Is Algebra Necessary?

New York Times ^ | July 28, 2012 | ANDREW HACKER

[reaganaut1]

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

[tiki]

I didn’t get it either but I could figure that out and there wouldn’t be any Xes or parentheses.

[BobL]

“well I live in a state with high taxes for property”

I hear you, I’m in Texas - we have maybe the highest rates in the country (although people in some other states pay more due to their property values).

But we don’t have an income tax, so I just lump all the taxes together and consider it the cost of living in the state.

[real saxophonist]

At GA Southern, first time I took Algebra I got a D. Second time, I got a B. Typical music major

I'm surprised no one has made this reference: Little Rascals/Our Gang

[Reily]

its really really unfortunate that creating kids isn’t as hard as raising them !

[cubreporter]

Awesome. What a great article. I bet kids learn under this man because he KNOWS how to teach!!! Those kids... all grades should get down on their knees and be thankful because they have someone in such an important subject who CARES...genuinely cares about them without all the “fluff” that it out there today. Besides... St. Ann’s was the name of the 8 year elementary school we attended as well. :) Thank you!!!!

[cubreporter]

Awesome. What a great article. I bet kids learn under this man because he KNOWS how to teach!!! Those kids... all grades should get down on their knees and be thankful because they have someone in such an important subject who CARES...genuinely cares about them without all the “fluff” that it out there today. Besides... St. Ann’s was the name of the 8 year elementary school we attended as well. :) Thank you!!!!

[taxcontrol]

I am of the opinion that there needs to be two math vectors. An engineering oriented track with the Algebra requirement and a business oriented track that focuses on structuring word problems, ratios, spreadsheets, accounting principles, maintaining a check register, calculating loans and interest, i.e general math topics.

Those that want to pursue an engineering degree can do so and those that want more business oriented path can also follow that program as well.

[Skepolitic]

This is just the academic version of “everybody gets a trophy”.

The curricula for engineering and real science disciplines require demonstration of college-level literacy. Is it really too much to expect that all bachelor degrees require at least high-school-level proficiency in mathematics?

If present trends continue, it won’t be long until it’s possible to get a PhD without understanding elementary mathematics like algebra. This is probably already true in some of the more dubious fields of study.

[muir_redwoods]

I needed both algebra and calculus to complete my MBA. It’s impossible to design an efficient assembly line, for example, without calculus. Statistics and probability require both algebra and calc as well.

[staytrue]

“Why do most of these students need math at all? All the fast-food registers do the math for them.”

I usually find that if my bill is $17.61 and I give the cashier $20.61, I usually get back my 61 cents in change and then get back an additional $2.39.

[LurkedLongEnough]

Amen, FRiend. Root cause: Teachers are the ones who should not be granted degrees for failure. LLE

[lonestar]

Can you even imagine having to teach kids to diagram a sentence today? They don’t think or speak in sentenses!!!

[Calvin Locke]

I stopped reading at this point.

"New York Times" is enough to cast doubt on the veracity of any column, particularly on the opinion page.

The are very few real "social scientists", even less competent and honest ones. The rest, >99.44%, are merely useful idiots.

[Lonesome in Massachussets]

Thanks, it reminds me of Feynmann’s complaint about mathematics textbooks when he was reviewer for the Berkley school department. One book, in particular, consisted of nothing but blank pages. When he called the publisher, she apologized and said that all the reviewers had been accidently sent blank trade show props, with the correct glossy covers. Yet some of the reviewers had already submitted favorable recommendations!

I hated high school math, and in freshman year in college we were taught by a Chinese TA who could barely speak English, and then not intelligibly. (I got 795 on the SAT math level II achievement test, but never did math homework, I was somewhat like Lockhart, but I plugged through the hateful experience, because I needed a j-o-b.)

[reg45]

How much mathematics is needed to swipe an EBT card?

[E. Pluribus Unum]

TRANSLATION: Eric Holder's people can't even read, much less solve a quadratic equation, no matter how much money we transfer to the teachers unions, so let's just dispense with quadratic equations because we don't want Eric Holder's people to feel inferior.

And just because Eric Holder's people can't be held to the same standards as everyone else, don't you dare say they are inferior.

[Skepolitic]

Slide rule? Man, you’re really dating yourself! Did you use a Pickett or a K&E?

[Grams A]

but you need to associate them with real things.”

I agree with you 110%. With our current approach we end up with people who are book smart but have absolutely no idea how to apply what they have learned to anything practical.

My oldest grandson had a very difficult time with math but was blessed by having a 4-H leader who was absolutely awesome. Each of the kids in their small group had to design and build a small storage building for the food for their animals. Suddenly things fell into place and made more sense to him. Building was successfully completed and we even had a ribbon cutting session. He was so proud.

[cartan]

What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² - y²)² + (2xy)² leads to more credible political opinions or social analysis.

Mathematics is the art of pure thinking. If your brain is not capable of doing math, it is not capable of thinking. And if your brain is not capable of thinking, then any kind of “social” or other “analysis” it comes up with is going to be entirely worthless.

Unless…the kind of “social analysis” this guy is having in mind is the whiny, liberal, illogical emoting you find in the rest of the NYT.

[arderkrag]

I still don’t know how to diagram a sentence. Completely useless, even to those who have plans to write as a career.

[driftless2]

The aim of the teaching of algebra, and other upper-level math classes, is not to give students something they can use later on in life. It is a separator. Something like an aptitude test to see what students will be able to negotiate careers that best utilize their respective brain talents. Let’s just say that if I’m an employer, I’m going to look more fondly on prospective employees who did well in math. High math skills, to be blunt, is an indicator of high intelligence...and I’m speaking as someone who did poorly in algebra and geometry in high school.

[American in Israel]

I’m one of those who just could not grasp Algebra...

I was exactly the same, was told by the teacher to give it up I would never be able to comprehend it. Ended up having to take Algebra in College just to take the programming class I wanted. The first day in class the teacher put an equation on the board that took up the entire board. He said, by the end of this class you will be able to solve this. I broke out in a sweat.

Funny thing was I passed that class with a 4.0 grade. I loved it. What a difference a competent teacher makes.

[BobL]

“The aim of the teaching of algebra, and other upper-level math classes, is not to give students something they can use later on in life. It is a separator. Something like an aptitude test to see what students will be able to negotiate careers that best utilize their respective brain talents. Let’s just say that if I’m an employer, I’m going to look more fondly on prospective employees who did well in math. High math skills, to be blunt, is an indicator of high intelligence...and I’m speaking as someone who did poorly in algebra and geometry in high school.”

...and you ‘drifted’ into the real reason for these seemingly unrelated requirements. The FACT is if you hire a college graduate, you expect them to be able to do at least Algebra 1. If they cannot even do that - then they may make some REALLY BAD decisions and screw you over. And it also implies that they don’t have much of a brain...or (more likely) much perseverance. Either way, you don’t want them.

College transcripts have pretty-much taken the place of the now-outlawed pre-employment exams.

[Skepolitic]

just don’t call the process high school, call it what it is,

vocational training adolescent daycare.

FIFY.

[Reily]

my freshman class was the last class at VaTech to be taught slide rule!

[driftless2]

"not grasp algebra"

I'll bet you could grasp it easily now. I assume you're appreciably older now than when you took the algebra. When I was a freshman in high school, I was put in a class where every other student had been taught the rudiments of algebra in the eight grade. My school didn't. I struggled to understand the basic concepts.

Jump almost thirty years and I'm attending college. To prepare for a college intermediate algebra course, I purchased a basic algebra primer. I'm sure they had many of the same problems and type of tests that befuddled me when I was thirteen. I found the book to be extremely easy. Because I was thirty years older and simply smarter. You'd probably find it a lot easier too.

[arrdon]

Why is it that America is the only land that finds it ‘too hard’? Waaaaaaagh! ‘It takes up too much of my Facebook time!’

[Beagle8U]

“If we are going to drop the algebra requirement, what need is there to warehouse children until they are 18? They may as well go onto an apprenticeship, grunt work or a trade school.”

The problem with that is the fact that almost every apprenticeship requires algebra, geometry, and trigonometry.

[Cuttnhorse]

My thought too...what the heck is a college student doing in Algebra??

I had a very difficult time with math in high school and college...all the way through calculus. Was not easy but it is required to earn a B.S. in geology.

Have I ever, ever, used calculus in my career as an exploration geologist of over 30-years? No! Did struggling through math make me a better geologist?? Most definately!

[arderkrag]

Employment tests haven’t been outlawed - you are required to take at least one and sometimes several for any type of apprenticeship program.

[Sacajaweau]

Hand calculators were just becoming available BUT “slide rule only” was at the teacher’s command. It was great.... builds concentration....probably K&E. I’m 70.

[formosa]

BS. Kids are capable of it. The public schools and parents have failed in teaching them to think or even use common sense. Not many people flunked out of Algebra when I was in school and I do not believe that kids have suddenly gotten dumber. They just do not know how to think.

[papertyger]

Ridiculous!

The critical skill learned from the study of Algebra is how to use what you DO know to find out what you DON’T!

[BlatherNaut]

But I do think there are different categories of math that require very different mental skill sets.

Agree. And an additional mental skill set to effectively communicate concepts (a skill set that many technical writers and instructors clearly lack).

[BobL]

“Employment tests haven’t been outlawed - you are required to take at least one and sometimes several for any type of apprenticeship program.”

In some cases, you’re right, but not where I work - due to this:

http://en.wikipedia.org/wiki/Griggs_v._Duke_Power_Co.

[Reily]

Bingo!
The whole heart of the matter!
Modern (meaning left-oriented!) education undermines the concept of "knowns (ergo what you know!)" and refuses to teach you the skills to find out what you don't. All that you will be told at a later date by your betters!

[Talisker]

Is Algebra Necessary?

Yes. For everyone. It teaches how to find concrete unknowns amongst a sea of apparently unrelated facts in a logical manner outside of feelings.

Something that utterly horrifies the New York Times.

[KarlInOhio]

Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.

That statement makes no sense at all. Teachers can pick out which students don't understand the topic, which ones do and which are chomping at the bit to go further. If you reduce the student's math requirements, schools won't keep the same number of math teachers just waiting for those bright students for individual teaching. Instead the schools will reduce the number of math teachers and hire ones teaching whatever subject the schools decide will be the replacement.

Maybe the bigger problem is the forced egalitarianism that all students must be taught the same and that fast tracking some students over others is discouraged. My high school had Accelerated Algebra I to separate the best students from the rest.

[Tammy8]

Yes the right teacher is the answer to understanding Algebra. I flunked every Algebra class I had in my younger days- chose my college major from a short list that didn’t require it. A few years ago I decided to take some classes at a University branch...took remedial Algebra, had the greatest teacher ever, finally understood the basics and was able to go on to pass intermediate and college Algebra. I had no reason to do this other than a challenge to myself, at my age not likely to use it much and don’t remember a lot now but did prove to myself I could do it. There are just not enough Math teachers out there that are even decent much less good or great.

My oldest daughter is another example of the problems of poor Math teachers. She struggled with Algebra all through school while excelling at all other subjects. My daughter went to junior college and as luck would have it ended up in the Algebra class of a great teacher. Daughter excelled after that and ended up being the paid Math tutor for her nursing class when she went to nursing school.

[papertyger]

Modern (meaning left-oriented!) education undermines the concept of "knowns (ergo what you know!)" and refuses to teach you the skills to find out what you don't.

Exactly.

These leftist SOBs would like nothing better than to have opponents who lack the skills to PROVE them wrong.

Without the skills to achieve mathematical "certainty" for ones conclusions, it all becomes "just your opinion."

[Chode]

gotta tell ya, in all my years at work i have needed and used extensively, geometry, trig, statistics and physics, but i have never needed algebra to do any job... lucky me

[BwanaNdege]

“...numbers matter, but you need to associate them with real things.”

EXACTLY!

Mrs. BN is finishing her degree On-Line. She needs a College Algebra class to graduate, but this particular course has two Algebra prerequisites, which would require an additional two semesters. If she can pass a Math Competency exam, she will gain exemption from the prerequisites.

However, the Mrs. has not had a math course for 45 years, so she was a bit “testy” (aggravated) when the subject of a required Algebra course came up.

“Why does anyone need Algebra?”

After a few minutes of my using Algebra terminology to describe some of the problems we’ve recently had to deal with, she began to nod her head, saying “OK, now that makes sense to me. Why didn’t they do it that way when I was in High School?”

BTW, if anyone needs a math refresher, or if “Teach Myself Calculus” is on you Bucket List, I highly recommend this site:

http://www.khanacademy.org/

[stormer]

I have an advanced degree in a hard science. I've taken more math classes than I ever wanted to - some of them I struggled with and still can't quite determine why they were relevant. I have always thought that the main reason for the overall lack of success was the quality of math instruction in primary school; it perpetuates the fear and loathing of math - would you want to learn how to swim from someone you know is floundering themselves? That said, you've hit on something I had not considered: instructors who “used to be engineers and cannot remember ever learning math”. You hit the nail on the head - my father was an engineer and I distinctly remember asking for his help on some middle-school math problem over 40 years ago. He was a man at the top of his field, but simply couldn't relate to the fact that I wasn't able to get from Point A to Point B - I never asked him for math help again. The problem is in the teaching - not the learning. Anyway - most folks aren't going to need to factor equations or understand quadratics, but the basic arithmetic, the Cartesian System, how to understand a table of values, a^2+b^2=c^2, y=mx+b, and some familiarity with probability and statistics are essential.

[Talisker]

Without the skills to achieve mathematical "certainty" for ones conclusions, it all becomes "just your opinion."

Very good point - without algebra, a person doesn't even have the experience that it's possible, not just in math, but in the logic behind it.

Try to imagine not being able to imagine that logical derivation of truth is possible.

Then look around at liberals with new eyes.

[MCH]

Of course, it looks like the Dems want 50% of the population to just be on the dole anyway, staying home and watching the TV all day.

Of course. But if you read the words of the genius "social scientist" that wrote this article, he's concerned with promising future degree holders in the fields of "art and history" being thwarted early on.

Really!? Do we really need more history and liberal arts majors than we have already? The job market would seem to indicate that we have a huge glut. And historically, many excellent artists haven't necessarily had a lot of schooling anyway. You don't need to pay extortion money to the education establishment to get an art "degree" in order to be a world class artist.

[Vendome]

There are less than 10 useful formulas in Algebra.

I don’t find learning useless things interesting at all.

Funny, how I got C’s and D’s in Algebra but received A’s in Mechanical Drafting where I used some formulas.

Supposedly Algebra makes you a better thinker.

I was chess champion in high school and didn’t feel the effects of algebra....evuh.

[GladesGuru]

“I say this as a writer and social scientist whose work relies heavily on the use of numbers.”

Counting on your digits doesn’t count as higher math.

True, but you forgot to mention that social science is mostly ‘social’ with very little real ‘science’. It is plagued with continual confusion of “correlation” with “causation”.

Given the statistical courses “social scientists” often have, to confuse correlation with causation can only be understood as a willing acceptance of deliberate duplicity.

Oh my! “Deliberate duplicity” is harsh . . . . would “ambitious ambiguity” be more acceptable?

[stormer]

https://www.facebook.com/?sk=lf#!/pages/Algebra/109398995745084

[newzjunkey]

Why did you need a summer at Sylvan to know what your daughter hadn't been taught in math?

Are you that hands off a parent that you're unaware of what she'd been taught six or eight hours a day for months or years?

It's your job to know and your failure that you didn't. That blame doesn't lie with the school, it's in the mirror.

[Reily]

so you set the problems up using the principles of “geometry, trig, statistics and physics “ but had someone else or something do the mechanics at arriving at the answer?