Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field?...To close those gaps, New York City’s previous mayor, Bill de Blasio [set the policy that e]very middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed take it.... New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.
AND: From the comments at the NYT:
Retired middle school teacher here. My last year in the classroom (2 years ago), I had an 8th grade section of English with 29 students, 7 of whom were identified as gifted and 8 of whom had an IEP (individualized education plan) for learning deficits. In order for all students to be successful in this heterogeneous classroom, my district’s one word answer was this: differentiate. I was supposed to come up with about 3 different lesson plans/expectations for the variety of learners in my classroom, so that everyone was challenged appropriately and no one felt superior/inferior. How do you think that worked out in reality? I’m human, not superhuman. And we wonder why teachers are leaving the profession in droves.
Sigh. Insert a toilet-flushing sound here as America’s dominance swirls down the drain.
पोस्ट्स
११८ टिप्पण्या:
Yes, let’s force bad students into algebra so they can fail. And then let’s take away algebra from better students so they can fail.
Our elites are idiots.
In the world of the all-powerful, public-school Teacher's union, priorities for student achievement come 'last', and it shows up by direct measurement - over, and over again.
Should middle schools eliminate algebra to level the playing field?
Why are these bigoted contemplations always given a prominent seat at the liberal table?
A friend immigrated from PRC, where she was an average math student, to CA middle school, impoverished. Never had to study for HS math. Everything had been covered in school in PRC.
Identify the smart minorities and put them on the same track as the smart whites and Asians and Indians and Jews.
They will succeed and we can get rid of DEI because we'll know who is worthy and who is an idiot.
But the last time I checked, California does not administer IQ tests to black children because most scores are lower than whites.
That's beside the point. It would identify the smart kids and give them a chance.
You need to have basic competence in math to attempt algebra of course were not focused on that
How preventing some from getting ahead helps those who have fallen behind eludes me.
As a teacher, you are supposed to believe, "All students can learn." Which is, of course, true in the sense of "everybody can learn something." But it is very much untrue in the sense of "everyone can complete a rigorous college program." Or even, "everyone can understand algebra."
Most students can solve the problem, "I buy two shirts for 28 dollars and pay with a hundred dollar bill. What is my change?" But fully half have great difficulty when it's changed into "If C = B -2x, where x is 28 and B is 100, what is C?" People who are mathematically proficient can't understand how that can be true--after all, the two problems are the same logically--but it is.
So maybe half of students simply aren't going to get algebra. This is a nightmare for educators because 1) algebra is the gateway to STEM, and 2) a disproportionate number of those who don't get it are going to be "under-represented minorities".
This reality is too awful to face, so educators hope and fiddle. And it never works.
In the words of hundreds of tee shirts (just google), "And then Satan said, 'put the alphabet in math.'"
These math gaps are "opening up" because ever since COVID schools have been utter dysfunctional.
The only kids that learn math right now learn it at home.
Dude1394 said...
Yes, let’s force bad students into algebra so they can fail. And then let’s take away algebra from better students so they can fail.
Our elites are idiots.
The average Democrat is an idiot. The average Uniparty flunky is an idiot.
The people who own the Democrat party, the Romney Republicans and the media know exactly what they are doing.
Equity apparently requires cutting people off at the knees if they start to be taller than others…
Yea, by all means, let’s NOT teach students algebra when they’ve shown they’re ready to learn it, because it might hurt the feelings of those other students over there who are not ready for it (and may never be).
Might as well ban private schools and colleges and universities in the name of DEI. After all, how can we allow those students to learn at college when not all students will make it that far (or want to).
How preventing some from getting ahead helps those who have fallen behind eludes me.
That's because you don't understand the goal. The goal is not to help anyone. The goal is to make everyone equal. The left mostly would rather everyone have $1 in purchasing power, than to have one have $100 and everyone else have $5 in purchasing power. There are exceptions to this. If there is a person with a perceived disadvantage in a current key social category, then the goal is to elevate that person above all other until a new special case can be found. the other exception is that the elite are exempt.
I went to a lily white school in rural PA. Only 30 kids got 8th grade Algebra. I was one of the 30. I had to pass a standardized test to get into the class. Not everybody is a math person. I am a terrible speller, but great at equations. I was 1 of 6 girls.
Fast forward, my daughter in Catholic school, has Honors Math in 7th grade. Now I need to recall my Algebra. She had to have a minimum Math score in 5th and 6th grade and a minimum on their standardized test. There are 8 kids in the class (out of 30). There are 2 girls.
In the local school district, where houses start at 800K and go over 2 MM, 40% of the 8th graders are NOT proficient in math. We are mainly a White and Asian community. Our neighboring districts are 50+% NOT proficient in 8th grade math. This is NOT algebra, but the basics.
The moral of the story is: it is not demographics, but teaching methods. The Catholic school uses a traditional curricula and the kids score better. Some kids are Math kids. It just is...
To master any subject at any particular level, you need a certain cognitive ability.
Not everyone has the cognitive ability to master any subject at any level.
Cognitive abilities vary greatly between individuals and groups.
Therefore, not everyone can master any subject at any level, and for any subject at any level there will be people who cannot master it.
Groups will differ in their ability to master certain subjects at certain levels.
This shows up in different test scores and levels of achievement.
In the U.S., the wrong groups show lower scores/levels.
This is intolerable; something must be done--anything to avoid Facing Reality.
On the right track, but the goal is not to make everyone equal; the goal is to have a submissive populace that will keep the government, the politicians that support it, and the factions that profit on it in power. What do they care about anyone or anything else?
"offer a chance" is a weird way to spell "pass them even if they can't do the work"
My sweet mom & my fourth grade teacher gave me a pass on math. I never learned basics. It destroyed my dream of being a pilot. (At my age, I probably would have died flying Phantoms off a carrier in Vietnam, so oh well)
I ended up getting the only degree available at the time that didn't require math, BFA in Design. I took Deductive Logic in summer school in the Philosophy department to bypass math, 2 hrs per day, five days a week and made an A, B, C, D, F & passed.
I ended up in business & when learning Borland Quattro (yes, told you I was old) from an owner's manual (remember those?) I looked at the formulae one day and said: Holy shit! this is freakin algebra. I should have paid attention.
"That’s why middle school math is this flashpoint. It’s the first moment where you potentially make it very obvious and explicit that there are IQ gaps opening up."
Fixed it for you.
Deny reality ai your peril.
Algebra?
Of course it should be offered. But so, so many would-be students of algebra have not thoroughly mastered arithmetic. And with math generally its study requires, without exception, a knowledge of the building blocks. The left decries rote learning and memorization, calling them Drill & Kill. When in reality those exercises are Drill & Skill. When arithmetic basics are implanted into a child's brain such that they become automatic, taking further steps into math is simply a naturally progression.
Algebra is both cornerstone and lynchpin to succeed in modern commerce.
"In the world of the all-powerful, public-school Teacher's union...."
Okay, what relevance does the first sentence in your dystopic science fiction novel have to the topic at hand?
There are plenty of atrocious, low-skilled, and likely low IQ teachers out there. They contaminate the students with bad habits and bad attitudes. Decades ago a talking Barbie doll was skewered for saying "Math is hard." Well, many teachers express that "math is hard" all the time.
Offer advanced placement algebra to all, but put the same students into real-world job math classes such as statistics, accounting, and...physics...then watch for similar or worse failure rates. Tracking students per academic potential has been common for generations. There is no alternative.
Merit is a privilege of the productive. Every child left behind is equitable and inclusive, is progressive: one step forward, two steps backward, and a source of forward-looking redistributive change. #NoJudgment #NoLabels
Harrison Bergeron was not a how-to manual.
And then let’s take away algebra from better students so they can fail.
The kids with parents who can afford it get tutoring so they are learning anyway. The only ones who are hurt by this are the smart kids with poor parents - precisely the ones who need these classes in school so they can get scholarships and break out of poverty.
Everyone taking courses that are pathways to college is just as bad. It's part of the "everyone must go to college" mindset. It's the mindset that looks down on service and labor jobs. Some kids are happier up doing things than they are sitting at a desk. They would do well in vocational classes that would help prepare them for a career as a plumber, electrician, mechanic, or carpenter. Something that would potentially allow them to support a family. Instead they'll take a few semesters of college and work as a barista, paying back student loans that benefited no one other than the college and perhaps a loan officer.
Education requires aptitude, investment, and interest. That said, diversity of individuals, minority of one.
84% of black kids are deficient in math. This can only be remedied by lowering standards so that simple arithmetic becomes the standard after which no more math is taught. Laughable to think this cohort can close the gap. Laughable to believe it is the fault of teachers or the education system.
I returned to teaching after 15 years of retirement - inflation. And I'm here to tell you that algebra teachers for middle school and upper math teacher (calculus, trig, geometry, statistics) are very rare commodities at the rural Florida high school where I teach. And if you do find one it's an even 50/50 they don't last the year.
Child aptitude, investment, and interest gaps are evident from grade school, perhapa earlier, and are predictive of achievement. The solution may not be academic.
As the Great Experiment in Socialist equality--the USSR-- demonstrated, the only solution to economic equality in the face of human diversity is poverty. Or, to the academic gap in IQ, ignorance. The blank slate denial of the reality of human diversity which has become the essence of the liberal or progressive view, has set them on a path of destroying Western Civilization, economically, intellectually and culturally.
Addendum: after walking in and out of classrooms since 1973 I'm here to tell you that Drill, Kill and Skill with rote memorization is THE way to go through 8*th grade. By the 9th grade you can allow students to start thinking in small doses.
55 years ago I tested into algebra in 8th grade. There were about 10 of us in our town, and we took it at the high school 1 hour before middle school started. We also had to take normal 8th grade math with our regular class. I still remember our wonderful algebra teacher Mr. Koval - genuinely one of those special teachers one remembers all their lives. It wasn't rocket science to set it up, and no one in our regular class felt like they were "failures."
And forget Brown, Taupe, and Albinos.
There was a viral video going around the other day where a guy with a camera was asking college students basic math questions like what is 2 cubed, what is 2 times 2 times 2, what is 11 x 6 etc. He even took the time to show the students who got the questions right, but one can only be filled with pessimism by sheer numbers of college students who couldn't tell you what 4 x 7 is.
You have to be willing to track students in elementary school- if you don't, you are still practicing destructive discrimination, but doing it to the smarter kids. I could have handled algebra by the time I was in at least the 3rd grade but didn't get a class in it until I was in the 9th grade, along with everyone else.
LatinZ... lost in leverage. There’s the problem.
And forget Brown, Taupe, and Albinos whose lives don't matter.
I've tutored individuals in math, mainly algebra, periodically over the past 50+ years. Always free.
The last example was a neighborhood kid (white if that's relevant). It became clear he was scared of math and barely functional in arithmetic.
His mom's goal was that he squeak out a D because, as she said in front of him, "He's stupid in math like me". Ouch.
A couple of arithmetic games loosened him up. Instead of theory I taught him "clues" to look for when solving (e.g.) quadratic equations.
After a few weeks mom was thrilled. The teacher told her he had a solid C going, would raise his hand to participate and even volunteered to explain at the chalk board.
I asked if I could have him a little extra in the lead up to finals because he could end up with a B the way he was progressing.
"Nope" says Mom. He and his Dad always take a week off this time of year for a fishing (hunting? I can't recall) trip. Momm tells the school he's sick.
Kid got an F on the final, but still squeaked out a D for the course.
I was the only one not thrilled.
Home life counts.
I was in school a long time ago (>30 years).
I was interested in the Teacher's comments. Hmm, that's exactly what teachers did back then. ~30 students, some gifted, some not-so-much. They learned how to teach a range of subjects with students with a wide range of ability.
In short, that teacher is why students are so inadequate, today.
(Yes, it's a 'back in my day' story).
Algebra I in the 9th grade was the first 'F" I ever got, and I had to go to summer school to make up for it. I took Algebra II as an elective in my senior year, but lost the thread after the first month and gave up my dreams of a STEM career. (F #2.)
Just kidding, I have never been very interested in most STEM topics.
Had enough good credits to graduate anyway; I'm no longer sure why I signed up for it, and devoted the attention I wasn't paying to Mr. Vernon to things like history books and classic scifi. It was a second study hall just for me.
In college I passed jock physics and symbolic logic, and took geography classes that had lab sections requiring some math. It was enough.
I like studying history partly because, other than literacy (in as many languages as make sense) there's no threshold like there is in STEM. You only have to be curious about the past and willing to learn the sources. High IQ is nice, and the best historians IMHO have very high IQs, but the field is open to anyone, even math dolts like me.
Do bias and inequality keep Black and Latino children off the fast track?
Yes. It's called the "soft bigotry of low expectations," and it's prevalent among educated leftists. When a white liberal looks me in the eye and asserts that "the average IQ of blacks is 87"* as a justification for affirmative action, DEI, and/or limiting the educational opportunities of children of color, then we see this soft bigotry in action.
Should middle schools eliminate algebra to level the playing field?
No. The principles underlying algebra are easy enough to state and explain, so the parents who care about what their children are learning can -- and will! -- teach it to their kids anyway.
___________
* No, I don't know where they got this number. Junk science? Some old KKK publication?
Everything, everything, points to the average black IQ being 86. A black with an IQ of 86 should do as well as a white with an IQ of 86, when everything is working. That should be the target.
Target higher and it will just be another failure.
Obviously the schools aren't doing even that well, rewarding acting out and chaos instead, which puts blacks even with whites with an IQ of 50 instead.
I don't see anything in algebra that prevents an IQ of 86 from doing fine in it, by the way. It can be done quite by rote. That's one of its flaws as far as teaching gifted kids. It bores them to death.
Example, before I took algebra:
x + 2 = 10
well, if two things are equal, then subtracting two from each they're still equal
x + 2 - 2 = 10 - 2
If you figure out the right things to do to each side, you wind up with
x = 8
Is that cool or what.
When you take algebra, you don't learn that. You learn move the 2 to the other side and change its sign. Pure rote, no reason, no deep puzzle. Boring.
Stymie:
Come on, Algebra. This is no place for you.
Middle school math (non-Algebra division) is the third year in a row students are instructed to multiply and divide fractions.
High school math (non-Algebra division) is the first year they give up teaching fractions to whole groups of students.
you CANNOT BE more racist than algebra. JUST LOOK AT IT!!
x is NOT EQUAL to y RACISM!!
x is GREATER Than y RACISM!!
y is LESS THAN x RACISM!!
x = b ± √ ((b*b) - 4ac)/2a The DEFINITION of RACISM!!
"How preventing some from getting ahead helps those who have fallen behind eludes me."
Welcome to Equity, coming soon to an intellectual abattoir near you!
What is AOC's position on this controversy?
I think Algebra is one of the first subjects in school where there will be some normal children, (meaning no significant learning disability), who will likely not ever gain competence in it. There are other children who not only will gain competence in Algebra but will do so much much faster than most children. Limiting the latter group's opportunities to protect the former group's self-esteem is profoundly unfair, and produces no good societal benefits to justify the cost. People worry that the slower students will get dejected and give up on learning if they see other students exceling where they do not. Those slower students become slower adults and at some point will have to deal with the fact that many other folks are sharper than them. The longer it takes for for this to happen the more effort is wasted. Algebra isn't a requisite for leading a good productive life. What's more when students are separated out by ability then then some start to understand what their talents and gifts are. We want people who are interested and talented in Algebra to pursue STEM careers, we want those who aren't interested or talented to not pursue them.
You need to have basic competence in math
Students have problems with calculus because they cannot handle algebra. They have problems with algebra because they cannot handle division. Math education in this country is a disaster.
I can remember taking algerbra in middle school. It was no big whoop. If the math teacher noticed you were doing well on all the basic math, he just asked you if you wanted something more challenging and gave you the algerbra textbook and had you work on that.
I've never been clear on why there is an obsession with advanced math in HS and middle school. Even though I've worked in finance and other professions that used numbers (before I swtiched over to HR) I've never had to use algerbra or calculus in my entire work life.
I suppose its a way to identify people who can do engineering, Computer Science, etc. but the whole calculus/algerbra, etc. classes are just a waste of time for 90 percent of college graduates.
BTW, I can remember doing "Fractions" in elementry school and I've never had to do a "Fraction" problem in real life in the last 45 years.
in the New York, about TWENTY FOUR THOUSAND DOLLARS are spent PER STUDENT, PER YEAR..
About HALF of students there are NOT proficent at grade level..
WHAT are they getting for that money.. (about a quarter of a MILLION dollars for 12 years)
You Can't Tell Me, that kids wouldn't be better off if we Just GAVE them the $288,000
Now, neighsayers will neigh: "OH! NO! They'd Just WASTE IT on iPods and Shoes!"
So, tell me; neighsayers.. WHAT DO the kids get for their $288,000 dollars?
Blogger RCOCEAN II said...
BTW, I can remember doing "Fractions" in elementry school and I've never had to do a "Fraction" problem in real life in the last 45 years.
Do you not cook, or have never had to make adjustments to proportions of something else? You may not actually write it out on paper but I'm assuming at some point in the last 45 years you did something along the lines of this was for X amount of people/days/servings but instead I need it for Y. Perhaps your teachers did such a good job and getting you competent in fractions you don't even have to think about them.
I moved during winter break in 6th grade, from an inner city school in Norfolk to a quite ethnically diverse but not inner city school next to Kirtland AFB in Albuquerque. (It may be worth noting that Sandia Labs is right there too. My younger siblings went to the public elementary school that served the kids of Sandia Labs employees.)
Anyway. At my new middle school, in the math class into which I was placed, they were just introducing this weird concept of "x" that could mean all kinds of things. My memory of that time is that I spent a good two weeks frustrated almost to tears by the cognitive leap this idea required, from manipulating concrete quantities to dealing with unknown ones that could become known through manipulation, but it probably wasn't more than part of a week.
And overnight one night, as if possibly in a dream that I didn't remember, something clicked, and suddenly it just made sense to me. No further problems.
I think about the fact that quite a few cultures never developed the concept of zero as a number. Algebra was a huge stride. The calculus (which I got through two semesters of but can't really say I ever really understood except definitionally) was gigantic. (I now have one kid who's a banker, one kid who's about to get her degree in math and finance, and another who's going into his junior year in mechanical engineering, and you, or I, can thank their dad for that.) Math is hard, for lots and lots of people, and not everyone has the capacity for it.
I suppose its a way to identify people who can do engineering, Computer Science, etc. but the whole calculus/algerbra, etc. classes are just a waste of time for 90 percent of college graduates.
It's helpful to identify those with the math IQ to succeed at more demanding jobs (definitely not HR). Some find it difficult to even spell algebra.
By the way, I am reading Glenn Loury's book, "Late Admissions." It is terrific that he was able to overcome so many barriers, some self created.
Over-compensating Non-combat "vet" Howitzer Howard: "Algebra is both cornerstone and lynchpin to succeed in modern commerce."
Which is precisely why your team seeks to destroy the teaching of it.
The "good" news from a dem/left/LLR perspective: more time for secretly transitioning and sexualizing vulnerable kiddos without parental notification as well as more drag queen story hours with dildo props to hand out to first graders along with pornographic books!
Actually I probably shouldn't have written those factual things given how...agressively motivated...LLR-democratical And Violent Homosexual Rage Rape Fantasist Chuck gets when these specific topics involving young children pop up.
It's a poor mind that can find only one way to spell a word.
As for fractions, I'm talking that whole demoninator/numerator nonsense i learned. Y'know 1/2 times 1/4 = whatever. And then when you 1/2 divided by 1/4, you flipped it and got whatever. Its much easier just putting in the excel spreadsheet/calculator: .5/.25 = 2 or .5 x .25 =.125
Algebra is the easy stuff. But you can’t fake it. Which means lots of practice using equations. And IT IS USEFUL
THE Asians out shine American teens so far here that ditching math is analogous to legalizing marijuana.
“In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes.”
The only way to solve that problem is to eliminate advanced math, period.
“I suppose its a way to identify people who can do engineering, Computer Science, etc. but the whole calculus/algerbra, etc. classes are just a waste of time for 90 percent of college graduates.”
And boy, does it show.
stlcdr said...
I was in school a long time ago (>30 years).
I was interested in the Teacher's comments. Hmm, that's exactly what teachers did back then. ~30 students, some gifted, some not-so-much. They learned how to teach a range of subjects with students with a wide range of ability.
In short, that teacher is why students are so inadequate, today.
(Yes, it's a 'back in my day' story).
********
I may have mentioned this here before, but my "back in the day" story has me attending 1st and 2nd grade in a one-room schoolhouse outside rural Somerset PA, a mile or two from Shanksville where United 93 went down.
Grades 1 through 8, about 30 kids, ONE teacher. No teacher's aides. No running water. Outhouses out back.
Somehow, our teacher maintained order and got us kids taught. I can still remember wondering what all those numbers were, spread across the blackboard.
It was long "division".
Just today, a continuation high school in a black SF neighborhood revealed it has an absenteeism rate of 96%. The math on that says invest in blue tents.
What, "algebra and calculus are just a waste of time for 90 percent of college graduates"?!
I hope that this 90% understands the concept of cost per unit (fractions!), or velocities (mph) -- tiny bits of algebra and calculus that we all use in our everyday lives, or at least I hope so.
Innumeracy, especially in the clerisy (journalism, law, politics) but of course in the general population, is actually one of the most important general conditions bringing the USA down. The average voter (and most of the clerisy) cannot grasp the magnitude of the federal debt and deficits, the rather simple equations for benefit programs and pensions driving it. Their eyes glaze over at the second sentence. One can almost hear the echoes of "I was told there would be no math...." As Charles Murray discovered, any rigorous statistical analysis elicits frustration and rage. As others here have remarked, mathematical reasoning itself has been openly identified as White Supremacy, by the critical theoreticians who have seized control of credentialed academia.
Somewhat related, I watched a recent Joe Rogan episode with Terrance Howard. Howard begins a rant about physics by arguing that one times one actually equals two. It just gets crazier from there, and Joe seems to take it all seriously for the whole three hours. Of course, he also believes that UFOs are real and the moon landing was faked, so I wasn’t too surprised, but still…
It is another example of trying to cure the symptoms rather than the problem, combined with trying to game the system to get the desired result without actually accomplishing anything useful.
If a student is ready for algebra in 8th grade, the student should take algebra in 8th grade. If the student could have been ready for algebra in the 8th grade but is not for other reasons, perhaps reasons that happened 10 years ago, it is too late to do anything about it now. You needed to fix it 10 years ago. Trying to force is likely to result in failure.
JAORE said...
His mom's goal was that he squeak out a D because, as she said in front of him, "He's stupid in math like me". Ouch.
The consummate devouring mother.
The most useful math course I had in high school was freshman geometry. It was taught the old fashioned way, the axioms were given and the student wrote most of the text by proving the theorems in progression. It taught logic and proof, skills which many college students find extremely difficult because they have never encountered them before.
My second son, now 48, is scary-bright. They had him skip Grade 3, and at the beginning of Grade 4 the class was handed a new Maths text ad told they'd be reviewing Grade 3 for the next two weeks. At home he was crankier than I'd ever seen him. Off to his room; agitated and clearly stressed, as soon as he got home from school which, because we were in Québec, was all in French.
After those two weeks, he handed the book back to the teacher and said "I finished the review. Could I have this year's book, please?" Having missed Grade 3 Maths entirely, he mastered all of Grade 4 Maths in two weeks !! It was then that we and the school understood what we had on our hands. At the time, his mother and I combined six degrees in the hard sciences, and we still found it daunting.
The schools helped him in every way possible, allowing him into higher grades' Maths classes. In the end, he earned a B.Math from Waterloo in Ontario, of only four schools in North America even offering that degree, the others being MIT, CalTech, and Stanford. Of the 22 students in that program, he was one of only two non-Asians [east and south], and he graduated in the middle of the pack. His primary education had been in a town of 600. His secondary -- due to Québec's longstanding voucher system -- was in a small regional city of 80,000.
In the States, where Merit is now "racist", and Maths, too, he'd have been held back at every step of the way so as not to embarrass fatherless and semi-feral students of certain ethnic and cultural groups, and "offend" their FEELZ.
There's more than one reason the Canadian education system has long been in or near the Top 5 in the world, whilst the US now struggles to remain n the Top 50.
Nothing destroys K-12 education faster than refusing to separate students by ability.
Tina848 and others here pick out traditional schooling and methods such as "drill and kill" and rote memorization as the lost skills of building a good knowledge base. They're so right. Add in discipline and consequences, and who cares if some people or even entire cohorts have lower IQs: they're prepared for life.
These methods are abandoned on the rationale that they are "rigid," "white," and "Western." But there's deep creativity to be found in memorization and repetition (of the right things). Both teaching and learning it. Ask an engineer, an athlete, a mathematician, or an actor.
We have lost the freedom of formality.
My favorite math joke:
We all know that 6 was afraid of 7 because 7 ate 9.
But, why did 7 eat 9?
Seven knew the importance of eating three squared meals per day.
When a white liberal looks me in the eye and asserts that "the average IQ of blacks is 87"* as a justification for affirmative action, DEI, and/or limiting the educational opportunities of children of color
No white liberal has been willing or able to assert that average racial difference in public since The Bell Curve was published in '94. There's a reason Murray was attacked and Steve Sailer writes in backwaters and only has invited guests attend his current book tour. Now all BIPOC academic gaps are solely down to systemic racism, requiring reparations, etc. If they could be honest, they might be able to make a rational argument for AA or at least useful vocational ed instead of ruining education for everyone.
We were introduced to algebra at the end of 6th grade in my lily white, tracking public school--by a black man. I can't remember my integrated 7th grade math class at all, it was that boring. My parents put me in private school for 8-12.
RCOCEAN II said...
BTW, I can remember doing "Fractions" in elementry school and I've never had to do a "Fraction" problem in real life in the last 45 years.
Keep This in mind, when rcocean tells us, that 100% of Gaza casualties are women and children
The most useful math course I had in high school was freshman geometry. It was taught the old fashioned way, the axioms were given and the student wrote most of the text by proving the theorems in progression.
That describes my liberal farts college geometry course for math majors. I hope we went further for our expensive tuition. For part of the final, the prof threw a curveball and wanted us to draw and describe how to do something (trisect an angle?) with compass and straight edge, neither of which we'd used at all in the course.
As a teacher, you are supposed to believe, "All students can learn." Which is, of course, true in the sense of "everybody can learn something." But it is very much untrue in the sense of "everyone can complete a rigorous college program." Or even, "everyone can understand algebra."
It is just preposterous that anyone still hangs on to the “tabula rasa” view of human achievement. I don’t care how smart you are, there are limits to what you can learn. I was always the smartest or second smartest kid in my classes, took all the highest level math courses in high school that I could, flashed through calculus and statistics and physics in college, and ground my way through DiffEq and linear algebra with somewhat more effort, but mastered the material. And then I got to Complex Analysis and Partial Differential Equations, and found my own personal “pons asinorum”, the Donkey’s Bridge beyond which a jackass will not pass no matter how hard you whip him. Everyone from a brain damaged moron to Stephen Hawking has a limit to their abilities, and the limit is different for each individual.
Lawyers have to understand ratios and basic statistics the better to understand expert witnesses BS. It’s just a tool in your head rather than getting out a slide rule.
But that helps in all calculation of dad old man Money.
A surprising percentage of outlier kids are homeschooled because their parents don't want to constantly wrangle with bureaucracy to get appropriate educations for their kids. Aren't bureaucrats always carping on about "equity?" Not fixing this problem means that only people with means get an appropriate education. How is that equitable?
I had no problems in geometry; in fact I was one of the better geometers in my class--my lady teacher even showed everyone my unique solution to one particular stumper. I won't swear it used fewer steps but it might have--I do know I started at a different place than the others
and she seemed impressed with that.
My standardized test scores were always among the best in whatever grade I was in, but they were definitely better in verbal than math (like the smart girls, and I am not ashamed).
Which explains why all those women kept insisting that I should make better grades.
All in the almost entirely lily-white public schools of east Memphis in the 1960s; there was a lot of class and faith diversity, but not so much in race. That came later.
Ralph L - if your geometry professor, on your final exam, wanted you to trisect an angle with ruler+compass then he hated all of you and was just f**king with you.
(Or possibly, it is you trying to screw around with us?)
There are some behaviors that Black people call Acting White. I wonder what behaviors Asian people call Acting White?
Has anyone here ever taken linear algebra? Partial differential equations? Fourier analysis? See any blacks in your class?
Everything the public education industry pushes out is designed to make it easier for teachers who get dumber and dumber every year but none of it makes sense to the kids. Now we have a math curriculum requiring 15 steps and advanced reading skills to subtract 4 from 20 when the obvious solution is for the kids to just fucking memorize the easy shit and move up from there.
RCOCEAN II said...
BTW, I can remember doing "Fractions" in elementry school and I've never had to do a "Fraction" problem in real life in the last 45 years.
****************
You sound like my wife. When she cooks, she always makes the full recipe----even if it's "Enough Moo Goo Gai Pan to Feed the Peoples Liberation Army"---because she can't scale down the fractions.
For example: if cooking 1 cup of rice takes 1 1/2 cups of water, how much water do you need to cook 3/4 cups of rice?
MANY recipes with multiple ingredients require that kind of math.
(Yes, we have a lot of moo goo gai pan leftovers in our fridge.)
One of the reasons why we spent the money to send our daughter to a private school K-12. They had Algebra in 7th-8th grade, and with that basis, I taught her derivatives over a weekend in maybe 8th grade. For her, not understanding math was not an option. Told her that if she wasn’t at the top of her class in math, we would spend our weekends together doing math, instead of skiing, etc. Didn’t need that threat. She is the 4th generation with a math/engineering degree. Ended up with a BS w/honors in Physics and Math, and a PhD in mechanical engineering, where her work requires significant use of partial differential equations, etc.
It’s weird. My partner has a photographic memory, and is quite bright. But algebra never made sense to her. Her older brother told her to ignore that it doesn’t make sense, and just do it. She did, and got As in math. How can it not make sense? If 2X=10, X is obviously 5. She is just too literal for that to make sense. Now, if I told her that 2 books cost $10, she would know that they cost $5 each. But what does X have to do with it? She just literally cannot abstract that way, while everyone in my family does it instinctively. On the flip side, we had a new refrigerator delivered to her room yesterday. It’s big (30 cubic feet), but she had a 1/4” to spare with the door opening and maybe 1” with the doors getting it in. She can space plan that well by sight alone. It’s uncanny.
I had the pleasure of working with two Black African women engineers, one electrical and the other chemical, both educated in Uganda. They knew their stuff.
The word algebra, I learned today, comes from Arabic. Math transcends cultures. It's not only that math teaches logic and abstract thinking, although that's a great benefit. The value of math is more philosophical, or spiritual even. Growing up, the one place where I routinely encountered the truth, unchanging and verifiable truth, was in a math classroom. Maybe that's why I loved math so much then. Not everyone has an aptitude for math, but we should do everything possible to make sure everyone has access to a math classroom.
“Has anyone here ever taken linear algebra? Partial differential equations? Fourier analysis? See any blacks in your class?”
Of course, and no. Daughter’s PhD program (ME) was mostly White (including dot Indian and Middle Eastern), with the remainder Yellow. Daughter uses the latter two heavily at work. She follows her mother there. My preference was for the more abstract math. As an undergrad, Linear was the cut class - if you couldn’t hack it, they wouldn’t let you major in math. My Abstract Algebra class wanted us to write a paper. So, I summarized my Linear Algebra class with the equations we were using in that class. My favorite though was Non-Euclidian Geometries. Spent the term playing “let’s pretend” every day in class. In Euclidian geometry, parallel lines never intersect, and the sum of the angles of a triangle equals 180°. It’s a useful generalization but not actually accurate.
“Most students can solve the problem, ‘I buy two shirts for 28 dollars and pay with a hundred dollar bill. What is my change?’ But fully half have great difficulty when it's changed into ‘If C = B -2x, where x is 28 and B is 100, what is C?’ People who are mathematically proficient can't understand how that can be true--after all, the two problems are the same logically--but it is.”
Would this hold true in Russia or China? I suspect not. So either Russians and Chinese are genetically superior in their math aptitude, or there’s something seriously deficient in our educational system or our culture. I don’t buy the genetic explanation.
“I suppose its a way to identify people who can do engineering, Computer Science, etc. but the whole calculus/algerbra, etc. classes are just a waste of time for 90 percent of college graduates.”
Confusing cause and effect. It’s a waste only if you don’t learn it well enough to do anything with it. If 90% don’t, that’s not an indictment of math, it’s an indictment of our educators or our culture that so many don’t learn it.
The top 5% of kids go on to make the world work. Sure, let's prevent them from taking algebra, what could go wrong?
The teacher's unions in inner cities have created terrible schools. Notice that black kids who go to Catholic school in the same neighborhood do well.
FWIW, I was told that back when geometry was the logic theorem/proof class, some kids took to it and didn't do so well in algebra, and others did the reverse.
When I volunteered at a local elementary school in Madison, they gave me a hands-on curriculum for teaching solving linear equations (of one variable) to third graders. The kids seemed to figure out the mapping of unknowns to symbols, and how to do simple manipulations, easily enough--which appear to be two of the big conceptual issues with algebra.
Asians overseas see acting white as the First Marines killing them all . But once they get here they desperately want to own real estate like the Chinese do.
Sebastian said: "This is intolerable; something must be done--anything to avoid Facing Reality."
I read that book, too. Charles Murray has spent his intellectual life insisting that we should all face reality. Hasn't been easy for him, either. But, it's reality, so you might as well face up to it. Avoiding it does no good.
I've never had to do a "Fraction" problem in real life in the last 45 years.
You must not have a job where analysis is required.
Analysis requires division.
Reminds me of my favorite math joke:
Terrible math student: Where will I use this in the real world?
Math teacher: Oh, YOU won’t.
Yes intro algebra needs to by taught in Jr. High.
But to me, the Biggest Problem is Parents. Parents, not teachers are responsible to see their children get the need education and skill set to be a fully functioning adult.
m
I'm mystified that kids cant read. That is not a 2024 problem Its a 2005 problem. Those kids never learned whats important.
The fact is our educational system has been degrading for 50 years. The Democrat Party has created idiocracy.
I had a little set to on line with someone that thought SS was a great value. The said, after 2.5 years they have already gotten out 50% of what his lifetime submissions have been! He was going to get out, way more than he paid in.
So I got on line found a an investment web site that had a calculator on the front page. plug in monthly deposit, annual interest, monthly compounding and years contributing and, there is is. 45 years and you have $1 million cash.Iof you take just the interest generated only you have more than twice what SS is paying out, and when you die you leave h your heirs $1million
I learned that in high school in the 70's(after Dad laid it out one day while raking hay)
Schools are not teaching compound interest, or when two trains leaving the station at the same time will meet each other.
It is much easier for the govt to scam the stupid. Biden just opened up the strategic Oil reserves trying to keep gas from jumping when summer blend switch over happens. Because the people are stupid
There are public schools in Milwaukee in which no one is proficient in math and reading as shown by standardized tests. But students from the zip codes served by those public schools do well in Catholic schools, in charter schools and even in the suburban public schools to which they can escape due to Milwaukee's enrollment policies. This is why I believe that a part of the problem, a very large part, is lack of discipline and phonics in the public schools and that there is a solution (discipline, phonics) which would create a literate, capable group of graduates in place of the illiterate, bitter graduates (and non-graduates) the public schools turn out. But the Teacher's Unions oppose this solution. Their "solution," if you can call it that is is an applied DEI in which teachers and principles get dinged if their students do well unless that success is in the same proportion as the demographic distribution of the races in the class.
In my opinion nothing but slavery itself has ever been as dangerous to the black citizens of this country as promulgating the rule that if you are in a class with black students you will not be allowed to do better than them. I think this is a policy which will simply not be enforced - like Prohibition. It's not wanted by anybody except Our Betters. And who thinks they know what they are doing?
If you know a bright 7th or 8th grader who isn't getting the math teaching he or she deserves, try the Wondrium or Teaching Company offerings that are available online and at many public libraries. They are inexpensive, come with workbooks, and have exceptionally good teachers.
I found that algebra, geometry, trig, and calculus lifted me from the dull (albeit necessary) mud of arithmetic. I would have benefitted from resources such as the Wondrium courses.
Sadly, smart kids today need to understand that there are lots of adults out there rooting for them to fail in their educations, and that they are going to have to go out of their way to defeat them. Intellectual competence frightens leftists. Promote intellectual competence.
According to progressives, everyone is the same. Any difference in outcome must be due to systemic issues, like racism or sexism or ableism. It can’t be due to the fact that different people have different abilities.
"Intellectual competence frightens leftists."
Of course it does. Those are the people who claim to be unable to define the word "woman". Their policies cannot withstand critical evaluation.
Algebra was a 9th grade subject when I was in school. What's the big hurry now? Obviously kids are not any brighter just because it's 2024.
Anyway, if kids stop taking progressively harder math then they forget all the simpler math including arithmetic.
If you make it "relevant" to everyday life then you lose its lovely other-worldly abstraction and render it mundane.
In short, everyone is wrong.
I see that someone else thought of Vonnegut's story Harrison Bergeron. Yeah, in ten years we'll be wondering why everyone goes to China or India for tech stuff, surgery, and lots more besides. We'll be a third world country in 50 years. And I'm no raging conservative. It's a simple matter of common sense. I was never good at math, got a degree in the humanities, and did OK. I can balance a checkbook and do day to day math. Don't need higher math, but I wasn't in a field that required it. If you are or want to be, you have to learn Algebra, trig, and so on. If you can't learn it, choose another field. Your self esteem will take a short term hit. Work through it.
David-2 said...
Ralph L - if your geometry professor, on your final exam, wanted you to trisect an angle with ruler+compass then he hated all of you and was just f**king with you.
I believe it must have been the right angle, a special case. It didn't give me much trouble (it might now), but then I did get a non-zero score on the Putnam--on my second attempt. Some of my classmates were put out by the problem, though there was no time limit.
Do bias and inequality keep Black and Latino children off the fast track?
No, stupidity, laziness, and lack of discipline keep Black and Latino children off the fast track, as well as many "white" and Asian kids.
Sometimes, howe3ver, the stupidity and evil that keep them off the fast track comes from the adult scumbags pushing "equity".
Reality check: to a good first order approximation the ONLY racism in America is anti-white and anti-Asian. For all intents and purposes, essentially every single bad thing that happens to blacks and hispanics in America is their own damn fault.
And 90%+ of what isn't their own damn fault, is the fault of the leftists those blacks and hispanics vote into power
Another "back in the day" story:
I went to a rural one room school for eight years. One, yes, just one, teacher taught all eight grades and all subjects to all eight grades. Basically, I think she disregarded what
"grade" each student was supposed to be in, and she taught the material until the student learned it or learned it to the best of their ability. Did that result in a good education? Well, at our high school graduation eight of the ten top students were educated in one room schools. Nuff said.
she had a 1/4” to spare with the door opening and maybe 1” with the doors getting it in.
When we gutted and installed a new kitchen in the 80s, I knew we had at least a 30.5" wide opening for a new 30" fridge--but when we tried installing, it wasn't the same 30" at the counter and the floor, so the new baseboard had to come off the side wall.
I think about the fact that quite a few cultures never developed the concept of zero as a number. Algebra was a huge stride. The calculus (which I got through two semesters of but can't really say I ever really understood except definitionally) was gigantic.
Even when particular cultures' (positional) numbering system did include a “zero”, it was typically merely an (empty-column, placeholding) zero symbol—as with the Babylonians (base-60), the “Arabic numerals” (base-10), and the Mayas (base-20)—which kind of zero had utility only in a positional numbering system, and was otherwise not a fundamental advance.
Contrariwise, the only culture to develop “the concept of zero as a number” [emphasis added] was the (East) Indians, in the guise of their (Jain) mathematician Brahmagupta—who (writing in Central India around the year 628 A.D.) invented the concept of the number zero (that is, the integer 1 less than 1, 1 greater than -1), as well as (bonus!) negative numbers, together with the rules for manipulating all numbers: negative numbers, positive numbers, and zero-the-number—then taught it to the rest of us.
Incidentally, though one still finds occasional folk arguing that the number zero (along with typically the negative numbers) ought not to be considered a real “number”—i.e., only the classical integers [1 to just shy of infinity] should be allowed in that set—nevertheless, it's worth recalling in this regard that originally, in the very early days of the development of the concept of “number,” even the number 1 wasn't considered a number—i.e., the “numbers” really began with 2! (with at least duality).
____
(Carl B. Boyer and Uta C. Merzbach, A History of Mathematics, 2nd Edition, 1991, John Wiley & Sons, Inc., New York)
Michael McNeil, excellent added context! Thank you!
I started writing something, then deleted it, started again, and deleted it...
At 68, having observed a lot of people over the years, it's extremely difficult to write anything on this subject without sounding racist.
Some people have no problem with abstract work. Others do. It's innate- and really, there's noting that can be doe about it. Keep teaching people more and more advanced math until they can't learn any more- then stop with those that fail. No point in going on. My failure was at LaPlace Transforms and Fourier Equations. I understand the concept of the latter- but can't use or manipulate them. I thin part of my problem is is that up to then- I never had to study. Anything. Still don't for most things in real life. I either A. Understand or B. Don't, and then I move on. My son the electrical engineer has no problem with LaPlace Transforms and Fourier equations. And calls me for problems with electrical troubleshooting. And sometimes we speak the same language, but it means different things. The ignitor on his furnace didn't seem to be working. I told him to check the resistance across it- zero was bad, open circuit was bad. He came back, "It's 16,000 ohms, it's good." And I told him, "No, it's bad, you need to replace it." "But you just told me..." With stuff he works on 16,000 ohms is a valid measurement. With stuff I work on- 16,000 ohms is an open circuit... There's a piece of dust or something on the break. He looked and found the minute crack on the ignitor.
I use algebra and geometry all the time. I just don't call it that. I call it troubleshooting and repair. The same is true of anyone who uses it all the time- they use it and call it something else.
There are people who get lost at multiplication and division. They're going to have a tough time in life. If they can't get that, they probably can't read very well either. Or understand anything abstract. Used to be jobs for people like that. They no longer exist to any great extent.
The unasked question is the article is, and the question a lot don't want to ask us- what do we do with dumb people? When there are no jobs for them? I've had this discussion with my children. One solution we've discussed- work camps. What we shouldn't do is subsidize people to do nothing. Which is what we're doing. We tell people- you want to eat? Work. Everything today is mechanized- but doesn't need to be. For centuries, millennia even, everything was done by good old fashioned manual labor. Pick some nice to have but not actually required infrastructure, let's say, hiking trails or bike paths, and establish a work force to construct. using pick, shovel, wheelbarrow, and manual labor. Hire former NCOs to run the base camps and the work crews, and provide housing, food, and some spending money to the work crews. The cost to actually build the trails is immaterial. The idea is, keep the otherwise unemployed and idle from being idle and criminal. The infrastructure they create is a byproduct of keeping them busy.
one still finds occasional folk arguing that the number zero (along with typically the negative numbers) ought not to be considered a real “number”—i.e., only the classical integers
well, that is Wholly Natural
"The unasked question is the article is, and the question a lot don't want to ask us- what do we do with dumb people? When there are no jobs for them?"
We could stop increasing the minimum wage. When some people can't climb any higher than the bottom rung of the employment ladder, removing the lower rungs ends up being counterproductive if the goal is to get people working.
Leftists, however, would prefer to force those people to sit on their asses and be dependent on the government because apparently, telling people you're not smart enough to hold a job is kinder than allowing them to actually do a low paying job.
Gospace: good ideas, not racist. But to make it happen at all, we have to impose consequences on our various underclasses for neglecting their children. Men as well as women need to be held responsible for parenting and going to work -- with supportive services and punitive ones.
And first we need to close the border and send millions of illegal residents back to their home countries, as well as limit legal immigration to re-build our own aspirational middle class.
There's no will anywhere in the political classes to do any of this, and until you witness it in person, it's hard to understand how far we have gone down the road to ruin. For decades, urban teachers reveled in their students' helplessness and dysfunctional homes: now a few brave ones are admitting they're scared and regularly brutalized by their students. They're also terrorized by the State into maintaining silence, and persecuted if they're white, but most are also empowered by the chaos if they support this status quo. 20 years watching this happen in Atlanta (now also south of the city and in the exurbs) has left me very pessimistic.
And not in Atlanta. Couldn't stand the lies, couldn't endure the consequences of being honest about it, and tired of watching my peers stupidly endorse it. It's not as if you can escape any of this outside cities, but you get less of it, and you still see a lot of creative bootstrapping.
Wholly Natural - I see what you did there, gilbar!
JSM
@Gospace - That sounds like the Civilian Conservation Corps from the great depression.
Robert Kaplan's "The Nothing That Is" is accessible even to a math dolt like me.
Has anyone here ever taken linear algebra? Partial differential equations? Fourier analysis? See any blacks in your class?
Yes. And no.
I had the pleasure of working with two Black African women engineers, one electrical and the other chemical, both educated in Uganda. They knew their stuff.
I've had the same experience in the medical field with doctors from Ghana and Nigeria. Quite capable indeed. Jumping through all the the hoops necessary to go from a hut in an African village to chief of Internal Medicine in an American hospital is a real accomplishment.
Africa has a lot more human biodiversity than any other place. A Bushman and a Senegalese and an Ethiopian are all more genetically divergent from each other than an Englishman, a Vietnamese, and a Patagonian Indian. There are certain tribes (the Igbo of Nigeria, notably) that have a markedly higher mean IQ than others, along with certain genetic markers that are known to correlate with high intelligence.
Other characteristics of Africa that contribute to the success of their best students include their devotion to order in the classroom, parental dedication and involvement, and lack of obeisance to politically correct pieties about how any child is equally capable of learning any given academic subject. African schools often cost the parents at least a moderate amount of money, giving them a stake in the outcome that is often lacking in the parents of public-school students in America. Success in school is a source of pride for family and clan. Insolent, disruptive, or lazy students are vigorously whipped, first at school and then again at home. Students who are unable to keep up with the curriculum receive no special consideration or coddling, and will be dismissed if it is obvious that they are unsuitable for the level of education they aspire to. There are no self-esteem exercises or gay pride days in African schools. In short, they retain many of the characteristics that folks my age will recall from their own school days, but which have been almost entirely lost under the rule of today's nonbinary purple-haired educrats.
@Achilles-- Let's see a quote from any Republican officer holder at any level, whether a Romney supporter or a Trump supporter, who favors eliminating junior high algebra in order to promote racial "equity." I dare you to find even one.
After college I was talking about math with a theater friend mentioned she understood nothing of algebra, but was able to get through Algebra I by sheer rote memorization. That says something interesting both about her impressive memory and the way teachers tend to set up algebra problems.
I suppose that I am late to this article and thread. Nevertheless, I'll add this comment: It doesn't matter the student's race if, at middle school, the student hasn't yet mastered arithmetic. They should not be offered algebra at all, let alone during middle school, even if the course would be available.
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