32 votes

NYT Asks, "Is Algebra Necessary?"

The dumbing down of America continues? Or a good argument?

[NYT] - 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.

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A state lawmaker from a southern state,

seeing that his son was having a particularly difficult time remembering Pi and how to use it, submitted legislation to have Pi rounded to a whole number, three, demonstrating the adage that the apple does not fall far from the tree. Fortunately his idea for making math easier did not sit well with most of his fellow legislators.

New Hampshire and Ecuador.

False.

It was Indiana in 1897. And the bill died in the senate. Not only that, none of the formulas in the bill included an even rounding to 3. And I don't recall it being in response to his son's inability to grasp the concept of irrational numbers either, but I could be mistaken.

There have been several rumors about this subject floating around, some say Kansas, some Oklahoma, some Tennessee, some Alabama and the latest was ascribed to a Georgia legislator in an attempt to smear the TEA Party there. All of the imaginary bills were blamed on Republicans by Democrats.

I heard it from Andre Marrou in 1992.

He included it as one of three humorous examples of idiocy by lawmakers. I may have the wrong states matched up with these stories but thinking about it now I'm sure one was Texas, "and I was born in Texas," he added. He also told another about a legislator from another state (Louisiana?) who objected to plans for a statewide nine-eleven emergency number. "It'll never work," he said, "there's no eleven on the telephone dial!." His third story was about a legislator in yet another state who took strong issue with any attempt by the state to accommodate Spanish speaking people: "If English was good enough for our Lord and Savior Jesus Christ it oughta be good enough for them folks!" The occasion was Marrou's address to both houses of the New Hampshire legislature. He got loads of laughs.

So who's Andre Marrou you ask? He was a former Alaskan legislator, he was Ron Paul's running mate in 1988 and he became the Libertarian Party standard-bearer in 1992. I was his 1992 New Hampshire coordinator. Biggest highlight of the campaign was "winning" in Dixville Notch, the first votes cast in the first-in-the-nation primary.

New Hampshire and Ecuador.

Leave it to MSM to ask the

Leave it to MSM to ask the wrong question, and leave it to simpletons to bite on the misdirection and undertake the futile endeavor of answering it with vapid emotion: "Math is important! Math is necessary!"; or "I think English and communication is more important!" etc etc, ad nauseum.

Back it all up. Scrap that nonsensical article and nonsensical question.

Liberty is the answer to every question asked, and all you need to do is trace the implication of that to whatever subject is being discussed.

So in this instance:

Q: Is algebra necessary?
A: It doesn't matter. There is no subject matter on earth so important that its dictation to any segment of the population should be compulsory, nor would any truly free society accept the compulsory dictation of any particular subject based on the judgment of its importance by survey of a collective group, but especially by a bureaucratic group.

Furthermore, a free market in education- like anything else- would ensure the appropriate allocation of knowledge and specialty in any given field.

To simplify further:

Q: Why the hell would a hair stylist married to an investment professional need to have taken algebra classes?
A: She did take and pass algebra classes; doesn't remember a damn thing about the material covered; and furthermore has absolutely ZERO need in her life for this knowledge; and would either develop of her own volition- or otherwise outsource for- that knowledge if it was ever truly required in her future.

Last note: You should all get familiar with "unschooling" and the many forms it takes, at a minimum. And read this from the NY state teacher of the year: http://www.cantrip.org/gatto.html?seenIEPage=1

I hope this helps.

You are correct, except where you presume someone would "need"

a subject specifically as to the purpose of studying it.

Math is not taught primarily because people will need to use it in its various forms.

It is taught because the study of it is the easiest way to teach logic.

If you can find a better way, or an equally good way that doesn't involve math, by all means - bring it forth and save the world from the boredom of Algebra.

That doesn't mean I think there should be requirements for it, but I recognize why it is used in education.

I think what you proffer here

I think what you proffer here is very misguided, though I appreciate your thoughts.

When you said: "You are correct, except where you presume someone would 'need' a subject specifically as to the purpose of studying it."

I would clarify that I believe someone would seek to acquire knowledge of a given topic for one of two reasons: 1) necessity in its application in their life; or 2) sheer interest/curiosity.

Then you said: "Math is not taught primarily because people will need to use it in its various forms. It is taught because the study of it is the easiest way to teach logic. If you can find a better way, or an equally good way that doesn't involve math, by all means - bring it forth and save the world from the boredom of Algebra."

Here, if I am taking your words in their context correctly- which I believe I am- then you are apparently presuming that everyone should learn logic (which is a subjective and judgmental value proposition on your part), and further, that algebra is the primary- or only- effective means by which people learn logic.

This is a problematic perspective on your part, easily refuted; but more to the point, it does not address at all what I have actually argued: namely, that no form of education should be compulsory, and that a free market would ensure that what knowledge was necessary to a functioning society would be acquired, voluntarily, and by the means most effective to the acquirer in his or her pursuit of such knowledge.

Any arguments to the contrary, in my estimation, arise merely as a result of a lack of imagination on the part of such an advocate of compulsory education.

In fact, if we just take the inverse of one of your statements, we can find an entirely different and profound perspective towards the same end: "Math is not [learned] primarily because people will need to use it in its various forms. It is [learned] because the study of it is the easiest way to [learn] logic."

If this is so, then you need not worry about anything as it pertains to the subject matter of algebra; and it would be entirely supportive of what I've argued thus far.

A republic, if you can keep it...

I have no problem with people not learning logic, as long as those people are not allowed to vote. If, on the other hand, voting is guaranteed for everyone, then learning logic (among other things) needs to be compulsory. Only someone living in a fantasy land thinks you can have an uneducated electorate and keep a republic limited to ensuring individual liberty.

Note that a free market (even if we had one) is not self-sustaining in this respect either. A free market works by encouraging a person to take actions that help others by making those actions benefit said person rather directly, and roughly in proportion to the value said person provides. Understanding and supporting an appropriately limited government that maintains a free market does not provide such direct and proportional incentives. In a free-market-only system, individuals are encouraged (by the system) to be "free riders" -- to let others create the environment for them to make their living, and spend the time thus saved making themselves more money or just enjoying life.

"a free market would ensure that what knowledge was necessary to a functioning society would be acquired, voluntarily"

No, it would not. See above. Furthermore, a free market can't ensure anything if there's no free market! And as long as there is an ignorant electorate that does not understand the importance of a free market, there will be no open and sustainable free market.

Your comment here is littered

Your comment here is littered with strawman arguments and statements pregnant with authoritarian premises, not to mention stupidity, through and through.

For starters: "I have no problem with people not learning logic, as long as those people are not allowed to vote. If, on the other hand, voting is guaranteed for everyone, then learning logic (among other things) needs to be compulsory."

Let's tackle this.

1) Who said people won't learn logic? You start off arguing against a strawman.

2) You make an affirmative argument that learning logic should be compulsory if voting is available to all. Leaving aside anything else (and make no mistake, there is much I am leaving aside); this opens up a can of worms that I would really love to see you attempt to contain; namely, and foremost, please define logic. Then, define the method by which it should be taught to all. Next, assure me that all who are taught will adequately grasp it to the extent you imagine is suitable since all are eligible to vote. Moreover, define who should teach it. After that, define the metrics by which 'learning' shall be measured. Tell me who creates the criteria by which all of this is accomplished. Furthermore, define what criteria make this/these individual/individuals collectively qualified to render this judgment... etc etc forever and ever amen.

3) You advocate compulsory education for logic; what distinguishes your advocacy of this compulsory education from, say, compulsory service in the armed forces? If you distinguish them at all.

That's just 3 select (and HUGE) problems with your first 2 sentences.

I don't even need to bother with your intellectually empty nonsense about the free market and free riders.

I mean, to highlight just how pointless it is even to have wasted as many words on you as I have already, let's take a look at an observation you make towards the end of your idiotic post:

"Furthermore, a free market can't ensure anything if there's no free market!"

How profound!!! You mean to tell me that, "the sun can't shine if there's no sun!"

Goodness, my! I am so enlightened for you having pointed this out to me!

EDIT (no response from you as of the time of this edit): For someone who advocates compulsory learning of logic, it is quite ironic that you so clearly lack any demonstrative ability in it yourself.

Oy!

"Who said people won't learn logic? You start off arguing against a strawman."

I said it (which FYI means it's not a straw man). People (in general) don't learn logic now. Most could. They don't.

More to the point, I brought up logic in the context of being an educated voter -- having the necessary skills to make a good choice about whom to vote for. The fact that people (in general) do not currently possess the necessary skills (and/or incentives) is essentially self-evident, unless you wish to argue that Obama and/or Romney qualify as a good choice for President.

"namely, and foremost, please define logic"

From wikipedia: "the study of modes of reasoning (which are valid and which are fallacious) and the use of valid reasoning"

Note that I am not talking about some vague idea of logic, or "common sense", or anything like that. I am talking about formal logic -- a mathematically-precise algebra of reasoning about what is true (which, if you are like 95+% of Americans, you have never been exposed to so you may not have any idea what I'm talking about -- if so, there are various resources you can tap such as this).

"2) You make an affirmative argument that [...]"

We have various legal requirements for education right now. Most of your questions have been addressed (perhaps not well, but they have been addressed) in other areas (math, science, English, etc.) and you provide no reason why the same can not be done in the field of logic. That still leaves one point you raised unaddressed though:

"Next, assure me that all who are taught will adequately grasp it to the extent you imagine is suitable since all are eligible to vote."

There is no need for that. I am not some fantasy-land idealistic absolutist, but a pragmatic realist. We don't need perfection, just an electorate that is sufficiently educated. Some people will never understand logic (and will make bad voting choices), but if the majority did understand logic (and had the other tools and incentives needed to make good voting choices), that would be sufficient.

"what distinguishes your advocacy of this compulsory education from, say, compulsory service in the armed forces?"

I am only pointing out the links between education, voting, and the results of voting, and suggesting that we should deal with the reality of these relationships rather than pretend they don't exist or pretend they will simply fix themselves. There is nothing arbitrary about that -- reliably making good voting choices requires a certain amount of education (and information, but that's another topic). On the other hand, tying voting to service in the armed forces would seem fairly arbitrary.

"How profound!!! You mean to tell me that, "the sun can't shine if there's no sun!"

How blind, that you can not recognize a key and required part of a complete and consistent logical argument. Since you failed to grasp it, I'll spell it out for you in a pseudo-algebraic form and see if that gets through your skull:

1. X requires Y
2. Y requires Z
3. no Z
4. therefore (by 2 & 3) no Y
5. therefore (by 4 & 1) no X

X = "what knowledge was necessary to a functioning society would be acquired"
Y = "the free market would exist"
Z = "the electorate is sufficiently educated to understand the importance of a free market"

#1 was derived from your "a free market would ensure that what knowledge was necessary to a functioning society would be acquired, voluntarily" statement (and from a tentative assumption that you are not saying other things besides a free market would provide for X).

My "a free market can't ensure anything if there's no free market" statement encompasses #5. You can't leave #5 out of the above line of reasoning or it is incomplete (does not reach the "no X" conclusion).

WoW

seriously? our country is seriously being dumbed down. it is true that some subjects aren't suitable for all high schoolers, but algebra?

i really believe that our public schools turn our children into the lowest common denominator. there are so many talented smart kids who are encouraged to cut up and misbehave by the less capable children in school. we should really split children up and give them different options, otherwise we're wasting our money.

If you cant do algebra dont go to college

Of course if you cant do algebra you probably cant manage risk so get a job and get your capital by savings and work. Formulas are the gateway to any job with a quantitative component-- accounting, business, science, engineering. If you cant do algebra you cant use formulas. I suppose some people are good at letters and could benefit by enhancing their writing skill for a couple years. But college seems an awfully expensive way to be an intern for a journalism or arts job

The problem comes from too

The problem comes from too much government involvement. Each student and their parents should be able to choose the appropriate path for their education. While algebra is child-splay for engineer bound students it is impossible and unnecessary for others.Some students would be better served if they were taught math with more practical applications for their future lives. If the requirement for everyone to take algebra was removed then the algebra classes could be made much more rigorous which needs to happen if we are going to compete with the rest of the world. Right now the algebra classes are dumbed down because everyone has to take it and few principles would allow a teacher to fail 50% of their students.

Keep the class. The problem isn't Algebra or its perceived

utility. (which has more to do with learning processes than with the math itself)

The problem is pointed out perfectly in the last sentence.

"Right now the algebra classes are dumbed down because everyone has to take it and few principles would allow a teacher to fail 50% of their students."

Particularly these two parts: "the alegbra classes are dumbed down" and that principles would not "allow" a teacher to fail 50% of their students.

If students fail. They fail. A principle, even the teacher, should have no say in altering that mark. It's up to the teacher to find a way to get the concepts through to the student. It's up to principles to make sure teachers are doing that.

It is NOT the job or the place of the principle or the teacher to so arrange the curriculum or the results of testing to ensure that students do not fail. It is their job to teach the students at the level needed and let the chips fall where they may.

If the chips fall on the failing side, then the teacher and principles need to find ways to reach the students without dumbing anything down for everyone else.

There's your problem - administrators and the asinine notion that the solution to failure is to lower the bar which defines it. Any teacher or administrator who does this should be fired without question and sued for back pay as damages, if not also barred at least for a time, from having any employment in the field of education.

How about Choice?

Everyone is debating what subjects are essential and what are not. The thread is sounding pretty statist with strong opinions about what is taught in forced government education.

How about we let students, parents and counselors select career paths that are appropriate to each student?

Want to be an engineer? Ok, you're taking calculus. Not good at advanced math? Here is a course plan that introduces you to multiple skilled trades and practical math associated with those trades. Want to be a writer? Take basic home/business finance essentials math and then focus on literacy, literature and writing courses.

Right now every student gets the same education and the same required courses. Schools are teaching to corporate (Pearson) high stakes tests. I am a teacher, and that test score is EVERYTHING in the eyes of the government.

Every student is expected to go to college and find a white collar job.

Well not every student is meant for college, not every career requires college. COLLEGE IS DEBT - Every student is now expected to begin their adult lives in debt to the US government $20-30+ grand. That amount is climbing at an alarming rate.

We need such a complete revolution regarding "education"...

...that we probably need a formula to figure it out. ha ha

Really, how can so many people still be mimicking the line of reasoning that has been preached for decades in govt. indoctrination centers about why EVERYone, HAS to learn algebra and that you are essentially a failure if you don't?

Please don't stone me, but don't enough of you who are naturally good at math know enough algebra for those of us who can not stand the thought of having it forced upon us?

Some people LOVE chess, my family has played tournaments, hosted tournaments. I don't even want to know what the role of each piece is and that is okay. I am okay with not playing chess or really most games for that matter.

Shouldn't people be encouraged and helped along(hopefully by those who love them most -their mother and father) to find out what they were created by God to do and to pursue their individual path?

This one size fits all is for the birds, kind of like most pages of the NYT, as bytejockey suggested. But, I think the political scientist may have a point here, even if I don't agree for the same reasons.

WHO is to say WHAT we ALL really NEED to know? Is that not collectivist thinking at it's essence? Let the free market as CSA1861 stated be the decider.

I am for peace: but when I speak, they are for war. Ps 120:7
--
Better to be divided by truth than united in error.
--
The local church(not a building -a people) is the missing link. The time to build is now.

The study of mathematics is

A good question! Necessary? Probably not. Makes for a better education? Probably so.

The study of mathematics is the study of logic. If more Americans actually develop skills in logic, perhaps the general public would be able to better understand economics and realize the two party system is a charade. Ron Paul can do algebra. So can I. Granted, I think the whole public school system should be eliminated (or at least locally governed and funded). However, if I started a private school, it would contain algebra and geometry for sure.

Ron Paul 2012

Amen, I want to see a massive reform away from "sküle" and if

I did start my own curriculum with a place to engage in it, the result would likely resemble something like the trivium and quadrivium. There are institutions currently that use both, and there are home school programs patterned off them as well.

That doesn't mean they are the end-all be-all. Certainly there is plenty of market space for trades and skills education, and I dare say, all of them are important for everyone to at least be introduced to. Doing so is part of discovering what one is good at, or interested in.

World & American History, Civics&Law, and Business Finance

are all MUCH more important. Higher level mathematics is for the college science & engineer bound person.

But for everyone else, all the high school students SHOULD be educated much more in those General Use, General Knowledge subjects such as World History, American History, American Civics and Business Finance.

When you walk out of High School, all students should be able to tell you the value of ANY business. Most of all, they should know WHAT numbers to ask for to determine ruff value. America used to be a nation of shop keepers and manufacturers and entrepreneurs. We would hang around our Universities and listen and learn about the discoveries that the engineers and scientists made; then we'd go build a business around them. Not today, sadly.

And history... what angle and perspective should it be taught? I submit it should be taught from the perspective that FREE MARKETS & PRIVATE PROPERTY RIGHTS are "the good", and the two dangers to the Free Market are Big Business and Big Government, the two entities that often collude to suppress and subdue the Free Market & Private Property Rights.

Treg

Yes, please BUY this wonderful libertarian BOOK! We all must know the History of Freedom! Buy it today!

"The System of Liberty: Themes in the History of Classical Liberalism" ...by author George Smith --
Buy it Here: http://www.amazon.com/dp/05211820

I would say that up to

I would say that up to algebra is needed, beyond that should be optional.(calculus etc; when do you use calculus+ in a job that doesnt require a degree?)
I guess I am too smart to understand, but I dont get why people think basic algebra is hard. The basic concepts in it are whats used by lots of people, not nessisarily the math itself.
I did get a degree in engineering though and I have to say that quantum mechanics is the hardest math there is. I still dont understand the math for it all that well, but the concepts I get alot better.

To climb the mountain, you must believe you can.

If it were possible to teach calculus without algebra as a

foundation, I'd say swap them out.

Calc is much easier in my estimation to grasp, and much more useful.

But algebra is, as has been noted above, more about logic than about math.

the Al-Gebra threat

New York (CNN). At John F. Kennedy International Airport today, a Caucasian male (later discovered to be a high school mathematics teacher) was arrested trying to board a flight while in possession of a compass, a protractor and a graphical calculator.
According to law enforcement officials, he is believed to have ties to the Al-Gebra network. He will be charged with carrying weapons of math instruction.

Read more

There's more to the story.

Officials became suspicious when the would-be passenger jotted down some numbers on an envelope using Arabic Numerals, the same as terrorists have been known to use.

Seriously, the golden age of Islam when algebra and trigonometry were invented, when advances were made in astronomy and medicine, and when Arab traders were the most successful in the world seems a far cry from the self-wrought state of poverty that prevails in many Islamic countries today.

New Hampshire and Ecuador.

"In the interest of maintaining rigor"

Who needs hard work and critical thinking? Not me. I just want to get paid for doing nothing and being useless. Maybe I'll become a social scientist.

Too harsh?

Sorry, sometimes I forget that social scientist are people too.

I really think this author

I really think this author has gone off the deep end. Not learn algebra? Are they serious? Everybody uses algebra in some form or another on an almost daily basis. If you don't, nearly everything you use was designed or developed with some form of algebra.

Coming from an engineer,

SAY WHAT? Understanding of simple algebra separates blue collar jobs from white collar. 3 times more algebra for everyone would be my recommendation.

To clarify, are you saying

To clarify, are you saying algebra classes should be mandated at 3x what they are now? Or just that your best judgment ("recommendation") is that everyone should attempt learning algebra with 3x more effort than they are now (whatever that may mean)?

Or do you mean something else?

Just want to leave you an out, b/c I aim to bring you down a notch if you're saying what it appears you are saying.

But Gym, Art, and Lit and essential??

I'm terrified of where we're headed as a nation.

Yes, literature is ABSOLUTELY essential....

more essential than math, IMO. Lit has been deemphasized in favor of math and science over the past decade or two, and we have a large number of dumb, gullible sheeple as a result. Lit builds not only literacy skills but also interpretation, debate, and comprehension skills.

I don't play, I commission the league.

Coming from a social sciences person...

...who is also a bookworm....I'll just say that in my honest opinion, Mathematics IS the single most important subject to learn - just a tad above reading.

Want to be a store manager? I have run into many people whose managerial careers came up short because either they didn't know the math - or weren't willing to catch up on the math. Sure accounting systems do all the work for us - but the user still needs to understand "balance" and numbers sense. Let's not even get started on scheduling...

Want to be a master electrician who is promoted to projects manager? Better be good at math - or else - it ain't gonna happen. I know a master electrician who regrets not taking math seriously in high school. He's blames that shortcoming as the one thing that nails him every time a projects manager opening is available.

Want to make a voice recognition system with a very high success rate for word recognition accuracy? Want the success rate to continue outside the language "accent" and prompt boundaries? The biggest phonemes, chunks, word and phrase dictionary in the world does go a long way - but in the end it is the mathematical sliding scale scoring system that nails it in the end. I know...I'm speaking from experience.

Want to know the modified crossing input to utilize in a spoke length calculation program for a bicycle wheel that uses a paired hole hub in a standard drilled rim? Geometry gets you there...

http://www.mrrabbit.net/wheelsbyflemingapplications.php

Spreadsheet has tabs for just that...

Funny thing about math is the following:

Our brains, especially as they mature, naturally see a way to solve a problem - the barrier though is that we DO NOT naturally have a symbology and language process that can be applied each time for a workable solution.

That's what mathematics is - our abstract logical and symbolic way of
representing what our brain recognizes - and taking it a step further - coming up with an applied system that provides a solution in a reliable manner that is repeatable by others.

All those individuals in the past 1000 years who have "discovered" and passed onto us Algebra, Geometry, Calculus, etc, were geniuses.

Do we really want to downplay it - or at the worse - wave it off?

Bad idea...IMHO...

Helpful Hint:

If you are struggling with Algebra, it's probably because most if not all of your math teachers in the earlier grade levels did not teach enough of - or under pressure from above - did not provide total and in-depth exposure of the number line throughout. What you probably got instead was all the other "creative" "innovative" "authentic" stuff for number sense.

Math through beginning Algebra is linear folks...that's your number line.

=8-)

Conservative AND Libertarian!!!