need to draw a table of all options while in Linear Algebra or numerics of differential equations I have a quiet good intuition.
Wait, the finest minds and educators in their respective fields are providing observational data that gifts are a real phenomenon, literally contradicting "reject ideas of natural gifts and talents". This is tremendous news that should have been a clarion call to seek out and elevate the gifted and invest every possible effort to nurture their gifts.
Yet the conclusion is somehow the exact opposite: that "gifts" are a falsehood used to malignly, even if unconsciously and unintentionally, dissuade people. How is this possible?
This is not evidence that natural talent is not needed, it is at best some evidence that minorities and women maybe don't think they have the requisite natural talent.
> Negative messages, either explicit (“I think you’d be happier if you didn’t take that hard mathematics class”) or implicit (“I’m just not a math person”), both imply that only some people can succeed.
To say the evidence for stereotype threat is "weak" is charitable at best [1], and multiple replication attempts have failed entirely.
Overall, the evidence that was cited is simply not sufficient to justify the principles you list.
[1] https://replicationindex.com/2017/04/07/hidden-figures-repli...
It's not whether gifted students exist - it's the extent they should be catered to. Society benefits more when you raise the average than when you foster the top 0.1%. Even Soviet mathematicians who moved to and taught in the US after the fall of the Soviet Union said something to the effect of "sucks for talented folks, but better for society" when they compared it to Soviet education.
With that context, whether they exist or not is really a rounding error. Most gifted students will do well eventually whether we have special programs for them or not. And it's challenging to show strong net positives for society if you did have those programs. As in, actual data that supports having them, vs mere anecdotes.
> Gifted will do well regardless whether we have special programs for them or not.
This is very much not true. Only gifted with rich or caring parents will do well. Others might suffer a lot. Being in a program for gifted for me made the difference between being thrown out of a school because I never did the homework and being invited and having my flights paid to a conference in Japan where I gave a presentation while in the last grade of school.
The state can provide this without believing you have a naturally innate ability in mathematics. They can still construct programs for people who are performing better in math.
The discussion is about innate talent, not whether we treat people who do well in math differently.
I have direct experience with this problem. I was labeled as a gifted student in elementary school but offered no opportunity to take enriched or accelerated classes. Out of boredom I quit trying and my grades collapsed. I dropped out of high school at age 16. Now I am an undergraduate student in mathematics, age 37, trying to put the pieces of my life back together. I have been forced to make friends with classmates half my age. All but 2 of my friends from elementary school have moved on.
True. However the state can not provide this "regardless whether we have special programs for them or not". You migh not have intended to but
>>> Gifted will do well regardless whether we have special programs for them or not.
is a claim which has policy implications orthogonal to any discussion about the innateness of talent. It is in this component that i disagree with you. I couldn't care less whether people being good at something is being caused by something innate or taught as far as that is not relevant for pushing the being good at further.
If it turns out that "natural talents and gifts" are really just due to a better critical period for the child, then the liberals here are really shooting themselves in the foot with this argument.
That said, twin studies do provide substantial evidence that giftedness is highly heritable and probably significantly genetic.
I am well aware of how twin studies but any claim about the genetic component kinda falls apart for me based on them as the children were in the same pregnant mother at the same time.
> any claim about the genetic component kinda falls apart for me based on them as the children were in the same pregnant mother at the same time.
They do somewhat control for pregnancy by comparing identical vs fraternal twins, and finding a higher correlation in intelligence between the former, as well as a far more similar brain structure in regions known to be related to intelligence (frontal cortex).
Anyway, it's impossible to get rid of all confounds via twin studies. But this doesn't mean that twin studies provide zero evidence. It just means the evidence can't be fully conclusive. It just strongly points in the direction of genetics.
Predicting IQ from genetic information alone should remove all the of compounding factors (except those introduced by IQ measurement itself) but can only serve as a lower bound unless predictor overfitted the study data.
> The truth is most likely somewhere between those two.
> but can only serve as a lower bound unless predictor overfitted the study data.
Genome studies are only good for lower bounds. They're a new methodology that isn't good with complex traits. For example, they can only explain 20-30% of the variability in hair color even though we know that hair color is almost 100% genetic due to the observation that identical twins always have the same hair color. Intelligence is much more complex than hair color, so it's no surprise that this method has failed to explain more than 5%. Further, these studies often rely on weak proxies like educational attainment because of the difficulty of IQ testing at scale, and the studies that do try to IQ test at scale suffer from small sample sizes which impacts the ability to find results due to being underpowered.
Also, IQ becomes more correlated with parents as you age, suggesting childhood environment plays a less important role.
In addition, the jump in correlation from fraternal to identical suggests more role for genetics than merely a few %.
But I remember they found a surprising amount of similarities in twins brought up in different environments.
Of all the things to evaluate the policy on, this is a real poor proxy as whether there are gifted people or not usually has little bearing on the overall health of math education across a very highly populated state.
I never disagreed with whether they exist or not. I just don't see why this is such a sore point for people. I can virtually guarantee that the existing education system in CA didn't really benefit the gifted folks either. If I were setting up the program for a whole state, whether it will be good for a Jacobi/Euler/Gauss is totally irrelevant. We're not going to make people who show up once every 50-100 years be a major factor in educating millions of people.
Your reply is that we shouldn't design a state-wide math program for extreme outliers. But no one said we should! We only said that we should design a math program that acknowledges a diversity in innate math ability (as proven by the existence of extreme outliers, and the many, many less extreme outliers).
To me, it seems these changes are oriented towards helping everyone succeed in STEM, even those who don’t think they’re math people. Which, again, is less to do with their actual abilities and much more to do with their mental dialogue.
This makes a ton of sense. Basically any skill or habit you might want to develop can be easily thwarted if you’re struggling mentally with discipline, focus, self-image, etc. In my opinion, the “mental game” is crucial to nearly everything and doesn’t get enough focus. (Think of how in sports, a bad mental game can easily loose you the physical game even if you’re an incredible athlete.)
I doubt these educational changes would ever have much of an impact on bonafide geniuses, because they are operating in an entirely different context.
It should be both.
This is not a flawed assumption with respect to baseline high school learning.
People can be taught much more mathematics and science than they normally learn.
This is not limited to STEM--people can be taught to write much better than they normally learn, as well.
The trick with the students is getting to the students before the "I'm not a <X> person/<X> isn't for me" kicks in. That means you have to get them in the 5th-8th grades--5th is a bit early/8th is a bit late.
I don't disagree. But holding back advanced students is no way to accomplish this.
My father (a high school teacher for almost 4 decades) used to say: "I can't stop an advanced student even if I wanted to--sheer boredom will propel them to do something." For him, dealing with an advanced student was the easiest thing in the world and took practically no effort--a little extra work with a slight bit of focus and they're off and running. At that point, he could practically forget about them until they raised an interrupt.
My own personal experiences in school also reflect this. Most of my teachers forced me to turn in "normal" homework, pointed me at something more advanced, and let me at it while occasionally checking in on me or offering advice. Sure, they did this so that they could get me off their plate to focus on someone else. But, to be fair, what they had me doing is also the essence of learning--self-directed engagement with an unfamiliar knowledge base via intrinsic motivation.
And, to be fair, if your "advanced" student can't operate in that regime, are they really that "advanced" after all? Far too many parents think their children are "advanced" when they are merely a touch above average and really do fit inside the "standard" curriculum.
The real problem in high school is motivating average to below-average students who want to be anywhere but in class. Video games, hanging with friends/dates, vaping/CBD, etc. is way more compelling than anything having to do with school. Getting through to those students is difficult and has very little to do with the curriculum.
The biggest irony is that the same people who preach that there are intrinsic differences always seem to forget that concept when it comes time to hire and pay teachers. Funny that.
And that is the real problem for parents looking for an "accelerated" track at school.
All they really want is a program that will challenge their kids and surround them with an equally motivated peer group that has a goal of getting into a selective university.
That is what drives private school enrollment, selecting public schools in areas with high property tax revenues, and accelerated tracks within public schools with lower socio-economic status.
You have part of that right. What most parents want is a magic piece of paper that says "Good for one admission to Prestigious University." The achievement of their child and whether it brings down other students is irrelevant to them. The credential is everything.
We see this with AP (Advanced Placement) programs. Parents will sue the district to get their child put into the AP class (who almost always also has an ADHD exemption for extra time on all tests due to "anxiety")--who is completely unequipped for the class and then doesn't succeed in the class and scores a 1 on the AP exam afterward. This is practically a tautology because if the parents were actually engaged in their child's education, the child would already be in the AP class by credential.
This, of course, brings down the children who do belong in the AP class. But the parents don't care because now their child is punching above their weight in terms of credential.
This is the standard "Something ceases to be a good metric once it becomes known to be a metric."
What does that say about the district?
Every student, no matter how capable, benefits dramatically from instruction tuned to their level and ability. Claiming advanced students will take care of themselves is an absolute failure in an instructor’s duty of care towards them, an excuse to make the teacher feel better about not having the time, interest, or knowledge to provide proper instruction. There is no merit to the notion.
Sorry. That's not even close to being a valid argument.
> Every student, no matter how capable, benefits dramatically from instruction tuned to their level and ability.
Oh, I agree. And the research supports it. However, when you tally up the bill for 2 teachers per every 10 or fewer students to make that happen, suddenly everybody starts screaming and objecting.
And curriculum has no bearing on any of that.
If you want to hear screaming and objecting, try to suggest that teachers need to be competent and tested in the areas in which they teach. Yes, if we had an entirely different educational system with an intelligent, competent teacher for every 5 students instead of a semi-literate, incompetent teacher with 30 kids in every classroom, some of these "reforms" might make more sense. But that isn't what we are seeing. Advanced math and gifted programs are being eliminated with the same semi-literate, incompetent teacher still responsible for 30 kids. Only now the few bright kids and the few kids who work very hard to excel will have no opportunity to do so. They will sit at the back of the class and scroll on their phones while the barely competent teacher struggles to crawl through a remedial lesson that the dumbest 10 kids in class cannot master. But we'll have equity when all of them are handed the same worthless diploma after 12 years.
"It must be nice to think about a world in which every boy and girl is an equally-capable blank slate. But we do not live in that world. We live in a world where some people are tall, and somewhat more likely to be successful basketball players. And boys find math easy, and are somewhat more likely to succeed in math.
When you start out with flawed assumptions, it's not surprising when your prescriptions (no advanced math for anyone!) are foolish and counterproductive."
This is what society used to believe. How was that productive and wise?
Learning Mathematics: for All
Introduction
Students learn best when they are actively engaged in questioning, struggling, problem solving, reasoning, communicating, making connections, and explaining. The research is overwhelmingly clear that powerful mathematics classrooms thrive when students feel a sense of agency (a willingness to engage in the discipline, based in a belief in progress through engagement) and an understanding that the intellectual authority in mathematics rests in mathematical reasoning itself (in other words, that mathematics makes sense) (Boaler, 2019 a, b; Boaler, Cordero & Dieckmann, 2019; Anderson, Boaler & Dieckmann, 2018; Schoenfeld, 2014). These factors support students as they develop their own identities as powerful mathematics learners and users. Further, active-learning experiences enable students to engage in a full range of mathematical activities—exploring, noticing, questioning, solving, justifying, explaining, representing and analyzing—making clear that mathematics represents far more than calculating.
Research is also clear that all students are capable of becoming powerful mathematics learners and users (Boaler, 2019a, c). This notion runs counter to many students’ ideas about school mathematics. Most adults can recall times when they received messages during their school or college years that they were not cut out for mathematics-based fields. The race-, class-, and gender-based differences in those who pursue more advanced mathematics make it clear that messages students receive about who belongs in mathematics are biased along racial, socioeconomic status, language, and gender lines, a fact that has led to considerable inequities in mathematics.
In 2015, Sarah-Jane Leslie, Andrei Cimpian, and colleagues interviewed university professors in different subject areas to gauge student perceptions of educational “gifts”—the concept that people need a special ability to be successful in a particular field. The results were staggering; the more prevalent the idea, in any academic field, the fewer women and people of color participating in that field. This outcome held across all thirty subjects in the study. More mathematics professors believed that students needed a gift than any other professor of STEAM content. The study highlights the subtle ways that students are dissuaded from continuing in mathematics and underscores the important role mathematics teachers play in communicating messages that mathematics success is only achievable for select students. This pervasive belief more often influences women and people of color to conclude they will not find success in classes or studies that rely on knowledge of mathematics.
Negative messages, either explicit (“I think you’d be happier if you didn’t take that hard mathematics class”) or implicit (“I’m just not a math person”), both imply that only some people can succeed. Perceptions can also be personal (“Math just doesn’t seem to be your strength”) or general (“This test isn’t showing me that these students have what it takes in math.” My other class aced this test.”). And they can also be linked to labels (“low kids,” “bubble kids,” “slow kids”) that lead to a differentiated and unjust mathematics education for students. A fundamental aim of this framework is to respond issues of inequity in mathematics learning; equity influences all aspects of this document. Some overarching principles that guide work towards equity in mathematics include the following:
⦁ Access to an engaging and humanizing education—a socio-cultural, human endeavor—is a universal right, central among civil rights.
⦁ All students deserve powerful mathematics; we reject ideas of natural gifts and talents (Cimpian et al, 2015; Boaler, 2019) and the “cult of the genius” (Ellenberg, 2015).
⦁ The belief that “I treat everyone the same” is insufficient: Active efforts in mathematics teaching are required in order to counter the cultural forces that have led to and continue to perpetuate current inequities (Langer-Osuna, 2011).
⦁ Student engagement must be a design goal of mathematics curriculum design, co-equal with content goals.
⦁ Mathematics pathways must open mathematics to all students, eliminating option-limiting tracking.
⦁ Students’ cultural backgrounds, experiences, and language are resources for learning mathematics (González, Moll, & Amanti, 2006; Turner & Celedón-Pattichis, 2011; Moschkovich, 2013).
⦁ All students, regardless of background, language of origin, differences, or foundational knowledge are capable and deserving of depth of understanding and engagement in rich mathematics tasks.
[1] https://www.cde.ca.gov/ci/ma/cf/documents/mathfwchapter1.doc...
could be replaced with:
> All students deserve powerful mathematics.
and still make the same pedagogical point, that all students should be taught with the expectation they will succeed at learning mathematical concepts.
Putting the emphasis on believing people do not differ in natural ability, is obviously false and therefor detracts from the overall goal.
The rejection of "ideas of natural gifts" is rejecting that success in math is tied to natural gifts (as opposed to say hard work or careful study.)
It is not rejecting the idea that some students will have an easier or harder time learning!
> “gifts”—the concept that people need a special ability to be successful in a particular field
Perhaps ability to consistently do hard work is also a natural gift.
That is not surprising to hear as it was written by people that have invested a large part of their careers in the educational system.
"Those who can't, teach. Those who can't teach, teach Gym."
People might talk a lot of woke on twitter, but nobody is going to willingly handicap their own children in the name of some nebulous greater good.
It's exactly the same as liberal NIMBYs. Preach tolerance and acceptance until somebody who doesn't look, talk, and think exactly like you, wants to live in your neighborhood and alter your precious neighborhood aesthetic.
I think long term, wokeism will kill those universities. A not insignificant part of the population isn’t impressed with slogans like “decolonise maths”, and the perception that they are handing over diplomas in the name of social justice, rather than skills, inflates away the value of those diploma. My own modest contribution to their demise is to give equal consideration to CVs of candidates from less prestigious universities. And I have seen enough idiots graduating from top universities to think that this credentials system was broken even before wokeism.
And I think it's a good thing. I much prefer the German system which, as I understand it, doesn't rely on a small number of elite universities, and where you have to evaluate the candidate rather than its credentials.
I was interested as I was ready for Algebra in 6th grade, but was unable to take it until 8th grade. If you don't get into Algebra before high school, there is no chance of taking a reasonable calculus class before college, which puts you way behind the curve if you get into an engineering program.
I went to a state university that had a strong engineering program. The students that I knew who were having difficulty and eventually dropped all had first seen calculus at the university. These were smart, talented people, but they were not given the chance to succeed.
And so, we get posts like this: public ed as a 'pipeline to STEM careers'.
The reductionist view of public education-as-career-training is one of those contentious topics. I myself find it absurd. An ed system driven by vocations and political/ideological nation-state goals has been so genuinely harmful to people it's hard to know where to begin.
And that doesn't even list the people with remunerative interests, teachers unions, textbook publishers the testing/test-prep industry, the for-profit outrage machine., etc.
I'm having trouble finding the right words to describe myself, but I vividly remember how many moments of epiphany I had when I took Calculus and Linear Algebra. I don't directly use either of them at all in my day job, but I feel like they were foundational in developing reasoning skills.
Only 59% of schools offer algebra in 8th grade.
There's a map showing percent of schools with 8th grade algebra by district. There's another map farther down shown percent of 8th graders who took it by school district. (The maps can be slow to load).
Overall 80% of students have access to algebra I in 8th grade. Breaking that down by type of school it is 88% in magnet schools, 81% in traditional schools, 60% in charter schools.
It is 86% in suburban schools, 75% in urban schools, 75% in rural schools, and 76% in town schools.
That is access. Enrollment is another matter. 24% of 8th graders actually take it. By gender that is 25% of the females and 22% of the males. By race 34% of the Asians, 24% of the Whites, 23% of the two-or-more race students, 14% of Pacific Islanders, 13% of the Hispanics, 13% of the Natives, and 12% of the Blacks.
It's important to remember that children are not tiny adults. At an early enough developmental stage, a child may be physically unable to learn algebra. The number of such children is much higher in middle school than freshman year of high school. Note that developing later doesn't mean you're not very smart nor that you have aptitude. A student I had many years with this issue now has his PhD in mathematics.
By delaying algebra, you give a large chunk of students time to move forward developmentally so they can engage in the material. The current system ill suits them for a few reasons. One is that curriculum (somewhat necessarily) assumes high mastery of pre-requisite concepts, when it turns out this isn't the case students tend to not understand the material and get very frustrated. That frustration and anger often causes lasting damage that may never be undone.
My mother was a math educator during the years when Algebra first moved into middle school fought heavily against it. According to her the push came mainly from professors of Mathematics (with no educational training) who wanted better trained students. I think this has worked out for some of the top schools. If you're smart and a little precocious algebra in 8th grade is good, but I think net we lose out on a lot of talent.
A central pillar of Equitable Math is that this disparity sustains White Supremacy in math, and thus all children should always be in the same class, up until the last year of high school.¹
This is the central point of contention, and not whether some children benefit from a delay of Algebra past middle school, and nor whether all children ought to learn Calculus.
Could you cite a more direct source for this? It's in direct contradiction with the materials the site you linked provided me [0]. If you go to page 17 "September Who are my students?" they do not discourage different classes or tracks existing, they discourage placing students in different tracks without input from the student or their parents. As a former educator that seems sensible to me. Sometimes a student isn't quite ready to enter the more advanced mathematical track but could be made so with if provided some guidance on how to self study. I've seen many high school freshman apply themselves more readily when I laid out the long term consequences of different math tracks.
[0] https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
The applications of math that everyone clamors for in high school eduction became far more apparent once I got to college.
Yes, primary and secondary curriculum matters, but in the same way a church musician parent will politely nod approval at the elementary school musical show knowing full well that real musical development for children usually happens in the home with parental involvement -- a mechanical engineer or e.g. actuary parent living in a small or under-schooled town will also politely acknowledge the child's remedial math homework assignments, yet know enough to be able to seek out quality instruction for the child, even if it means utilizing community college or other nearby resources.
Given the same family and upbringing, something tells me that Scott would still excel in math as a HS student in today's California, were he there and that age now.
The author needs to re-work this so that the first paragraph tells me everything that I need to know, and the rest of the essay/letter/memo can elaborate on things that I should or might want to know.
If they aren't willing to do that then they are going to continue to remain out of touch to most people.
I think we lane people out of STEM way too early, which is what I believe some of these curriculum changes are trying to redress.
If you don't have students repeating basic math (and chemistry) in college, they can do deeper on an elective track involving a STEM because because their STEM credit hours aren't spent getting a rerun of Calc I.
It would have been a huge shame if I was slightly worse at math, didn’t even take Calc and thus wasn’t accepted into a CS program upon graduation.
So much stress and consternation is spent on saving one calculus corse in college (and it’s used as gate keeping to get into an elite college stem program).
It's a lot easier to become oppressed when you don't possess these most fundamental tools for understanding the nature of that reality. Maybe that's what we need to keep this shit show moving along for another generation.
(I kid, this sounds disasterous).
For my own sake, I want everyone to think computers and programming are incomprehensible magic.
Why can‘t we behave more like highly limited occupations like medical doctors?
“every child must master algebra, preferably by eighth grade, for algebra is the gateway to the college-prep curriculum, which in turn is the path to higher education.” But that's not the life path for perhaps 90%+ of the population. I don't think we can justify burning tax dollars to exclusively and solely support a tiny minority of kids at the expense of nearly all the other kids.
I would not be bothered by mindless STEM boosterism if it were not for pages like this:
https://datausa.io/profile/cip/electrical-engineering#tmap_o...
It offends me as a EE type person that the top job title for graduating engineers is software dev, where they'd have been better off with a CS degree, or no degree. Meanwhile I'm told by the other side that we have a terrifying massive shortage of engineering grads, despite that clearly not being the case and it being VERY difficult for new kids to get a job in the field. I'm led to believe by "shortage" they actually mean a "shortage of people willing to work 80 hrs/wk for minimum wage and no bennies" or "shortage of experts with decades years of masterful experience willing to accept apprentice level pay scales"
We simply seem to have too many STEM grads for our economy to support. I don't see any realistic reason for future improvement in that situation. Meanwhile public education policy, meant to serve EVERYONE, is telling most of the kids to go to hell. And those are the kids running the rest of the economy and we're relying on them to grow the economy enough to support the 5% of STEM workers whom are the only important people to educate according to "public" education, which is now really only college prep STEM education and F every other kid.
This path cannot possibly end well.
The best way to handle algebra education as applied to the entire student body, is to acknowledge that for 95% of the population, learning how to change the oil in a car or how to identify when someone is using statistics as propaganda, would be a more valuable life skill. Yes I acknowledge STEM is and will remain important for a tiny subset of both kids and future jobs, but...
Sure, but that's not what they're objecting to. They're objecting specifically to cutting off avenues to those advanced paths, and in ways that harm underprivileged students more. Quote:
> the bottom line is that rather than trying to elevate under-served students, such “reforms” reduce access and options for all students. In particular, the CMF encourages schools to stop offering Algebra I in middle school, while placing obstacles (such as doubling-up, compressed courses, or outside-of-school private courses) in the way of those who want to take advanced math in higher grades. When similar reforms were implemented in San Francisco, they resulted in an “inequitable patchwork scheme” of workarounds that affluent students could access but that their less privileged counterparts could not.
No, we don't. STEM grads makes way more money than most other grads, hence there is no glut of them if it were then STEM grads salaries would fall until they make the same as business grads or even literature grads or other fields where there is a glut of people to do the jobs. Engineers go to software since it pays more than their main field, but their main field still pays way more than a typical grad job.
https://www.cde.ca.gov/ci/ma/cf/documents/mathfwchapter2.doc...
Why are they integrating and layering the religion of social justice and gender ideology onto math? I would be just as alarmed if Christianity or any other religion or dogma or ideology was embedded with math and how it's taught. This document is pushing evangelical-level indoctrination and is certainly less about teaching math than our current system. At the very least it's orthogonal to learning how to add and subtract.
"Teach Toward Social Justice"
"Teachers can take a justice-oriented perspective at any grade level, K–12"
"teachers need to work consciously to counter racialized or gendered ideas"
"Students are able to take what they noticed and named – in this case, how gender played out in the problem"
"Learning is not just a matter of gaining new knowledge—it is also about a change in identity. As teachers introduce mathematics to students, they are helping them shape their identity as people"
Do we have data that it helps/worsens?
We've been playing games with education in the US for a while now. This identity stuff is the newest, but you can go back every decade or so for some 60 years and find some fad that was really big at the time.
Now look at the test scores over time. Up? Down? Flat? Break it out into race, socioeconomic class, religion, however you want. Check again. Up? Down? Flat?
We pretty well know how to teach things like math. It's a lot of drills. It's a lot of homework. It's word problems. It's all the things that both teachers and students hate, because it's annoying to do and annoying to check. But math is more or less like learning a language. You have to immerse yourself in it and do a lot of practice.
And, in the end, you have to accept that some people are just not going to cut it. They will top out at about 8th grade basic Algebra. And that's okay! Cramming some kid who can't cut Calculus into a Calculus class just because you need to count a certain number of different colored noses is daft and unproductive. School should educate people to their maximum ability, and everybody's maximum ability is different.
It doesn't matter if it makes you feel better to attribute somebody's poor performance to some vaporous societal ill. That's not helping. That's trying to shoehorn your preferred reality into actual reality. The hell of it is that it completely shafts those who really did earn their way into the top ranks. There is always the spectre that they're there because some administrator needed enough $IDENTITY to make their Powerpoint presentation look good.
But ... again do we know this based on data, or it's patting our own back for finding a logical consequence that seems to nuke the whole affirmative action system?
> math
I think the real problem is that we should not teach math, nor most of the abstract arts. We should teach learning, acquiring skills, and ... picking and sticking to strategies.
And then it makes sense to help them learn whatever they want.
"The process of teaching a person or group to accept a set of beliefs uncritically."
What I see in your examples does sound like teaching a set of beliefs, but there is nothing that I see where it is done uncritically. For example, there are stereotypes in our society about what genders and races are good at STEM and which are not. If a word problem reverses those stereotypes, do you think that encourages or discourages the reader to think critically about their own biases?
> there is nothing that I see where it is done uncritically.
I mean, how is it going for those criticizing CRT-ification of education? It doesn't seem like its advocates are actually interested in criticism of the dogma.
From what I can tell in our local area it seems to be going about as well as they hoped.
First they rail against about some weird graduate-level field most people have never heard of that isn't related to anything taught in our elementary schools. Then they interpret the eyerolls from the other parents and patient administrators attempting to keep the conversation focused on relevant topics as attacks on their freedom and they get to play the martyr.
"Before the Great Proletarian Cultural Revolution there were 48 students in class one in Qunli Elementary: During the six years of obliteration by revisionism on the educational system, 13 students dropped out. All 13 students were from the worker or poor peasant families. Compute how many students from the worker or poor peasant families dropped out and how many were retained due to the obliteration by revisionism?"
[1] https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.98...
And you yet you immediately say:
> there are stereotypes in our society about what genders and races are good at STEM and which are not
Your post is a good example for why it is very difficult to make any critique of the DIE "teachings" in a public / classroom setting. DIE only makes sense if front of a mob.
If you disagree, you are against the DIE (diversity, inclusion and equity) virtuous teachings. Unlike other theoretical fields, to understand is to agree with DIE and its apparent virtues.
And DIE should stay away from any serious academic setting, especially young students, because it's a widely discredited field: https://areomagazine.com/2018/10/02/academic-grievance-studi...
Usually spelled DEI, for the obvious reason that "dei" isn't an English word meaning death.
I don't get it... what about this is so scary to you? Is it the word 'identity'? Because as a standalone statement, I actually think this is a healthy approach to education.
I get that "social justice" and apparently now "justice" are loaded terms in our modern political discourse, but countering racialized ideas and framing education as a part of our identity as people/citizens... I mean, that hardly seems like objectionable to me.
This is one of those statements where part of your brain goes "well, I guess there might be atom-sized kernel of truth to this". But in reality, I doubt anyone is tangibly affected by the congruent use of Male/Female names in word problems that map to traditional Male/Female gender roles. I believe this is a result of a hypersensitive social-justice filter which results in an astonishingly large false-positive rate.
Quite frankly, I just fail to see how gendered language in word problems not only 1) reflects math being inherently cultured and identity-based, 2) harmfully reinforces malicious stereotypes (people can just as easily write Alice makes $50,000 a year, Bob needs 10 onions from the store), and 3) are odious enough to justify a substantial, near fundamental, change in math education.
Word problems are pain in the butt, but they teach the skill of converting an abstract problem math symbols which can be solved
I guess it's just I think that the pursuit of knowledge shall have nothing to do with any one 'identity' or 'ideology'. It is orthogonal to that, or it just doesn't work and then why teach something that does not work.
I can also agree that it is very difficult to do and learn Calculus when your understanding of Algebra is limited or out of practice as someone who went back to get an undergraduate degree after almost 2 decades of not doing math. Is Calculus actually essential for critical thinking ? No and it does serve as a stand-in for this in many STEM degrees and if someone is lacking in understanding of the basic principles of algebra then it is going to feel like torture to solve calculus problems even if you can understand the concepts.
Now the conventional wisdom seems to be that you do have to be a math person, and teachers had better work hard on cultivating a “math person” identity, because otherwise there’s no way their students can learn math. I think this is a false belief that will make education quite a bit worse if acted on. I would never have learned to write well if teachers told me I needed to identify as a writer first!
From: https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
> As a visual indicator, we italicize the terms used to identify white supremacy characteristics as defined by Jones and Okun (2001). They are as follows: • Perfectionism • Sense of Urgency • Defensiveness • Quantity Over Quality • Worship of the Written Word • Paternalism • Either/Or Thinking • Power Hoarding • Fear of Open Conflict • Individualism • Only One Right Way • Progress is Bigger, More • Objectivity • Right to Comfort
I would personally say that this is sort of a manifestation of hierarchicalism which can be predominantly connected to white people in the United States but really transcends the racial dynamics and instead focus on accepting and promoting social structures that make those who have power over others feel like their power is justified and that those who question it or don't accept it are wrong.
For instance here is how they define paternalism:
decision-making is clear to those with power and unclear to those without it
• those with power think they are capable of making decisions for and in the interests of those without power
• those with power often don't think it is important or necessary to understand the viewpoint or experience of those for whom they are making decisions • those without power understand they do not have it and understand who does
• those without power do not really know how decisions get made and who makes what decisions, and yet they are completely familiar with the impact of those decisions on them
Here they present some antidotes:
make sure that everyone knows and understands who makes what decisions in the organization;
make sure everyone knows and understands their level of responsibility and authority in the organization; include people who are affected by decisions in the decision-making
Is this directly related math, not necessarily and should it be tied exclusively to white supremacy culture, I would argue no but it can certainly be the case that the corporate culture of our hierarchical society has a lot of these problems. I just wouldn't lump it under a racial lens because I feel like that misses the mark.
I also agree that the short list included is sort of a disservice/reductionist as it doesn't explain how these are problems or how they can be overcame whereas the source document at least provides context and explanation.
I find this an absurd and utterly indefensible statement.
You cannot find any examples of "hierarchicalism" outside of white people in the United States? Seriously?
You put the weasel word "predominantly" in there, but I think most human civilizations through out history have featured these kinds of dynamics.
First, they are listing words cited in an academic study, to set up the language used for the rest of the document. Claiming they are saying "objectivity in math is white surpremacy" is like saying "critical race theory is taught in high school".
Second, the overall message is that "roteness" is a bad way to teach. Sure, they link it to how "my way or the high way" authoritarianism is linked to how the downtrodden have been treated in America and make a parallel between that and rote memorization style of teaching. How is that unreasonable in a document talking about the experience of black people in highschool?
Maybe you are the willfully ignorant one here?
I understand roteness is bad. But please explain:
1. How roteness is linked to white supremacy.
2. How objectivity is linked to roteness. They are not related at all. You can be objective and creative. E.g., Ramanujan.
3. Asians are well known for rote learning. I am Indian. I know how rote it can get and I agree it is bad. But stop conflating that with objectivity.
4. > Claiming they are saying "objectivity in math is white surpremacy" is like saying "critical race theory is taught in high school".
Did you read the document? That is exactly what they say and imply in multiple places. Roteness is different from objectivity. You are defending a straw man. Words have meanings. If they mean't roteness, use that.
Here is an example of what this document is talking about (in unnecessarily obtuse language, but the authors probably did not expect readers primed to read it with a negative interpretation): A *very* common wasted opportunity is the following. A student is given a problem to solve. They solve it by method A. The teacher wanted method B and grades the student poorly because method A is objectively different from method B. An opportunity to learn was wasted because the teacher used something they would consider "objective" or call "expecting perfectionism". "Objective" is a weasel word in this context that just absolves the instructor from considering the particular situation of the student and teaching to them.
It seems you would be incredulous that this is my reading of the document. On the other hand, until six months ago, I was absolutely incredulous that anyone would read anything different in this document. It sounded crazy to me that people would read it the way you do. But I guess I have to concede that the document was written poorly and it triggers a lot of people.
For context, if you care, to me the reading I presented seems obvious because I have read other pedagogical research literature that gives the same advice without discussing race. So the (tangential) mention along the lines of "ideologies of supremacy use the same language as inflexible teachers incapable of adjusting to the needs of their students" seemed like a curiosity, not like something over which to grab pitchforks.
And what is academic passion if not a combination of identity, desire, and education? I think it's a nice framing, one that engage students more than 'you will learn math because we say you must learn math.' One that ensures teachers are aware of their role in shaping the identity of students.
If you trace back the history of math, it's not uncommon to make math a passion, a part of your identity (think of the Pythagoreans, for a historical example). When you become a mathematician, is math not then a part of your identity? That's what I interpret from:
>As teachers introduce mathematics to students, they are helping them shape their identity as people.
So the idea is to have teachers be aware of the impact of math and education on people's identity. It is a consciousness thing.
The vast majority of high school math students will not become mathematicians.
It's not a question of preferability (one view is not mutually exclusive of the other), and I didn't claim high schoolers should all become mathematicians (where did that come from?). In either case, I fail to see how training instructors to be aware of their teachings' effect on identity can be harmful. I'm not particularly scared nor threatened by the idea of it, and the idea that there's no connection between education and identity doesn't make sense to me.
That's all I have to say.
Math deal with concepts, forms and quantities and their relationships and their abstractions, not personal identity. There are more proper academic fields for this (such as language and art), although it doesn't remove the fact that DIE is a discredited field and should be done away with anyway.
What does it mean that learning mathematics changes your "identity"? You are still the same person you were before, but now you know some math and can do and can understand some things you couldn't before.
I fail to see how it is "clearly" indoctrination as it is taught critically (as is well evidenced in the link) unless you are some sort of "anti-SJW warrior" against any sort of modernization of our curriculum.
Then you are doing mathematics and science wrong.
The whole point of those disciplines is to eliminate human bias in favor of objectivity in order to accurately understand the world, or to make correct conclusions or predictions based on axioms, observations, and data.
If you introduce biases like gender ideology into those subjects, you are defeating the purpose.
Right now there is tremendous societal pressure and varying outcomes depending on _who_ you are (race/gender/other socioeconomic factors) and the entire point is to remove that from the equation to lead to better outcomes overall.
To do that, you need to be aware of those factors and control for them. That is very basic science.
You seem to be advocating putting ones head in the sand and saying that those factors don't matter and should be removed.
> "teachers need to work consciously to counter racialized or gendered ideas"
Is this wrong? Is it indoctrination?
> "Are there word problems that challenge gender stereotypes?"
I don't see the issue here. Should all word problems reflect 1920s America and ask about the challenges with the dust bowl harvest and how many bathroom stalls you need to serve a particular crowd, accounting for segregation? No that's silly. We want word problems to reflect the world we live in today, which means sometimes having physician Alice and nurse Bob.
> "Learning is not just a matter of gaining new knowledge—it is also about a change in identity. As teachers introduce mathematics to students, they are helping them shape their identity as people"
There's lots of discussion about how women especially, but also lots of minorities, seem to leave STEM after primary school. To me, this seems to be reminding educators that they should make an effort to keep these classes engaging and inviting for people who leave, in case the cause has historically been something in how we do math education.
> "Students are able to take what they noticed and named – in this case, how gender played out in the problem"
This is talking about teaching critical analysis (in the "how do I analyze a text" sense, not the "race theory" sense), where the teacher uses a math word problem as one of a number of places to do this. There's nothing wrong with this, in fact its actually really good to read critically in all contexts!
You can argue the best technique to accomplish the goal, but `social justice` just means that you believe every person deserves an equal opportunity to thrive. That is not a religion, that is the American dream.
Social Justice is simply the idea that we actually need to work towards providing the American Dream to everyone. That shouldn't be controversial.
No. That is the surface level definition which insidiously hides the conflation between opportunity and equity that underlies the politicized restructuring of our institutions. Equality of outcome is only possible by hindering high achievers.
In part it is the purely faith based belief in the tenet of tabula rasa that makes this movement resemble a religion. There is no quality science which suggests that all people are equally capable given identical environments; in fact such an assertion would completely deny the realities of genetics and culture.
b. It sounds like you are arguing for Equality based on merit, allowing each person a chance to thrive. I agree, that would be great. But what is actually happening is different: equity, where in practice most implementations stunt growth and paper over achievement gaps.
c. I want a equal opportunity to thrive. But "social justice" is also extra-judicial justice. It sounds nice, but isn't waht I want.
See also "motte and bailey".
Your statement "That shouldn't be controversial" encapsulates this perfectly.
> ...the National Society of Black Engineers (NSBE), which set in 2015 a goal to double the number of African American students taking calculus by 2025.
Which would be a step towards improving educational opportunities for everyone.
The new California standards are arguably going in the opposite direction.
I find this to be a trend, that many pushes for "equity" in education seeks to achieve this by reducing the success of high achieving groups to match that of the low achieving groups, instead of figuring out how to get the low achieving groups to the level of the high achievers.
The subsequent exercise suggesting a close reading of the gender roles in said word problems ... doesn't seem to have a lot to do with learning math, I'll grant.
This isn't about avoiding stereotypes though. This is about pushing a belief system and an agenda. A dangerously misguided one at that. Equity is about equal outcomes. Which you can only get through force because people have different preferences, different abilities and make different choices. Choices necessarily lead to different outcomes.
Equality and equality of opportunity, yes, please. Equity, absolutely not.
So in a way, the letter is arguing for a regression to an earlier status quo which itself contributed to the very conditions we're seeing now. Societies don't really rewind like that.
If you think we can teach CS at any sort of non-trivial level without an understanding of math beyond grade 7/8 you don't really know what computer science is. Even if you mean "programming", kids want to primarily build games which involves tonnes of HS math. Even shop courses often involve questions like "find the center of an object".
Math didn't "click" with me until well after college, when I eventually caught up on a lot of calculus, discrete math, probability and stats, to the point where I ended up doing math most of the day as a data scientist.
Before I learned math I used to feel like you did, and would argue that math wasn't necessary to be a good programmer.
Funny thing is that only once I learned a lot of math did I realize how insanely applicable it was to a wide, wide range of problems I was working on. Because I had to learn it late in life I learned math more enthusiastically than most of my data science peers and so find that even in that domain people don't realize how often they can use math to solve problems better and faster.
I wish I had had better teachers in HS that were able to make me realize just how important math is to so many interesting and fun problems.
It's sort of shocking to me, looking back at HS, how many math teachers didn't have a good answer to "when are we going to use stuff?". I wish I could take some of my friends making high six figure salaries with a penchant for late night partying to explain to HS students exactly how math is useful because it lets you get a job where nobody cares how much weed you smoke, how late you sleep, and pay your more than many doctors all because you can do some basic calculus tricks. Plus you get to work on really fun problems.
Well that is a strong argument for separate tracks. Advanced math courses for those intending to study STEM in university, CS and shop for those intending to get a job directly out of high school.
(And yes, CS as "programming" and not an academic discipline is something you could learn well enough to get a job right out of high school, or maybe with a couple more years technical education, at most.)
Also, is that true that most trades can be learned on the job without prior training? I thought you needed a decent amount of training to be a plumber, electrician, etc.
"The modern use of the term liberal arts consists of four areas: the natural sciences, social sciences, arts, and humanities."
So no, math is not "generally thought" to be part of the liberal arts.
Interesting.
One was almost entirely conceptual and provided a fantastic base with which to reason about the world. Everything was explained completely without math and then a little bit of math (usually no higher than basic algebra) was used to describe what we had just developed to fulfill basic requirements of the curriculum. People had wonderful conversations about how things worked and understanding was developed from observation and intuition.
The other was almost completely the opposite direction and calculus based. I often found errors in the application of math and reasoning about the subject. There was a moment where the teacher couldn't be convinced that something he said was wrong because of the math he was looking at. Years later, in a college Physics course, a similar core concept was covered and I was internally vindicated.
Einstein/Feynman were known to be highly conceptual and the math was often worked out after a thought experiment. A famous quote by Einstein, "Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater."
It all depends on how it is taught.
All of that being said, Mathematics is an excellent tool to sharpen ones ability to reason.
Academic areas that are associated with the term liberal arts include:
Life sciences (biology, ecology, neuroscience)
Physical science (physics, astronomy, chemistry, physical geography)
Logic, mathematics, statistics, computer science
Philosophy
History
Social science (anthropology, economics, human geography, linguistics, political science, jurisprudence, psychology, and sociology)
Creative arts (fine arts, music, performing arts, literature)
is something lost when someone learns about propositional logic and set theory without learning about the vienna circle and logical positivism? yes. does it matter very much practically? probably not, and stem people who are interested in that kind of thing can probably pick it up on their own.
I hated my humanities courses all through middle and high school and college. I took as many advanced math/science courses as my high school had. I graduated from a well-regarded technical university.
My humanities courses have probably had more positive impact on my career earnings than my tech courses. I feel like I should find my old English teachers and apologize to them.
Students probably shouldn't be falling hard on one side or the other any earlier than they already do lest even more of them believe they are completely unrelated.
Be able to write well to communicate your ideas clearly and persuade people to your position.
Be able to apply math to a variety of practical problems.
I think that prepares you to specialize in any field later.
I think the complaint from the left is that minorities don't end up in the higher math offerings because they are either not offered at certain schools or, for whatever reason, unattractive to those students. That's the problem that needs to be fixed. Whether any public school can do that is questionable.
We've got molten lava in our mouths that we can neither spit nor swallow.
A neighboring district has a similar school geared towards Healthcare.
These schools obviously teach all necessary subjects but have more advanced classes geared towards those subjects than your average school would have.