July 29, 2012

Algebra class is hard — so should we stop requiring it?

That's what polisci prof Andrew Hacker argues in a NYT op-ed:
Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white.... Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job.... Of course, people should learn basic numerical skills: decimals, ratios and estimating, sharpened by a good grounding in arithmetic....

Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey....

Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.”... It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.

181 comments:

rhhardin said...

There's always been poets' physics courses.

It's time for women's math.

traditionalguy said...

He is an idiot. Algebra is easy and is also a very useful tool used in every day life.

Pogo said...

Barbie was right!

Peter said...

Regardless of what Andrew Hacker may think, the fact remains that the majority of marketable college majors require math. Usually lots of math.

madAsHell said...

This is more dumbing down for the ......

Pogo said...

The teachers can't teach and the parents don't care, so teach them moron math so at least they can count their Food Stamps and Medicaid income.

BigFire said...

Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house.
--Lazarus Long, "Time Enough for Love", (Robert A. Heinlein)

Shanna said...
This comment has been removed by the author.
Borepatch said...

Whatever happened to the idea of excellence? Are younger generations less capable than previous generations? Or is it the teachers?

The question is rhetorical. When all else fails, lower your standards. Oh, and raise the teachers' pensions.

rhhardin said...

"A great deal of what we learn at school is of little use in later life. This is especially true of mathematics..."

Carl E. Linderholm _Mathematics Made Difficult_ "Guess the Next Number" p.89

Shanna said...

By all means, let's have less math.

Idiot.

Regardless of what Andrew Hacker may think, the fact remains that the majority of marketable college majors require math.

My required 6 hours, including Calculus (also, finance, econ and stat). I'm pretty sure Poli Sci only required some sort of ridiculously basic math.

Shanna said...

Also, I took Algebra in 9th or 10th grade. What the heck are they planning to teach if they knock that out?

Writ Small said...

I think we could solve the problem by giving a trophy to everyone who attends an algebra class regardless of performance.

Also, we could ask China and other countries whether they would do the same to keep the playing field level and all.

Dan Jelski said...

I agree with Mr. Hacker. Any computer can do algebra better than any human being. Solving quadratic equations by pencil & paper is a completely useless skill. Functional relationships are important, and students should be able to draw simple, free-hand graphs of linear, quadratic, cubic, and trigonometric functions, but otherwise it's silly.

People will get jobs doing things that computers can't do. Your telephone can do algebra better than you can. Why are you wasting your time?

Ross said...

Get rid of math? Sure! Let's get rid of history while we're at it so we don't realize we're making the same mistakes as previous generations...

rhhardin said...

Lautreamont O Stern Mathematics.

He who has not known you is a dolt.

ricpic said...

The problem is that if it were proposed that the multiplication tables be taught by rote and taught thoroughly (repetitively) the objection would be that that would shackle students' "creativity" or some such.

edutcher said...

When i was getting my Computer Science degree, there were 2 types of Calculus courses; the regular ones and what was called Concepts of Calculus for the managerial types.

We called such things, "Computing for the computer-impaired". This sounds similar. One of William Ayers' brilliant ideas, no doubt; can't have the proles learning to think for themselves, can we?

Sorun said...

You peasants don't need math to understand ObamaCare or climate change. You only need to be able to read the The New York Times.

Barry Dauphin said...

I guess we can teach whatever will enable the citizens to swallow AGW whole cloth: How to mis-measure temperature trends over the past century.

Sumbunnyluvsu said...

I just got a job as an adjunct business/accounting teacher at a for profit college. The first thing they asked me to do was teach a young lady algebra. And I am not a math major. I figure that this girl had probably taken algebra at least twice in public school and when I got her, she was on her third try in college. I have never taught anything before. She passed the class with an 86% and finally got her AS. I'm having trouble understanding why she couldn't learn from her previous teachers. My biggest clue was when I met her, she told me several times that she had ADD but couldn't take her medicine because she was pregnant. She ended up surprising herself.

Quaestor said...

Poli Sci was invented to give idiots on atheistic scholarships something to major in. That someone hired to teach a subject fit only for inferior minds thinks math is too hard is not surprising, just depressingly predictable. What's also not surprising is the NY Times giving that loser a soapbox on which to utter his mathophobic bleats, since the former Gray Lady has been busy devolving into a dingy old whore.

AJ Lynch said...

I got the NY Post the other day. It reported NYC has 3 Million people on Medicaid and it costs, in total, over $28 Billion which is more than $9,000 per person per year. I thought WTF? That is a lot of money for health insurance. I wonder how this idiot Polisci prof would obfuscate about that math?

kimsch said...

Oh my Lord.

Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job..

I am just finishing an MBA course called "Quantitative Reasoning for Business" and guess what? There's a heck of a lot of algebra in it and that algebra is necessary to the course and understanding the material.

wv: shookil

Ignorance is Bliss said...

— and include discussion about which items should be included and what weights they should be given.

Just what we need. Less classes based on right and wrong answers, and more based on a discussion about how we want things to be.

For the non-college-bound, I'd be willing to trade some of the existing math, such as algebra, for some practical, but still rigorous, alternatives.

Things like Probability ( No, you're not going to win the lottery, ) Statistics ( Here's a newspaper: identify the way the statistics are misused in each article ) and Budgeting ( No, your new cell phone is not an investment. )

I'd also quite happily trade some literature or social studies for a course in rhetoric, particularly in identifying logical fallacies.

Skyler said...

I'm more inclined to conclude that polisci is not an academically rigorous field since this man is clearly an idiot. Algrebra is not in the least bit difficult.

Bob Ellison said...

Algebra teaches young minds an important skill: how to guess whether a fact (like the possible values of x) is knowable.

People unschooled in this skill are called politicians.

Unknown said...

My theory is that the more squishy types hate math because it's one of the few disciplines that has correct and incorrect answers. Nothing about you, your politics, or your style will make an incorrect answer correct. Math lacks heart, therefore it cannot be important.

Paco Wové said...

I'm sure Dr. Hacker would have no problems with taking some advice from the Math Dep't. on which of his courses could be eliminated from the catalogue.

David said...

It's too hard mommy. Make it go away.

Algebra is not hugely difficult if you do the work to learn it day after day as the lessons progress.

Unless you are highly gifted, it's damn near impossible if you don't.

There's no room for bullshit on a math test.

Michael K said...

"This is more dumbing down for the ......"

This battle was lost years ago in Los Angeles. I remember the debates in 1995 when they LAUSD decided that every student should be given a chance to "FAIL ALGEBRA." That was when they dropped pre-algebra from middle school.

The curriculum wars were lost long ago. Now, we have Ivy League graduates who know nothing, like our community organizer in chief who thinks Austrians speak Austrian.

Those who know algebra will rule the world if they can hang onto their guns.

An Old Sergeant said...

ANY subject that is not subject to the rigors of mathematics and logic should be considered a 'boutique" degree. A degree created solely to elevate the self esteem of the 'student' and of no real worth in the real world. These degrees have given us educated idiots with no marketable skills!

t-man said...

When liberal policies are clearly doomed because the math doesn't add up - get rid of the math.

paul a'barge said...

Sure thing. Replace it with Poly Sci. Or Women Studies. Why not? The world can always use a few more morons.

Astro said...

So - Someone at the NY Times allowed a web troll to write an article that they agreed to publish? His thesis is ludicrous on its face, so the only purpose of this can be to provoke responses. [To that extent, I guess, it succeeded; but only to that extent.]

Is this moron/troll unaware that the movie 'Stand and Deliver' is a true story? That 'dropout' kids were capable of learning calculus, in high school?

t-man said...

By the way, in my day, the advanced kids were taking Algebra in 8th grade. Now, my daugher just finished it in 7th.

NorthOfTheOneOhOne said...

Dan Jelski said...

I agree with Mr. Hacker. Any computer can do algebra better than any human being. Solving quadratic equations by pencil & paper is a completely useless skill.

Sure, hear hear, I agree 100%! All we need is for tomorrow's Americans to be able to understand math so they can program the computers to do math!

Oh, wait.......

Sorun said...

Don't probability, statistics, and computing the CPI all use algebra?

Maybe I've forgotten the precise definition of algebra, but it's pretty basic math. I think they start teaching it in middle school.

wef said...

First, you are again referencing the power-worshiping proglodytes at the lickspittle, crony-capitalist nytimes. Why?

Second, this high-IQ idiot is shilling for the "relevant" bs that makes contemporary pedagogy the miserable mediocrity that it is. If anything, as a teacher myself who has to deal with many stupid-thinking bright young minds who spout "everybody says" crap, let me testify that it is the practice in abstraction that eventually liberates the mind to think - to allow youth to make their own models and comprehend a series of complicated steps that take one from a problem to a solution. But liberating the mind, training youth to deal in abstract train of thinking is perhaps what the servile crowd wants. And it does not have to be algebra - it could be Latin or Russian grammar, the law, or the logic of theology a la Aquinas. But the foolish nonsense about relevancy is such bullshit.

yashu said...

As others have said-- ugh, what an idiot.

Instead of teaching students powerful mathematical tools for active problem-solving using their own independent reasoning ability and exercising those mathematical problem-solving skills, let's take the one hour a day of math class and inculcate leftist ideology (or whatever ideology the teacher wishes to instill) then too.

We want our children to be "informed citizens." And if they don't know math or algebra, they'll be less equipped to question or doubt whatever we teach as "citizen statistics" or the benefits of ACA or the impact of climate change etc. More "informed citizens" (who don't know math) means less skeptics (of Democratic policies): win win!

Lem said...

I propose an American Affordable Math Act... AAMA... with a penalty/tax to free riders... the people that rely on others for math.

Bob Ellison said...

I hope the "any computer" comments are all sarcastic. Computers don't do algebra. Asking your Mac to do algebra would be like commanding your oven to bake a cake.

JC said...

Both IIBliss and Unknown have put their fingers on the problem. You don't get partial credit for wrong answers in math/ (Unless you prove Fermat's Last Theorem in the margins or something).

Randall Monroe has a great comic: http://xkcd.com/1050/

If you're not reading XKCD, you're part of the problem

Luke Lea said...

I agree with the good professor. Give these kids the skills they will actually need and be able to use, including opportunities for more training in the industrial arts. And to get rid of the stigma make some industrial arts training a requirement. Everybody needs to know how to cook, use a screwdriver, and a few other things.

Lem said...

I hope they put in a sunset provision...
The last year of Algebra is to be taught outside the classroom.

Math is easy... comedy is hard.

Quaestor said...

Dan Jelski wrote:
I agree with Mr. Hacker. Any computer can do algebra better than any human being.

It takes a certain boldness to lend one's support to a cretinous proposition, so kudos for boldness, Dan Jelski.

However, you reasons for agreeing with Hacker's thesis are nonsense, but that's not your fault. Arguments in favor of a specious premise are themselves specious by default.

The value of algebra is two fold:
1) Algebra is the foundation stone of mathematics, which is reasoning with numbers. Mathematics is always a matter of logical inference, if a=b and b=c, the c=a, etc., as opposed to arithmetic, which is mere calculation. Machines are infinitely better than humans at arithmetic because the solution is as inevitable as the flow of electrons in a circuit. Computers know how to add the same way the switch on your wall knows how to turn off your light. Computers can't reason at all, however. Without algebraic logic you can even formulate a problem such that an algebra program can operate on it.

2) Algebra teaches basic rationality. No problem in mathematics is amenable to emotional displays and other sorts of histrionics, the likes of which our society has much too much of as it is. Teach a young mind to apply its native genius to a problem rather than sit and pout, complaining "math is hard", and you've rescued the world from yet another walking Barbie. So what if a lawyer might live out his career without revisiting the binomial theorem? Alegbra should be required if for no other reason than to weed out the Snookies. No high school should graduate a student without a year of algebra passed with a C. No university should admit an applicant without a year each of algebra, Euclidean geometry and analytic geometry. Too tough you say? Let it be tough. As Plato over his door, "Let only geometers enter."

Quaestor said...

typo: "then c=a" Damned fingers! Damn-ned, I say!

Cedarford said...

I'm all for making up two sets of schools - one the "hard track" full of math, science...the other the "social promotion track - far easier courses but students and parents told up front the outcome would be far less high value jobs for the grads.

Of course, if you ever tried it, it would be shot down as resegregating the schools.

Saint Croix said...

So Barbie says "math class is hard" and she gets in trouble.

Obviously she should have written a New York Times editorial instead.

Lem said...

But for most adults, it is more feared or revered than understood.

Algebra is the religion of peace.

Astro said...

Bob Ellison said...I hope the "any computer" comments are all sarcastic. Computers don't do algebra.
Apparently Bob, you've never heard of Mathcad, or Mathematica.
With either of these software packages installed on your computer you can type in an algebraic equation and the software (your computer) will solve it. Both have been widely available since the early 1990s.

Michael K said...

"
Is this moron/troll unaware that the movie 'Stand and Deliver' is a true story? That 'dropout' kids were capable of learning calculus, in high school?"

We know it is a true story but the polisci majors don't.

We have a developing tragedy in our inner city schools. There are kids who are capable of learning English and math who will never learn those subjects because racist lefties think they can't.

The City Journal articles about discipline and about curriculum point out that increasing numbers of black African and Caribbean immigrants are taking advantage of US policies that favor blacks and are intended for people who will never qualify.

I've met them myself. Some are my students. Black abortion rates suggest that self immolation may solve the problems. Middle class blacks are moving to the suburbs and the South and those remaining in the inner city seem to be killing each other and aborting the rest.

Unknown said...

“citizen statistics.”

Doesn't that just scream indoctrination!?!

Michael K said...

"With either of these software packages installed on your computer you can type in an algebraic equation and the software (your computer) will solve it. Both have been widely available since the early 1990s."

Do you understand that the person entering the equation has to understand it ? Did you ever do word problems in algebra to learn how to reduce a question to an equation ?

Jesuzzzz !

bagoh20 said...

I use and need algebra pretty often in my job and just life in general. I have paid dearly for not learning it well. Recently, it got to the point where I went on line and started learning what I didn't have a good grip on so I could be more effective. It's really useful since most questions involving numbers can usually be expressed as a word problem and a simple equation.

Very few statistics are beyond the reach of politics and it's biases. A valuable thing for people to learn early is how cons are run at both the micro and macro level. Learning how you can be used or manipulated by others is probably more valuable to people than just about any other single subject.

After that, learning how you can con yourself is next most valuable.

Of course, if people were educated in these things in high school they would probably avoid a lot of college.

Quaestor said...

Astro, don't think to advise Bob Ellison on software, and what makes it go. Just don't ok? It's like a buggy driver lecturing Karl Benz on automotives.

Lem said...

yashu @ 9:24

Quaestor said...

Attention Astro:
Read and be wiser.

Freeman Hunt said...

Nightmare world. Nice to read these comments and awaken from that dream.

Freeman Hunt said...

People who don't know what math is have ruined math for children.

Original Mike said...

Yeah, let's replace algebra with polysci. Wow.

Alex said...

Whatever happened to the idea of excellence?

What about basic competence? Expecting excellence of everyone is unrealistic. At the very least I want my fast food order taker to get the basic arithmetic correct.

Sayyid said...

Sorum: "Don't probability, statistics, and computing the CPI all use algebra?"

Yes. Thread winner for being the first person to point this out.

OP: "It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted"

Good luck understanding what mathematical weighting is without knowing algebra. Students would stare at the teacher wondering where the scales are.

Alex said...

Wow - with that attitude we'd be stuck in the Middle Ages. No computers, no MRI machines, no smartphones.

Alex said...

Engineering relies on calculus which is built upon algebra.

*THUD*

acm said...

But, if the kids don't learn algebra, then their souls won't enter their bodies (why yes, I am thinking of Philip Dick's "The Pre-Persons").

Clearly, Dr. Hacker didn't learn Dick when he was at school.

ad hoc said...

The reasons for learning algebra go beyond the fact that it's an essential foundation of mathematics; algebra is the beginning of using math to problem solve - using variables to represent numbers, understanding relationships to set up equations.

The idea that this is too hard to learn, so why bother teaching it is truly sad.

Levi Starks said...

If you could time travel back into the middle ages and the one thing you chose to take with you was a good working knowledge of modern mathematics, you would either rule the world, or be burned at the stake.

AndyN said...

...and include discussion about which items should be included and what weights they should be given.

I'm shocked - SHOCKED - that a polisci prof would want to reduce the rigor of the math curriculum and then encourage the students who've been allowed to neglect that part of their education to believe they have some valid input into how math is used in the real world. It's almost as if he's hoping that once fewer people understand how numbers relate to one another it'll be easier to convince them that his opinion of what numbers mean is actually fact.

Fen said...

NYTs Elites: "Can't teach the proles Algebra! They might wander off the work farm!"

O2BNAZ said...

The left has no use for a literate society...

Mark Nielsen said...

Well, I'm late to this thread. But as a Mathematics Professor, I thought I should chime in. However, there's nothing I could say that would much improve on
Quaestor's 9:42 comment. So maybe I'll just leave my contribution at recommending you go reread that. Pure gospel.

Pogo said...

Public schools have ruined reading and math, through Whole Language and Whole Math and a thousand other fads.

Now, due to their accumulated failures, they want to do away with math altogether, blaming the very subjects themselves for their inability to teach them.

They are Dada-ists of education, scrawling their mark on a urinal (for they cannot write or spell) and calling it graduation.

crosspatch said...

This sounds to me like an article designed to lay the groundwork for rationalizing "Education for Sustainable Development" which holds that people with a lot of education demand lots of "stuff" which increases their carbon "footprint" and is "unsustainable". People with little education live more simple lives, don't demand so much and are more "sustainable" to manage in large populations. Plus they just believe the bull you feed them.

This looks to me as a way to rationalize to the masses the elimination of math education but smells to me like it is coming from one of those "Sustainable Development" lefties.

Gene said...

Dan Jelski: People will get jobs doing things that computers can't do. Your telephone can do algebra better than you can. Why are you wasting your time?

Your cell phone does algebra? I have a smart phone but it's not that smart.

Unknown said...

Astro said..."Apparently Bob, you've never heard of Mathcad, or Mathematica.
With either of these software packages installed on your computer you can type in an algebraic equation and the software (your computer) will solve it. Both have been widely available since the early 1990s."

Indeed, Astro? And without having learned algebra, how would one know how to write an equation for the computer to solve in the first place?

Ignorance is Bliss said...

About 10 years ago I was doing a home improvement project that involved cutting a new doorway from the house to the garage. I had cut away the drywall and removed the studs that would be in the way. This left me with a slightly larger opening than needed. In order to figure out the spacing for the new framing I took out a pencil and started adding, subtracting, and dividing. My daughter, who was about 8 at the time, came over and asked me what I was doing. I said I was working on the doorway. She said Oh, I thought you were doing math.

That's what we call a teachable moment. She's now an engineering major at a top school, about to start her junior year, with a full tuition merit scholarship for the next two years.

Gene said...

I think Andrew Hacker's real goal here is to reduce the black-white achievement gap. It drives educators nuts because they can't figure out how to make it go away. Their current plan is to make education so easy everyone gets an A. Voila--no achievement gap.

Paul said...

So the failed state school system now says Algebra is 'hard' and, well, unnecessary?

No wonder Johnny can't read (or even add.)

yashu said...

[A]s a teacher myself who has to deal with many stupid-thinking bright young minds who spout "everybody says" crap, let me testify that it is the practice in abstraction that eventually liberates the mind to think - to allow youth to make their own models and comprehend a series of complicated steps that take one from a problem to a solution.

Well said, wef. And Quaestor @9:42 and others too. Even if a student never has reason to use e.g. the binomial theorem after graduating from high school, to learn algebra and geometry is in a very fundamental way to develop one's ability to think and reason, to exercise oneself in thinking and reasoning independently, rigorously, and at a high level. As opposed to depending on and regurgitating conventional wisdom and sophistry.

Levi Starks said...

Cell Phone doing Algebra? I have a trig app that I use all the time at work to solve work problems. but I still have to punch in the correct variables.

Michael K said...

"Recently, it got to the point where I went on line and started learning what I didn't have a good grip on so I could be more effective. "

There is an excellent book called Forgotten Algebra which is a great refresher after many years. She also has a book called Forgotten Calculus, which is just as good. I went back to school at age 55 and it was a great help.

For kids who were never exposed, I don't know what to say. The welfare office is just around the corner.

kimsch said...

And I'm actually glad for this refresher in algebra (first learned in 9th grade many years ago) because The Little Guy will be entering AP 6th grade next month and will have pre-algebra and algebra. I'll be able to check his work.

I've done some of my homework for this course in Excel and some by hand. I do it both ways for a couple of reasons. One, I can check my hand work with the Excel and check my Excel work with the hand work. Doing it both ways also helps to "get" it.

One can put all the steps into Excel or one can use the formulae that Excel has built in. Running the problem through all the steps by hand helps to understand how the formula in Excel works.

Way back in High School I also took a course in bookkeeping. At the time, I thought that course was more valuable than algebra because it taught how to balance a checkbook. I still think it's important to have a course that teaches personal finances in high school, but I also think that algebra is very important - even in personal finances...

I'll have to post this article and see what my classmates and Professor have to say about it.

Two more classes and I'll have my MBA. Accounting starts Tuesday and after that is Economics. More math. More algebra.

Yay math! \o/

wv: melayee

LakeLevel said...

Oh brave new world that has such idiots in it. Manhattan, Los Angeles and Chicago have become Huxley's brave new world.

Carnifex said...

The comments from Dan Jelski and his ilk just prove that P.T. Barnum was right all along.

Tell ya' what Danny boy, you're right. Algebra, science, math, all that hard "thinking" stuff? Don't let your kids learn it. Put your money where your mouth is, or shut the fuck up. Better yet, just don't reproduce. The IQ of the world will thank you.

Although speaking as a carpenter with over 4 decades of experience, I couldn't do shit without the Pythagorean Theorum. And that's just 1 instance of math used for practical purposes.

MMASRP63 said...

"Mathematics is the language of nature." --Max Cohen in the movie Pi.

One of my friends is a high school chemistry teacher. She has students in her classes who haven't learned the required algebra. These students are unable to understand concepts like pH that are defined in terms of logarithms.

Students who don't learn algebra may be able to achieve competence in biology (though they'll never understand even simple concepts like the Hardy-Weinberg Theorem).

These same students will never be able to learn more than the most basic chemistry.

Finally, these students will find physics to be utterly incomprehensible.

The fact that the vast majority of people, even those in professions that involve science and engineering, may not use algebra on a daily basis has absolutely nothing to do with the far more important fact that crucial scientific concepts are defined mathematically and cannot be truly understood independently of math. Once understood, the math can often be ignored, but one shouldn't overlook the fact that the math is always implicitly there.

Prof. Hacker's suggestion would produce students who are incapable of even beginning to understand the world.

kimsch said...

A great place online for refreshers is Khan Academy and the best thing is: It's Free!

Lem said...
This comment has been removed by the author.
AndyN said...

Ignorance is Bliss said...

I said I was working on the doorway. She said Oh, I thought you were doing math.


Summers during college I worked for a commercial drywall company. I'm not sure why this one example sticks in my mind, but there was this one framer I worked with who never used a square when he was laying out walls. He just used the Pythagorean Theorem to make sure he was keeping his right angles true. I'm positive he didn't have any formal education beyond high school, nor did he need it to do a job that he enjoyed, but if he'd gone to a school where even the "smart" kids were discouraged from taking algebra, he'd have suffered for it.

The same is true of most people I know who work in trades. Electricians, plumbers, masons frequently need to know more math than you'll learn if you stop before you get to algebra. It's just sad that any professor would think we should be sending kids to college with less math knowledge than they'd need to progress beyond being unskilled labor on a construction site.

kimsch said...

Andy N.

To find if a corner is square without using a square the formula is easy.

Measure 3 units down one side and four units down the other side of the corner. If the square is true, the diagonal will be 5 units of measurement.

The 3-4-5 rule.

Portia said...

Astro said:
Apparently Bob, you've never heard of Mathcad, or Mathematica.
With either of these software packages installed on your computer you can type in an algebraic equation and the software (your computer) will solve it. Both have been widely available since the early 1990s



The stupidity, it burns.

MadisonMan said...

How can a person who apparently doesn't understand math -- like Dr. Hacker -- argue about its worth?

I wonder how much he was paid for the op-ed. Too much, I'll wager.

Penny said...

It's like everything else.

Twenty percent of the people cause eighty percent of the problems.

The only reason that's KILLER to our country, is government regulations, and laws that have not only outlived their usefulness, but have now begun to destroy us.

Penny said...

And on a micro note...

I don't care if your kid doesn't want to learn math if you don't care that my kid will grow up to make more money.

Mimi Black said...

Shouldn't be, but am - amazed at the number of mentions of gender in the comment thread, and I find it very interesting that the insults are toward the gender that the said professor is NOT; so much for logical criticism.
The education system set a course for failure in the 60's when college became a rite of passage for being judged a "worthy adult", and it's gotten more ridiculous every year after, I think the singularity will be here soon. Who should go to college? How about people who want to study a subject because they want to study a subject. NOT every single kid, just because it's a status symbol. How many kids have gone to college in the last 5 decades JUST BECAUSE? And now we have Bachelor Degrees with low self-esteem issues because they are flipping burgers, and they actually think that flipping burgers is "BENEATH" them. WHO made them believe that an honest day's work is BENEATH anyone? SOMEONE did, they weren't born believing that. So they are taking jobs that someone could use who might actually take pride in their work. (I'm sorry guys, but if a job is "BENEATH" you, then what exactly do you think of people who do have that job? And do you honestly believe that only smart people go to college, and that anyone who did not get a degree is not as intelligent as those who did?) This entire country, and a lot of the world, has become a fishbowl of ignorant arrogance, and the dumbing down of academics is the most obvious symptom, never mind the oppression of peasants thing that most people seem oblivious to. (According to Yuri, that was already accomplished.) Another obvious symptom is the lack of ability of college graduates to discuss a subject without using personal insults and stupid sexist connotations that show a childish disdain for an entire group of humans. Everyone needs to GROW UP for God's sake, before it's too late, it's TIME.

Seven Machos said...

Three weary travelers stop into a hotel for the night. The room rate is $30, so each chips in $10.

The next morning, the general manager realizes that the travelers have been overcharged. The rate for their room is $25 per night, not $30. So, the general manager dutifully sends up a bellhop with five dollars to give to the travelers.

On the way to the room, the bellhop decides that giving the five dollars to three people equally is too complex, and so he gives each traveler one dollar and pockets the other two dollars.

Now, each traveler paid nine dollars. Nine times three is 27. So the travelers paid $27. The bellhop kept two dollars. That's a total of $29. But the travelers originally paid $30 total.

What happened to the missing dollar?

kimsch said...

But they didn't pay $9 each. They "paid" a total of $28. ($30-2) so each paid 9.33333333 to $28 and the bellhop made off with the $2 extra.

Seven Machos said...

Kim -- That is not correct. They did pay nine dollars each. Back to math class for you!

MMASRP63 said...

Seven Machos, you managed to stump me for more than a minute. Nice!

The way you wrote the problem is designed to trick the reader. The travelers originally paid $30, but after receiving part of their money back they paid $27. However, the amount of the bill is $25. The $2 difference between these amounts is what the bellhop pocketed. The appearance of $30 towards the end of your riddle is a red herring.

Thanks for the fun.

Saint Croix said...

There is no missing dollar. Each traveler was supposed to pay $8.33. Each paid $10. So each one was overcharged $1.66.

The bellhop gave each one a dollar and stole 66 cents from each traveller, for two dollars total.

Carnifex said...

@Kimsch

Okay show off, tell me whose portrait is on the .03 specie?

:-)

If ya get it right, I'll send ya $15 in new minted $3 bills. :-)

And while 3-4-5 is great to know, you are not always presented with such fine easy numbers in construction. I always made guys under me learn a square + b square = c square. They bitch at first, but appreciate later on.

Plus don't forget the golden ratio...something I always tried to incorporate when I designed something.

Seven Machos said...

MMASRP63 nails it. Good work!

It's really the sneaky properties of arithmetic, though, which, incidentally, algebra can really help you understand.

Lem said...

I have a suggestion for commenter yashu... please add an image to your profile to make it easier to spot you.

I'm lazy.. I dont read every comment.

I'm not an indiscriminate reader.

Seriously ;)

Erika said...

Algebra is hard? Whaaaa? I'm not gifted with natural math ability and I earned an A in algebra in the seventh grade. If I listened to the teacher while he explained things, did my homework every day and asked for help if I was lost, it was basically effortless to keep up. It's never occurred to me to think of algebra as hard!

allison said...

I am the founder of a 501 (c)3 whose mission is to help teachers, parents, and schools prepare children for algebra, so I might be considered biased or knowledgeable, depending on your point of view.

the reason algebra is now too difficult is because in the US, we have watered down the arithmetic in grades 3-8 so much that it has no difficulty. that happened in the textbooks, and in what teachers are taught. Basically, elementary educators do not understand how arithmetic works, let alone fractions and decimals. Their textbooks are riddled with errors, their professional development in mathematics nil.

Parents should be afraid, very afraid. the nominally high performing school is no better at the standard algorithms or equivalent fractions than the impoverished schools. If you do not learn math at home, you will not learn it period.

We are throwing kids off the ramp to successful tech jobs in 4th grade.

to plug my nonprofit:
www.msmi-mn.org

Palladian said...

The value of the study of a subject does not necessarily lie in the utility of the subject. Studying and attempting to master a subject such as algebra helps teach people how to think; it's training for the mind, as well as a useful tool.

I teach my college freshman drawing and painting classes with the same idea. Many of my students are studying graphic design or advertising and will likely never make rigorous graphite pencil studies of human anatomy again. The value of these lessons and exercises is that they teach my students the value of mental discipline, how to observe things, the manual dexterity necessary to translate observations into descriptive drawings. I also hope to spark an interest in the machinery of the human body, the beauty and mystery of form, a curiosity about science, and so forth

The job of a teacher is to help students realize that every rigorous subject strengthens the mind, and that a strong and curious mind is necessary for true freedom, true happiness and success in life.

That your computer can do something "better" is not the damned point.

Palladian said...

Okay show off, tell me whose portrait is on the .03 specie?

A shield within a six-sided star was on the first one, and Liberty was on the second.

If ya get it right, I'll send ya $15 in new minted $3 bills.

I'd prefer 5 of the US three-dollar gold pieces, if you don't mind. Email me for my mailing address.

kimsch said...

OK Seven, I see from MMASRP63's explanation what I got wrong. Math on the brain. I've been dreaming equations and inequalities and word problems. Final tomorrow.

Carnifex:

Math is beautiful. Golden ratio, Fibonacci sequence, nines.

9 x 1 = 9 and 9 = 9
9 x 2 = 18 and 1 + 8 = 9
9 x 3 = 27 and 2 + 7 = 9
9 x 4 = 36 and 3 + 6 = 9
9 x 5 = 45 and 4 + 5 = 9
9 x 6 = 54 and 5 + 4 = 9
9 x 7 = 63 and 6 + 3 = 9
9 x 8 = 72 and 2 + 7 = 9
9 x 9 = 81 and 8 + 1 = 9
9 x 10 = 90 and 9 + 0 = 9
9 x 11 = 99 and 9 + 9 = 18 and 1 + 8 = 9
9 x 12 = 108 and 1 + 0 + 8 = 9
9 x 13 = 117 and 1 + 1 + 7 = 9

and so it goes.

You can do nines on your hands too. Hold your hands out, backs up with thumbs toward each other. Bend down "one" (your left pinky), you're left with nine digits. Now raise the pinky back up and bend "two", your left ring finger. You have one up on the left and eight to the right. 18. Try with "three", you have 2 and 7, 27. It works all they way across. Cool trick huh?

wyo sis said...

Algebra teacher people how to think logically and strategically. It awakens the mind to possibilities. It makes no more sense to stop teaching algebra than it does to stop teaching literature. They are both about much more than they first appear. Imagine not being able to find or articulate relationships. It would be like not being able to read. Or being able to read, but not understand what you read.

Carnifex said...

As a child I saw how Chinese children counted on their fingers...way better than ours. Index- pinkie right hand is obviously 1,2,3, and 4. The right thumb is 5. Hold up an index finger and the thumb you have 6, and so on till you get to 9.

After 9 you hold up the left index finger...that's 10. hold up all four fingers of the left hand and you have 40. the left thumb is 50. So with 2 hands you can count up to 99.

Carnifex said...

@Palladian

No, I promised crisp new minted three dollar bills and I meant it.

Or I can send a nine and a six. It's up to you

(should made it 12, it divides up better 3 4's, 4 3's, 2 6's, 2 3's and a 6, 1 8 and a 4. damn!)

Seven Machos said...

What happened to the good old days when our kids used to sing songs about the Greatness of Obama?

techsan said...

Mr Hacker...way to set the Expectation Bar for our kids about knee high.

beast said...

Pretty much every degree in the College of Arts and Sciences at all seven of the colleges and universities I attended required exactly ONE algebra course to matriculate.The ones that didn't were the funny ones like Hard sciences and Mathematics itself.In the College of Business they had those Finance,Quantitative methods and Statistics courses.And the College of Engineering-let's just say I have something on the order of 75 Math related hours up to Partial Differential Equations.Strangely I've never viewed my sisters journalism degree as quite as rigorous as mine.Nor my other sisters ED degree(she had to take one quarter of calculus)-and she is a High school Math teacher.Reminds me of what my Dad said when I found out my sister was going to a fluffier state university to study English or such.He said"What, you think she can pass freshman calculus?".
Several years later we took the same Microeconomics course -she dropped after being unable to comprehend supply and demand curves.I passed with a perfect grade.

Steamshovel Operator said...

er....ah....uh....

avwh said...

California tried to make a high school diploma more rigorous a few years back. Required a test to graduate; the math level was what most college-bound kids would take in 9th grade, so any legit college-bound kid would have no trouble with this exit exam.

But the hand-wringing liberal local newspaper ran a story, about how heart-wrenching it was for those kids who had family expecting to go to their graduation ceremony, but the kid hadn't passed the test, so wouldn't get a diploma. The story had many quotes that said the only fair thing to do was give them the diploma anyway, whether they'd passed or not.

This dumbing down of the math requirements reminds me of that. That episode also was when I realized the liberal press would sell us down the river in a heartbeat for their mistaken and misplaced "compassion".

Carnifex said...

Early reporting here ans off topic(well it could be construed as on topic) A new report released by NOAA states they have over estimated the warming of the surface temperature by 3 times. The NOAA admitted that in every case when temperature readings in sites that didn't have dryer vents blowing on them etc. differed from those sites that did have artificial warming factors, the always, ALWAYS went with the aryificially inflated temperatures. These differences meant that the temps taken with good data were then multiplied by 3. The new NEW data suggests that the earths surface as been warming at about 1/10 of 1 degree per decade. Better get that sunscreen on!

Ain't science wonderful... when it doesn't have an agenda.

RAUF ARSHAD said...

It is hard to slove Algebra questions but they are constantly repeated in exams .

Sportsunplug.com

yashu said...

There's no appeal to authority, reliance on expert opinion, or ad hominem argument in algebra. You have to prove things for and to yourself. Can't have kids learning to think like that-- we need to make "informed citizens" (well-indoctrinated subjects) out of them instead.

(Aw Lem, thanks for the suggestion; I'm flattered and I'll consider it. I scan profile images when skimming through threads too-- useful to spot commenters and also to skip over them.)

Revenant said...

Before we discuss replacing algebra as a requirement, I'd like to hear more about what it is being replaced with.

virgil xenophon said...

The really ironic deal is that when one opens up a cover of the APSR (American Political Science Review) the inside looks like a mathematics/statistics text. Given the fact that the "Quants" have dominated Poli-Sci for the last 50 years--especially the gatekeepers of peer-review for the APSR--one wonders exactly how Dr Hacker ever got his PhD in Poli -Sci w.o. doing some serious math..

fivewheels said...

I strongly suspect that Gene has it right. Hacker might be protesting too much when he says it's "an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white." (Asians of course not mentioned.)

The proposal seems too stupid on its face to be sincere, without an ulterior motive.

Wren Bastol said...

I wonder why the Pacific Rim countries are all snickering behind their hankies at Hacker's remarks.

It appears Paul Krugman has sudden and fierce competition for the title of The Western Hemisphere's Most Overeducated Cretin.

rhhardin said...

As a child I saw how Chinese children counted on their fingers...way better than ours.

Use gray code and you can count to 1023.

Only one finger moves at a time as you count, is its point.

grackle said...

Two somewhat differing opinions:

Algrebra is not in the least bit difficult.

Algebra is not hugely difficult if you do the work to learn it day after day as the lessons progress. Unless you are highly gifted, it's damn near impossible if you don't.


Had trouble with algebra. Have always had trouble with math courses. Managed Cs at the college level by working very hard. However, I made mainly As in statistics and research techniques, both of which involve significant algebraic content but both of which were subjects that were extremely interesting to me.

Due to my family situation my education first through tenth grade(when I dropped out) was extremely chaotic. I changed schools a total of 8 or 9 times at four different schools – several times in the middle of a school year. Back and forth, back and forth. Subjects other than math, such as history or English literature, were easy for me. I could change schools, get my new textbooks and be caught up by reading them within a week or two. Also, that was back when our schools were still pretty good.

Someone mentioned logic. I LOVED logic! Did not expect to. Took logic at the university from a terrific teacher. Aced the course. Don't ask me why college level algebra was hard but logic seemed easy.

All 3 of my children were good to excellent in math, especially the youngest who began avidly reading books on analytical and Euclidean geometry at age 11. Nothing but As in math courses(and most other subjects). He now works in computer security for a large corporation. All three had stable educational experiences. All three are successful and thriving in their occupations.

I think math must be learned in a certain sequence because each new concept is built upon a preceding concept. You get any of that out of order and there are learning problems unless you are one of those gifted with a high mathematics aptitude.

Like some of the other commentors I think the author of the article is full of crap.

PLC said...

Ann

A good comparison would be to Tim Gowers's post "How should mathematics be taught to non-mathematicians?"

DEEBEE said...

And we can do away with English, since most people speak it anyway. Perhaps replace it with the Annals of Community Organizing.

We should be able to replace social studies since most of that stuff is about way back that has no chance of happening again.

And the Constitution is a living document and will catch up with modernity by the dint of our judu=icial system.

jaed said...

So: does this proposal stem from simple ignorance and stupidity, or is there an ulterior motive behind the suggestion to dumb down Americans by removing cookbook algebra from their education?

I can see it either way, but the multiple references to political shibboleths make me suspect the latter. (It's so much easier to rule proles if they're kept too ignorant to ever mention any inconvenient facts.) But it's possible I'm being too cynical.

Curious George said...

Algebra is a lot easier than learning Chinese

FleetUSA said...

Algebra has been taught to the educated for almost 2,000 years and should continue so.


However, there is a place for those not capable. It is called VoTech and attendees shouldn't be ashamed to go there as they might make more money than a college grad.

Joe Schmoe said...

Interesting piece. The author makes an assertion that high dropout rates in high school and college are due to kids failing at math. I think that's a pretty glib leap, and he doesn't provide compelling data to support it. He argues that dropout rates would go down if we revised our math courses, and more kids who are talented enough in other areas would complete school.

I don't necessarily buy his point that getting rid of algebra will suddenly eliminate high dropout rates. I am, however, sympathetic to the idea that kids just aren't that engaged with school overall.

Bob Ellison said...

Astro, you're right, and I should have been more precise. I remember the challenge in algebra as defining the equation in the first place.

This is what I mean when I say that algebra is important, because it teaches people to consider how and whether problems can be solved in the first place.

MadTownGuy said...

If you want to see what it would look like if we follow this course, look to what's going on in Argentina.

Craig said...

Try to balance a chemical equation without using algebra.

Robert Cook said...

I'm late to the party, so to speak, but this is ludicrous. If anything, we need to make schoolwork for our children more rigorous.

I say this as one who never enjoyed math and had no innate aptitude for it; I squeaked through Algebra with a "C" average and had an even harder time in Geometry. (I think Geometry, in retrospect, was probably easier than algebra, but my absolute disinterest in the subject mitigated against my ever really studying or learning the material.)

I regret my poor grounding in math and wish I had the opportunity to go back to my youth and kick my own ass to work harder at the subject!

It is this constant, incremental dumbing down of schoolwork by pedagogues trying to be "helpful" that has led to legions of high school graduates being functionally uneducated.

Robert Cook said...

I should add I never took another math class after Geometry; I have no idea what the inside of a Calculus textbook even looks like!

Joe Schmoe said...

The author loses me when he says, and I paraphrase, "solving (an algebraic equation) doesn't lead to better political opinions or social analysis."

Guh. Here he exposes his inner prog core. I don't think we need more political opinions or social analysis. Here he strongly hints at the idea that progs are empirical, and if more people were better at statistical empirical analysis, they would indubitably become Democrats.

Wrong, jackass. There are lies, damned lies, and statistics. It might be useful to use social analysis and political opinion to forensically explain something that's already occurred, but to use it to prognosticate or implement social engineering is useless and harmful.

We don't need more people manipulating statistics to try and create our utopian state. We need more people who want to work, to better themselves through their work, and in the process lift up the others around them. We don't need more academic desk jockeys like this guy.

Robert Cook said...

Or Trigonometry.

Pogo said...

Andrew Hacker is why Idiocracy is America's fate.

Astro said...

Bob Ellison said...Astro, you're right, and I should have been more precise. I remember the challenge in algebra as defining the equation in the first place.

This is what I mean when I say that algebra is important, because it teaches people to consider how and whether problems can be solved in the first place.


Thanks for your response, Bob -- Astro.


So:

Unknown said... Astro said..."Apparently Bob, you've never heard of Mathcad, or Mathematica.
With either of these software packages installed on your computer you can type in an algebraic equation and the software (your computer) will solve it. Both have been widely available since the early 1990s."

Indeed, Astro? And without having learned algebra, how would one know how to write an equation for the computer to solve in the first place?


Michael K said..."With either of these software packages installed on your computer you can type in an algebraic equation and the software (your computer) will solve it. Both have been widely available since the early 1990s." Do you understand that the person entering the equation has to understand it ? Did you ever do word problems in algebra to learn how to reduce a question to an equation ?
Jesuzzzz !


Portia said...Astro said: Apparently Bob, you've never heard of Mathcad, or Mathematica. With either of these software packages installed on your computer you can type in an algebraic equation and the software (your computer) will solve it. Both have been widely available since the early 1990s

The stupidity, it burns.


Unknown, Michael K and Portia, you can all go suck wind. Yeah, the stupidity. It burns.

Fernandinande said...

If everyone graduates from high school, then graduating from high school doesn't mean anything.

There should be more math required and fewer high school graduates, and far fewer college graduates, especially people in fields like political (pseudo)science.

"But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar."

Too bad for them: potential fast-food servants have the same problem. The poets and philosophers shouldn't have their useless hobbies subsidized by the state anyway.

Cato Renasci said...

How the f*** can anyone understand how to calculate the CPI without basic algebra?

No one should be permitted to obtain a bachelor's degree without demonstrating competence in first year calculus.

Bob Ellison said...

Well, great, Astro, now you're [succeeding in] making me look like a serial plagiarist! But I swear I didn't read, copy, paste, and then edit Unknown's remark!

I think you're being a bit harsh. Let's all agree that algebra is difficult for some people, and have a cookie.

Balfegor said...

This is simply atrocious. Honestly, someone who cannot grasp basic algebra seems to me less than fully human.

Ken Prescott said...

I'll provisionally accept his proposal if he accepts the following proposition:

Voting machines shall require the following to unlock the vote function:

1. Depositing the equivalent of 1 troy ounce of gold in US currency;

2. Solution of a differential equation.

Solution of the equation unlocks the voting function and refunds the voter's money. Incorrect answers result in the government keeping the money and no vote being cast.

Deal, or no deal?

Tibore said...

"... I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.”"

Leave it to a PolySci professor to want to politicize math.

If he'd restricted his criticism to the notion that math should be taught in a more practical way, with an eye towards reflecting how quantitative problems manifest in the real world, then I'd agree with him. Not strenuously, since there's also something important to be said for the abstraction involved in teaching math: Being able to abstract and go beyond what the real world shows in all its complexity is what has allowed humanity to understand basic concepts about our universe. But still, I'd agree in principle, and leave the messy details to be haggled over later.

But I'm not sure that's what he's getting at. His sentence "Being able to detect and identify ideology at work behind the numbers is of obvious use" reads straight out of a leftist deconstructionalist worldview, and reads as yet another instance of academic "my numbers are better than your numbers" argument. I feel less that this professor's point is less about decreasing practical innumeracy and more about politicizing its application. It's an easy thought to have, given that such actions are par for the course for far too many modern academics.

It's up to him to demonstrate that his purpose is to genuinely create a more numerate society, even if it contradicts academia's general leftist worldview. Just saying one's purpose is benevolent is lip service, nothing more.

Hagar said...

Sounds like this guy wants advanced mathematics taught without basic arithmetic and beginning algebra being taught first.
Good luck with that!

Crimso said...

"Before we discuss replacing algebra as a requirement, I'd like to hear more about what it is being replaced with."

With Citizen Algebra, comrade! Algebra is clearly a tool for oppression of those less fortunate. Citizen Algebra will result in equality ("inequality?")for all!

Robert Cook: I disagree with you on a lot of issues, but you're quite correct (I don't dare use the word "right"). If you're ever looking for something to stimulate your mind, do try calculus (you will have to work up to it). It is a different philosophy of math than that which precedes it, and it is exquisitely beautiful and enormously powerful.

For those who have suggested vocational tech and/or industrial arts so as to avoid the math, you've obviously never built a house.

CharlesVegas said...

I agree with crosspatch. This is just the Elites trying to keep the proles docile and stupid and willing to accept their Enlightened solutions (i.e., Edicts).

rhhardin said...

In 7th grade I thought algebra was really interesting, from a simple tip.

In the 8th grade when they started teaching it, it pretty completely killed off my interest.

The tip was, if A=B, then A+something=B+something, and you could add somethings to each side until the variable you wanted was alone on one side, and the answer would then be on the other.

This was so cool, compared to arithmetic.

When they started teaching it, this never came up. Instead you got rules, like change the sign of anything you move from one side to the other. The contact with reality was lost.

Scott said...
This comment has been removed by the author.
Crimso said...

A bonus of Citizen Algebra is that by using it, you can prove that taxing the rich their fair share will balance the budget.

Freeman Hunt said...

Rh sums up the problem with school math. They teach math as if it were a list of rules to memorize.

Peter said...

“You peasants don't need math to understand ObamaCare or climate change. You only need to be able to read the The New York Times.

And how many New York Times reporters could pass a reasonably rigorous algebra exam? Let alone one in basic statistics.

Consider (for example) the NYT article that proclaimed that the average temperature in Alaska had risen by seven degrees [Fahrenheit] in the last thirty years.

To get the number in the first place, one has to cherry-pick the data- which anyone who had the most basic competence in statistics would realize was a no-no.

BUT it’s followed by the idiocy of proclaiming that Alaska is “xx percent” warmer- apparently without realizing that the “percent warmer” number depends on the units (it would have been a larger percentage if they’d used Celcius). And what if the temperature had increased from zero degrees F to 0.01 degrees F- would that be an infinite increase?


So, perhaps the NYT should concern itself with whether its editorial staff is mathematically competent before trying to further dumb down the public schools.

Peter said...

"Hard America, Soft America: Competition vs. Coddling and the Battle for the Nation's Future" by Michael Barone explores this in some detail.


"America is divided into two camps, according to U.S. News and World Reports writer and Fox commentator Michael Barone. No, not Red and Blue, though one suspects Barone may taint the two groups in the hues of the 2000 presidential election. Barone's divided America is one part Hard, one part Soft. Hard America is steeled by the competition and accountability of the free market, while Soft America is the product of public school and government largesse." -- from the review by Steven Stolder.

Roger J. said...

I see Palladian is also a numismatist--the US has minted many coins and gold pieces that have seen only limited circulation--for example the "trime" a three cent piece in silver designed to pay for stamps. The problem was it was very small. And the US experimented with a four dollar gold piece (the Stella)--a beautiful coin but never went into circulation as far as I know.
Good job Palladian--coinage tells a lot about our society. The St Gaudens gold pieces, along with the standing liberty quarter and the 50 cent piece were beautiful coins. The St Gauden's double eagle is the most beautiful coin struck by the US.

Roger J. said...

I have always enjoyed mathematics--I really loved calculus but it got even better when I got to differential equations. The trouble with math, IMO, the higher you go in math the more it becomes increasingly abstruse (topology, for example) When you get into chaos and string theory, I am totally lost.

Matthew Sablan said...

I remember when I said algebra was hard, and my teacher just said: "So is life. Deal with it."

I dealt with it.

Bruce Hayden said...

To some extent, this all seems almost unfathomable, but a bit of bias here - my kid has a double major right now, including one in math, and that makes them the 4th generation (actually, my grandfather was a chemical engineer and artillery officer, and it was his sister who got the Master's degree in mathematics). But, that is higher math, and there is a good reason why it is often the major with the lowest work requirements, since truly abstract math is beyond a lot of people (where numbers can be almost non-existent throughout an entire semester of classes).

But Algebra? I can understand not learning Geometry or Trig, but Algebra is so fundamental to so much. When you hear that GDP grew by 1%, or we have an 8.x% unemployment, how do you understand that without geometry. Or figuring tips or whether you made or lost money this last year (since accounting is based on Algebra). Or figure your taxes (ok, you can use TurboTax, but it is a bit scary when the Sec. of Treasury uses it, fails to pay large amounts of taxes as a result, and is now helping to run our economy). How about commissions? A family budget? Comparison shopping in the grocery store? Gas millage? When to get an oil change? How long to get from point A to point B? And, yes, even how much to bill someone for your time or how much you should be making, given the time you work and what you are paid an hour.

This article is a bit scary to me. Algebra is a significant part of the basis for much of the basic competence to get through life in a modern society. Most of us use it dozens of times a day just getting by. It is scary that we have an entire, and apparently growing, subculture who mostly lack basic competencies in their every day lives as a result of this dumbing down of basic mathematics. Apparently, as Algebra becomes more important in life, less and less competence in it is required to be taught by our public school systems.

Matthew Sablan said...

Huh. When you put it like that, I never realized all the things I do with numbers that are algebra, just hidden behind mental tricks.

CWJ said...

So late, so late. Its easy to mock this Dr. Hacker, but such things have and continue to happen. For example, Geography in any rigorous sense of the word has pretty much disappeared from American K-12 education. Not sure why.

Rliyen said...

My family's Achilles Heel was math. Even with that fault, I looved Algebra. It made sense and was frikken easy for me.

Fractions, to this day, still beat me up and take my lunch money.

Bruce Hayden said...

I have been thinking about the idea above that you can get your answers to many of life's questions by using a computer instead of knowing Algebra. As noted in my previous post, I find this problematic. Nevertheless, I have envisioned doing a lot of those basic tasks on a computer (or, now, smart phone), and, yes, it may be doable. But, then, basic stuff will become like magic to those who use computers in such a manner. Imagine a tip program that takes your bill, and tells you what tip to leave. But, then, you would probably need to understand percentages as an input, so might have to have a selection of choices, such as 15%, 20%, etc.

I find this interesting because my first career was as a computer engineer, and my first computer science classes were taught in the math department when I was working on my math degree. And, for me, Algebra has always been essential to my knowledge of how to use computers. But, then, I started using computers, and programming them, long before their user interfaces were anything but crude in today's terms. Still, without understanding Algebra, you aren't going to be able to program - not that most computer users these days need to know much programming.

And, I will admit that I still program, though now mostly in VBA for Word and Excel. It is my hobby, and what I do to get centered again, just like others work in the garden or on their cars.

And, thinking of Excel made me think of how great spreadsheets are as an invention. You can think of them as a tool primarily designed to make using Algebra easy and efficient. Many think of them as a financial or accounting tool, but that is only because those applications are based on Algebra.

Michael K said...

"
Unknown, Michael K and Portia, you can all go suck wind. Yeah, the stupidity. It burns."

Do you really not understand why algebra is necessary to use mathcad ? Does someone smarter than you stand over you and tell you what to enter ?

I know where the stupidity is.

Anglelyne said...

July 1969 - this nation puts men on the moon.

July 2012 - this nation's paper of record tells its citizens that they shouldn't be taxing their children with basic algebra.

We lay down our harps and weep.

California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history.

If you don't have the intelligence necessary to simply pass three years of high school math, it's highly unlikely that you're intelligent enough for it to be worth your time, or anybody else's, for you to take up space in an alleged "institution of higher learning", acquiring a history degree.

Look, there's nothing wrong with the sort of vocational training Hacker describes as being given to Toyota factory workers in Mississippi. But what has that got to do with the millions of college students who can't master what even less able students were once expected to get through as freshmen in high school?

Nor will just passing grades suffice. Many colleges seek to raise their status by setting a high mathematics bar. Hence, they look for 700 on the math section of the SAT, a height attained in 2009 by only 9 percent of men and 4 percent of women.

What percentage of men and women in general does the good professor think should be in any college, in the first place? He seems to accept on faith that the current college racket isn't the gross distortion of purpose and waste of resources that it is. (Though a poli-sci professor would, wouldn't he?)

It'd be far too discombobulating to grapple with the real causes of poor student performance (some remediable, some irremediable). Best to just dumb things down for everybody. Heaven forfend that hick-ass, podunk colleges like Rice and Washington University demand some cognitive horsepower in their students. (Goodness gracious, whatever do people who don't go to the tippity-toppest universities need brains for, darling?)

Not to worry, China et al can carry the torch for mankind while we critically evaluate our idiocracy with non-quantitative statistics.

gregq said...

"It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given."

And how do we explain this "weighting" process, without using algebra?

What a buffoon!

gregq said...

For all the people saying "but my phone can solve that problem better and faster!"

Yes, that is true, so long as you've typed everything in correctly. If you understand how to solve the problem, then you have a chance of noticing if you screwed up, and got a wrong answer (i.e. What's the square root of 101? 10.something. If you accidentally type an extra 0 in the middle, you'll get an answer on 31.something. If you have a clue, you'll know that's wrong, and try again. If you don't, you'll screw up, and not catch it).

It's like spell check: it only does you much good if you know enough to know what the right answer should look like, and what are the potential mistakes (they're / there / their).

Shanna said...

Imagine a tip program that takes your bill, and tells you what tip to leave.

They've had those little tip cards forever, though, for people who can't seem to figure it out for some reason. I've never understood why that was difficult, but apparently some people find it so. Those aren't the people who should be making 'math education' decisions for the rest of us, clearly.

Shanna said...

If you understand how to solve the problem, then you have a chance of noticing if you screwed up, and got a wrong answer

This is so, so important. I use spreadsheets all the time to do math, but I need to know if it looks off because the spreadsheet won't give you a 'you did this wrong' notice. It just goes with the numbers you gave it.

Sunslut7 said...

Ann,
There is a very high correlation between ill-numeracy and poverty. The numerate are highly employable.Unfortunately, the ill-numerate are not.

Math skills are critical to an individual's survival in todays economy. it is the math majors who have jobs now. The humanities and social science majors generally do not.

If you want to flip burgers for the next ten years avoid developing your maath skills.ismaNe

Lonetown said...

Judging how the vast majority of IPCC "scientists" have modelled AGW, I'm pretty sure algebra is not being taught.

In fact its so weak I fear for science in the hands of these hacks and fools.

gerry said...

I don't think Obama can do Algebra.

That just seems so...true.

MikeR said...

Too much of this debate ignores the simple facts of reality. A considerable fraction of American youth are below average in intelligence. By definition, about half of them. They are not likely to benefit from algebra. They are likely to benefit from practical training in important skills. Make sure they know how to multiply, and to read competently. Shop class. Do not try to teach them algebra.

Another considerable fraction of American youth is above average in intelligence, again about half. Teach them algebra. For those that can, teach them calculus as well.

Deal with reality.

gregq said...

"A considerable fraction of American youth are below average in intelligence. By definition, about half of them. They are not likely to benefit from algebra."

EVERYBODY who wishes to be a functional member of society needs to understand algebra. You can not understand probability, or statistics, or the CPI, or pretty much anything else unless you can understand basic algebra.

Life in modern society requires you to understand and be able to use math. Deal with it.

Michelle Dulak Thomson said...

Peter,

BUT it’s followed by the idiocy of proclaiming that Alaska is “xx percent” warmer- apparently without realizing that the “percent warmer” number depends on the units (it would have been a larger percentage if they’d used Celcius). And what if the temperature had increased from zero degrees F to 0.01 degrees F- would that be an infinite increase?


"X% warmer" makes sense only in degrees Kelvin, because it's the only scale that has a non-arbitrary zero point. Of course, it does have the drawback that on the Kelvin scale even the most apocalyptic global warming predictions look trivial on a percentage basis.

Balfegor said...

Too much of this debate ignores the simple facts of reality. A considerable fraction of American youth are below average in intelligence. By definition, about half of them. They are not likely to benefit from algebra.

Look, I can see drawing the line at Calculus. Yes, maybe people who are of sub-average intelligence won't be able to understand Calculus, and they will have little need of it. Algebra is not that hard, though, and it's kind of important for anyone who expects to live an independent life in the modern world. If you're talking about someone who genuinely can't understand algebra -- not someone who was just badly taught by our abominable public education system, but someone who really lacks the basic mental capacity to understand algebra -- you're talking about someone who probably ought to be institutionalised. Maybe that's the bottommost 1% of the population. I cannot believe it's the bottom 50% of the population, in the United States.

Harrington said...

If you can read and know mathmatics, you can learn anything else on your own. There are any number of intelligent comments posted here, but Traditionalguy sums it up succinctly: "He is an idiot".

Big Mike said...

I guess Andrew Hacker would not have been voting for JFK after this speech.

Jose_K said...

Ortega y gasset. The reactionari author of Revolt of the masses (nan antiamerican panflet) , soerd by the defat in the cuban war said: que inventen ellos. That worked rally well for them

JAL said...

I wasn't going to bother to comment, but just wandered through older posts this evening (was out of town) and saw AA noted the nouveau algebra news.

I see the reactionary Althousians are ridiculing the wise educator.

So I shall pile on.

I use basic algebra regularly, in real life.

How else does one figure out an unknown which one needs to know when ... mmmm .... pick something really rare, like .... shopping!

Or when creating something which requires measurements some of which I may have to figure out? ("Mmmm "x" will be ....)

Basic geometry comes in handy in everyday real life, also. (How many square bales in a 4x5 round bale, while standing in a field?)

Shoot, forget algebra, now that we have all the electronic thigamigbobs which tell the cashiers how much change to give, and they go the fritz, the under 40 cashiers cannot figure out how to make change.

Given that all our electronic tools need to be *charged* ... it isn't a bad idea to have the basics -- and that includes Algebra I (and II) down.

The upside is the homeschoolers will eventually rule the world.

They can spell, they know where in the world Carmen San Diego really is, and they can do algebra.

manoj singh said...

Algebra is a major component of math that is used to unify mathematic concepts. Algebra is built on experiences with numbers and operations, along with geometry and data analysis. Some students think that algebra is like learning another language. This is true to a small extent, algebra is a simple language used to solve problems that can not be solved by numbers alone. It models real-world situations by using symbols, such as the letters x, y, and z to represent numbers.

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