December 5, 2011

Can adults pass school achievement tests?

About a half-dozen years ago, the Gates Foundation talked the L.A. school board into passing a rule that nobody could graduate from high school without passing Algebra II (as well as Algebra I and Geometry). Each year since, implementation of that edict has been delayed for a year, although, supposedly, this year's class of high school freshmen will absolutely have to pass Algebra II to avoid going through life as high school dropouts. We're Not Kidding This Time!

It's amusing to contemplate school board members trying to pass Algebra II.

Marion Brady writes in the Washington Post about a wealthy friend who is on a school board. He decided to take his district's test for 10th graders. 
“I won’t beat around the bush,” he wrote in an email. “The math section had 60 questions. I knew the answers to none of them, but managed to guess ten out of the 60 correctly. On the reading test, I got 62% . In our system, that’s a “D”, and would get me a mandatory assignment to a double block of reading instruction. 
He continued, “It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate. 
“I help oversee an organization with 22,000 employees and a $3 billion operations and capital budget, and am able to make sense of complex data related to those responsibilities. 
“I have a wide circle of friends in various professions. Since taking the test, I’ve detailed its contents as best I can to many of them, particularly the math section, which does more than its share of shoving students in our system out of school and on to the street. Not a single one of them said that the math I described was necessary in their profession."

My view is that it's very important that our society identify and educate the kids who can handle the standard algebra-calculus-and beyond math track required to be an engineer or the like. That justifies humiliating and wasting the time of the majority who can't master the standard math track through calculus ... up to a point. But there are huge costs, out of pocket and opportunity, to trying to lead horses to the well of higher mathematics and trying to make them drink.

For one thing, there are other kinds of math, such as statistics, that some people are relatively better at. More broadly, there are lots of  people who can't learn arithmetic at the fast clip necessary to get through calculus by 12th grade. But stuff like fractions and percentages are hugely valuable in life. 

But, does anybody know of a study of what % of jobs require somebody to use Algebra II level math?

77 comments:

Anonymous said...

According to Warren Buffett, investing only requires arithmetic. Unfortunately, most people on Wall Street are convinced that it requires advanced calculus and thus they create dangerous models that blow up randomly from time to time.

Anonymous said...

“I won’t beat around the bush,” he wrote in an email. “The math section had 60 questions. I knew the answers to none of them, but managed to guess ten out of the 60 correctly.

Absolute, 169% total B.S.

An entire test of obscure forget-after-school material? Trig identities? Finding the determinant of a matrix? Set theory? For all 60 questions?

No "solve for x" or "what is angle 'a' equal to"?

Yeah right.

Luke Lea said...

Well, I've had occassion to use Algebra II in the course of my life. 3 or 4 times in 50 years.

We will wait, but not for long said...

Pretty good-quality discussion over at Hacker News:

http://news.ycombinator.com/item?id=3314676

Anonymous said...

"According to Warren Buffett, investing only requires arithmetic."

I remember hearing Peter Lynch say the same thing on TV. He said that he never used anything beyond simple arithmetics in his work. I've always suspected that successful "investing" mostly requires connections, i.e. mutually-beneficial relationships with powerful people who have inside info before it becomes public.

ben tillman said...

Absolute, 169% total B.S.

Ditto.

Allison said...

http://www.nsf.gov/statistics/seind10/c3/c3h.htm

is the report on indicators in science and engineering produced by NSF's National Science Board.

According to that:
"The number of workers in S&E occupations grew from about 182,000 in 1950 to 5.5 million in 2007. This represents an average annual growth rate of 6.2%, nearly 4 times the 1.6% growth rate for the total workforce older than age 18 during this period."

Elsewhere, they explain
"Although there is no standard definition of an S&E occupation, NSF has developed a widely used set of occupational categories that it calls S&E occupations. These occupations are generally associated with a bachelor's level of knowledge and education in S&E fields. A second set of occupations, S&E-related occupations, also require some S&E knowledge or training, but not necessarily as a required credential or at the bachelor's degree level. Examples of such occupations are S&E technicians or managers of the S&E enterprise who may supervise people working in S&E occupations. Other occupations, although classified as non-S&E, may include individuals who use their S&E technical expertise in their work. Examples include salespeople who sell specialized research equipment to chemists and biologists and technical writers who edit scientific publications. The NSF occupational classification of S&E, S&E-related, and non-S&E occupations appears in table 3-1 ."

The whole report is interesting.

Nanonymous said...

That 'wealthy friend' knew answers to NONE of the Algebra II questions? If so, he has no idea about complex fractions, powers and logarithms. That's the same guy that has "a bachelor of science degree, two masters degrees"? Bloody hell, this shit makes me want to scream and cry alternately. Is this what we have become?

With this background, I somehow don't believe that he truly is "able to make sense of complex data related to overseeing an organization with 22,000 employees and a $3 billion operations and capital budget". Probably some dolt with MBA, maybe even affirmtive action one.

ziel said...

I've been receiving the "SAT Question of the Day" in my email for about a year since I signed my daughter up. I've gotten every single verbal question right, but some of the math ones stumped me - and SAT math is easy. Even the simple techniques needed to solve algebra I problems can be hard to recall years after they were learned.

Ray Sawhill said...

In my post-school life, I've never had to use anything beyond basic arithmetic. Forcing non-mathetically-oriented kids to study anything beyond geometry strikes me as completely unnecessary cruelty.

DaveinHackensack said...

"According to Warren Buffett, investing only requires arithmetic."

This is what Warren Buffett's mentor Benjamin Graham said (from the appendix on p.570 of the 2006 edition of The Intelligent Investor). Bear in mind though, that he's talking about investing in common stock. The math associated with options can be more complicated.

"Mathematics is ordinarly considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw therefrom. In forty-four years of Wall Street experience and study I have never seen dependable calculations made about common-stock values, or related investment policies, that went beyond simple arithmetic or the most elementary algebra. Whenever calculus is brought in, or higher algebra, you could take it as a warning signal that the operator was trying to substitute theory for experience, and usually also to give speculation the deceptive guise of investment".

Anonymous said...

ITT: calculus is scary.

DaveinHackensack said...

"I remember hearing Peter Lynch say the same thing on TV. He said that he never used anything beyond simple arithmetics in his work. I've always suspected that successful "investing" mostly requires connections, i.e. mutually-beneficial relationships with powerful people who have inside info before it becomes public."

Peter Lynch got some big winners by investing in chains that were successful in one part of the country and riding their growth as they expanded. He also stopped actively managing money in 1990 though. He wrote about investing in Fannie Mae in his books published in the early 1990s, and might have still owned it when it went bust if he were still managing the Magellan Fund during the financial crisis. Part of being remembered well is knowing when to quit.

I doubt Buffett has benefited from inside information with his investments in publicly traded stock. But Berkshire Hathaway also buys privately held businesses, and there Buffett has a unique advantage: he has a reputation for keeping existing management intact and letting them run their own shows. That makes Berkshire the buyer of choice for family-owned businesses.

Anonymous said...

According to Warren Buffett, investing only requires arithmetic.

Investment bankers don't really do math. Just arithmetic and maybe some basic algebra (like solving for one variable in a basic equation). Most of the actual work (as opposed to interpersonal stuff, meetings, etc.) is basic accounting and Excel stuff.

Traders generally don't know math either, and there are a good number of jock type guys that are traders.

Quant traders, however, have math and science backgrounds, often quite substantial.

Physics for Idiots and Poets said...

He didn't know the answer to even one of 60 questions in 10th grade math test?

This is what is expected of 10th grad math students.

I hope he was lying for dramatic effect and to score PC brownie points. I fear he may not be lying and there are many such 42-long cretins with BS degrees at helm who actually believe they "can make sense of complex data" despite being unable to answer

Anonymous said...

Buffett's Berkshire Hathaway also would have went bankrupt due to derivative bets if not for the 2008bank bailouts...

Anonymous said...

I trade options actively, and do very well trusting my gut. I don't need complex maths to tell me if something is over or under-valued.

The only times I did badly was in being over-leveraged and simultaneously failing to predict a major market drop that was due to crime or governmental mismanagement.

In these cases, even with the wisdom of hindsight, complex math would simply have been a waste of time. But knowing the right people, understanding human weaknesses and paying close attention to early warning signs would have made the world of difference.

Anon.

candid observer said...

I guess I can see how, at least in principle, a HS math test could be devised so that essentially every question hung on some technique one must explicitly remember (or be able to devise on the spot) in order to solve.

But how does a mature, educated adult get only a score that would represent a "D" on a HS reading test?

Unless there's something really hokey about such a test, I don't see how it manages to be much more than a reading comprehension test. And so how does an adult with multiple degrees get only a "D"?

There's something fishy about this story -- and/or the wealthy guy is quite the blathering idiot.

Lady Engineer said...

For those people who claim to only need arithmetic to get through their lives after they are out of school - you don't calculate car loans and mortgages? How about the amount of paint or carpet needed for your home? That all involves more than just basic arithmetic.

Maya said...

"No "solve for x" or "what is angle 'a' equal to"?"

Most adults can't solve for x. Over 90% of teachers at my school can't do percentages without a scientific calculator. Neither can the principal. It's painfully apparent during every after school meeting when we "analyze" data. Pathetic.

Ray Sawhill said...

Lady Engineer: "For those people who claim to only need arithmetic to get through their lives after they are out of school - you don't calculate car loans and mortgages?"

I don't own a car. For the living space, I got a fixed-rate mortgage at what seemed like a decent-enough rate, then paid it off really fast. No math needed, and I have a hunch that I'm better off than many people who spent a lot of time with calculators figuring out exactly how much house they could afford.

"How about the amount of paint or carpet needed for your home?"

Throw rugs and trustworthy workmen FTW.

I often manage to go for months without doing any arithmetic whatsoever. Can someone please explain why I needed to study algebra, trig and beginning calculus, all of which hurt my brain and all of which I forgot instantly?

Anonymous said...

I bet he's black.

It sounds like the next push is....

"Let's get rid of math altogether!!! We rich people don't need it...It makes the minorities feel bad! Heck, Steve Jobs took Caligraphy in college (fucker)!"

Anonymous said...

Algebra II is relatively easy, compared to geometry. Yet for some reason you take geometry FIRST, then algebra II.

Algebra II teaches you fairly useful computational skills, while high school geometry is completely, utterly useless.

Nanonymous said...

Over 90% of teachers at my school can't do percentages without a scientific calculator.

Heh. Reminded me of a successful realtor who had to grab a calculator to calculate 10%. We declined her services the same day. This was before I was even aware of 'g' but I suppose the concept is intuitively obvious.

Anonymous said...

I just tried the first set of myMCAS questions. Got 8 out of 11, did them in my head.

Two questions involved using this notation:||

I dont remember what that means, if I did I would, hopefully, have made 10 out of 11.

Anonymous said...

I just took this California Algebra II sample test for the fun of it. http://www.cde.ca.gov/ta/tg/sr/documents/rtqalg2.pdf I scored just a shade over 50% on it, only based on questions that I felt competent to attempt (ie no guessing). Fumbled a couple due to sloppiness/rushing. Most of it seemed familiar but some techniques I couldn't recall for the life of me (eg rules relating to logarithms). It's hard to believe that standards could be so different across school districts that a PhD candidate with a bachelors degree in Science (!) would not know how to solve any of these questions (he had to guess at them), but oh well, we can all forget some things.

Even if it's too much to demand all high school students pass a test of this degree of mathematical rigor in order to graduate, it doesn't change the fact that a large proportion of the material covered here has all sorts of real life applications. I would feel very short-changed if my high school hadn't covered all these topics.

Sawhill,

I often manage to go for months without doing any arithmetic whatsoever. Can someone please explain why I needed to study algebra, trig and beginning calculus, all of which hurt my brain and all of which I forgot instantly?

Obviously a person can get through life with next to no math, but why make a virtue of ignorance?

Anyway, here's my answer: do it for the fun of it. :) Imagine yourself back at the dawn of civilization. People were erecting shoddily-built structures all over the place and pulling their hair out in frustration doing it, when all of a sudden out of the blazes came a shiny new technique -- trigonometry, some called it -- that promised the people precision. In your mind's eye you can pretend you were right there on the scene, watching the math unfold throughout society and illuminate what had only theretofore been obscure. Then you can transport yourself forward in time and observe math work its magic time and time again. Isn't that fun?

Trader fellow,

You'll probably disregard this completely, but I'll say it anyway: it's ever so easy to be
'fooled by randomness' when you trade by 'feel.' You're very likely to attribute to skill what may only be a result of good fortune; and you're also likely to attribute to 'bad trading' what may only be a string of bad luck (these runs can last an awfully long time).

Silver

Anonymous said...

I dont remember what that means, if I did I would, hopefully, have made 10 out of 11.

Hah, that's 'magnitude'! At least most of the time. I think I might have seen that sign applied elsewhere, where it didn't mean magnitude, which can certainly throw a guy.

Silver

Anonymous said...

But but, the point is to be "well rounded".

Anonymous said...

I am a math mediocrity and a verbal 1 percenter; son of and brother of math one percenters. I realize that I live in a culture built by people like me but in a physical world built by people like my father and my brother.
I love good buildings more than anything in the blah, blah world.
Gilbert Pinfold.

John Mansfield said...

I did a double major in engineering and math and then an engineering PhD, so I'm one of those who uses plenty of advanced math every week. I never touched calculus until college, though. There was nothing in my high school past analytical geometry (stuff like relating equations of ellipses to their geometric definitions). I never heard of AP classes or tests, and I don't feel that waiting until college to learn college stuff set me back much. I have sons in 9th and 10th grade now. Last night the 9th grader was doing linear algebra Gauss-Jordan equation solving, and a couple weeks ago the 10th grader was doing work abstract algebra group theory. I didn't get to that stuff until my second or third year of college. I am curious if learning it in high school will make any difference for them. These are topics that most college graduates never learned, so maybe it will provide the nation of tomorrow with the sort of background knowledge that comes from high school. For example, the last formal instruction I received in geology came in 9th grade, yet my first engineering job was modelling groundwater flow.

Anonymous said...

Hearing this kind of shit is INFURIATING to a young 20s male starting out in the professional world

Anonymous said...

Algebra II teaches you fairly useful computational skills, while high school geometry is completely, utterly useless.

Really? My experience has been the opposite. I haven't used Algebra II since leaving school, but I still find a use for elementary geometry once every couple of months.

Anonymous said...

Actually, electricians *should* have a good grasp of algebra in order to make the correct calculations for able sizing.
In actual fact most don't.

SFG said...

You don't need algebra and certainly not calculus unless you're an engineer, physicist, etc.; plenty of people get by without it.

It's basically signaling value for high g, and as many here have argued, not necessarily the useful kind.

Camlost said...

I haven't taken a math class in 19 years, but I got all 11 correct on the 1st 10th grade quiz. It's not that hard.

Back in 10th grade I would have ripped through that in about 45 seconds, but it took me much, much longer now. And I only got a 750 on the math SAT, probably could have done better if I'd done any test prep or if I had taken the test more than once.

FYI, || means absolute value of what is inside that bracket.

JW Ogden said...

the L.A. school board into passing a rule that nobody could graduate from high school without passing Algebra II (as well as Algebra I and Geometry).

If they are smart, and I think that they are, they will have various levels of Algebra I, Algebra II and Geometry. After all their is no firmly fixed description of those.

Anonymous said...

"But, does anybody know of a study of what % of jobs require somebody to use Algebra II level math?"

According to eHow:
"Algebra II covers topics such as solving inequalities, graphing functions, factoring polynomials, solving equations with complex numbers, and dealing with logarithmic and exponential functions. In order to learn Algebra II, it's important to have a grasp of the concepts covered in Algebra I which include graphing equations, finding the domain and range of a function, finding absolute values and solving equations involving variables."

Alas, we see that the Bell Curve itself is a topic beyond Algebra II which is why so few can carry on an informed conversation about race and IQ. Most folks are unable to grasp why a 10 - 15 point lower mean for some ethnic groups virtually wipes out any chance that they will produce a meaningful number of candidates in STEM, medical, or legal studies (unless they constitute a population the size of India) because the tail of the distribution applying to them will effectively terminate before 120. It explains why Barack Obama, the African American supergenius, has the intelligence and cultural interests of a typical midwestern dentist. It also explains why Sonia Sotomayor writes pages and pages of cryptic gibberish sounding more like a Tarot card reading than a legal opinion.

Mr. Anon said...

In order to graduate from High School in California, I think that every pupil should offer an original solution to Fermat's Last Theorem.

That will solve a lot of problems.

Anonymous said...

Can someone please explain why I needed to study algebra, trig and beginning calculus, all of which hurt my brain and all of which I forgot instantly?


Signaling? The point of doing some of these difficult things is to show that you're capable of doing difficult things. Math tests are a proxy for IQ tests in this sense.

Eugene said...

As Car Talk's Tom Magliozzi (he graduated from MIT) says about high school math courses: "The purpose of learning math, which most of us will never use, is only to prepare us for further math courses, which we will use even less frequently than never." (Follow the link above for his extended rant on the subject.)

John Mansfield said...

Many are under the impression that high school geometry is about lines and circles. Really it is a course in logic, using the lines and circles as something to be logical about. On the occassions when I need to construct a tangent to a circle, and every now and then I do, I think back more to my high school drafting class than to my geometry class. When I need to construct a proof, I draw on the concepts I was first taught in geometry.

Anonymous said...

@ John Mansfield

As a former high school math teacher, I agree with you. It used to drive me nuts that my high school texts threw in so much math that I didn't start learning until I got to college. It was just too difficult for my students. Meanwhile something that was absolutely essential for them to understand was covered in only one lesson, and--unless you hammered on it repeatedly--quickly forgotten. Because social promotions were the norm, I seldom had a class that was capable of learning from the text book assigned for it. I wound up teaching remedial Algebra I and calling it Algebra II; and I considered myself fortunate if I had a class capable of learning even that. My number one goal was to make them learn something--anything they were capable of learning--and to make it hard enough that the real dummies wouldn't sign up for Pre-Calculus.

Mouth Breather said...

Hell, if you can't eat it, drink it or f*ck it what darn use is it anyway?

Now I gotta go lazyboy my double wide behind and watch me some football.

This thread reminds me of a Chris Rock routine on how some blacks view books.

TonyLast said...

"The margins of his electoral wins and his good relationships with administrators and teachers testify to his openness to dialogue and willingness to listen. "

Yeah, I am sure *that* is what it testifies to. Snort.

"and said he’d make his scores public. "

But he hasnt- who is this loser and what is the school system?

-----------

Flipping the presumptions of the columnist around a bit, what would we say if it was the expected case that a kid who hasn't studied for the final exam and hasn't been in class all year did pass? Wouldnt we all say that something is wrong with the school's standards?

That appears to be the case here- Mystery School Board member has done no review, no practice tests, and hasnt been in classroom for decades. When was their last experience as any kind of test taker?

They are unfamiliar with the current terminology and took no time to get up to speed- median, absolute value, leaf plot, calculating slope. None of those are hard concepts but you do have to know the definition before you can be tested on it.

Frankly they should be expected to fail!

Likewise is there any subject that they would pass in these conditions? Pass the history test without studying? Spanish? Biology- remember all of the names of the cell organelles? Even the Driver's Ed final might be tough with no prep at all.

WaPo tries to present this as a redectio ad absurdum that a college educated school board member (vacation home in the Caribbean! Influential friends!) was confronted with a Math Test too difficult to pass. The real absurdity would be if there was a test the majority of people could pass by not attending class or doing any preparation at all.

------

BTW the Massachusetts test here is a piss poor test for a 10th grader.

http://mymcas.com/Mm_g10/Mm_g10_S2009_ST1/quiz_mm10_03_09_st1.htm

Lots of problems that dont even need to be solved because the test maker has put in only one plausible answer. A functioning adult would only have trouble passing this if they werent familiar with the terminology.

Mr Mystery School Board member needs to be voted out of office for his stupidity and his grandstanding.

Anonymous said...

I would tend to dispute that prob and stats are that much easier than calculus. Most of the public seem to be incapable of discussing group differences in terms of mean and variance.

I think this has as much to do with incapability of understanding statistics than with PC indoctrination. IME a lot of people lack the smarts to grasp that a single exception does not invalidate the statement that "group A is generally Xer than group B".

The implication of this is that they are going to struggle with isteve, The Bell Curve and the like.

Kylie said...

"I just tried the first set of myMCAS questions. Got 8 out of 11, did them in my head.

Two questions involved using this notation:||"


I got 7 out of 11, did all but 2 in my head.

Anonymous said...

Absolute, 169% total B.S.


Agree.

I pick up SAT/AP study guides for my son and do a quick look at the questions. Easy. Period. And I am a stay home mom with a foreign language BA, not some highly trained techie.

Anonymous said...

Algebra II is relatively easy, compared to geometry. Yet for some reason you take geometry FIRST, then algebra II.

Algebra II teaches you fairly useful computational skills, while high school geometry is completely, utterly useless.



WHAT?!

Geometry is painfully easy. That is why they made it a full year course, so kids could EASILY get two math credits, back in the day when you only needed two math credits. We used to be able to graduate with only twenty credits (pass 20 of the 24 classes) and you could graduate with two Math of Consumer Economics math credits. That is what the slow kids and some vocational students took.

Anonymous said...

If they are smart, and I think that they are, they will have various levels of Algebra I, Algebra II and Geometry. After all their is no firmly fixed description of those.


Extended Algebra.

This is Algebra 1 spread out over two years. The slower pacing allows time for twice as much practice and remediation.

I guess they could do the same with Algebra 2.

Sheila said...

I've always had much higher verbal skills than math skills, but I did well enough decades ago back in high school through pre-calculus. I aced that, but then failed calculus miserably my senior year - I need a slow, step-by-step instructor in math and instead got one who stood at the board with the math whizzes and solved advanced problems, while I was left trying to learn calculus by myself by reading the text book. I got a refresher course in Algebra I and II while assisting my older son, who took it in 7th and 8th grade (in private school at age 11/12, having skipped two grades) and found the Christian Saxon Math textbooks easy to understand. The only problem was that while I tried to explain things step by step (i.e. the way I learned it), my son understood it intuitively and jumped ahead three or four steps past what I was trying to teach!

FWIW, I've never had a job that required more than basic math (vs. high verbal/writing ability), but even that seems beyond most people today. Cashiers who cannot do basic subtraction and give change if their do-it-all-for-you register goes out, clerks who need a calculator to figure out 10% off, or the price of 3 for $5.00, and so on. I could not recall most math formulae if my life depended on it, but such a dire situation has yet to occur. Meanwhile, my husband uses math every day (precious metals trader) and steps in to help where my memory fails me.

David said...

Years ago Robert Sheaffer said it doesn't matter what schools teach - as long as it's hard. That weeds out the smart from the dumb. He said the high schools could give nothing but courses in ancient Mandarin and achieve the real purpose of schooling.

I have my doubts. Wouldn't the truly smart kids rebel against using their brain in a useless and absurd way? I think the real geniuses would drop out, become autodidacts, and found businesses.

In most places education is indoctrination, aimed at making good factory workers (whether factory jobs are plentiful or not). Read John Taylor Gatto.

Hail said...

At first go-through, I read "Marion Brady" there as "Marion Barry".

The hasty reader might come away with the following from that paragraph: "Marion Barry...decided to take his district's test for 10th graders." Haha.

Anonymous said...

This article in the Bulletin of the American Mathematical Society is more honest than most of the talk one hears on this topic (the author urges that we "tone it down" about the necessity of algebra for job performance:)

http://www.ams.org/notices/201005/rtx100500608p.pdf

Here's another interesting one in which not one of 50 third grade teachers knows how to find the area of a rectangle

http://www.ams.org/notices/200502/fea-kenschaft.pdf

Gene Berman said...

Lady Engineer:

No, the processes you've mentioned are all merely arithmetic, though being somewhat more specialized than the 4 simple operations.

A somewhat greater understanding is required to solve some simple problems involving a single unknown (and head or book full of conversion factors--equivalencies--like pints in a gallon, gallons in a "barrel," specific gravities, or relationships involved in sides of triangles)--all still arithmetic, though dramatically more involved (or onerous) but routinely useful in construction, estimating costs of operation, etc., all of which are among the less-demanding of "head" tasks in engineering of many sorts. Such one-"unknown" problems are no more than slightly advanced arithmetic. I'd venture that actual "math" begins with algebra in which involve more than one unknown and "engineering math" is, specifically, calculus--a facility far more difficult to even appreciate, much less master.
Engineering--depending on type--may require not only those but, further, probablility theory and statistics (the last itself involving all the preceding, on occasion). Mining engineers solve problems ranging from specific equipment required to excavate, sort, crush, and, perhaps, separate values from a given over- burden to providing appropriate safety measures for workers. In like wise, the entire gamut of math (as well as specialized knowledge) is characteristic of electrical, chemical, and nuclear engineering. The problems you've mentioned are all simple stuff.

Gene Berman said...

Lady Engineer:

No, the processes you've mentioned are all merely arithmetic, though being somewhat more specialized than the 4 simple operations.

A somewhat greater understanding is required to solve some simple problems involving a single unknown (and head or book full of conversion factors--equivalencies--like pints in a gallon, gallons in a "barrel," specific gravities, or relationships involved in sides of triangles)--all still arithmetic, though dramatically more involved (or onerous) but routinely useful in construction, estimating costs of operation, etc., all of which are among the less-demanding of "head" tasks in engineering of many sorts. Such one-"unknown" problems are no more than slightly advanced arithmetic. I'd venture that actual "math" begins with algebra in which involve more than one unknown and "engineering math" is, specifically, calculus--a facility far more difficult to even appreciate, much less master.
Engineering--depending on type--may require not only those but, further, probablility theory and statistics (the last itself involving all the preceding, on occasion). Mining engineers solve problems ranging from specific equipment required to excavate, sort, crush, and, perhaps, separate values from a given over- burden to providing appropriate safety measures for workers. In like wise, the entire gamut of math (as well as specialized knowledge) is characteristic of electrical, chemical, and nuclear engineering. The problems you've mentioned are all simple stuff.

Polymath said...

I call BS on this guy, with his claimed credentials and demonstrated writing ability he could not have scored as low as he said.

Those Massachusetts 10th grade tests are excellent. There is nothing wrong with standardized tests being required of all students, but educators and politicians need to accept that the bottom quarter [of a 100-IQ-average population] will never be capable of passing "Algebra II" as it is currently generally understood to mean, and that dumbing it down does a disservice to the three quarters who could pass it. (Only the top half ought to be able to pass it routinely, but with a lot of effort and tutoring the third quartile, the ones with IQs in the 90's, will generally be capable of getting enough of the material for a passing score.)

Obviously the majority of teenagers from groups whose IQs average in the 80s will never graduate from high school if Algebra II is required and not dumbed down. But this is not to be discussed publicly by politicians and educators on pain of career truncation.

Jacob Roberson said...

Anonymous said...

Two questions involved using this notation:||


Looks like computer programming to me. But that wouldn't be on a math test.

K(yle) said...

"Hah, that's 'magnitude'! At least most of the time. I think I might have seen that sign applied elsewhere, where it didn't mean magnitude, which can certainly throw a guy."

It's absolute value.
http://en.wikipedia.org/wiki/Absolute_value

Anonymous said...

Those Massachusetts 10th grade tests are excellent.

I decided to take first 20 with a time limit of 10 min. Had 16 out 20 correct. Without time limit and paper/pen, it would be 20/20 no doubt. I cannot imagine even moderately smart guy (say, IQ 115) not getting at least 66% no matter how long ago he had any math class. Remembering what square root is and estimating sqrt(2) mentally is like riding a bicycle - can't unlearn.

Anonymous said...

"Two questions involved using this notation:||"

...absolute value eluded you?!

Yikes. Please make sure my fries are piping hot.

Anonymous said...

The whole idea of Algebra II or whatever is really parochial. I am English; I have no idea what is in Algebra II. Why is it the same throughout your whole massive country?

I did A-Level maths and I've never used any of the stuff I supposedly learned (I'm a software developer.) I probably shouldn't have bothered with it. On the other hand, A-Level physics knowledge I've used quite a lot in everyday life.

Conclusions? None.

But the whole idea of being a high school graduate or not is weird to me.

Anonymous said...

Info on the school board member and the test: http://www.washingtonpost.com/blogs/answer-sheet/post/revealed-school-board-member-who-took-standardized-test/2011/12/06/gIQAbIcxZO_blog.html.
The test is the Florida Comprehensive Assessment Test.
There are example tests here: http://fcat.fldoe.org/fcatrelease.asp
I looked at a 10th grade math test. At least in the first 25 questions, you don't need any knowledge beyond very basic algebra and geometry, and for many, you only need arithmetic and basic reasoning skills. The idea that this test is impossible is BS.

Elli said...

I got 20 out of the first 20 questions in the MA 10th grade math tests. I damn well ought to have, with a math degree. But there's no point in most of it for someone who isn't headed for a STEM career. Question 17 on order of operations was a time sink math puzzle, pointless except for amusement value, and a cruel panic trigger if you are not happy with math.

Most people need not much more than arithmetic - do a budget, double a recipe, calculate how much fertilizer or paint they'll need. Compound interest rates and a bit of probability would be helpful too, but real world stuff like poker and pregnancy, not abstractions. Four years of shop and home ec classes would do more to help the left half of the bell curve get a solid grasp of necessary math than four years of algebra-geometry-trig.

College material kids (real college material) ought to take statistics because there is a world of liars and wishful thinkers out there waving magic number wands.

Nanonymous said...

"Info on the school board member and the test"

Thanks, Anon!

LOL. So the "science degree" of this guy is in "education" and his masters are in "education and educational psychology". And he was a teacher in Orange Co.

I also looked at the test and the guy has to be an utter moron if he does not know answers to most of the questions: "According to the graph, in what year had the population grown to approximately twice that number?" - this isn't even a math, this is little more than a common sense!

Doug1 said...

For the life of me, I don't know why they don't teach first year college level statistics in high school instead of calculus for more advanced AP level students. Statistics is useful and important to know in most professional areas including STEM ones, whereas calculus is only in some STEM areas.

I found algebra II (not called that then, instead quadratic equations and trigonometry) pretty easy. I use algebra I at least and word problems into algebra all the time and I don't work in any STEM related field. Use it all the time in investing in fact.

Anonymous said...

Yes anon. Absolute value eluded me. If I ever learnt it at school Ive forgotten it and Ive certainly never had any cause to need it since. Ive quite literally never seen it used anywhere in everyday life.

If thats your cutoff for burger flipping I can only assume you move in far, far more rarified circles than I.

You seem to be confusing the ability to handle the equations in that test with the ability to recall the meaning of all the symbols used. There is a correlation but I think you will find they are not the same thing.

Now that I know what || mean you will be gratified to know that I got those two questions correct. Boosting my score from 8 out of 11 to 10 out of 11. Guess that means my burger flipping days are over.

You know what this means?

The anti-IQ folks are right, it doesnt test ability it just tests memory. Thats what you are saying because lets look at the facts, I just got more intelligent didnt I?

Elli said...

Even though I just said most people need only arithmetic, would do better with a solid grounding in arithmetic, I'd much rather send my children to school in Massachusetts than Florida, to judge by the tests, or by Mr. Roach, former teacher, trainer of 18,000 educators, school board member, sample of one.

My children are not most people. Could Florida schools actually be better for most people...some large minority of people? It's enough to make the upper middle class mind itch. Hell no, because you want someone teaching arithmetic to know it upside-down and sideways...and you sure can't count on that with Mr. Roach in charge.

gnome said...

The problem with all this emphasis on higher more abstract mathematics is that it detracts from the math which is not only useful, but would actually help people to become better citizens. As a student the larger fraction of your time is wasted on doing math you will never even use and because you never really spent enough time on understanding the basics those are quickly forgotten post-school. As an example, I would rather the general populace had a better grasp of basic statistics but whether they can factor a polynomial is of minor import. Even brighter students would benefit from taking more time on the fundamentals so that they get the time to really understand what they are doing instead of just doing it by rote. This will help them proceed in higher math far more efficiently.

and deliver us from morons said...

Steve, the **last** thing you want to teach to those too dumb for algebra 2 is statistics. Well, that and maybe financial trading with your money. Poor knowledge of algebra, much like poor skill in writing essays about Great Gatsby, cannot and does not translate into any real world effect. But the "I got edumacated in statistics, yessirree" type of guy makes an excellent stormtrooper on behalf of false government policy, "science", "medicine" etc. Such people can produce and consume fancy sciency-looking propaganda not just not recognizing the lies, but being incapable of conceptualizing the difference between truth and lies in this realm of discourse in the first place. Trying to convince them of their error would require to, snicker, make them actually comprehend the subject they were too dumb to learn in the first place. So yeah, better to keep them sloganeering about God's children and disturbing gaps, because nothing good will come from adding t tests and mathematical models of the climate to their rhetorical arsenal.

Anonymous said...

It's absolute value.
http://en.wikipedia.org/wiki/Absolute_value


Magnitude means the same thing, so I'm not sure why you chose to 'correct' me.

ben tillman said...

Info on the school board member and the test: http://www.washingtonpost.com/blogs/answer-sheet/post/revealed-school-board-member-who-took-standardized-test/2011/12/06/gIQAbIcxZO_blog.html

Thank you!

Wow, that test is easy. Sample multiple-choice question: Florida has 7.2 million acres of pine forest. Pine forest is either natural or planted by man. If 4.4 million acres are natural, how many acres are planted by man?

Anonymous said...

"FYI, || means absolute value of what is inside that bracket."

I'd forgotten that but was able to infer it from the answer selection.

Anonymous said...

Elli, you get the schools you deserve. Florida public schools are slanted toward Floridians, with all the social pathologies endemic to said benighted rathole. Public schools in Massachusetts have to answer to higher expectations.

Massachusetts public schools annually score in the top three on nationwide tests, even though the racial makeup of the Commonwealth is not lily white like Utah or New Hampshire (or lemon yellow, a whole other story). What most don't realize about MA is that every fall about 280,000 18-25 year-olds arrive to attend one of the 85 colleges and universities within a 50-mile radius of Boston, a fair number of these schools ancient and venerated (by American standards) centers of intellectual excellence. This includes the best and brightest of the NAM community. A certain number decide to stay after graduating, perpetuating the cycle of academic attainment.

That said, the local coffee shops here are full of these multiple-degree twits with so little real knowledge, common sense and comprehensible world view that they're unemployable.

Anonymous said...

"Florida has 7.2 million acres of pine forest. Pine forest is either natural or planted by man. If 4.4 million acres are natural, how many acres are planted by man?"

Why the hell is this called Algebra II? This is barely third grade level arithmetic.

Juan Bautista said...

It is irrelevant whether algebra is required to perform any particular task. Is weight training required to hit a golf ball? No, but it helps Tiger Woods perform.

The purpose of education is not to train pupils to perform specific tasks (such as answering SAT questions), but to train, develop and strengthen minds and bodies to perform whatever tasks they encounter in life as best they can. Not everyone can bench press 250 pounds, but everyone can bench press something and can profit by the effort.

Aaron Baugher said...

School subjects can look harder than they are when you look back at them as an adult. Math was my favorite subject; I got a 33 on the ACT without trying (when top was 35), and I liked calculus. Twenty-five years later, I'm tutoring some kids in 5th-grade math, and occasionally I look at their book and say, "Huh?" I can still divide numbers and calculate averages, of course, but sometimes the specific methods and terminology they're using today are different or escaped my memory after I learned the principles behind them. For instance, yesterday we did "short division." I don't remember seeing such a thing before; we did long division until I was ready to tear my hair out from being forced to "show my work," until teachers finally let us do it "in your head." Short division appears to be an intermediate step between the two, but it was news to me, and confusing for 20 seconds or so.

I think sometimes adults look at their kids' schoolbooks and have that kind of reaction, and assume that means their kids are doing harder work than they did, so the concerns about schools being dumbed-down must be unfounded hysteria (or may be true about other schools, but not their beloved South Union High). It doesn't mean that at all; it just means they don't remember all the details of the steps of the learning process.

But this guy is obviously lying when he says he knew the answer to ZERO questions out of 60. He's probably stretching the meaning of the word 'knew' to unrealistic levels ("Well, I was 99% sure the answer was A, but I didn't really know it."). Or the time spent working on those two masters degrees turned his brain to sludge.

The purpose of schools is to lock kids up during the day so their parents can get things done. If they stumble across some knowledge while they're there, that's a bonus. But the purpose of education is to learn how to think. Algebra II does that, as does studying ancient history, or Shakespeare, or classical music, or the structure of an atom, or the life cycle of the butterfly, or how rocks are formed, or how to combine pulleys to lift a heavy object. Aside from reading, writing, and basic arithmetic, you're probably not going to use anything you learned in school later in life unless you teach one of those subjects, or get a very specific job in one of them, in which case you could learn the basics that you picked up in school in the first couple weeks on the job (or in a trade school, which is designed to teach actual skills). I've never needed any of those things in my adult life, but studying them (mostly outside school) helped me learn to think.

True, some people aren't particularly good at thinking, and there's probably no good reason to try to force them through Algebra II (or Shakespeare, or Physics, etc.). They're not going to learn it, so one of three things will happen: they'll drop out (leaving you to devise new ways to force them to stay in), they'll cheat, or you'll cheat. It'd be better to teach them something they can handle but is a bit challenging for them, just as Algebra II is a bit challenging for the 110-120 IQ kid. The 90 IQ kid can learn to think better too, but a subject that completely confuses and frustrates him won't do that; he needs to study something he can get if he works at it. That wide-eyed, "Hey, it makes sense now!" look is a beautiful thing to a teacher, whether it comes from the smartest kid in an optional Latin class or a kid you're helping with fractions because he's been struggling with them for two years. (Maybe more so in the latter case, because the smart kid would probably get the Latin without your help.)

But if we did that, we couldn't pretend humans are blank slates that can achieve anything with the right willpower and environment.

Gene Berman said...

Anonymous (immediately preceding Bautista):

What you say about the obviousness is correct--but it's still essentially (in it's construction of method) algebraic. Like it or not, what is essentially a review of the mental steps involved in solving such a simple problem are fundamentally instructive even to those for whom its solution is a "snap" and the instructional process is intended to prepare all--the bright and the slow-witted as well--to the broad
extension of knowledge (and the capability derived from that knowledge) possible from the application of our minds' logic (of which math is a subset) to various problems encountered in life. Everyone who crosses a bridge, flies to a destination, or lives confidently in any urban agglomeration (where sufficient agriculture is out of the question) implicitly places a high level of confidence in the mathematical and computational skills of his fellows. We should all know something whereof our complex civilization is possible.