I recently came across an article on ZeroHedge I initially believed to be satire: 3 Examples That Show How Common Core Is Destroying Math Education In America. It wasn’t, though, as the reference to a Common Core textbook clearly shows.
One example of the innovations was a new and improved method for teaching retards how to subtract two integers. The old subtract-with-carrying method apparently doesn’t cut it any longer. Here’s how they do it nowadays:
Instead of performing one pass to get to the result, you start with the lower integer and incrementally increase it until you reach the larger number, and then you add up the increments. This is akin to a Rube Goldberg machine for arithmetic. While you can’t make morons smarter, you can most certainly stunt the intellectual development of smart kids by putting them into a classroom full of morons in which an imbecile tries teaching them.
This reminded me of the “FOIL method” of multiplying two linear binomials, e.g. (1x + 9) * (y + 7). It’s a completely superfluous rule that could be dropped if teachers instead focused on the applicability of the associative law. It boggles my mind that time is wasted on a special case that will only cause the average student to be stumped by more complicated mathematical terms.
The underlying issue the leftist education establishment tries to solve is easy to diagnose. They mistakenly believe that everybody is a potential genius, and if there are differences of ability, they must be due to societal oppression, or something along those lines. Thus, they look for supposedly friendlier approaches. The net result is that idiot children of idiot parents still won’t be able to get a grasp on elementary mathematics, while smart kids who suffer the misfortune of being exposed to such an environment waste their potential.
In the end, however, the left will succeed because everyone who got exposed to such a curriculum will be equally incompetent.
Quote from a middle school principal to my testing coordinator sister: “You can’t make chicken salad out of chicken shit.”
That’s something I have been thinking while studying Math on my own. The Soviet was much more realistic though. They designed their curriculum to be as rigorous as possible to select the brightest kids to send them to special schools, where they would receive specialized training. Russia in 1950s was basically the golden capital for pure mathematics. You have so many giants from this period: Kolmogorov, Gelfand, Piskunov and their students of course, just name a few. Even lesser intelligent kids got swept with enthusiasm for Math and science. The Soviet clearly understood humans are not equal in intelligence, yet their textbooks were to instruct even slightest motivated kids.
I still used to old Soviet books to enrich my Math understanding. Their style is terse, concentrated yet absolutely rigorous, to the point. Their exercises left you thinking for days. America does have great books though: Social Calculus is wonderful. His book on Mechanical Physics is incredible too.
Who is the author of those books and what are the exact titles?
too bad they couldn’t apply that math to their economy.
then again if they did that, they wouldn’t be soviets. gotta wonder how many of their best and brightest were sent off to siberia because they had figured this shit out.
Yeah, the Soviets were a really interesting case. They actually sent some scientists to the Gulag for believing in Genetics in those very same 1950’s. They had this belief that “Great Socialist System” could make anyone anything, and genetics kind of destroyed that world view. Basically, it was Cultural Marxism cult-of-equality stuff taken to the extreme.
It’s interesting to note that even within this extreme system, there were some clear thinkers who didn’t believe in that nonsense. They did the same with their Athletes as well, or at least their Hockey players, taking the best kids and giving them more training, progressively culling the lesser players constantly throughout each year, until only the best remained.
The same basic process occurred in the West though, with rep teams and the like. Basically you have just-for-fun leagues called House Leagues, then rep leagues which are the best players. In my country, Canada, there are even three levels of rep leagues starting at age 6, called AAA, AA, and A.
It has always seemed totally obvious to me, and pretty much anyone paying even the slightest attention, that segregating kids by ability leads to much better outcomes for all. The problem really is totally political, parents of the lesser kids don’t want to have to admit that their precious progeny isn’t above-average at insert-subject-here, and will complain about mistreatment. This is even worse in a society with a large black or NAM population, since they will be drastically over-represented among the bottom percentage, whatever cutoff level that is designated, at any academic subject decided truly on merit.
An interesting exchange I had with my Dad the other day. He’s really big into the whole “education standards are going down the drain” stuff. He’s fairly accurate in that assessment, but I think he doesn’t understand why. Consider some numbers:
In 1900, 7% of Americans had a university diploma
In 1960, 26% of Americans had a university diploma
In 2016, 40.4% of Americans had a university diploma
The same is true for high school graduation rates.
In 1900, 30.5% of Americans had high school diplomas, that’s over 90% now.
It’s pretty easy to understand why college professors constantly complain about having to teach remedial classes, they’re simply getting a worse crop of students to start with.
It also explains those people who bitch about how “the education system has failed, look at the advanced calculus that students were learning in grade 11 back in 1910, and yet 100 years later and kids are failing out of basic algebra.” Well, ya, no shit though, the students currently failing out of basic algebra at age 16 are the ones who would previously have dropped out in grade six, and gone on to have productive careers in the trades, or owing a small business, etcetera. But nowadays they have to stay in school and we have to pretend like it’s societies fault that they can’t do what they genetically can’t do. I suppose it’s must be societies fault that 5’2 people can’t play in the NBA.
And then they use utterly stupid metrics of societal success, like “percentage of people who graduate high school” because they’re so fucking stupid that they think “well high school graduates do better in life than non-high school graduates, if everybody is a high school graduate, everyone will make more money and be more successful.” Which of course, gives them huge incentives to reduce the difficulty of High School, which they happily do. It’s just the absolute stupidest attitude you could possibly have.
There gets a point where leftists have ruined something so much, that it’s beyond angering and just depressing.
Who is the author of those books and what are the exact titles?
You can check “Differential and Integral Calculus” by Piskunov, a venerated text for Soviet technical schools. It was widely popular in Hispanic countries. I am studying this text together with Spivak.
An older textbook is of Fichtengoltz. I am not sure his Fundamentals in Analysis is the same as his 3 volumes book on Integral and Differential Calculus. The text is clean. I don’t have them personally
Kolmogorov was basically the greatest influencer on the Soviet Math and science education. He was the editor of books for high school students.
For Linear Algebra, you can check out his Linear Algebra. The original title was Introduction to the theory of Linear space. I intend to finish this book after studying basic Linear Algebra .
Most famous texts would be published in English by Mir publisher. Lots of them are available for free.
For more basic topics: Gelfand series Algebra, Trigonometry, Method of Coordinates, Lectures on Linear Algebra are great. I haven’t dared to touch the last book. All suitable for self learning.
For Combinatorics, Vilenkin book is of great fun and depth.
Thanks! I was asking about the authors of the American books, though, in particular “Social Calculus”, as I could not find a reference online.
Sorry Linear Algebra is authored by Georgi Shilov, not Kolmogorov. Shilov was also a n extremely prominent mathematicians. Basically the greatest minds of Soviet science were in charge of the education of their children. Unlike American modern textbooks company which only week to milk students money, their books are cheap, light and of high quality.
OK greatly sorry, that is heavy typo. I am actually talking about Spivak Calculus. I am on my phone so…
I have been saying this all along. But, some say if idiot kids from idiot parents can’t do well in school, how come all of Finland do better in PISA? I find that to be a hilariously stupid argument. But how do you explain what PISA is to a leftist?
Their argument is indeed ridiculous. Finland is more than 99% white, of course it does well on the PISA test. The same is true for Hungary. There’s no question that educational standards certainly have some affect on student performance, but what students bring to the table is far more important. The idiot kids in Finland from idiot parents probably don’t do all that well on the PISA test, there are just less of them.
BTW, as much fun as it is to bitch about common core in America, and it really is terrible, if you look only at White-Americans they do okay, not great, but okay when compared to white kids in other countries on the PISA test. Asian-Americans also do okay, again not great, compared to asian kids. It’s the NAM’s that drag the score of America down, same as Sweden.
The problem is that there are two different goals that you are trying to achieve when you tech math. One is to give kids some useful skills for actually doing arithmetic. The other is to give kids an understanding of how numbers work – prep for doing higher math.
In trying to achieve both these goals, they muddle and mix them together and achieve neither. The idea of “see what you have to add to the smaller number to get the larger” is maybe a useful idea in conveying what subtraction is about. But to teach that idea, they are teaching it in the manner that you teach arithmetic skills – execute the procedure by rote, grade the kids on conforming to the prescribed way of doing it. It’s nuts, and what’s more important is that it ain’t working.
It doesn’t help, of course, that the kinds of people that go into teaching are not the kinds of people who themselves have a deep understanding of math.
https://terrytao.wordpress.com/career-advice/there’s-more-to-mathematics-than-rigour-and-proofs/
You can read this about mathematical education from Terence Tao, a Math prodigy. We can argue that you need to take geniuses away from the classes because they will disrupt the normal kids, not to mention the fact that they could cause embarrassment to their high school teachers.
But generally, no how smart you are, you need great teachers. If you are a genius, you teacher should be a genius himself, unless you are Ramanujan, of course.
I think it’s pretty simple: Stupid kids will be soon stupid adults. Stupid adults are easy to manipulate and to control.
The Zero Hedge post with the Grade 8 exam from 1912 is really depressing. I am positive a pile of university grads would fail that completely. Nowadays, the only way to fail high school where I live is to not attend school.
While we may be getting dumber, as “temp” points out, it was entirely feasible for people one hundred years ago to not finish high school and end up working in the trades and living in a reasonable state. In eastern Europe, by around grade 8 they either funneled you into preparation for university or trades school and that seemed to be a lot more intelligent approach than trying to pretend we all can be astronauts and surgeons.
I would just like to make clear that I don’t think people are getting dumber, just that graduates are due to the reduced selectivity. Sort of like how if everyone went to the NBA then NBA players would no longer be taller than average. It’s not a comment on the genral population.
In the 19th century Mark Twain wrote an article ridiculing the difficulty of such text books and pointing out that most children could not get the correct answers. (I read it in a Twain anthology.)
Today the difficulty of such texts is taken as proof that the people of the past were vastly smarter but I’m not sure that’s true.
There is irrefutable proof that people are getting dumber and dumber. My favorite example are the mathematical entrance exams at some Swedish university, which have been unchanged for decades. I assume they change the numbers in their calculus questions. What happens is that this university observed a gradual decline. Year on year it may seem negligible, but decade over decade it is quite shocking.
I can attest to this. My exam on Calculus is almost the same as our homework. 60% of our classworks are graded, 3 term exams are only 40%.
Instead, in Vietnam, as a non-credit student who sit for Sino-Nom classes (basically classical Chinese-Vietnamese literature and language), the exams are much tougher, requiring true dedication. Even the take-home exam is not easy. You basically have to wade through Chinese handwritings in cursive forms. I don’t think many students will survive this. Even I find it difficult.
Over the years, there are discussions about how to make teaching and learning Math more interesting and “fun”. Understandably, it is productive to focus on new technology to help normal students to visualize difficult concepts in intermediate Mathematics. But I can’t refrain from making a comment that: For average students, it won’t be that more interesting. For those who have a natural ability to indulge in mathematical concepts and thinking for hours, or even worse, barely escape the abstract of mathematical symbols, it’s the subject itself that is crazily fun and interesting, you don’t need preach them about those qualities in Math.
What makes Math interesting and fun? Rigor, Logic, Patterns and Proofs. That’s all.
It’s a good thing there isn’t a country of 1.3 billion people, with an average IQ of 105. With no political correctness and no low IQ minorities that just became active in world affairs a generation ago. No wait.
There is a saying that ability to explain something to a clueless person is related to how well you understand the subject yourself.
According to that line of thought math curriculum should be designed by top tier mathematicians or rather subset of them who happen to also be good communicators and not people who have background in education or psychology.
Agree with the overall point here, but the reality of this (extremely) touchy subject is considerably more nuanced. Terry Tao’s blog above is a good source for commentary on research-level mathematics (he won gold on the International Mathematical Olympiad several times and is considered one of the best living mathematicians). See also (just a small selection of relevant links):
http://www-history.mcs.st-andrews.ac.uk/Extras/Hardy_Tripos.html
http://nymag.com/news/features/27840/
https://www.amazon.com/Mastery-Robert-Greene/dp/014312417X
https://www.bloomberg.com/news/articles/2017-05-01/odd-lots-one-of-the-world-s-top-chess-players-talks-chess-computers-and-options-trading
https://chessdailynews.com/wp-content/uploads/2015/11/Bringing-Up-Genius-The-Chronicle-of-Higher-Education1.pdf
http://www.dailymotion.com/video/x2iwz26
https://www.youtube.com/watch?v=IIDLcaQVMqw
http://fair-use.org/rampart-journal/1965/03/teaching-and-the-expanding-knowledge
The general theme of the links above is it may actually be effort (properly applied), not raw ability per se, that leads to exceptional performance in the long run. Also, hopefully you are able to see the dailymotion video in your country (it’s an upload of Chris Rock’s “Never Scared” standup special). Listen closely to what he says around 49:00-51:00. The main idea there, if true, paints an incredibly damning picture of what likely happened over the past centuries historically. See also G. K. Chesterton’s essays, in particular Eugenics and Other Evils.
For more detailed commentary on this general subject (along with many great anecdotes from the physics world), see Steve Hsu’s blog, infoproc.blogspot.com. I believe he has a project with the Beijing Genomics Institute to profile the actual genetic architecture of intelligence.
Effort alone won’t lead to good results. Without a strong foundation, i.e. IQ, all efforts will be wasted. I briefly listened to Chris Rock’s piece, for about twenty seconds. I don’t think there is a factual basis that there was selective breeding among slaves to get “super slaves” as they were used for tasks that required different levels of physical strength. However, if the goal of his routine is to make the point that the big bad white man simply bred blacks into utter stupidity, then he deserves only ridicule as the historical non-slave population of blacks by far outnumbers the number of slaves. That didn’t raise collective IQ over time either.
What do you think about people who come from a STEM background like me (Math) who own businesses or work in finance and business related fields because they are more lucrative?
What else would you do with your degree in mathematics? Academia is a big gamble, so going into finance or business isn’t a bad choice at all.
Math and Computer Science go hands in hands.