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> Nelson and Boaler’s very public beef is rooted in a controversial debate over how to teach math to California’s K-12 students.

> Boaler is behind the ongoing effort to change the math curriculum framework in California that includes, in part, increasing equity, pushing algebra 1 back to 9th grade and applying social justice principles to lessons.

Every time I hear anything about math education in the US, I leave convinced that "professors of education" should have nothing to do with it. And this opinion doesn't have anything to do with contemporary politics, since as far as I can tell, they've had a malign influence for at least a century (e.g. math education in the US was dumbed down by the "education experts" in first half of the 20th century, until the requirements of the space race and cold war forced a turnaround in the 60s).

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Let’s say you flip the recommendation to “smarten up” math education K-12. Teach Algebra gradually over K-6, do Geometry 7-8. Trig in 9, Calc 1 & 2 in 10-11, and Real Analysis in 12.

What do you think the outcome will be in aggregate? I’ll bet my hat it does nothing to produce better outcomes while furthering the race-influenced class divide. We literally have 4 living generations of people who’s only lasting association with math is “that thing that was needlessly hard and useless.” It’s the education equivalent of peacocking. It says nothing about you other than your family circumstances afforded you ample time to waste. Nobody remembers a damn thing about Trig, Geometry, Formal Proofs, or Calc unless they went on to a STEM field where they kept the knowledge fresh and even then they were still retaught it all in college anyway. But let me tell you everyone remembers the stress.

I say this as someone who has two degrees in math and tutored half my damn class just to get them through trig and calc. High school math is garbage and pointless. “Oh but it teaches you how to think analytically.” The hell it does, the nuggets of creative problem solving are buried in mountains of rote memorization and bullshit trivia.

If you want to raise the tide for all ships I would just do two years of algebra so people actually understand it completely instead of rushing them to the next thing only to flail for 4 years barely keeping their heads above water and then just stop. Then let people who are genuinely passionate about maths (or need it because they want to do calc based physics which would also be optional) opt in to that track, and crucially, don’t reward it in any way except as “nerd extracurricular” so people aren’t pressured into it.

The world is getting more complex, rather than less and the requirements to compete in that world are increasing.

Giving up on math is giving up on the future.

See here’s the thing. I completely totally agree with you. Which is specifically why I want to drop the math curriculum that is 4 years of blinding speed though material with just enough understanding and blind memorization to pass an exam it before forgetting it all.

I want a world where people come away not afraid of maths and feel like they can use it as a tool to solve real problems. But that doesn’t happen unless you sit with the material for a while. What you see as dumbing down I see is actually having a whole generation of people understand and remember algebra which is way better than we have now.

Just to add an anecdote about rote memorization -- not one teacher or textbook explained the "why" behind the area of a triangle being base times height divided by two. Just had to memorize that along with everything else.

It wasn't until years later I saw something online that showed two right triangles stacked on top of each other forming a rectangle. And then further illustrations on how you could bisect triangles of other shapes to make two right triangles that you could double up to make rectangles. Then it was obvious why you had to take the formula for a rectangle's area and divide it by two for triangles.

Similar visualizations are useful for other shapes too. But for some reason (unless I spaced out during that lesson) this was never brought up in any high school or college math class.

I don’t love the idea of ‘dumbing down’ maths, but I think there’s a needless race slant that gets added here (not by yourself, almost by US society).

Im from the Uk, went a state school, with a Masters in Engineering, and a father who was an Engineer. My perspective is that the curriculum that I grew up with failed to properly teach me maths. Further, as much as I don’t personally like some of the policies implemented in the US education system (positive discrimination), I find myself agreeing with some of the policy/curriculum changes suggested.

The largest difference between myself at university and my peers who went to paid or selective schools was that they knew how to learn. This was the hardest but most valuable lesson I learned from my prof in my first year. I remember trying my hardest, and in hindsight trying to learn in the most ineffective ways- copying out of textbooks. Seems stupid ? But that’s essentially how I was taught maths at school from 2000 to 2010 at school.

I can see 100% how upbringing currently has an outsized impact on maths attainment, far beyond other subjects. - and the impacts on social justice.

K-6 is way too early for Algebra I or anything like that, but what you can do is smoothly transition from arithmetic to "pre-algebraic" thinking, most commonly seen in complex word problems. Geometry can be taught alongside math throughout the whole K-9 or so curriculum, laying the prereqs for trig, so-called "precalculus" and calculus in 10-12. This is not a fancy approach, it's basically how math has always been taught outside the U.S. When you hear amazing things about "French math", "Russian math", "Singapore math" or whatever, that's what it's about. It's a smartened up form of traditional teaching: no need for useless Ed-school woo about how "students should just learn their math by themselves".

The big transition in thinking comes when you realize that there is a difference between arithmetic and math. And that kids can absolute hate arithmetic, but fall in love with math.

This doesn't change the fact that algebra is extremely unintuitive for a young kid who only knows arithmetic. Working on complex word problems - as was common in traditional math teaching, even as far back as ancient times - can help bridge that gap.

It’s not hard to teach basics of algebra to small children. When you work with teaching analogies like “has two apples” all the time, it’s actually not that hard to get kids to understand that you can you can do math with “things” and that it doesn’t matter what the “things” are, so two apples and five oranges becomes 2a + 5b…

I don’t expect a 9 year old to do complex algebra but the fact that you can do math with placeholders is definitely within their grasp.

> it’s actually not that hard to get kids to understand that you can you can do math with “things” and that it doesn’t matter what the “things” are, so two apples and five oranges becomes 2a + 5b…

It's hard if you want to do it prior to 8th grade let alone 6th grade, and that isn't even the most challenging part of what Algebra involves; you might as well just teach them Dragonbox and hope they all grok it. The common approach of introducing algebraic thinking gradually via complex word problems has very much stood the test of time.

> Let’s say you flip the recommendation to “smarten up” math education K-12. Teach Algebra gradually over K-6, do Geometry 7-8. Trig in 9, Calc 1 & 2 in 10-11, and Real Analysis in 12.

That's a straw-man, no one wants to make math education that aggressive.

> What do you think the outcome will be in aggregate? I’ll bet my hat it does nothing to produce better outcomes while furthering the race-influenced class divide.

If you dumb down math education, you will probably just end up "furthering the race-influenced class divide":

http://www.csun.edu/~vcmth00m/AHistory.html:

> Modeled on Summerhill, and supported by the challenges at that time of structures of authority, both within education and the larger society, "free schools" proliferated, and eventually helped give rise to the Open Education Movement. The Open Education Movement was nothing new; it was just a repetition of progressivist programs promoted in the 1920s, but the idea of letting children decide each day what they should learn at activity tables, play corners, or reading centers, was once again promoted as profound and revolutionary.41

> The effects of the Open Education Movement were particularly devastating to children with limited resources, due to their lack of access to supplemental education from the home, or tutoring in basic skills outside of school. Lisa Delpit, an African American educator who taught in an inner city school in Philadelphia in the early 1970s wrote about the negative effects of this type of education on African American children. Relating a conversation with another African American teacher, she explained, "White kids learn how to write a decent sentence. Even if they don't teach them in school, their parents make sure they get what they need. But what about our kids? They don't get it at home..." Summarizing the effects of the open classroom movement from her perspective in 1986, Professor Delpit wrote:

>> I have come to believe that the "open classroom movement," despite its progressive intentions, faded in large part because it was not able to come to terms with the concerns of poor and minority communities.42

> Another prominent educator, Nancy Ichinaga, came to similar conclusions about the effects of the Open Education Movement on low income students, based on her experience as principal of Bennett-Kew Elementary school, in Inglewood, California. Ichinaga began a 24 year career as principal of Bennett-Kew in the Fall of 1974, one month before scores from the California's standardized test were released. At that time the school included only grades K-3 and it was called Bennett Elementary school. Bennett's 1974 third grade students ranked at the third percentile in the state, almost the absolute bottom. The school was then in its fourth year of the "Open Structure Program" and the student body throughout her tenure as principal was nearly 100 percent minority and low income. Reacting with shock and dismay at the test scores, Ichinaga confronted the teachers who admitted that their program was not working. The entire student body was illiterate and the student centered mathematics program was in shambles.

> With the collaboration of her teachers, Nancy Ichinaga introduced clearly defined and well structured reading and math programs which included practice in basic skills. After a few years, test scores increased to well beyond the 50th percentile, and by the end of the 20th century, her school had earned national acclaim and became a model for others to emulate.43 At an education conference held in May 1999, Principal Ichinaga described the situation in her school in 1974:

People who claim that education was "dumbed down" conveniently forget that until after WWII, most people in America didn't even graduate from high school. Until after WWI, or just over a century ago, most people didn't even go to high school.

Education didn't dumb down. Students now learn robotics, foreign languages, and advanced laboratory sciences in good districts (and even some of the crappy large ones like LAUSD). The good ones learn more advanced topics, and at a younger age, than people in previous generations.

There are simply many more students than there were before, so while the performance of the good ones got better, and there are more of them, the average performance got worse.

Many students can’t read though: https://calmatters.org/commentary/2020/01/functional-illiter...

> most people in America didn't even graduate from high school

Mostly, they didn't need to. A good quality junior-high education could feasibly reach what today would be high-school standards. And such was all that was needed for the kind of manual work that would've been common prior to the advanced factory manufacturing that only became common post-WWII.

> There are simply many more students than there were before, so while the performance of the good ones got better, and there are more of them, the average performance got worse.

This might most accurately describe the performance of teachers, not just students. If really good teachers are inherently very rare, then average performance might indeed get worse as numbers increase. What one could raise issue with though is the recurring claim that modern educational methods are more effective than earlier ones. There's simply too little evidence for that theory.

" in good districts "

And therein is one of the bigger problems.

http://www.csun.edu/~vcmth00m/AHistory.html (just some random link, but it seems to cover things I've read elsewhere):

> The prescriptions for the future of mathematics education were articulated early in the 20th century by one of the nation's most influential education leaders, William Heard Kilpatrick....

> Reflecting mainstream views of progressive education, Kilpatrick rejected the notion that the study of mathematics contributed to mental discipline. His view was that subjects should be taught to students based on their direct practical value, or if students independently wanted to learn those subjects. This point of view toward education comported well with the pedagogical methods endorsed by progressive education. Limiting education primarily to utilitarian skills sharply limited academic content, and this helped to justify the slow pace of student centered, discovery learning, the centerpiece of progressivism. Kilpatrick proposed that the study of algebra and geometry in high school be discontinued "except as an intellectual luxury." According to Kilpatrick, mathematics is "harmful rather than helpful to the kind of thinking necessary for ordinary living." In an address before the student body at the University of Florida, Kilpatrick lectured, "We have in the past taught algebra and geometry to too many, not too few."9...

> In the 1940s it became something of a public scandal that army recruits knew so little math that the army itself had to provide training in the arithmetic needed for basic bookkeeping and gunnery.24 Admiral Nimitz complained of mathematical deficiencies of would-be officer candidates and navy volunteers. The basic skills of these military personnel should have been learned in the public schools but were not.25 As always, education doctrines did not sit well with much of the public. Nevertheless, by the mid-1940s, a new educational program called the Life Adjustment Movement emerged from the education community. The basic premise was that secondary schools were "too devoted to an academic curriculum." Education leaders presumed that 60% or more of all public school students lacked the intellectual capability for college work or even for skilled occupations, and those students would need a school program to prepare them for every day living. They would need appropriate high school courses, including math programs, that focused purely on practical problems such as consumer buying, insurance, taxation, and home budgeting, but not on algebra, geometry, or trigonometry. The students in these courses would become unskilled or semiskilled laborers, or their wives, and they would not need an academic education. Instead they would be instructed in "home, shop, store, citizenship, and health." ...

> By 1949 the Life Adjustment Movement had substantial support among educators, and was touted by numerous federal and state education agencies. Some educators even suggested that in order to avoid stigmatizing the students in these programs, non-academic studies should be available to all students. Life Adjustment could meet the needs of all American students.26

> Progressive education was forced into retreat in the 1950s, and even became the butt of jokes and vitriol.29 During the previous half century, enrollment in advanced high school mathematics courses, and other academic subjects, had steadily decreased, thanks at least in part to progressive education. From 1933 to 1954 not only did the percentage of students taking high school geometry decrease, even the actual numbers of students decreased in spite of soaring enrollments. The following table gives percentages of high school students enrolled in high school math courses.30

But that wasn't the end of it:

> The NCTM Standards reinforced the general themes of progressive education, dating back to the 1920s, by advocating student centered, discovery learning. The utilitarian justification of mathematics was so strong that both basic skills and general mathematical principles were to be learned almost invariably through "real world" problems. Mathematics for its own sake was not encouraged. The variant of progressivism favored by the NCTM during this time was called "constructivism" and the NCTM Standards were promoted under this banner.54

> ...Criticisms of educational constructivism, as in this article, were not well received by the education community. In an address before the California State Board of Education in April 1997, Hirsch described the treatment of this paper. "After a so-called peer review, Educational Researcher turned down the article, and agreed to print only a section of its critique of situated learning. This decision would have been unremarkable except that the three authors of the article happened to be among the most distinguished cognitive scientists in the world, John Anderson and two other colleagues at Carnegie Mellon, Lynn Reder, and Herb Simon. The latter happens also to be a Nobel prize winner."56

> ... Education leaders presumed that 60% or more of all public school students lacked the intellectual capability for college work or even for skilled occupations ...

This is a significant point that's unfortunately buried in this article. Progressive ideology prior to the 1960s or so was extremely bigoted, what we would nowadays call classist, sexist and racist; it went hand-in-hand with the promotion of things like eugenics. (Some people might even convincingly argue that the toxic bigotry is very much still there beneath the shiny surface, but that's beside the point here.) So this attitude that intellectual thinking should be explicitly discouraged in the bulk of the student population was actually quite functional to that sort of authoritarian ideological stance. The meaningful question is how on Earth it is still considered proper for Ed-schools to focus entirely on this sort of garbage, and neglect actual, useful direct teaching of students at all achievement levels. We expect "college for all" but drop the ball re: teaching the sort of traditionally-valued skills and attitudes that would enable that underserved 60% of the population to do good work in college.

Couldn't agree more. Its all lunacy.

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