Earlier in the summer, veteran sociologist Andrew Hacker caused a stir by arguing that algebra shouldn't be a mandatory course in high schools and colleges:
Education Realist reviews the numbers and responds:
These numbers, on the surface, don’t support the conventional wisdom about math performance: namely, that elementary school teachers need improvement and that the seeds of our students’ failure in higher math starts in the lower grades.
Elementary students are doing quite well. It’s only in advanced math, when the teachers are much more knowledgeable, with higher SAT scores and tougher credentialling tests, that student performance starts to decline dramatically.
What these numbers do suggest is that as math gets harder, fewer and fewer students achieve mastery, or anything near it. What they suggest, really, is that math knowledge doesn’t advance in a linear fashion. Shocking news, I know. We have all forgotten the Great Wisdom of Barbie. ...
Anyway. With numbers like these, it’s hard not to just see this entire debate as insanely pointless. In California, at least, tens of thousands of high school kids are sitting in math classes that they don’t understand, feeling useless, understanding deep in their bones that education has nothing to offer them. Meanwhile, well-meaning people who have never spent an hour of their lives trying to explain advanced math concepts to the lower to middle section of the cognitive scale pontificate about teacher ability, statistics vs. algebra, college for everyone, and other useless fantasies that they are allowed to engage in because until our low performers represent the wide diversity of our country to perfection, no one’s going to ruin a career by pointing out that this a pipe dream. And of course, while they’re engaging in these fantasies, they’ll blame teachers, or poverty, or curriculum, or parents, or the kids, for the fact that their dreams aren’t reality.
If we could just get whites and Asians to do a lot worse, no one would argue about the absurdity of sending everyone to college.
Until then, everyone will divert themselves by engaging in this debate—which, like many kids stuck in the hell of unfair expectations, will go nowhere.
I'm a little less cynical.
First, America has made a vast effort since 1983 to teach students more math, and the test scores suggest that it has been mildly successful.
Second, it's worth trying to pound some abstract math into everybody's heads just to find out which ones can do it.
Third, there are massive diminishing returns to pounding, however. The Gates Foundations' pushing for requiring Algebra, Geometry, and Algebra II to graduate from public school is overkill.
Fourth, we need a lot of effort and publicity put into figuring out what kinds of non-abstract math are useful. Consider construction, for example. Economic historians sometimes use carpenters' wages as an index to compare wages over the centuries because carpenters have been around since before Jesus, and will probably be around for a long time in the future, too. Think about five categories of individuals in regards to construction work:
- Unemployable
- Laborer
- Carpenter
- Contractor
- Developer
The differences between Unemployable and Laborer are presumably mostly due to character. But differences in math skills can matter in moving up the ladder. It would be useful to have a curriculum for mastering practical arithmetic for students who don't have what it takes for abstract math.
Fifth, the algebra v. statistics question is a good one. I was always mediocre at pure abstract thinking, but, for some reason, am good at very simple statistical thinking (and I am good at pulling up examples out of my memory). That's a major reason why my insights are so orthogonal to almost everybody else's. I don't really know why that is.
Would teaching more statistics at a younger age do much for the quality of discourse in America? I don't know. In some ways, probabilistic thinking is an old man's game. It may not appeal much to the young, who are more imaginative, abstract, and idealistic.
Would teaching more statistics at a younger age do much for the quality of discourse in America? I don't know. In some ways, probabilistic thinking is an old man's game. It may not appeal much to the young, who are more imaginative, abstract, and idealistic.
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109 comments:
Uhh, you are working on your Tony Scott obituary, right?
Hey, Steve. Thanks for the argument.
I don't think we're that far apart. Most math teachers in high school could think up a thousand interesting ways to teach practical math, and it would involve some algebra. I remember a while back that you did a post on a sample low-level vs. mid-level algebra problem (searched for it but couldn't find it).
But we are shovelling kids into algebra simply for politics and ideology, not because research has found it educationally appropriate. On that point, I am not cynical. Tom Loveless has made the same observation.
There's not much wrong with putting an uninterested kid through algebra, particularly if we wait until he's a senior. But most high schools require three years of math, and they don't offer anything except geometry and algebra II after algebra. In California, schools take a *huge* hit for any kid who is taking math below algebra. Most high schools don't even offer pre-algebra anymore.
So we're not talking about disinterested kids being required to take algebra, but being required to then sit through geometry and Algebra II. Their only option to avoid moving on in math is fail the class they're in.
I have no objection to kids taking basic math for freshman and sophomore year, algebra their junior year, and then, if they want, taking geometry their senior year.
But what's happening in many Title I schools is that 30-40% of kids are failing algebra their freshman year, and that's the second time they've taken it. Then another 30 percent fail geometry their sophomore year--which isn't counting the 20-30% of juniors who fail geometry after passing algebra the third time they took it. So juniors and seniors are now sitting in algebra and geometry classes with absolutely no hope of graduating, along with freshman and sophomores, some of whom have the skills to be there, some of whom are going to be those juniors and seniors in a couple years.
Meanwhile, classes beyond geometry are a complete joke because with all the kids failing for doing no work at all or missing months at a time, the kids who don't understand a thing but show up and work get a passing grade. So now they are taking advanced math despite, in most cases, not being able to successfully identify the slope of a line.
By the way, NAEP scores don't show much success in teaching math once we get past 8th grade, so I'm not sure we can even say that going through this crap has been even mildly successful. The bulk of the push occurred in the past 10 years.
"Third, there are massive diminishing returns to pounding, however."
If by "diminishing returns" you mean "making over half the kids in any class higher than algebra feel worthless" and "wasting billions of dollars forcing kids to retake math classes they will never really understand simply to get them to go through the motions enough to graduate" then yeah.
Re: statistics:
It may not appeal much to the young, who are more imaginative, abstract, and idealistic.
If there is a youth-oriented branch of mathematics, it would have to be topology. Imaginative, abstract, idealistics, extremely visual. Perfect for the video-game / Internet / ethernet generation.
^^^ Ha ha ha. I think you are confusing topological maps with the mathematical branch of topology, which have little to do with one another. There is nothing visual about almost any higher level math, least of all topology.
Pound the difference between Edward Greydon Pickels and Arnold Orville Beckman into the kids' heads starting in kindergarten. Pickels invented the ultracentrifuge but Beckman made all the money off of it.
Oh, and if Bill Gates wants to really educate kids, he might start with the political economy of the network effect, which is what made him the world's richest man because he happened to be in the right place at the right time.
"That's a major reason why my insights are so orthogonal to almost everybody else's."
Orthogonal? Does it have something to do with plunging?
My middle-school-aged kid has been getting a solid foundation in statistical thinking as part of the core math curriculum. Uh... parochial school.
Anyway, she understands it, even likes math at times.
The school uses a variant of the Singapore Math Method.
My wife points out what the Gates Foundation would have to say in order to make their position a good one: Students should have to have passed those three subjects in order to go to college. That solves a bunch of problems right there, I'd say.
As far as probability and the young, I'd argue that many kids would get a lot more sensible a lot faster if they got some significant exposure to those ideas in high school. Feynman's mercifully brief and readily graspable "QED" in a physics course, plus a statistics module in math and maybe something else... Such a curriculum would offer a quick and pretty painless grounding in how a lot of important aspects of reality actually function.
Why do so many white people do something that is bad for them, or bad for them in the long run? People don't think in terms of the long run--or at least lie about it to themselves in their obsession with short-run advantages.
If all these anti-white measures were to hurt all whites equally at once, I think whites would wake up. But anti-white-ism in America is geared so that will not hurt all whites at once. Indeed, it will greatly help one bunch of whites while hurting another bunch of whites. The whites it helps are especially the affluent, privileges, and intelligent whites. Just look at the likes of Billy Boy Clinton. Or Tom Brokaw, Bob Costas, and etc. Such people have much to gain by promoting anti-white-ism. They are favored in college, promotion, jobs, elite positions, and etc. They are patted on the back for their 'progressivism' and 'compassion'. Though they ostensibly work to undermine evil white privilege, their participation in the anti-white crusade pays off nicely. How much did Tom Brokaw make? MILLIONS!
And the global elites who engineered this system know all about how it all works. Imperialists did the same when the took over places like India. They found native allies who were rewarded profusely for collaborating with the imperialist authority. If imperialists came down hard on everyone, they would have been far less effective. They were effective because they favored enough of the natives who would benefit greatly by going along with the new order--even if it meant bowing down before the authority of alien rulers.
This is why dealing with anti-white-ism is a difficult matter for 'white nationalists'. Too many white people will benefit from it before their descendants will suffer from it.
We suffer from anti-white-ism, but look at all those whites in Harvard and Yale. They have so much to gain by sucking up to globalists and chanting Obama, Obama.
Why teach math in public schools? The rich kids these days send their kids to Kumon, which is a Japanese company so you know it must be good.
"That's a major reason why my insights are so orthogonal to almost everybody else's."
Another reason could be that your "insights" are a collection meaningless anecdotes that are supposed to lend support to one of your favorite dumb themes (Steroids! Blacks are dumb! The Gay Jew Mafia!)
a little OT, but I can't wait for steve to review this movie
http://www.imdb.com/title/tt1870529/
i saw the trailer - its a huffingtonpost.com/ feminist narcissit fantasy..
I was just discussing this with my son last night as he did his algebra homework. He's an 8th grader in an ordinary Japanese public school. His class started algebra from the beginning of the school year in April and they're already pretty far along in it. He was surprised to hear that many high school kids in America couldn't do his homework, and that this keeps them from graduating. I asked him how many of his classmates just don't seem to get algebra at all yet. He thought maybe 5%.
David Davenport said...
Are you a gay black-Jewish body builder?
How many of these exist? Many of these categories are for all practical purposes mutually exclusive.
This is absurd. We are talking algebra, not calculus. Of course students should be able to do elementary algebra before receiving an education certificate.
Why not concentrate students' efforts? Mastery of english grammar; arithmetic; elementary algebra; and the fundamentals of American history, geography, and civics. Natural sciences, english literature, foreign languages, advanced algebra and calculus, and European history can be reserved for a minority who attend academic secondary schools. The rest go to trade school after finishing with algebra.
When I went to school in socal in the 60s, Algebra I wasn't required to graduate. I took it anyway, because it was college prep.
As much as I hate to see schools relax requirements just to boost self-esteem, I really think they need to backtrack on this effort and revert to the old status quo. Saying every student should pass Algebra II is like saying every student should be above average.
Algebra? Who cares! The guy who directed the Top Gun movie killed himself.
Of course high school kids should learn algebra. That is, in a reasonably well functioning advanced society.
My wife is Japanese. Early in our relationship, I asked if she knew calculus.
She responded, "Of course I do", in a tone that an educated American would use if asked whether he knew arithmetic.
According to her, all the high school kids get calculus in Japan.
Algebra is a pretty low bar. That anyone is even seriously discussing whether junior high school kids, much less high school kids should study algebra is an indication of how far we've already slid down the 3rd world slope.
Geometry should be taught before algebra, and if only one is taught, it should be geometry.
Geometry is a better introduction to abstract mathematical because the objects of geometry - lines, points, circles, squares, etc. - are more accessible to people and because it introduces basic, simple logical thinking and constructing proofs.
Relevant from 2:20 onwards:
http://www.youtube.com/watch?v=rrFZ_1xCrIQ
I completely disagree with Andrew Hacker and Education Realist. Teaching algebra is just as important as teaching the basics of grammar. Also, the idea that higher level mathematics such as Calculus is harder than Algebra is not completely true. Go to any Calc 1 class in America and what are the kids struggling with the most: Algebra.
I don't need no algae bra.
We're not talking about elementary algebra; we're talking about two full years of algebra, plus a full year of geometry.
What's a high school diploma supposed to mean? Today, we've decided that it means you you showed up and made a decent effort for four years and weren't entirely unteachable. We expect pretty much every kid to get a high school diploma. Given that, it's unreasonable to expect all of them to handle advanced algebra.
If, on the other hand, we only expected the top 50% or so of kids to earn a diploma, then it would make sense to require advanced math -- along with physics and chemistry, a couple of languages, etc. But that's not what high schools are for.
I never understood why statistics and probabilities were saved for senior year, since they seemed far easier than the other subjects to me. More interesting, too, since they relate to sports stats, gambling, playing games, and plenty of other real-life uses. You need a little math to understand standard deviations, but you certainly don't need two years of algebra under your belt.
If we could just get every kid through a couple weeks on the difference between correlation and causation, it'd be a big improvement.
truth is a harsh mistress: good instruction SPREADS OUT outcomes - high ability students gain FAR MORE from good instruction than do low ability students. good instruction does not help 2-digit IQ-ers learn Algebra. (minor footnote: good instruction does not help triple digit IQ students who have only 2-digit Spatial ability learn Calculus or Physics). Quick, we have to pretend what I just wrote isn't real (when really it's 99% of ALL that matters) -- panjoomby
http://www.buzzfeed.com/rosiegray/how-management-killed-the-village-voice
http://www.davidbordwell.net/blog/2012/08/19/nolan-vs-nolan/
Elementary students are doing quite well.
How couldn't they? Elementary school has hardly any factual content at all.
"Algebra is a pretty low bar. That anyone is even seriously discussing whether junior high school kids, much less high school kids should study algebra is an indication of how far we've already slid down the 3rd world slope."
Have you looked at the composition of our population lately?
There aren't too many Japanese in it.
AAre you a gay black-Jewish body builder?
How many of these exist? Many of these categories are for all practical purposes mutually exclusive.
OK, draw us a Venn diagram to show which of those properties you believe are not in the intersection of sets.
Got thru an entire working life without ever having to use algebra. Come to think of it, I can't remember the last time I had to use long division. I get Steve's point that you gotta ask most kids to give algebra a try, if only to see who might be up for it. But, practically speaking, in my case, everything that was inflicted on me past basic arithmetic: pure torture, and completely useless and pointless.
Hey, I'm super-ultraglad there are people out there who are competent at the harder kinds of math. But why should everyone have to be?
(thanks for the LINK, not argument. Duh.)
I don't agree with Hacker. I'm saying it's a pointless discussion. Hacker, like the people who disagree with him, thinks everyone is capable of achieving at the same level.
Those of you who are saying "Everyone should have to pass algebra" are missing the point. Again.
In California:
1) Everyone must take algebra in 8th grade.
2) No one can take anything less than algebra in high school.
3) Everyone must take 3 years of math in high school (Cal mandates 2 years, but most schools mandate 3 to get a decent API score).
All other states have similar requirements.
So the argument isn't really about whether or not everyone should take algebra, but because algebra is required in early grades, it's about whether everyone should take algebra, geometry, and algebra II/trig.
And no, rich people's kids are not taking Kumon, which is for the middle class. Newsflash, folks: if you've heard of a tutoring company or an approach, or a curriculum, the rich aren't using it. Kuman's worthless. Singapore Math is a decent way to teach smart people math, but that covers about 20-30% of the population, most of whom get math without Singapore.
And really, are some of you really arguing that everyone can understand algebra? On THIS blog? Good lord.
Algebra no, statistics yes.
Of course I'm talking about "baby stats": statistics for people who aren't necessarily good at math. In other words, How To Read a Political Blog Post. You can teach all the basics of statistical inference at a practical level to students with hardly any math background. If the teacher and the material are good, it can even be interesting: stories torn from today's headlines, and all that.
That said, even baby stats is hard to teach without some really, really elementary high-school algebra, like maybe the first month or two of Algebra 1.
I may have a solution. Introduce sociology and other SWPL subjects into schools as an alternative to algebra.
The less math oriented kids could take such courses without being tagged as 'dumb'.
Teach the test, by which I mean the GED. Once a kid passes that (and the younger he passes the smarter he likely is) he can start taking college classes. These folks seem to be on the right side of the competence vs credentials debate.
http://www.wgu.edu/
If college isn't for them, put them into Job Corps vocational classes (yup, carpentry's on the list).
http://recruiting.jobcorps.gov/en/benefits/careers.aspx
Steve,
You may find this pretty interesting:
http://www.fortbendisd.com/docs/curriculum/high-school-program-guide-2012-13.pdf
Most people who are smart enough to participate in these kinds of discussions have a very inaccurate concept of just how stupid a person with a median IQ is, not to mention a -1 or -2 SD IQ.
If ~25% of the population isn't earning a high school diploma, then the threshold for success at high school is at about -0.67 SD (IQ of ~90).
In the Japanese population, that would be about a 14% success rate, assuming a Japanese IQ of 106. A quick web search suggests the actual Japanese graduation rate is more like 2%. It's not obvious if the Japanese graduation criteria is as hard as it is in the US. If it is, then Japanese students have more going for them than IQ alone would indicate.
I should add that that bit of quantitative reasoning was brought to you without the use of algebra.
The less math oriented kids could take such courses without being tagged as 'dumb'.
It's mostly the educrats, teachers, and some parents who are worried about kids being labelled as dumb. For real dumb kids, being dumb, and being labelled as dumb, is the ultimate in street-cred.
I had as much difficulty with the x-axis and y-axis as the Allies had with the Rome-Berlin-Tokyo Axis. Out of every one of my algebra classes I emerged in post-traumatic stress.
So, should a passing grade in algebra be required of every high school freshman? Yes, indeed. Purely because if I had to endure it, so should they. Mwah-ha-ha-ha-haaaa!
A good argument for some indoctrination in math beyond arithmetic is that it dispels magical thinking, the hallmark of savages and primitives.
Although not frequently lauded, mathematical and analytic thinking are as much a cornerstone of western civilization as all the rights of man, Locke, Hume stuff (which is indispensable also).
A little bit of math demonstrates that certain things can be determined with precise accuracy with no room for argument, feelings, wishfulness, spin, stroking, eagerness, or zeal.
But all those things that seem to matter so much nowadays in our PC era and the rationalists are increasingly seen as unfeeling and harsh, so it isn't surprising that even a forlorn remnant such as algebra or geometry is now under attack.
Ex Submarine Officer said...
A good argument for some indoctrination in math beyond arithmetic is that it dispels magical thinking, the hallmark of savages and primitives.
The same can be said for the unglamorous aspect of computers known as programming, or coding. There seems to be less emphasis on that now, and more on the Web, networking, using and customizing apps and skins, etc. School-level computer instruction in the 1980s, however - mostly programming dumb things in 8-bit BASIC - was a good exercise in logical thinking.
A little bit of math demonstrates that certain things can be determined with precise accuracy with no room for argument, feelings, wishfulness, spin, stroking, eagerness, or zeal.
But all those things that seem to matter so much nowadays in our PC era and the rationalists are increasingly seen as unfeeling and harsh, so it isn't surprising that even a forlorn remnant such as algebra or geometry is now under attack.
Have the "social causes" types realized that they could do much more for their feeling-filled causes, and be more effective crusaders, if they master some higher mathematics, programming, and logic?
It's not obvious if the Japanese graduation criteria is as hard as it is in the US.
There are no requirements for junior high schoolers (grades 7-9) to advance or graduate. Entering high school, students are sorted by ability into different schools with different ciriculums. They must pass their tests to progress, but there is always the option of transferring to a less academically demanding school. A student could graduate from a very low-level high school without being expected to do much algebra. As far as I know, there are no prefectural or national graduation requirements.
What I really fear is Wallgebra, the math used on Wall Street.
Like Education Realist, I'm really surprised by the comments I'm reading here. IQ distribution is one of the foundational principles Sailer keeps harking back to. The idea that there are minimum IQ floors for the successful completion of certain tasks I thought was part of that.
Below a certain level of IQ, a person is incapable of learning algebra, critical thinking, logic and the like. The belief that you can dispel magical thinking from low IQ people through the use of some sort of magical teacher or course is in itself magical thinking.
We need to face the reality that there is a certain section of the population who, frankly speaking, are too stupid to educate above a certain level. They will continue to read horoscopes, see fortune tellers, and spend what little discretionary income they have on lottery tickets, drugs etc. and use credit cards to do the buying.
If we don't want these sort of people in our society, education will not work. There is only one solution, and that is to lower fertility rates for such people (and stop new ones coming into the country via immigration).
Glad I can say this anonymously, because it sounds awfully harsh.
There's a difference between teaching some basic algebra and teaching a full algebra I & II curriculum. There's also a difference between the type of algebra most likely to come up in certain real life jobs / situations and the type that the average person will only see on a GMAT, SAT, or other weeder test. And there's no reason that some basic, useful algebra (and some basic, useful statistics) can't be taught to average, non-college track students.
The logical approach is to split off college track students from non-college track students by junior high, or by freshman year of high school, at the latest. The college track students can take something like California's current curriculum. The non-college track students can take a more practical math curriculum, the contents of which wouldn't be determined solely by educrats, but would be determined in consultation with major employers of high school grads -- the military, leading companies in manufacturing, skilled labor unions (carpenters, plumbers, electricians, etc.). The practical math curriculum could be spread out over 4 years of high school to make it more digestible. Enough basic statistics to grasp the most basic political issues could be sprinkled in too.
"can't be taught to average, non-college track students. "
68% of high school graduates go to college.
Public school, as it exists now in America and other Western societies, is obsolete, and so badly broken, there is no hope left. This is not an issue of algebra vs. geometry, phonics vs. whole language, or blacks vs. whites vs. other races.
Why bother with the 19th century anachromism of public school, or even school at all, if education can be done with a combination of the Internet, educational software, brick-and-paper libraries, tutors, and a little self-motivation? It's been the same with smart kids and smart adults all through history. They have always found a way to educate themselves. And now, we got the technology to make it easier for everybody. The only magic ingredient is motivation (and vocation); no amount of technology nor draconian discipline can replace it.
Albert Jay Nock pointed out the difference between religion and The Church that most modern people seem to grasp, and suggested we apply it to government and The State. How about education and The School? Religion without churches is possible and doable. I suggest education without school.
Have you ever seen the standard of algebra and geometry problems that ALL Japanese High School students are expected to master upon graduation?
Or even some of the awesome Finnish exam papers?
Both theses subjects are very g-loaded. Whilst perhaps having no 'practical' benefit for 99% of students who are forced unwillingly to learn these subjects, the training of the mind they engender in cold, hard, rationalist g-loaded thinking - and the subsequent application that has to contests based on pure mind power (which basically is how the 21st century will be won or lost), cannot be undersestimated.
"Most people who are smart enough to participate in these kinds of discussions have a very inaccurate concept of just how stupid a person with a median IQ is, not to mention a -1 or -2 SD IQ."
Exactly. If you've ever worked a truly mundane, low skill entry level job, a job in which you're surrounded by lifers doing the same tedious routine day in and day out, you probably have met and gotten to know some folks who have -1 or -2 SD IQs. And if you have, you understand that they just don't have the ability to learn higher order math. At all. Never did, never had a chance.
We have let tens of millions of these people settle here with little hope that their children will be any brighter. Our standard of living is slipping accordingly.
The Left is not going to admit that IQ is a biological phenomena, rooted in the genome. If it did, the entire narrative would start unraveling. So my suggestion is to attack the public school teachers with full moral rage at their failing to educate our students of color. It's cynical, but at some point, the teachers (most of whom are progressives) will have had enough demonization and will join the HBD bandwagon out of pure self preservation. And once you start thinking in terms of HBD, you can never go back to the narrative.
There begins the takeover (or reclamation) of our public institutions. Until the institutions are de-politicized, there is little hope of stopping the Left and all its inherent madness.
Actually, a highly skilled carpenter needs a very good grasp of the more abstruse branches of solid geometry, in constructing such things as hipped, pitched roofs with dormer windows, staircases with winding steps etc.
Surprising as it might seem to some here carpentry (at least how it used to be practised), can be a highly technical field of operation requiring not only years of practical training but hours of work understanding the intersections of dihedral angles as applied to a 2D scale drawing of something that is 3D and 100 times bigger, in fact some of the most mind bending exercises in practical imagination as applied to reality you'll ever find anywhere.
Sigh. Most of you simply don't understand what we're dealing with. How could you? Most of the "stupid" kids from your own school days were perfectly capable of using cashier registers by the age of 16, and most of the girls you knew as dumb ditzes went on to become RNs, kindergarten teachers or, at the very least, waitresses. These people might have struggled in math, but they were able to earn a fair "C" with some effort because none of them were actually below average.
I sponsor the homework and snack hour after school, and I teach the extended school day standardized testing prep to our 5th graders (a lot of whom are 12). These kids are incapable of understanding fractions. I've cut many a pizza, many a cake and many an apple to prove that 4/4 is the same thing as 2/2 which is the same thing as 8/8. I had them cut their own donuts, do drawing and coloring exercises, all in addition to explaining it, of course. Nothing. They are also unable to get that the larger the nominator the larger the number and the larger the denominator the smaller the number. i explained that the fraction is how much pizza they get to eat and the top digit is how many pizzas there are while the bottom number is how many people have to share these pizzas. I demonstrated on actual pizza. that's too much mental gymnastics. Me: "So, do you get to eat more pizza if it's just you and your mom sharing one between the 2 of you, or if it's you and your 7 cousins sharing one pizza between the 8 of you?"
They: "The other one! With the cousins! More people, more pizza!"
Me: "But the pizza man delivers just one pizza to your house regardless of whether it's just you and your mom there, or if your 7 cousins are visiting, and it's the exact same size pizza that everyone in the house has to share equally. So do you get to eat more when it's just 2 people sharing, or when 8 people are sharing just one pizza?"
They: "Eight people! because 8 is bigger than 2, so you get more pizza!"
Even after playing out this experiment on actual pizza and realizing that a group of 4 gets to eat more than a group of 8, they are unable to get the concept once they are back in their chairs.
Algebra? Statistics? Are you friggin' kidding me? If we're lucky and diligent, we'll be able to memorize the table of multiplications (we sing and dance it out). If we're even luckier, we'll know where multiplication can be applied in real life.
My great-uncle who had an eighth-grade education helped us build a house once. He knew how to calculate the length of rafters based on a 3-4-5 or 5-12-13 triangle, but he'd never heard of Pythagoras. He just knew how to calculate it with a carpentry square. A lot of practical labor is based on some basic algebra or geometry, but that doesn't mean the people doing it need years of training in the theory. Truck drivers don't need to understand differential equations to know when to hit the brakes.
I'm all for learning for learning's sake (heck, I teach Latin in my spare time). This isn't a utilitarian argument. The problem is that we have a goal and a belief that are contradictory:
1) Everyone must get a high school diploma.
2) A high school diploma should require rigorous study in some difficult, abstract subjects.
This requires us to pretend not to know that many kids simply can't handle those subjects, and spend billions trying to fix things that aren't broken.
Maya, you're spot on. Everyone who thinks we should push all kids through two years of algebra should have to tutor an 80-90 IQ kid in fractions for a year. And yes, I say a year, because it'll take that long, and he still may not have it. You can draw pizzas, tear pieces of paper into equal sections, get out cups and measuring spoons, and whatever else you can think of for examples, and he'll still look at you dumbfounded. When he does get it right, odds are he'll be aping you, and the next time he'll switch the numerator and denominator. When you do think he's got it, and he's able to answer a bunch of questions correctly, you'll send him home triumphant, only to have him come in the next day and get it all wrong again.
After a year, maybe you'll have drilled it home -- he still won't really understand it on a deep level, but he'll be able to fake it -- but he'll be a year behind the kids who got it in a week. And this kid is going to pass an Algebra II test in a few years? Not a chance. If he could, his 100+ IQ classmates would be taking advanced calculus by that point.
Of course, to say such a thing will be taken as giving up on the kid and relegating him to the horrors of a blue-collar existence, which can't be contemplated by decent people these days. So we punish the kid instead.
Everyone who thinks we should push all kids through two years of algebra should have to tutor an 80-90 IQ kid in fractions for a year.
IQ 80-90 is on the HIGH side of the curve for the NAMs.
Just to the immediate left of average for the NAMs, you're looking at IQs in the 70s, 60s, 50s, 40s, and beyond.
Anonymous said...
Algebra? Who cares! The guy who directed the Top Gun movie killed himself.
DAMN STRAIGHT.
You think they didn't need Algebra to create all those F-14s?
Or to create the recording technology to preserve all those Righteous Brothers hits?
F*CKING A, MAN.
PS: Greatest Vampire Lesbian Movie of All Time [or maybe second-greatest, if you're a really die-hard Ingrid Pitt afficionado].
PPS: Greatest HBD Soliloquy of All Time, bar none.
F*cking A, man, f*cking a.
I never understood why statistics and probabilities were saved for senior year, since they seemed far easier than the other subjects to me. More interesting, too, since they relate to sports stats, gambling, playing games, and plenty of other real-life uses. You need a little math to understand standard deviations, but you certainly don't need two years of algebra under your belt.
Agreed. I sometimes have slipped STDEV into 9th grade science classes and most students had little trouble with it.
I'd be interested in your all's/Steve's take on language instruction in our educational system. I think it's truly bizarre that we require 2/4 years of foreign language classes to graduate high school-yet, as we all know, bilingual Americans are a rarity (this isn't restricted to high/low iq kids, either).
In essence, we are requiring kids to memorize arbitrary stuff for 2 Years, which will not be used again. For all intents and purposes, we could invent a fake language and force kids into 2 years of memorizing it, and get the same educational benefit that current language traing yields.
I'm not saying learning foreign languages isn't valuable (I personally enjoy studying languages, and have self-taught to read one as well as learned tourist-level understanding in two others). Rather, I'm saying a language (probably Spanish) should be studied for all twelve years of school, with the goal of having a usable tool (I.e. understanding of that foreign language) upon graduation. It's the current practice:studying something arbitrary for two years, with no expectation of any level of understanding, that is so completely ridiculous.
anon(sorry for errors above:ped on an iPad).
I was educated in the '60s and learned math up though differential equations. Now retired, I would guess that not 1 out of 100 jobs require knowledge of even basic algebra. What I find is that most people can't quite grasp fractions, percentages, and proportionality and at least half the population can't grasp these at all. These subjects need to be repeated ad nauseum. Geometry, trig, algebra, calculus are a complete waste for all but that top 1% who will actually need them in their working life.
Another reason could be that your "insights" are a collection meaningless anecdotes that are supposed to lend support to one of your favorite dumb themes (Steroids! Blacks are dumb! The Gay Jew Mafia!)
Not one tiny corner of the Earth for the heretics! They must all buuuurrrnnnnnnnnn!
Anon is right. Geometry is actually fun.
It's interesting to read all these anecdotes about dealing with low IQ people.
I travel to Third World countries all the time, mainly in South East Asia and India, with very low published IQ scores, and always marvel at how these people don't really seem that dull at all. I always expect to encounter massive stupidity on a vast scale, but everyone always seems fairly competent and intelligent. The people definitely seem, on the whole, less alert, less mentally flexible, than in the West, but not by vast magnitudes. And I interact with the average people extensively. Granted, I am not trying to teach them fractions, but I would bet I could, to most of them. The kinds of interactions I, as a tourist, often have with them, do not seem less complex than fractions. Many random people who just chat me up on the street in these countries often have a pleasing wit and make comments that suggest a reasonably complex and nuanced understanding of life and society.
Interacting heavily with low-IQ people has led to the opposite reaction with me - not, wow, they're so dumb, but huh, I expected them to be much stupider.
The differences are certainly noticeable, though. When you go to Japan, say, average people seem markedly more efficient and mentally alert than, say, Cambodia.
Interestingly, the country where people who seem the stupidest from on the ground impressions - to me at least - is far from the least developed country in the region; Thailand. Average people here seem dumb as bricks. In an ironic twist, I think the more developed a low-IQ economy is, the more decent-IQ people get siphoned off to professional jobs, leaving the rock bottom dumb to work in the laboring professions. The average cashier or waitress in Thailand seems miles more retarded than her counterpart in, say, Cambodia, which is a far less developed country.
I also found day to day, average Indians to be perfectly intelligent and mentally alert. I kept on marveling how the whole country seemed like it was falling apart, yet everyone I interacted with seemed to be quite intelligent and competent. Didn't quite make sense. I couldn't understand how these seemingly perfectly intelligent people could mess up a country so much.
"the training of the mind they engender in cold, hard, rationalist g-loaded thinking - and the subsequent application that has to contests based on pure mind power"
'We do not rise to the occasion. We fall to our level of training.'
"The Left is not going to admit that IQ is a biological phenomena"
but they'll gladly accept racism as one and then eradicate it.
"These kids are incapable of understanding fractions. "
One section required that one explain the differences between two graphs comparing the breakdown of fats, carbohydrates, and proteins in the average American’s diet in 1910 and 1960, respectively. One question asked for an explanation of the change in the percentage of fat — 12 percent in 1910, and 42 percent in 1960. Many students mistakenly answered that the percentage of fat had risen “30 percent.” Of seven faculty colleagues I queried, only one, an Indian chemistry professor, knew that “30 percent” (as opposed to “250 percent”) was an incorrect answer. The others had all rated the answer, “30 percent,” as correct.
Dumbing-down is evidently a two-way street."
"Ray Sawhill said...
Got thru an entire working life without ever having to use algebra."
You mean you've never had to figure out, that if five beers and a $5 cover charge cost $40, what was the price of one beer? Nothing like that, ever?
Aaron, Maya, and some of the anonymii get it. I actually wrote a post about this here:
http://educationrealist.wordpress.com/2012/07/01/the-myth-of-they-werent-ever-taught/ which I also linked into the article.
But I do not want to give the impression that I think people of low-mid ability/IQ are worthless, "stupid", or incapable of educating. And, while I think that racial IQ means are largely accurate, I also see smart, poor kids of all races every day. Very few teachers ever assume anything about a student based on his or her race, although the expectation that all races can achieve equally is enough to make the most idealistic teacher deeply cynical.
JOhn talks about his surprise in discovering that low IQ people aren't dumb. No, they AREN'T "dumb". They are just largely incapable of grasping abstract concepts. You would not discover this in day to day conversation.
Muhammed Ali has an IQ of 75, or did back when he was in high school (I think Steve has mentioned this before). Nothing about his persona is inconsistent with an IQ of 75. But I bet most people think Ali is "smart" because of his quick wit and rhetoric. Teaching him algebra would, however (assuming his IQ test was accurate) reveal the same issues.
We need to upgrade our educational system for our top kids. We need to improve the education we give our lower-mid- ability kids by making it challenging, content-rich, and CONCRETE. And, as Steve writes often, we need to reduce immigration--not just illegal immigration, but also the family chaining--to give our low-to-mid ability kids a better chance at jobs that will allow them to make a living without defining their lives.
"John said..
Interestingly, the country where people who seem the stupidest from on the ground impressions - to me at least - is far from the least developed country in the region; Thailand"
------------------------------
Me: Thailand ruling and business class is Chinese, but they have Thai names and speak Thai language.
Is the reverse of Malaysia, the Chinese kept their language and identity and they are limited to business by the Malay Muslim ruling elite.
i doubt Ali was accurately measured.
one of your favorite dumb themes (Steroids! Blacks are dumb! The Gay Jew Mafia!)
Because no one takes steroids to gain advantage?
Because blacks are really smart and its only a white conspiracy to hold them back?
Because gays and jews never cooperate with other gays and jews to gain advantage? Thats just a dumb conspiracy theory and there are no conspiracies because thinking like that is dumb. (Unless its YT holding back the brothas of course)
Have you any idea of just dumb most elementary and HS teachers are?
Dan Kurt
All this talk about how we shouldn't force algebra on certain kids because they don't get it misses the point.
We need to force algebra (and other stuff) on some of these people to remind them that they are stupid, others aren't, and that they really shouldn't get to puffed up about themselves.
This is the reverse of the self-esteem cancer infecting our society today.
While I was on the advanced math track in school, I was not one of those students who grasped it all with ease, nor could I teach myself. I struggled a bit with algebra I in 8th grade, enjoyed geometry in 9th, struggled a lot with algebra II in 10th, and finally got a teacher who broke everything down and explained it, step by step, in my pre-calculus class. I took pride in my success and was even able to explain things to other students. Then I took calculus as a senior - while the handful of math geniuses worked it all out in a corner of the blackboard with the teacher, the rest of us had to learn it from the book. I "passed" with a D. Thus ended my math career.
My kids (at opposite ends of the IQ spectrum) have had the benefit of private school, and Abeka/Saxon/Singapore math. Even I was able, with the step-by-step explanations in the books, to help them with their homework and clarify new concepts (particularly now with the younger boy, who has trouble with abstract concepts). Simple equations and algebra can be taught to the 80-95 set, but requires the type of explanation and instruction that is wholly absent in today's public school math texts and their topical chapters. Personal, hands-on tutoring is obviously a huge help, as well.
Perhaps advanced math is not useful for most students but it would be a pity if exposure to this beautiful creation of the human mind were confined to the mere 1% who might use it professionally.
JOhn talks about his surprise in discovering that low IQ people aren't dumb. No, they AREN'T "dumb". They are just largely incapable of grasping abstract concepts. You would not discover this in day to day conversation.
Amen.
Saying "I talked to him, and he didn't seem low IQ" is like saying "I talked to him and he didn't seem unable to run the forty in under 6 seconds."
Retards have BOTH low IQs and something seriously wrong with their brains. Low IQ is correlated with "stupid," "dumb," and "retarded" but it isn't the thing itself. Retards also tend not to run the forty too fast.
I agree with Education Realist and the other "pessimists" and suggest that the optimists read "The Misplaced Math Student: Lost in Eighth-Grade Algebra", available online. It mentions the following NAEP math questions for 8th graders:
There were 90 employees in a company last year. This year the
number of employees increased by 10 percent. How many employees
are in the company this year?
A) 9
B) 81
C) 91
D) 99
E) 100
Only 36.5% of students get the correct answer, D. It is unlikely that such students can learn algebra, much less apply to solve a problem in real life.
<<>>
I handed over the credit card, signed and saved the receipt, filled out the expense account and was done with it. Aside from figuring out the tip and adding up the "expenses" column: zero math.
If I can venture two points:
1) You geeks and engineers may not take much note of it, but the country is full of people who create ads, design things, lay out catalogues, write the copy in quarterly reports, sell things ... None of these people -- none -- have a need for anything beyond basic arithmetic. Most of them realized they weren't destined for a math-heavy life at a pretty early age. Insisting that such people spend hundreds of hours studying a subject (or at least sitting thru a class) that to them is nothing but brain-hurting and useless is a little perverse, if not actually cruel. Algebra I and II may have been wonderful, useful, enlightening for you, and even fabulous mental exercise and discipline. It wasn't (and isn't) for the non-math crowd. Hard to believe, I guess, but there are people out there who AREN'T LIKE YOU. Oddly enough, many of them would be better off cultivating and pursuing their own peculiar interests and talents than snoozing thru math class. I'm totally cool with releasing the math crowd from studying Advanced English Lit and/or The History of Graphic Design and/or Intro to Ballet. So how about you release my cohort out from those damn math classes?
2. I can't help but notice that these discussions seem to take absolutely no note of motivation. It's all about aptitude -- IQ and such. I think motivation deserves a lot more attention than it gets. Math isn't easy -- in addition to needing some mental horsepower, a kid has to WANT to be able to do it and get it. What if a given kid simply doesn't have that desire/interest/drive? I know loads of pretty-smart to smart people who simply didn't like math, couldn't see the point of it where there own lives went, who had other interests/drives/pleasures .. A few of us even went on to have satisfying, reasonable lives despite the lack of math interests and training. In my own case: I always tested well where math aptitude went but I always hated the experience of being in math class. Result: hundreds of hour of boredom, snooziness and resentment. I'd have been better off spending that time reading books, playing music, learning some Game ...
I know something of this topic. I taught statistics as as second job for five years. I had taught calculus in grad school to MBA students. I have never actually taught a course in algebra. I only taught algebra as a means of humiliating my stat students.
I took a lot of math in grad school. I was a math whiz - among business and government students. At Cal Tech I'm sure they would have laughed at me as a hopelessly innumerate boob, but I didn't choose to compete in that arena. I worked in administration. For years I was always the only guy on the floor who could handle math.
In government administration, math skills are very, very weak. Many government executives can't calculate a percentage reliably. Private businessmen are better but not much. I once applied to a consulting company located at Union Square in San Francisco. They gave a math ability test to all applicants who came through the door. In my class of about twenty I was the only one to pass the test. The test was nothing but long division.
The other applicants left after working on these tedious hand calculations for a half hour or so. There was no time limit so I continued for hours checking and rechecking my work. It was of course really a perseverance test not an ability test. My ability was to recognize it for what it was. Anyone who stayed long enough could have done what I did and gotten a job offer.
The point is that they jumped on me. They gave this test everyday. Almost no one who wanted to be a management consultant (nominally a job that took some brains) could actually do long division. They wanted to hire me badly. Only later did they mention that it was a 90%+ travel job. I walked away.
When I taught statistics I gave a lesson on "Smurf" algebra. The kiddie cartoon show had had an episode in which there was an Arab character who solved a practical problem with algebra. This episode was supposed teach an appreciation of the Arab contributions to math.
I did this several times with undergraduate students at a four year college. No one in any class ever could solve this very simple problem. And algebra was a course prerequisite.
Algebra is simply beyond the reach of almost all liberal arts students. They can be forced to learn it but it rapidly leaks out of their heads.
Women I've noticed usually are totally bamboozled by algebra. They can do geometry well enough but algebra is too abstract. It seems to require circuitry that they just don't have. OTOH women seem to do OK in statistics.
There are only about three or four concepts in elementary business statistics. Typical students who earn a 'B' or 'C' usually master perhaps two of these ideas. These ideas include: The Neymann-Pearson Lemma, the Central Limit Theorem and the various Probability Distributions. If you're lucky you will get one student who understands all these concepts. For the rest, you just just drum into them nostrums like "correlation isn't causation", the "sample isn't the population" and the "median is preferable to the mean for skewed distributions".
I was a very, very good stat teacher - in years three and four. The first two years I didn't know what I was talking about. The fifth year I knew everything but I was bored and boring. I switched to teaching computer subjects. Most full time stat teachers are going to be boring for most of their careers. The problem is that business stat is a rather small field of study and quite static. The last major advance was the introduction non-parametric statistics in the fifties.
I taught data communications thereafter - a bigger field and much more dynamic. A field that keeps the teacher on his toes. Stat teachers are always going to be boring.
Albertosaurus
"I was educated in the '60s and learned math up though differential equations. Now retired, I would guess that not 1 out of 100 jobs require knowledge of even basic algebra. What I find is that most people can't quite grasp fractions, percentages, and proportionality and at least half the population can't grasp these at all. These subjects need to be repeated ad nauseum. Geometry, trig, algebra, calculus are a complete waste for all but that top 1% who will actually need them in their working life."
Nobody understands statistics whatsoever. To some extent it reflects a lack of common sense. I recall my freshman year of college I took a general biology course to fulfill a science requirement. During the section on the environment, we had some quizzes which had a few questions about human population growth. One of the questions was "approximately how many people were on earth in 1900?" The choices were 1 billion, 3 billion, 10 million and 1 million. A slight majority of the class picked "10 million" , which was of course incorrect. This was at a flagship state school, so the students were at least IQ 105 or so. Yet they were under the impression only 10 million people were around in 1900. They didn't even take into consideration that 7 billion people exist now or the population of the state they live in which is about 5 million. It just floored me that college students at a decent school could be so ignorant of such a basic concept.
"68% of high school graduates go to college."
Not only do 1/3 drop out, but plenty of people go to bogus colleges -online or otherwise.
I thought Bill Gates was going to make sure that all American High School kids finished math through Algebra II.
He still hasn't found his African Einstein yet, apparently.
"Muhammed Ali has an IQ of 75, or did back when he was in high school (I think Steve has mentioned this before). Nothing about his persona is inconsistent with an IQ of 75. But I bet most people think Ali is "smart" because of his quick wit and rhetoric. Teaching him algebra would, however (assuming his IQ test was accurate) reveal the same issues."
Much of the most sophisticated rhetoric Cassius Clay employed was scripted for him by the Nation of Islam.
I figured out who broke into my house using algebra.
I didn't know I had used algebra to identify the suspect until Sailor posted this article and I went to wiki to get the definition and read this:
from Arabic al-jebr meaning "reunion of broken parts"
Then it all "clicked". When I reconstrocted the event and what led up to it, the "image" it produced was missing a piece that only the suspect perfectly fit.
Isn't that algebra?
Using the known to determine the unknown?
Would teaching more statistics at a younger age do much for the quality of discourse in America? I don't know. In some ways, probabilistic thinking is an old man's game. It may not appeal much to the young, who are more imaginative, abstract, and idealistic.
This is why poker and craps should be taught in the schools.
You mean you've never had to figure out, that if five beers and a $5 cover charge cost $40, what was the price of one beer? Nothing like that, ever?
So you write this out as an equation and then solve for x? Really?
Rather, I'm saying a language (probably Spanish) should be studied for all twelve years of school
Make that some language other than Spanish.
Speaking or teaching Spanish in North America should be actively discouraged.
"So you write this out as an equation and then solve for x? Really? "
LOL
"Most of them realized they weren't destined for a math-heavy life at a pretty early age. "
but, but..
I know precisely where I lost my battle with math, the moment I was informed clearly and unequivocally that I simply wasn’t “a math person.” My seventh-grade math teacher, an otherwise lovely man, called each of his students up to his desk one by one in order to write a “1” (for the honors track) or “2” (for the standard track) on the school’s official math placement forms. As I watched from over his hunched and courduroyed shoulder, he wrote a beautiful, decisive and neat “1” on my form.
There it was, in permanent ink. I was good at math.
“Jess, could you come back up here for a minute?” he asked as I floated back to my seat.
He reclaimed my form, and carefully overlaid that beautiful “1” with a dark, clumsy “2,” pressing hard with his black pen in order to make sure the ink obliterated any evidence of his indecision.
And from then on, I wasn’t good at math anymore.
For real dumb kids, being dumb, and being labelled as dumb, is the ultimate in street-cred.
I heard that made explicit a few years ago on a S.F. bus. Kid tells his friends proudly, "I get all D's." Chinese kid.
"
Only 36.5% of students get the correct answer, D."
I'm glad you put the correct answer there.
A few months ago, I went for a work lunch with three other guys with whom I was working on a short-term temp project.
My companions were a 37 year-old welder, a 38 year-old construction manager and a 19 year-old musician/laborer. Two Hispanics, one white Mormon.
We forgot to request seperate checks, and it was going to be serpetine for the break the check apart after it was delivered so I volunteered to split the check manually.
We all had different priced entrees, and our drink choices ranged from water (me) to two beers, so it was not a simple matter of dividing by four. Although I did not think any adult with some college would be unable to do it.
Now I took some shortcuts in dividing the bill, as to where it was not accurate to the penny; I added up everyone's purchases correctly, but I estimated slightly on the tax we each needed to pay, for alacrity; and doubled the tax and divided by four (roughly) for the tip.
You should have heard the comments:
"Oh ho-ho, Mr. Math genius..."
"Look at the big brain on "Truth" he must be a genius..."
etc., etc. It was a bit of an eye opening experience, doing 9th grade math amongst normal adults.
He reclaimed my form, and carefully overlaid that beautiful “1” with a dark, clumsy “2,” pressing hard with his black pen in order to make sure the ink obliterated any evidence of his indecision.
And from then on, I wasn’t good at math anymore.
Boo hoo hoo, what a touching liberal parable.
"I:" wasn't good at math any more? Why not?
Because "I" (a) lacked the aptitude or (b) because "I" or he let the seventh grade math teacher demoralize him, even though he had sufficient mathematical aptitude?
Either way, the otherwise lovely teacher was correct in his assessment.
It's a tough, cruel world. One shouldn't let mean people get one down.
While I was on the advanced math track in school, I was not one of those students who grasped it all with ease, nor could I teach myself. I struggled a bit with algebra I in 8th grade, enjoyed geometry in 9th, struggled a lot with algebra II in 10th, and finally got a teacher who broke everything down and explained it, step by step, in my pre-calculus class. I took pride in my success and was even able to explain things to other students. Then I took calculus as a senior - while the handful of math geniuses worked it all out in a corner of the blackboard with the teacher, the rest of us had to learn it from the book. I "passed" with a D. Thus ended my math career.
Yeah. I do get the impression that math teachers, unlike other teachers, don't seem very interested in teaching. The purpose of math class seems to be less to help children learn and more to find and identify those children with a pre-existing math aptitude.
Is math "hard"? Being really good at anything is "hard". But I see no reason why ordinary people should be unable to master basic math skills, including algebra and trigonometry. With better math teachers this could happen.
I heard that made explicit a few years ago on a S.F. bus. Kid tells his friends proudly, "I get all D's." Chinese kid.
That kid was probably a straight-A student and violin virtuoso trying to build some cred so nobody would pick on him.
I'm fine with more language instruction, but it should be a language like Latin that helps you to understand English better, trains your mind to think logically, and introduces you to some of the great works and history of Western Civ.
Please, no Spanish. I'm tired of being told that we need to learn Spanish so we can talk to our domestic help. I know several people who had two or more years of Spanish, who understand none of it as adults despite Dora and all the other bilingual stuff floating around. The former Latin students I know remember *far* more of it, despite never speaking it.
The former Latin students I know remember *far* more of it, despite never speaking it.
All I remember from Latin is "amo amas amat" and that Gaul is divided into three parts.
[I]t would be a pity if exposure to this beautiful creation of the human mind were confined to the mere 1% who might use it professionally.
Absolutely. I don't think even the most cynical of us would suggest that advanced math should be denied to the non-genius students. Enthusiasm counts for a lot, and all the teachers and tutors that I've known would gladly put in extra time and materials to try to help a kid who's slow but really wants to master a tough subject. I'll take that kid over the lazy one or the apathetic one any day, even if he requires more attention.
We're just objecting to requiring it of all kids, including those who have neither any aptitude for it nor any interest in it, who will be lucky to "master" it long enough to pass the test and forget it the next day. Learning has a value in its own right, but not if the main thing they're learning is to hate the subject and the system that seems to be punishing them with it.
I was a math wiz, but I couldn't do art to save my life. I'm sure glad I wasn't forced to spend three years in art class and required to do a good self-portrait before I could graduate. My one year of art taught me a smattering of things about painting, sculpture, calligraphy, and so on, and piqued my interest in some kinds of art, without forcing me to struggle at it until I hated it. I was expected to do my best, but also understood that it wasn't critical to my future. That's probably how math should be presented to a lot of kids.
"Please, no Spanish. I'm tired of being told that we need to learn Spanish so we can talk to our domestic help."
Well hey, Chief, therein lies the conundrum:
One who can afford domestic help does not need Spanish, in five years, one who cannot will.
Wow, you're saying that most Americans are innumerate and have no ability to think abstractly.
In other news, dogs tend to bark...
If algebra is taught to seventh graders, what are the schools prepared to teach to seniors?
Will high schools teach differential equations in the twelfth grade?
goatweed
"Eric said...
""You mean you've never had to figure out, that if five beers and a $5 cover charge cost $40, what was the price of one beer? Nothing like that, ever?""
So you write this out as an equation and then solve for x? Really?"
I wouldn't, no. But whether you write it out or not it's still algebra.
Will high schools teach differential equations in the twelfth grade?
Yes.
http://dhsmathandscienceacademy.weebly.com/course-offerings.html
[I]t would be a pity if exposure to this beautiful creation of the human mind were confined to the mere 1% who might use it professionally."
Yeah, they should have math appreciation classes like they have art history classes. So the professor explains all about how it is done and famous problems and why they are important etc. Like watching the olympics. They just show you people doing it. You don't have to do it yourself, but it is cool to see how it is done.
My one year of art taught me a smattering of things about painting, sculpture, calligraphy, and so on, and piqued my interest in some kinds of art, without forcing me to struggle at it until I hated it.
I was forced to do it for 4 years.
I wouldn't, no. But whether you write it out or not it's still algebra.
I would have called it arithmetic. How is 40/5 algebra? This is something you do in third grade.
Some currently used language, Spanish or French or German or whatever, is pretty valuable, both because learning a second language teaches you a lot about your own language, and because you can travel and rea more widely. But what's needed is not "Yo quiero Taco Bell" level grasp of the language, but rather enough to actually use it--the endpoint should be an ability to carry out a decent conversation And read books and articles in the language you studied. As with algebra, that takes rather more work than going through the motions, though I think any person of anything like normal mental capacity can learn a new language.
Algebra comes from India, via Arabia.
"The differences between Unemployable and Laborer are presumably mostly due to character."
Mostly? No, many people are not physically cut out to be a construction laborer.
That circuitry that women (and maths disabled males like me) seem to be missing are a decent pair of parietal lobes. It's also the probable reason why many women (including smart ones)have a poor sense of direction.
Verbal intelligence and behaviour control seem to be controlled by the frontal lobes, but to be good at math you also need good parietal lobes. Damage to the parietal lobes also tends to have a very adverse effect on maths ability.
Interestly there have a been a few tests showing temporary improvements in mathematical ability following stimulation of the parietal lobes by TMS.
"Eric said...
""I wouldn't, no. But whether you write it out or not it's still algebra.""
I would have called it arithmetic. How is 40/5 algebra?"
You already got it wrong. The answer is 7, not 8. Maybe YOU should write it out. Again, whether you write it out, it IS algebra.
When I went to high school in the mid 1950s, students were given a math choice of business math, record keeping, years of bookkeeping, clerical practice, business machines, and practical math such as how to fill out check books, do your tax forms, and pay your rent or mortgage. The commercial-academic course also allowed taking courses in typing, shorthand, and business practice. If you didn't like math, there always was the clerical practice course. Friends who took this course sometimes went to college and majored in teaching secretarial studies, bookkeeping, moved on to accounting courses, if prepared for them, or else took courses in full-charge secretarial bookkeeping. An executive secretary with a high-school only education could reach 120 wpm shorthand (Gregg or Pitman) and 70 wpm typing skills, apply for a government job and work for civil service. Now that shorthand went out and dictation machines came in, people are still hired as office managers, even for the government where one might end up with perks, pension, and vacations, including health care coverage after retirement. Good old days when one could take the commercial course, if one wanted.
I agree with the general premise that average IQ people are not able to genuinely understand authentic algebra, intermediate algebra, pre-calc/trig, calculus, and so on. I am saying this form the experience of having taught high school math. Of course, many teachers and many schools simply water these courses down to the point that they are only "algebra" or some other math subject in name but not in substance. Then they pass the students through and claim the students successfully learned the subject when the students were never even presented with the subject. I have personally witnessed this at numerous schools. There is one contention in your interesting post that I would like to question. That is the idea that American students are doing really well in the elementary grades and not failing to understand math until the more advanced levels. In fact, I do not believe at all that students in America on average are doing well in the elementary grades in the subject of math. I believe it appears that way because the tests which say so allow them to use calculators or otherwise use artifice to inflate the student scores. Most American students that I question about their elementary math education tell me that they have been using calculators without limit since early elementary school and are always allowed them for all tests. I find that these students have little number sense. Because they have always had a calculator as a crutch in the crucial years when students are learning arithmetic, they do not understand the basics of arithmetic including manipulating positive and negative numbers or adding/subtracting/multiplying/dividing fractions. These American students who are dependent on calculators for doing arithmetic are crippled in their ability to comprehend advanced mathematics. Frankly, most of these students would not understand advanced math regardless. However, unfortunately, many students who would have the capability to understand math are also caught up in the terrible scheme of having always had a calculator as a child when they should have been learning to add, subtract, multiply, and divide without one.
Part two: I find it challenging to navigate the modern world of lies--statistic fulls of lies, studies full of lies, newspaper articles full of lies, government propaganda full of lies. So I ask the truth for myself. Basically, I ask enough questions to students and their parents to ferret out their true math educational background, abilities, and understanding. Certainly, often in America, the person's self assessment does not match reality. Students here usually think they have more math knowledge or ability than they do because their egos and grades have been inflated since their early years. Their first clue that they are not doing well in math generally comes when they receive their SAT scores or place into remedial college math or begin doing poorly in college math classes. But when this reality check occurs, they are unable to believe the truth and often resort to claiming that they are just poor test takers or other unrealistic beliefs that they use to patch together their cognitive distortions. I have also noticed a general pattern of parents and students themselves claiming the student is bright, brilliant, advanced, very smart, and so on. It seems I never meet a parent who does not make this claim now. Decades ago, even parents of truly gifted students did not describe their children in this manner as a matter of course. In fact, back then, such a description would have been rare and probably part of a factual and involved discussion. Back then, the WW2 generation of teachers were taught to grade on a curve. A's were generally hard won often even by the top students in class. People had a more realistic assessment of their own or their children's academic abilities. No longer. They are all little Einsteins now, at least they think they are.
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