New math
Ace writes about Common Core math pedagogy:
Common Core needlessly complicates the simple. They complicate the simple, supposedly, to impart “number sense” to kids, to get them to understand not just that 9 +3 = 12, but why 9 + 3 =12.
That’s a very ambitious goal.
I suppose we should ask this question, however: Given that teachers are currently failing in the less-ambitious goal of simply teaching that 9+3= 12, why do we believe they’ll be better at the more-ambitious goal of teaching why 9+3 =12…
Pedagogues have been doing this sort of thing for ages. In fact, Tom Lehrer got their number back in the early 60s when he lampooned what was then called “New Math.” Enjoy this; it’s timeless:
Speaking of timeless, I was lucky enough to be educated prior to such abominations, although even in my day there were tiny hints of what was to come. For example, my grandmother used to tell a favorite story about something I did as a child. I have no memory of the incident, but it sounds about right. When I was in grades one and two there was a big push to get us to see that the simple math tables we were learning had practical real-world applications. This bored me no end, but I knew that if I failed to label my math problems properly (one apple plus five apples equals six apples), I would be marked down even if I got the right mathematical answer.
I hated it, but I complied. And according to my grandmother (who’d been a teacher back at the turn of the century—that’s the turn of the 19th century into the 20th century, by the way) I applied it. When I was around six or so I was playing with some toys in her apartment while she was talking to a friend (also a former schoolteacher) about teaching children their math tables by drilling them with flash cards and the like. They didn’t think I was paying attention—why would I be?—until I suddenly cried out, “No, no, no!”, leapt up, and imperiously and impatiently said, “That’s not how you do it!”
They were sitting in front of a dish of cookies, and I took four out of the plate, lined them up in two rows of two, and pointed. “You have to say two of these and two of these!” I insisted, having learned my lesson.
This is like very painful mind control.
I had the New Math inflicted on me by about third grade, which finally and forever educated me out of any interest in mathematics. I scraped through high school algebra and got a high enough score on the SATS by dint of being fairly intelligent, but anything more than figuring percentages makes my eyes glaze over.
Learning the relationship of binary, trinary, and so forth to decimal, really made math into a kind of relativistic spectacle.
Yeah, St. Mom, I’m a victim of that stuff too. Fortunately, my father had been a math teacher, so he showed me, 1). How to get the right answers with the tried-and-true, and THEN 2). How to please the teacher with the New Math nonsense. Dad had a low opinion of new smarty-pants ideas of pedagogy – he’d often say that the best school was a log with the student and Aristotle sitting side-by-side on it.
Math educators are very concerned with getting students to “think” about what they are doing. At an elementary level, it is better to simply learn to DO IT. An elementary student doesn’t need to elucidate the differences between phonics and whole language approaches to learning to read- he or she simply needs to learn to read. Ditto with math.
The issue of transferring math skills to the “real world” has always been there. I am not sure what the best way is to effect this transfer of math skills to the “real world.” I did very well in math in high school, in a New Math program which involved a lot of proofs. I loved it. I recall not liking Physics in high school- the math wasn’t “pure” enough. I didn’t like the messy numbers you got in lab. But that is the way that real world measurement goes- you are always going to get approximations to the equation. It took me a while to realize that.
In college, I didn’t like math as much as I did in high school, because in college there was more emphasis on doing problems instead of doing proofs. Years later, in preparation for a second career- which turned out to be a short one- as a math teacher, I took a Liner Algebra course. The problem sets involved a lot of proofs. I was one of the few students who did well in the class- because most of my fellow students didn’t have previous experience in writing proofs. Conclusion: my high school math experience, of doing a lot of proofs, was an outlier.
I did not get exposed to New Math until high school- in my case it was University of Illinois Committee on Secondary Mathematics – a.k.a. Illinois Math.
I got the best of two worlds. I got a good grounding in traditional add and subtract, multiply and divide arithmetic. I did not get New Math taught by math-challenged elementary school teachers, who invariably would have shorted their students on knowing multiplication and division etc.
[I had a teacher in college who had met Max Beberman, the godfather of Illinois Math. He had asked Max if Illinois Math should result in a de-emphasis of basis arithmetic skills. Not at all, replied Max. Students should still learn to add and subtract, multiply and divide, Max said. Unfortunately, when New Math was in the hands of elementary school teachers, a substantial proportion of whom are math-challenged, a de-emphasis of basic arithmetic skills is precisely what occurred. New Math worked with math-skilled teachers with bright students- the University of Illinois lab school where Max developed his program. With less capable teachers, not to mention less capable students, it didn’t work as well. I would also point out that in my high school, Illinois Math was a hit with the top 1-5% or even 10%, but it didn’t work well for most.]
A further point about “thinking” about math- from my experience it doesn’t work until you have a good grounding in the basic facts. While I liked the proofs I got from day one in 9th grade Illinois Math, I had a good grounding in basic arithmetic.
From 9th grade Illinois Math, with its emphasis on the distributive and commutative principles of addition and multiplication, I independently saw that theses principles could be used to estimate answers. 19 X 72= (20-1)X72= (20X72) – (1X72). I became very good at estimating answers, which is a very useful skill. But I couldn’t have “thought” this about math if I didn’t already have a good grounding in basic arithmetic principles.
I’ve been causing problems at my son’s school for several years. He scores near perfect on state tests in math. He consistently got a 75% on the “problem of the week.” Once, he got the correct answer, showed his work, explained his reasoning. But he said, “Subtract a from b to find the difference.” The note from the teacher said he didn’t explain why he used subtraction to find the difference. And this was in 5th grade.
LisaM, the irony about the teacher’s note is that, given the math-challenged characteristic of many or even most elementary school teachers, is that the odds are that the teacher wouldn’t be able to do very well on the “whys.”
Could the teacher elucidate the “whys” of high school algebra or geometry, by writing out proofs in those subjects? I doubt it very much.
The teacher’s groundings in the “whys” of elementary school math are most likely very shallow. Very shallow.
I did so poorly in math beginning in elementary school & all along. It was so bizzare to be in the high achievers for reading
ability & comprehension, English grammar etc. and be relegated
to the *struggling group* for things mathematical !
I have often wondered if I took an algebra class now would I be any better at it or would it plunge me into full blown
Alzheimer’s ?????
I learned arithmetic by memorizing the math tables. It wasn’t until many years later that I got into the axioms of arithmetic. I don’t think children have the intellectual maturity to understand the theory of arithmetic.
http://en.wikipedia.org/wiki/Peano_axioms
Ray:
I don’t think children have the intellectual maturity to understand the theory of arithmetic.
Certainly not elementary school children. The Peano axioms at your link bear a certain resemblance to what I did as a 9th grade New Math student, so in limited doses, bright high school students can hack them.
My daughter is a junior in high school here in CA and starting to be inflicted with CC. She believes the problem with CC is that the questions are so abstract and indiscernible that only a very small percentage of students have the ability to figure out what the questions are actually asking and what they are supposed to be doing. Those students who have very high levels of cognitive abilities to begin with should be fine (according to my daughter). All other students are continually lost. It’s very sad and even potentially tragic to think what these students will be losing because of some very silly ideas about education.
Of course Common Core needlessly complicates the simple, but there is nothing needless about it. The educational administration cadre and the teachers, who as we all incessantly hear, do it “For the children” in ever-increasing numbers, have needs too. They need to be employed, and to be obeyed. Having a semi-inscrutable Common Core (so thoughtfully named), which troubles and is resented by the commoners, is a stroke worthy of Bill Ayers.
I haven’t followed the Common Core debate at all. As to this particular issue, people’s brains work differently. For abstract thinkers, the “why” might be important. For concrete thinkers, the cookie count might be the way to go. For teacher’s pets like me, I was going to learn to memorize anyway because it was in a book, so I wanted to learn it.
That abstract thinker may go on to be a great theoretician; the concrete thinker, an engineer. Generally, the more top-down the system gets, the worse it’s going to be for the education of the kids. But that’s top-down in method. We’ve got to have a standard level of expectation of results. Actually knowing the multiplication tables, for example.
Thank God, I had nuns who taught phonics and made us memorize times tables. The best one, however, was our not-too-bright geometry teacher. About 5 of us in the class would do problems and solve theorems when she was out of the room so that we could show her up. It was great fun, and we became sort of heroes to the class, which actually learned something from our exercises.
It’s a shame we can’t get rid of ed schools. Bill Ayers things math class should be used to teach social justice.
Well I agree with you about modern math and how it’s taught, but… As an engineer, if you don’t pay close attention to those cookies and apples (we call them units in engineering and science) you will make mistakes. The kind that get people killed
That particular practice of keeping your units consistent is indispensable and they drill that into you with a vengeance in engineering school. You might get a complicated answer numerically correct, but without defining the units, it’s next to meaningless and a good professor will give maybe 5% for your answer.
So even though it seems silly at the grade school level, the discipline has a real world and vitally important role. Believe it or not.
Southpaw – Meters per second is a completely different concept than meters per second squared. And when you start getting into force and energy and stuff, yikes, sometimes those units are the only way to tell you’ve mangled the equation.
Schools of education in colleges and universities are the problem. They’ve latched onto fancy theories like Critical Thinking in an effort to gain academic respectability. Teacher training should have stayed in the old normal schools.
It’s just like business. If it was simple, with few taxes and rules, then the competition could usurp the market share of the big boys. The teacher unions, by making things complicated and hard, will be able to keep out the competition and crush them, thus preserving their monopoly and control over the kids, their renewable resource.
Southpaw…
NASA lost a spacecraft it Mars mission because of exactly such a cross-up calculation!
###
I found the tempo of my elementary education to be brutally slow.
My weird home life drove me into autodidacticism.
I have no memories of either parent reading to me, ever.
I’m puzzled as to why such basic (3Rs) material is hard to get across.
I used to teach — when I was young and still in school. I’d end up having to re-explain, to rework, this or that lesson to my peers.
It’s a bad habit that has dogged me all of my life.
%%%
The no-child-left-behind brain fart was a backwards step of significance.
The ONLY way that the ‘system’ can meet its metrics is to slow the progress of everyone down to that of the mental cripples.
White America has an IQ norm of around 100ish. (by definition going back a century)
The nclb scheme must include those with an IQ as low as 77 because there are sure to be a LOT of White American kids within 1.5 SD of 100.
The slow tempo is sure to generate ‘deportment problems’ as there is only so much needless repetition a kid can take.
Urban youth norms to 87ish IQ, with SD of around 12. Consequently, the tempo has to reach down to that of an IQ70 child. Such low g metrics largely explain why Baltimore has an illiterate underclass.
Rather than dance around with Common Core and other political nostrums, policy should shift towards profiling low IQ students so that they can be directed into classwork that is at their tempo. Life is a lot more fun when you’re with people of your own age, maturity, and abilities.
The other policy shift that’s overdue is the rapid removal of disruptive students. In particular, very aggressive boys need to be taught in a boys-only setting — and by a man — never a woman.
If the priority is to be ‘for-the-children’ then strong men are going to be required in the classrooms of urban America. Some attempt ought to be made to hire retired military vets. A graduate degree in education is completely unnecessary for such men.
Being a Fogey who learned by rote, I am not sure what New Math actually is. Surely, I tried to help my daughter with New Math at some point, but I don’t recall the concept.
Math was never a strong point for me. But, when I was learning to program–in machine language–we had to have some instruction in the concept of number systems and to start thinking in terms other than a decimal system. We were also introduced to the concept of scientific notation –at least it was introductory for me. All pretty fascinating. In today’s world i would expect the school system to introduce those ideas at some point.
Regarding precision. I had occasion to instruct some Japanese Air Self Defense Force Officers on the performance characteristics of a plane they were buying. We, of course, did some work with charts and graphs; but, in some areas I spoke to them in “rules of thumb” and mental interpolation because that is how you fly. At least in America. Would not do. They needed very specific numbers in every instance. I never saw them plan a mission, but it must have been pretty tedious.
IMO the department of education should be abolished. The best thing “for the children” is to keep DC far away from children. As noted by Ann, above, requiring elementary teachers to have degree in ‘education’ does not produce a teacher with a well rounded knowledge in the basic subjects; instead it produces teachers indoctrinated in ‘educational theory’. When it comes to high school, teachers should have degrees in the subjects they teach. Yet we still wonder, after decades of experimenting with theories, why Johnny can’t read and Susan can’t do fractions.
“The other policy shift that’s overdue is the rapid removal of disruptive students. In particular, very aggressive boys need to be taught in a boys-only setting – and by a man – never a woman.
If the priority is to be ‘for-the-children’ then strong men are going to be required in the classrooms of urban America. Some attempt ought to be made to hire retired military vets. A graduate degree in education is completely unnecessary for such men.”
I agree, lack of discipline must be addressed, with special schools for some students; and end the idiocy of making young thugs stay in school until age 16. They are children of brutal streets and unlikely to ever change; sad but true.
wow… it only took you more than a decade to notice…
amazing…
and the new math that tom lehrer made fun of was not the thing they teach now… ALSO, if you did learn a better way of doing it, you were not punished for using it, but now, your punished from using it.
the point is to make people equal…
how do you do that?
you erase the old culture (erasing racists who love it), by removing it one brick at a time.
if kids do well because their parents are educated, then forbid the education of parents, impose a different method, and then the population goes forward on equal footing.
right?
except that its wrong…
funny thing is that this has to do with school, and socialism in the school, and i said, read “school of darkness” Bella Dodd… head of the teachers union and CPUSA… duh.. i also recommended Iserbyt (who worked at one time making such plans for the feds), and Gallo
its like shouting out the answer and having to wait months before the rest catch up
by then they forget that you said the answer way back… and when they catch up, they do not realize the implication that you were trying to wake them up to (as much as a decade earlier!)
its very frustrating.
How long it will take to make the connection between these people EXPERIMENTING on other peoples children (told you Joseph Mengele is normalized now, we not only intervene in their lives to mold them for a future designed by people who follow a later branch of the same root tree Joseph came from), and basically making sure that over time, they will be completely defenseless. (i think with all the people who will just pick sides and then having the side people wish for being present to rationalize it, they choose that one like all the answers are right and you get what you pick)
You equalize with other lesser states, and you end up in WAR…
Kids that cant do math, grow up into adults who cant do math. they become adults who have a problem reading and following directions in order and applying logic.
the converse also points out that this means that the people who will be needed to defend and fight would be best and brightest, making a war, a good way to equalize on top of the cannon fodder they are making.
War in Europe? Ukraine and the Threat of Wildfire
http://www.spiegel.de/international/europe/how-the-ukraine-crisis-is-stoking-fears-of-war-in-europe-a-966504.html#
[edited for length]
Richard Feynman hated the New Math crap, too. Taught his son the most direct and efficient way to solve math problems. The California Board of Ed wanted him to vet some science textbooks of theirs, and he would be in his basement workroom, cursing long and volubly. Had a lot to say about it.
That led me to look him up, and I found this trove of Feynman quotes. Enjoy!
http://en.wikiquote.org/wiki/Richard_Feynman
(When he was young, he looked almost exactly like Cornel Wilde.)
when they try to hide it or play games with it, you get articles like this
Global grade: How do U.S. students compare?
How do U.S. students compare to students in other countries? It’s not as bad as some say, but there is room for improvement.
http://www.greatschools.org/students/academic-skills/1075-u-s-students-compare.gs
the best were the teens from finland (at that time)
Students in the United States performed near the middle of the pack. On average 16 other industrialized countries scored above the United States in science, and 23 scored above us in math. The reading scores for the United States had to be tossed due to a printing error.
the rest of the article tries to use the finns as an example of what to do to socialize the US school system… from homogenizing the courses, to pre-school, etc.. the whole menu.
they do not point out that finland is very homogeneous in terms of race and small…
when you have a country trashing and stoppoing bronx science students from achieving, race balancing, feminism, and so on… you might not notice that they are not doing it for entertainment.
how about something a bit more recent…
U.S. Students Slide In Global Ranking On Math, Reading, Science
http://www.npr.org/blogs/thetwo-way/2013/12/03/248329823/u-s-high-school-students-slide-in-math-reading-science
American 15-year-olds continue to turn in flat results in a test that measures students’ proficiency in reading, math and science worldwide, failing to crack the global top 20
“In mathematics, 29 nations and other jurisdictions outperformed the United States by a statistically significant margin, up from 23 three years ago,” reports . “In science, 22 education systems scored above the U.S. average, up from 18 in 2009.”
we are on the eve of the next world war…
and we still do not realize the seriousness of it.
top scores?
Shanghai (China)
Singapore (China)
Hong Kong (China)
Taiwan
South Korea
Macao
Japan
Lichtenstein
Switzerland
Netherlands
Estonia
i don’t see a population to equalize to in those places (nor the rampant ideology that wants to. do you?)
The math scores of students in Shanghai showed that they are “the equivalent of over two years of formal schooling ahead of those observed in Massachusetts, itself a strong-performing U.S. state,”
The U.S. was slotted between the Slovak Republic and Lithuania in the overall results, two spots behind Russia.
oh.. you mean we are now scoring UNDER them?
While our scores in reading are the same as 2009, scores from Belgium, Estonia, Germany, Ireland, Poland and others have improved and now surpass ours – Harvard professor Jan Rivkin
the improvements did the opposite..
if we left it the old way, we would still be outperforming
(but then again, we would have to accept that some groups due to genetics, do not score, and will never score like others – though they may be subsumed by others over time)
hopefully neo didnt delete the part that shows training time and performance of our defenders are tightly coupled with the abilities of the population those defenders come from.
Putin’s tiny army: Russian child soldiers trained in battle tactics, weapons and hand-to-hand combat to ‘repel any enemy of the Motherland’
http://www.dailymail.co.uk/news/article-2588013/Putins-tiny-army-Russian-child-soldiers-trained-battle-tactics-weapons-hand-hand-combat-repel-enemy-Motherland.html
Children as young a five sent on marches, trained in hand-to-hand combat
our kids are untrained and performing below the above
while i am not suggesting training, how bout school?
from the washington times
Tactical advantage: Russian military shows off impressive new gear
Tanks-to-troops modernization
want to go back and notice that every rebuttal to war with Russia says they have no equipment, what they have is old, and so on
been telling you for years, and even showed the hiding game
“It just seems to me from watching the films that their arrows are pointing up and ours are sadly pointing down.” retired U.S. Army Maj. Gen. Robert Scales
What they see are the fruits of a modernization plan begun in 2008, not just in tanks and vehicles but all the way down to the individual warrior
[edited for length by n-n]
rats..
way too long
read it while you can..
Stephie Says:
April 30th, 2014 at 1:58 pm
I can’t help wondering if this isn’t the desired outcome. Are elite private schools, such as Sidwell Friends, using Common Core?
It’s clear that progressivism, or socialism, is actually regressive: it leads to a sort of modern feudal society of hereditary nobility and commoners. The nobility may believe it is in their interest that the commoners are educated to a lower level. Less competition that way. And commoners who struggle with mathematical concepts and logical thought, and have a poor grounding in history and literature, will be easier to manipulate and propagandize.
Possibly the best short essay about the problems of modern education was “The Comprachicos”, written by Ayn Rand way back in 1970. It appears in her collection The Return of the Primitive, and I also found a downloadable PDF here.
I agree, Art. We are being set up for attack and defeat. There’s just no other way to read it.
What Stephie said. The general trend over the last couple of decades has been to render students dumber and more at sea … while making them believe that they are the absolute bees’ knees, intellectually speaking.
And look – I have seen it, over and over. The student intern volunteers that I supervised twenty years ago at the military radio station overseas were innocent of the ability to spell simple words and punctuate. God only knows what it is like now.
Yes, modern pedagogy seems determined to keep all but the elite classes barely literate, ignorant, and as dumb as stumps. All the better to control the masses, my dear.
Artfldgr:
I noticed it a long time ago.
And of course the New Math Lehrer made fun of is not the same approach or technique. I didn’t indicate that it was. But the basic criticism is still funny and relevant, and the song is still funny.
I have a friend who homeschools her children. She has pointed out that they are given tests each year by the school system that her children have to pass, in order to be given credit for what they learn in homeschool. She thinks the Common Core math will make it impossible for homeschooled kids to pass the math sections of the tests, because they demand answers that describe the Common Core method of how the problem was solved, not just the plain “oldfashioned” correct answer.
This will be part of the new attempts to outlaw homeschooling. The other things that are taught in Common Core will soon be the materials you have to teach your children, or they will close you down as a homeschooler.
There used to be a comic strip called “Pogo”, about a porcupine that lived in the Florida swampland. I loved it, and bought all the Pogo books, too–this was back in the 1950s and 60s. In one of the story-arcs, the swamp denizens had to set up speakeasy schools, like prohibition’s speakeasy bars, because some of them wanted their children to go to good schools that welcomed all students who wanted to learn. This was the era of Civil Rights, when the Democrats were closing schools rather than integrate them. You would have to take your child to the hole in the log, or an alcove amidst a pile of rocks, and say, “Joe sent me.”
I can’t believe how many of Pogo’s story-arcs are now happening in reality, just with a different emphasis, but with the same enemy–the Progressives. Of course, the author, Walt Kelly, thought of himself as a Liberal, but like I said, the enemy was and is really the Progressives.
(There is another story-arc where the reporters couldn’t find the critter involved with the story they were covering–a two-headed Russian puppy–so they turned to each other and interviewed themselves about what they might have found had they actually found and interviewed the puppy.)
Minta, the Leftist alliance is not merely America’s enemy. They are humanity’s enemy. Enemies of humanity are to be given no mercy or sanction.
Art….
WRT Ukraine…
Putin is engaged in a repo operation. The vast bulk of the Ukrainian military leadership is STILL composed of Russians living in “the near-abroad.” (aka Ukraine)
So regardless of Kiev’s sentiments or any other reality, Putin already has his military forces in control of Ukraine.
And even beyond the generals… the average trooper in the ranks has no motivation to fight off an atomic super-power. Their attitudes must approximate those of the Iraqi army squaring off against the US Army.
%%%
Art…
On your math statistics: for political reasons, DC never breaks out American educational achievements by race.
Whenever this is done, White America skews high, typically beating all comers.
(It’s the Ashkenazi effect. This mathematically adept crowd is always folded into the White America category. Though few in number, they pull the metric straight north.)
America’s metrics ALWAYS drag down low because America is always being flooded with immigrants from lands that have essentially no educational system of any kind. (Haiti, Somalia,…)
Rock bottom scores by ‘students’ who can’t even write their names pull the national average down sharply.
https://www.youtube.com/watch?v=LPjzfGChGlE
^^^ Roy Beck makes a solid case that importing poverty can’t solve anything. (6 min)
People are not to be treated as gadgets on an assembly line. Yet, that’s pretty much what Common Core does.
It’s simply a disaster to force children who are way behind to track with those who are flying ahead. Slowing down the bright kids hurts all of society — and makes them into lousy students. When the pace is too slow, intelligent kids develop bad habits.
It’s also a first class disaster to bring in children from the Third World who can have no chance of getting up to speed. Their IQs being stunted before birth, they have no hope of gainful employment in a society that needs brawn less and less.
In the case of Iraq, Saddam deliberately starved the Shia — as a slow motion genocide. This heinous crime will echo down the century. There is no cure for fetal privation, when the brain is wired up.
What’s actually happening is that America is brain-draining the rest of the planet. WE are thereby throttling the growth of those societies.
This happened within the domestic American economy when the USSC overturned Jim Crow. The first Blacks to leave the ‘hood were those most dynamic, most educated, the brightest — the leadership of their communities.
Promptly thereafter, social cohesion broke down. Low IQ Blacks are NEVER going to accept or track White American cultural norms. Rappers make this explicit. They want their own culture — and it mostly takes the form of rejecting White culture.
Thus Reverend Wright, Farrakhan, …
American Jewry has made common cause with Black America. The reward has been Al Sharpton and riots.
Black America dumped Donald Sterling like a good habit.
Black American culture is largely a rejectionist ethos. I don’t think that such an orientation can be changed.
If anything, Barry and Eric have made this anti-White creed more intense. In a nation that’s looking to get past racism — we’ve placed the two biggest racists in America into the top slots! They come into every squabble from a totally racist point of view — and never get called on it.
The hypocrisy is off the scale.
It sounds like the global powers that be have decided that white-majority nations have an insurmountable advantage, so henceforth there will be no white-majority nations, in order to make everybody “equal”.
Of course, when whites are the minority, the fact that every other race has been systematically taught to hate us will come into play. I expect to see a lot of forcible ‘redistribution of wealth’.
I had always heard that the Khan Academy gets great results. I wondered what their secret was. So, I checked out some of their online video lessons. Like this one:
http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/linear-equation-word-problems-tu/v/basic-linear-equation-word-problem
Just about the way it was taught to me. I have read that some teachers are using these video lectures in their classrooms and then using their time to help the students work on problems. Makes sense to me, but that doesn’t fit with the grand scheme of the progressives.
Math, algebra, geometry, and calculus are mostly about doing problems until you have the basics down pat. I managed to get through college math through calculus by using memorization and drill. When I was 29 (1962), the Navy sent me to a year of Post Graduate School. The emphasis was on physics, math, and leadership (business management). It was there that I began to see some of the reasoning and logic behind the problem solving. I was going over old ground and seeing it in new ways. What blew me away was that humans had dreamed this system up to describe the world around them. Just having a system to measure distance and time – huge steps. We stand on the shoulders of many giants.
During my year in PG School we worked with a room-sized IBM computer learning how to develop simple programs with punch cards. The vacuum tubes reigned supreme then, but the silicon diodes were just starting. I’m sitting in front of a computer that has more computing power than the huge IBM that we used. 52 years of progress. But the progs will reverse that if they can.
I think blert has a point about the comparisons of our students’ scores with those of other countries. In most countries, if you aren’t academically gifted, you don’t get to attend what we know as high school. They shunt less gifted students into trades or directly to work. Its comparing apples and oranges. Also, this is the only country that I know of where you can fail or drop out of school at some point and return. Two of my high school classmates flunked out of college and spent three years in the Navy. They came back and both became Veterinarians. That’s not an unusual story here. It is in other countries.
JJ,
It is easier here to go back and learn what you didn’t get in school. For my college science class, I took organic chem. About 7 years later, I was a social worker in a clinic and I realized I needed some basic biology to better understand the medical situations, so I took a night school course in intro biology. There were some med school guys in my circle of friends, and I would sit on the floor listening to them talk for hours about the classes they were taking.
Later on, after a move, I applied for a job as a copy editor with a medical publisher. I got the job because of the grammar I had learned in school, and from then on I read medical papers everyday. Sometimes in order to correct an error, I would dig into textbooks trying to figure out what the author of the paper might be trying to say. Sometimes I would actuallly have to practically rewrite a paper (these were review papers, not the original research papers). I later moved on to a research facility and there I could talk with the people who wrote the papers, so I learned even more.
The point is that you can learn as you go if you are allowed, and if you aren’t held too strictly to your credentials but are treated as an intelligent person willing to learn by your co-workers. There is no degree that would have prepared me specifically for the work I did. Some scientists don’t write well. Some editors have huge gaps in their science knowledge. But if they work together and learn from one another, they can make a good product.
Teachers don’t need advanced degrees in education theory. They need real-life experience interacting with students and they need mentors who share what worked for them when they faced a particular challenge. Isn’t the problem with many of our braniac betters that they have never had real-life experience, but have spent their whole lives in a bubble of theoreticians? These are the people who try to scare their underlings by telling them that a problems has increased by 100% in the last 2 years without telling them that previously the incidence was 1 in 300 mill and that last year the incidence was 2.
Expat, the system they are under is similar to totalitarian militaries. Individual initiative and bottom up hierarchies aren’t allowed. Autonomy isn’t allowed. Personal initiative, not allowed. As a result, their individual efficiency and efficacy drops over time, it does not improve like in a freehold system.
Ironically, one of the better civilian bottom up hierarchies enforced by social conformity is in Japan. They have the senpai and kouhai system to allow bottom level up initiative and mentoring. It is very easy for Westerners to forget about things like this, because there’s often no social delineation or word to describe it. It’s as if the Left tried to use Alinsky tactics, but nobody had ever read Alinsky. First the ideas must be recognized as valid by a large group of people before the applications of the idea can be engineered. In America, we’re all supposed to be equals, but we know that it is not so.
What totalitarians and enemies of humanity wish for is Absolute Obedience, not backtalk or even wealth.
For teachers to be able to learn from their seniors and teach/mentor their juniors, a certain level of delegated power and autonomy must be insured. Totalitarian systems will never allow or forgive such things.
JJ, I’ve heard similar stories about Khan. Khan is an example of internet non tax freedom that allows individual solutions to apply to social groups and customer market shares.
This is why the MPAA and the Leftist alliance will overturn the control of the internet, and put it back under the plantation and slave master’s control. With high taxes, 50%, to ensure that no competition will arise to challenge Hollywood, the ATF, Democrats, teacher unions, or anybody else on the Leftist alliance for that matter.
“Math, algebra, geometry, and calculus are mostly about doing problems until you have the basics down pat.”
I’m not sure about that, JJ. Math, yes. Geometry, I don’t know, because I never really got that down. Algebra and calculus are more about understanding the concepts. You have to solve problems to get the mechanics down, sure, but without an understanding of them, you can’t tell what to use when. They’re things you can regurgitate on test day, rather than tools you can use on a daily basis.
Nick, your comment is correct. Had I gone into engineering it would have required that I be able to understand the concepts at a deeper level. My employment after college was working as a field geologist for an oil company. We needed to understand basic math, geometry, and trigonometry. Most of my work was making surface geology maps using a plane table and alidade. From our surface maps we made orthographic projections of the strata to try to get an idea of where an oil bearing formation might be in the subsurface. Pretty straightforward stuff. My tenure there was cut short by a call from Uncle Sam. From then on I was involved in Naval Aviation and the airlines as a pilot. Good math skills and ability to think in three dimensions were what were required there. My stint in PG School was a chance to appreciate the whys of algebra and calculus, but I never used it much after that. I also got a deeper understanding of the way physics developed as a useful way to study and describe the natural world. Made my life richer, but wasn’t necessary in order to make a living.
parker,
There are a lot of martial arts businesses making money due to lack of rules and taxes. It seems the Democrats don’t have a martial arts union dictating things and taking a cut, so they haven’t muscled in on that territory.
That resource base of manpower would be a good start to creating schools that combine physical and mental education. Teach the thugs and crime lords how to control violence, while giving them a better alternative than the thug life. That way, people in a community can take care of their own problems before it explodes in a flash riot at our own neighborhoods.
I am one of those people for whom math is not a second language, but THE first language.
Even the pricks teaching math in school could not beat it out of me. So, naturally, when I got to college, (already sporting a full term of Calculus taken at the local JuCo), I took still more math — I have, in fact, more math credits by far than any other, even though I did not wind up majoring in Math.
I note this because, while they did not teach “New Math” (i.e., the 60s version) where I went to school, I know something of the complaints about it.
The relevance is that, studying math deeply, I quickly encountered the basis for it.
It is possible, using set operations, to demonstrate the existence of the counting numbers. And from the Counting Numbers, one gets to Integers. And thence to Rational Numbers…. and Irrational Numbers… and Imaginary Numbers… and all the other stuff that surrounds them under the rubric, “Mathematics”.
The nature of the New Math was, essentially, to try and teach children this “natural” path to number understanding (that it was “so” natural that we only came to it literally millennia after we learned to do more than count using marks and fingers was utterly lost on these multi-level idiots).
And that might STILL have worked, mind you — except that what they FAILED to do was to teach TEACHERS what the eph they were teaching.
Teachers had no freaking clue what the hell was going on, why you did ‘x’ to get the results you were supposed to — and thus could not possibly begin to impart any actual understanding about what the eph they were teaching.
And this is, in the end, the real problem with public education. It’s all about process, not about results.
Follow the process. Be a good little sheep and do what you’re told. No, don’t ask questions. Don’t make waves. Don’t argue. Do it THIS way and no others.
This is the educational pattern that produced Nazi Germany — the “Germanic System of Education”.
And you should fear it. It’s well along the way to eliminating that essential individualism that is at the heart of the American character.
The next 20 years will be…. interesting.
In the apocryphal “chinese curse” meaning of the word.