Is Algebra Necessary?

[coda]

Is Algebra Necessary?

By ANDREW HACKER

Published: July 28, 2012


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.


http://graphics8.nytimes.com/images/2012/07/29/sunday-review/29ALGEBRA2-1343429652118/29ALGEBRA2-1343429652118-articleInline.jpg


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.

Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia.

Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.

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. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.

“There are students taking these courses three, four, five times,” says Barbara Bonham of Appalachian State University. While some ultimately pass, she adds, “many drop out.”

Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.

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. And it’s not just Ivy League colleges that do this: at schools like Vanderbilt, Rice and Washington University in St. Louis, applicants had best be legacies or athletes if they have scored less than 700 on their math SATs.

It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.

Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III (http://jsmith.wiki.educ.msu.edu/Vitae), an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required. Toyota, for example, recently chose to locate a plant in a remote Mississippi county, even though its schools are far from stellar. It works with a nearby community college (http://topics.nytimes.com/top/reference/timestopics/subjects/c/community_colleges/index.html?inline=nyt-classifier), which has tailored classes in “machine tool mathematics.”

That sort of collaboration has long undergirded German apprenticeship programs. I fully concur that high-tech knowledge is needed to sustain an advanced industrial economy. But we’re deluding ourselves if we believe the solution is largely academic.

A skeptic might argue that, even if our current mathematics education discourages large numbers of students, math itself isn’t to blame. Isn’t this discipline a critical part of education, providing quantitative tools and honing conceptual abilities that are indispensable — especially in our high tech age? In fact, we hear it argued that we have a shortage of graduates with STEM credentials.

Of course, people should learn basic numerical skills: decimals, ratios and estimating, sharpened by a good grounding in arithmetic. But a definitive analysis by the Georgetown Center on Education and the Workforce forecasts that in the decade ahead a mere 5 percent of entry-level workers will need to be proficient in algebra or above. And if there is a shortage of STEM graduates, an equally crucial issue is how many available positions there are for men and women with these skills. A January 2012 analysis from the Georgetown center found 7.5 percent unemployment for engineering graduates and 8.2 percent among computer scientists.
Peter Braunfeld of the University of Illinois tells his students, “Our civilization would collapse without mathematics.” He’s absolutely right.

Algebraic algorithms underpin animated movies, investment strategies and airline ticket prices. And we need people to understand how those things work and to advance our frontiers.

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 (http://topics.nytimes.com/top/news/science/topics/globalwarming/index.html?inline=nyt-classifier). 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.

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.

Many of those who struggled through a traditional math regimen feel that doing so annealed their character. This may or may not speak to the fact that institutions and occupations often install prerequisites just to look rigorous — hardly a rational justification for maintaining so many mathematics mandates. Certification programs for veterinary technicians require algebra, although none of the graduates I’ve met have ever used it in diagnosing or treating their patients. Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice. Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status.

It’s not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better.

I WANT to end on a positive note. Mathematics, both pure and applied, is integral to our civilization, whether the realm is aesthetic or electronic. But for most adults, it is more feared or revered than understood. It’s clear that requiring algebra for everyone has not increased our appreciation of a calling someone once called “the poetry of the universe.” (How many college graduates remember what Fermat’s dilemma was all about?)

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.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.

It could, for example, teach students how the Consumer Price Index (http://topics.nytimes.com/top/reference/timestopics/subjects/c/consumer_price_index/index.html?inline=nyt-classifier) 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.

This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry. More and more colleges are requiring courses in “quantitative reasoning.” In fact, we should be starting that in kindergarten.

I hope that mathematics departments can also create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet. If we rethink how the discipline is conceived, word will get around and math enrollments are bound to rise. It can only help. Of the 1.7 million bachelor’s degrees awarded in 2010, only 15,396 — less than 1 percent — were in mathematics.

I’ve observed a host of high school and college classes, from Michigan to Mississippi, and have been impressed by conscientious teaching and dutiful students. I’ll grant that with an outpouring of resources, we could reclaim many dropouts and help them get through quadratic equations. But that would misuse teaching talent and student effort. It would be far better to reduce, not expand, the mathematics we ask young people to imbibe. (That said, I do not advocate vocational tracks for students considered, almost always unfairly, as less studious.)

Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.


Andrew Hacker (http://qcpages.qc.cuny.edu/political_science/hacker.html) is an emeritus professor of political science at Queens College, City University of New York, and a co-author of “Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids — and What We Can Do About It.”


A version of this op-ed appeared in print on July 29, 2012, on page SR1 of the New York edition with the headline: Is Algebra Necessary?.


http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all

[black magick hustla]

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

idk what is the point of this article when clearly the problem are grading schemes and standarized tests rather than teaching algebra itself, because it goes both ways. a lot of mathematical people don't wanna listen to some windbag's opinion on literature and politics (AKA general eds university requirements).

[Book O'Dead]

I am perhaps the most incompetent person I know regarding arithmetic and mathematics, and I can tell you that the stupidity of the question was an instant magnet for me to open and read this thread.

Not even at my lowest, when I had to take remedial math in college in order to advance to higher courses, did I ever consider that algebra was anything but important, indeed essential!

I was lucky, though; I had two of the loveliest, most patient and talented math teachers any idiot like me could ever hope for in college. Not only were they good math teachers, they were natural pedagogues; teachers by vocation, as well.

It's always been a wonder to me that in the course of my life i have encountered so many generous, gifted people along the way who have lightened the burden of being me.

[MaximMK]

The question is not stupid at all. He is talking about advanced algebra. In my country in gymnasiums which are supposed to be general schools all students regardless of what direction they choose have to study algebra which is advanced and unnecessary for someone that chose to study philosophy or sociology. I agree totally that forcing all students to study advanced algebra that won't have any use to them in their everyday life unless they choose to be scientists or something is stupid. I admit that i hate mathematics even tho i understand it and all i just don't find it interesting. So i chose to study social sciences but according to our education i have to study algebra till the end of my education. Algebra which i will never use for i did not chose a direction or a job that requires it. Algebra is important but should only be studied by people who choose to and need it. It shouldn't be imposed on everyone for we are not all the same and everyone has different interests and potentials.

[citizen of industry]

I remember in highschool being all advanced placement in history, English, literature. Doing music and drama, and failing dismally in algebra and mathematics in general. I hated school because of math. I like economics. The author's point is that anything beyond general math and statistics is not necessary, and should be voluntary. Imagine how many hours I could have put into subjects I liked if I didn't have to waste so much time on math I've never used.

Why not demand flugelhorn proficiency for every student, and base college entry on flugelhorn proficiency? It's ridiculous, because flugelhorn proficiency isn't necessary and flugelhorn mastery requires personal interest, which isn't cultivated at all in schools.

[Revoltorb]

I remember in highschool being all advanced placement in history, English, literature. Doing music and drama, and failing dismally in algebra and mathematics in general. I hated school because of math. I like economics. The author's point is that anything beyond general math and statistics is not necessary, and should be voluntary. Imagine how many hours I could have put into subjects I liked if I didn't have to waste so much time on math I've never used.

How can you like economics and hate maths? Economics on anything more than a shallow overview necessitates a fairly high understanding of maths. Also, if the author's point was that "anything beyond general math[s] and statistics is not necessary," then why make the title "Is Algebra Necessary?" General maths is algebra and statistics relies heavily on at least basic calculus. If you don't know how to take the integral of a function you don't know how to find the probability-density for a given outcome. Or if you don't know how to use logarithms how will you solve any queue problems? The point is, mid level maths is necessary to understand statistics for anything more than rote regurgitation.


Why not demand flugelhorn proficiency for every student, and base college entry on flugelhorn proficiency? It's ridiculous, because flugelhorn proficiency isn't necessary and flugelhorn mastery requires personal interest, which isn't cultivated at all in schools.

Because flugelhorn proficiency (usually) doesn't teach you anything about how the world operates. A lack of understanding in a universal language like mathematics belies a lack of understanding in the world whereas not being able to play a flugelhorn could just mean you aren't very dextrous.

[black magick hustla]

I remember in highschool being all advanced placement in history, English, literature. Doing music and drama, and failing dismally in algebra and mathematics in general. I hated school because of math. I like economics. The author's point is that anything beyond general math and statistics is not necessary, and should be voluntary. Imagine how many hours I could have put into subjects I liked if I didn't have to waste so much time on math I've never used.

Why not demand flugelhorn proficiency for every student, and base college entry on flugelhorn proficiency? It's ridiculous, because flugelhorn proficiency isn't necessary and flugelhorn mastery requires personal interest, which isn't cultivated at all in schools.

i took algebra in 9th/10th grade. what is "advanced math" in general? how are you supposed to do statistics if you can't solve for a variable? i could be a further asshole and argue that to understand statistics you need to know calculus, but lets leave it there.

it is not really about math, really. it is about the fact that children are made to take classes in general that they couldn't give a fuck about. my lowest grades were literature classes and i hated them (even if i love literature), i shouldn't have to take it beyond junior high level if people are allowed to skip something as elementary as math.

[Book O'Dead]

I think that it's generally believed that musicians are more proficient at math than average people. In fact, most mathematicians are able to play some kind of musical instrument. That suggests that mathematics is an indispensable part of music.

[Kenco Smooth]

Forcing people to continue with subjects they don't care for really will do no good. That said mathematics shouldn't be underrated as it often is.


I think that it's generally believed that musicians are more proficient at math than average people. In fact, most mathematicians are able to play some kind of musical instrument. That suggests that mathematics is an indispensable part of music.

I'd be extremely surprised if there was any relationship between these beyond people who are good at one thing tending to be good at other things.

[Book O'Dead]

Forcing people to continue with subjects they don't care for really will do no good. That said mathematics shouldn't be underrated as it often is.
I'd be extremely surprised if there was any relationship between these beyond people who are good at one thing tending to be good at other things.

So, I'm guessing you didn't know that music is a highly mathematical art form?

A Google search titled Music & Math provided these interesting links (among others):

http://en.wikipedia.org/wiki/Music_and_mathematics

http://serendip.brynmawr.edu/exchange/node/1869

http://www.math.niu.edu/~rusin/uses-math/music/

[Misanthrope]

He fails to draw a correlation between algebra and the drop out rate. He could have picked any class and had the exact same argument. The point is that the current school structure promotes regurgitation of information and obedience rather than critical thinking.
Anyway, at least math/science classes have no social or political influence (for the most part) in comparison to humanities/social sciences. Math is hard but it really depends on the amount of effort you put in. Is algebra really the root of students failure? A more likely suspect would be the anti-intellectual sentiment that is ever so common in contemporary society or the structure of modern schools, not a class that I took in 8th grade. Modern schools aim for control first, learning second.

[NewLeft]

There is a "liberal arts" type of math class, where most of the assignments are analysis type questions etc. It's not really popular, probably because it's a pointless course and it's more difficult than regular math..


Anyway, at least math/science classes have no social or political influence (for the most part) in comparison to humanities/social sciences.
I wouldn't say so, we did alot of public policy type of bullshit in biology and even chemistry, but even that's just scratching the surface..

[MaximMK]

Dude i am forced to learn operations with complex numbers = i ( which are used in quantum physics ) in 2nd year of middle school. And i still have 2 more years of math + i never chose a direction for becoming a engineer, physician or something like that. One of my most favorite things about socialist Macedonia is that back than people that chose societal sciences didn't have to learn advanced math past year 2 middle school so they learned only what they actually needed for everyday life and nothing more advanced.

[Misanthrope]

There is a "liberal arts" type of math class, where most of the assignments are analysis type questions etc. It's not really popular, probably because it's a pointless course and it's more difficult than regular math..


I wouldn't say so, we did alot of public policy type of bullshit in biology and even chemistry, but even that's just scratching the surface..

Yeah I expected someone to point things such as these out. I mean with creationism even being accepted as biology in some cases.. I personally have never dealt with such trouble because I'm lucky to have teachers that actually respect science. Obviously maths/science courses aren't perfectly run but in comparison to social science classes especially they are a lot more acceptable, but being revolutionary marxists we shouldn't accept "acceptable" as ideal.



Dude i am forced to learn operations with complex numbers = i ( which are used in quantum physics ) in 2nd year of middle school. And i still have 2 more years of math + i never chose a direction for becoming a engineer, physician or something like that. One of my most favorite things about socialist Macedonia is that back than people that chose societal sciences didn't have to learn advanced math past year 2 middle school so they learned only what they actually needed for everyday life and nothing more advanced.

OH. MY. GOD. ARE YOU OKAY? I just hope that you don't turn out to be an engineer or physician. THE HORROR!!!!!

[MaximMK]

You don't get it man. Im gonna spend over 100 hours in that classroom doing stuff i will never need and never want to. Im just pointing out an injustice of the educational system here.

[Misanthrope]

You don't get it man. Im gonna spend over 100 hours in that classroom doing stuff i will never need and never want to. Im just pointing out an injustice of the educational system here.

I didn't make the connection. Coercion is definitely a horrible part of modern secondary schooling.

[Admiral Swagmeister G-Funk]

I don't understand it, don't want to understand it. I was always told that I needed it but teachers could never really explain why.

I'm not saying that there aren't uses for it but how it supposedly translates into real-life is something I see no proof for. If this can be explained to a lay man, please do.

[Misanthrope]

I don't understand it, don't want to understand it. I was always told that I needed it but teachers could never really explain why.

I'm not saying that there aren't uses for it but how it supposedly translates into real-life is something I see no proof for. If this can be explained to a lay man, please do.

It's not the application which is valuable; it's the process of learning it.

[Revoltorb]

I don't understand it, don't want to understand it. I was always told that I needed it but teachers could never really explain why.

There's your problem. Apathy is the biggest impediment to understanding everything from maths to socialist organisation.


I'm not saying that there aren't uses for it but how it supposedly translates into real-life is something I see no proof for. If this can be explained to a lay man, please do.

Algebra at its most basic is simply saying "We can produce x widgets a day and we need y number of widgets to satisfy demand for widgets, how many days do we need to keep the plant running?" Higher level maths are just more ways to solve these problems that aren't as simple. Maths is completely necessary in any sort of management, from personal resource allocation to federation level planning.

[black magick hustla]

Dude i am forced to learn operations with complex numbers = i ( which are used in quantum physics ) in 2nd year of middle school. And i still have 2 more years of math + i never chose a direction for becoming a engineer, physician or something like that. One of my most favorite things about socialist Macedonia is that back than people that chose societal sciences didn't have to learn advanced math past year 2 middle school so they learned only what they actually needed for everyday life and nothing more advanced.

complex numbers are used a lot in electronics/electric engineering, and virtually anything that involves waves and oscillations.

anyway, school is unfair in general. school is not about "learning" but discipline. i am just annoyed that people single out mathematics because it is not really taking a look at the source of the issue.

(besides math makes $$$$$$$$$$$$)

[The Jay]

That article was a pile of crap.

[Ocean Seal]

You should know algebra, especially if you are a philosopher. I wouldn't trust anyone who didn't know algebra, it isn't a lofty mathematics bar, its basic math. How can you even know if you'll like math if you haven't understood algebra, my god.

[The Jay]

You should know algebra, especially if you are a philosopher. I wouldn't trust anyone who didn't know algebra, it isn't a lofty mathematics bar, its basic math. How can you even know if you'll like math if you haven't understood algebra, my god.


If the article was about differential equations then it would have a case.

[Ele'ill]

Most subjects suck when they aren't relevant to the person being forced to learn them. I constantly failed math but did well in lit courses because I liked comic books, fantasy/sci-fi/horribly tragic stories/violence and wanted to learn about new imaginary universes on my own for fun until I discovered drugs which made reading seem pretty irrelevant until I discovered reading while on drugs. I think math would have been a lot more interesting if it was combined with some trade or even some task of some sort. Sitting in front of pages full of numbers and studying like three or four sections per test was too much and I was constantly wondering what the fuck I was doing and looking at. I'd get to tests and just not remember anything and just hand the test in blank within the first five minutes. I think it would have been cool to be like 'oh yeah I can reversally isolate the samoflange' on test day instead of 'i remember pages of numbers here let me redraw them in the right order from memory

[RedMaterialist]

math teaches you logic

[Ele'ill]

math teaches you logic

How?

[RedMaterialist]

"We can produce x widgets a day and we need y number of widgets to satisfy demand for widgets, how many days do we need to keep the plant running?" Higher level maths are just more ways to solve these problems that aren't as simple. Maths is completely necessary in any sort of management, from personal resource allocation to federation level planning.

A better example might be "Worker produces $X of value per widget per hour; capitalist sells the widget for $X+$Y and pockets the difference, Y-X as profit. How is this possible?

[Revoltorb]

A better example might be "Worker produces $X of value per widget per hour; capitalist sells the widget for $X+$Y and pockets the difference, Y-X as profit. How is this possible?

Maybe in a capitalist society but when production is for use and not profit, such questions will be unnecessary :lol:

[The Jay]

How?


Math is logic, or a form of it. It's formal logic written in a more precise language.

[citizen of industry]

i took algebra in 9th/10th grade. what is "advanced math" in general? how are you supposed to do statistics if you can't solve for a variable? i could be a further asshole and argue that to understand statistics you need to know calculus, but lets leave it there.

it is not really about math, really. it is about the fact that children are made to take classes in general that they couldn't give a fuck about. my lowest grades were literature classes and i hated them (even if i love literature), i shouldn't have to take it beyond junior high level if people are allowed to skip something as elementary as math.

That's exactly my point. I didn't like economics until much later in life when I was receptive to learning and could choose topics I was interested in and study at my own pace. Some people don't do well with structured learning, and school cheats kids of exercising their intellectual abilities. You should have been able to forgo literature and spend more time with math, and become an even better mathematician. I should have been able to forgo math and spend more time with literature. It's not an attack on algebra, it's an attack on people being forced to learn algebra at a level they feel is more than socially necessary for themselves, then being put to standardized testing where their performance in math is used as a basis to deny or limit them higher education. But, alas, education problems are not to be solved under capitalism.

[cynicles]

Yes.

I hated English but it helped me learn critical thinking and that's important as a life skill regardless of career. I definately wouldn't remove it just because I had trouble with it, only -As.

[mew]

i hated math and almost didn't graduate because of it. i've heard that the way math especially algebra and beyond is generally taught in american schools compared to a lot of other countries makes it unnecessarily confusing/hard though. this could be hearsay though.

[Kenco Smooth]

So, I'm guessing you didn't know that music is a highly mathematical art form?

A Google search titled Music & Math provided these interesting links (among others):

http://en.wikipedia.org/wiki/Music_and_mathematics

http://serendip.brynmawr.edu/exchange/node/1869

http://www.math.niu.edu/~rusin/uses-math/music/ (http://www.math.niu.edu/%7Erusin/uses-math/music/)

Of course I know that, anyone who has ever been anywhere near music/a history of mathematics/ancient greek philosophy is well aware of that fact. But I very much doubt maths is relevant to actual performance more than a general factor across mental abilities accounts for. 'Doing' music and maths are two completely different things. Maths only comes in explicitly once you get into issues of sound engineering/high level digital work.


Dude i am forced to learn operations with complex numbers = i ( which are used in quantum physics ) in 2nd year of middle school. And i still have 2 more years of math + i never chose a direction for becoming a engineer, physician or something like that. One of my most favorite things about socialist Macedonia is that back than people that chose societal sciences didn't have to learn advanced math past year 2 middle school so they learned only what they actually needed for everyday life and nothing more advanced.

Except indepth engagement with modern social sciences typically does require a knowledge of mathematics beyond what is taught in secondary education. Qualitative social science is becoming more and more niche next to the quantitative stuff.


i hated math and almost didn't graduate because of it. i've heard that the way math especially algebra and beyond is generally taught in american schools compared to a lot of other countries makes it unnecessarily confusing/hard though. this could be hearsay though.

My gut feeling is it's hearsay simply because if the tests were needlessly difficult it would be very easy for politicians looking for points on education to scale the difficulty back to foreign levels and see large increases in school success. Sadly it seems more likely that it's the American education system being especially underfunded and unsupported is the reason.

[cynicles]

You're forgetting the profitability of standardized tests.

[Jimmie Higgins]

While it's true that the way people are taught in the US is not really relatable to many of the skills that people will end up needing, I think there are some seriously problematic things argued here stemming from a lack of seeing this in a larger context.


Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III (http://www.anonym.to/?http://jsmith.wiki.educ.msu.edu/Vitae), an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required. Toyota, for example, recently chose to locate a plant in a remote Mississippi county, even though its schools are far from stellar. It works with a nearby community college (http://topics.nytimes.com/top/reference/timestopics/subjects/c/community_colleges/index.html?inline=nyt-classifier), which has tailored classes in “machine tool mathematics.”
While the skill and education level of a workforce is important to capitalists, they are not moving to towns based on trade-based education vs. a traditional public education, they are moving for labor costs and an easier ability to raise exploitation rates.

What's dangerous - for workers - in this article is that while the author (according to the blurbs on Amazon.com from his other book) is aware and seems to care about education inequality, his arguments would actually aid the attempts to undermine public education. Mathmatics programs were pumped up and empasized in public ed in the post-war era when the US needed skilled workers at many levels of the workforce. This hasn't been the case for a while now, but bureaucratic public institutions don't restructure as fast as the capitalist's demands on labor does and so for a couple of decades now there have been various attempts at public education (de)reform. Part of this project has been to refocus resources on "achievers" while making education for the rest of us more standardized and ridged. It's this atmosphere in which Obama has been able to push characterization and people like Newt Gingrich have suggested that poor (specifically black) students don't need education, and can just go to school to work as janitor-interns so they can learn "practical skills". In this larger context, arguments like the one in this OP-ed would only provide a liberal cover for basically the same argument - just made in a more sympathetic way.

The author may have good intentions, but under present conditions, it would only lead to more educational inequality - and therefore even slimmer chances for individual advancement and inter-class mobility for working class people.


You're forgetting the profitability of standardized tests.While there are certainty profits for some companies through these tests, I think their current purpose is part of the attack on public education and teacher's unions, not a money-making scheme. "Standards" are a way to Taylorize teaching - making the job a series of goals to meet based on a time-schedule - and low-test scores allow schools to have funding withheld or to get rid of tenured teachers for "low-performance".

EDIT: I worked for a testing company grading essays for a summer. A room full of minimum wage college grads doing the work of higher paid teachers for a fraction of the cost - standardization also helps speed up the process so we went through tons of tests each shift. I wasn't a revolutionary at that point, though I had become interested, but the whole process made me feel sick because basically it didn't matter what the kids wrote as long as they repeated some key phrases - and that a bunch of office-temps are assigned duties that can help or hurt people's chances of getting into higher education without knowing anything of the kids potential or situation or whatnot.

[coda]

I fall on the elective side of the controversy.

Anyhow, here's an interesting follow up on the article by Sanjoy Mahajan, a professor at MIT, past Physics Professor at Cambridge, Ph.D in physics from Caltech. http://www.inference.phy.cam.ac.uk/sanjoy/

http://www.freakonomics.com/2012/07/31/dump-algebra/

Dump Algebra

http://www.freakonomics.com/images/authors/sanjoy-mahajan.jpg Sanjoy Mahajan (http://www.freakonomics.com/author/sanjoymahajan/)
07/31/2012 | 1:24 pm

Being a good teacher, I like to think, requires a curious and freethinking mind. A supporting example is Andrew Hacker, described by a former Cornell colleague as “the most gifted classroom lecturer in my entire experience of 50 years of teaching.” His book Higher Education?: How Colleges Are Wasting Our Money and Failing Our Kids—and What We Can Do About It (http://www.amazon.com/gp/product/031257343X/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=031257343X&linkCode=as2&tag=freakonomic08-20)http://www.assoc-amazon.com/e/ir?t=freakonomic08-20&l=as2&o=1&a=031257343X, co-authored with Claudia Dreifus (http://sipa.columbia.edu/academics/directory/cd2106-fac.html), convinced me that tenure is harmful (http://www.freakonomics.com/2011/07/14/another-salvo-in-the-tenure-debate/). His latest broadside, “Is Algebra Necessary?” (http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html), in last Sunday’s New York Times, is as provocative.


He argues that we should stop requiring algebra in schools. Despite the vitriol in several hundred comments (“We read them so you don’t have to.”), he is right.

Support for Hacker’s view comes from the observations of engineer and senior executive Robert Pearson (published in his article “Why don’t most engineers use undergraduate mathematics in their professional work?”, UME Trends, October 1991). Based on his “fifty-four years of experience as a design engineer, as an engineering manager, as a member of management assigned to help alleviate engineer-shop design and manufacturing problems, as a product cost and reliability analyst, as a corporate executive, and as an undergraduate mathematics instructor,” he asks, ”Why do 50 percent (probably closer to 70%) of engineering and science practitioners seldom, if ever, use mathematics above the elementary algebra/trigonometry level in their practice?” If algebra is the limit for most engineering and science professionals, why does a typical citizen need algebra?

As Hacker says, much more useful than algebra is quantitative literacy: being able to estimate, judge the reasonableness of numbers, and thereby detect bullshit. Our world offers plenty of practice.

My only disagreement with Hacker is small: whether, as he says, young people should learn to “do long division, whether they want to or not.” I teach mathematics and have written a mathematics textbook (http://streetfightingmath.com), but long division I haven’t used for at least three decades.

[cynicles]

Ew, freakonomics, read with caution (http://shameproject.com/profile/steven-d-levitt/).

[coda]

<<Ew, freakonomics, read with caution (http://www.anonym.to/?http://shameproject.com/profile/steven-d-levitt/).>>

eeks! thanks for the heads up. never heard of Levitt before- googled the follow up led to it.

[La Comédie Noire]

I used to hate math and be pretty terrible at it, but with time, patience, and a little extra curricular reading I became fairly good at it. The problem is the way grading and math classes are set up it punishes failure harshly so students get discouraged from trying and intuitively grasping the subject. (It's also the nature of the subject itself, you really can't bullshit a math test like you could an essay.)

A lot of math and sequential thinking involves chipping away at a problem and failing a lot in the process. So when people get a few steps in an equation wrong, they give up and say "ugh! I'm just not a math person!" when in reality they are becoming a math person by learning patterns of thought and mitigating human error. And do understand there will be lots of human error which is why your math teacher is always nagging you to check your work!

[MarxSchmarx]

I was doing well in school around age 12 except for algebra class. I built a whole edifice of an argument about why it wasn't necessary and useless and that it wasn't a real measure of a person's ability. I even (tried to) read some of the work on nonlinear dynamical systems that argued that you can get deterministic uncertainty and tried to argue that therefore math was useless because the world is just too unpredictable for maths (like I said, I was 12 - although maybe I wasn't so far off). I still think the person who taught the algebra class was a douche and didn't know what they were doing. One of my math teachers would throw the chalk on the ground, step on it to break it, and point to it yelling "this is you!". But nevertheless. I was complaining about my homework to my Trotskyist father. I used the same arguments some of you raised- that arithmetic is important, but beyond that what's the point. I wanted to be a chef at that age.

He then came up with this crazy problem that made me rethink my crusade against the class that was giving me bad marks:

Suppose you're making a meal, and you know that your customers want about 100g in the vegetables. You also know that the ratio of food weight in your vegetables needs to be about 5 units of brocolli for every 2 units of carrots, because they like a little more than twice the amount they like carrots. So how much brocolli and how much carrots shoudl you put in to get 100g of vegetables?

2*x + 5 * x =(2+5)*x = 7 * x = 100

Solve for x. Then the amount of brocolli you need is 5*x grams and the amount of carrots is 2 *x grams.

Thanks dad.

[MaximMK]

Math is not logic. I think that more logic is needed in real life situations in solving problems and stuff like that. In math you just need to remember the rules of how a particular task is solved and just keep doing it with different numbers. Math doesn't increase logic or intelligence like people say it does. The majority of people i know like math have some really stupid ideas and beliefs.

[Luís Henrique]

Math is not logic.

No, but logic is math.

Luís Henrique

[citizen of industry]

I was doing well in school around age 12 except for algebra class. I built a whole edifice of an argument about why it wasn't necessary and useless and that it wasn't a real measure of a person's ability. I even (tried to) read some of the work on nonlinear dynamical systems that argued that you can get deterministic uncertainty and tried to argue that therefore math was useless because the world is just too unpredictable for maths (like I said, I was 12 - although maybe I wasn't so far off). I still think the person who taught the algebra class was a douche and didn't know what they were doing. One of my math teachers would throw the chalk on the ground, step on it to break it, and point to it yelling "this is you!". But nevertheless. I was complaining about my homework to my Trotskyist father. I used the same arguments some of you raised- that arithmetic is important, but beyond that what's the point. I wanted to be a chef at that age.

He then came up with this crazy problem that made me rethink my crusade against the class that was giving me bad marks:

Suppose you're making a meal, and you know that your customers want about 100g in the vegetables. You also know that the ratio of food weight in your vegetables needs to be about 5 units of brocolli for every 2 units of carrots, because they like a little more than twice the amount they like carrots. So how much brocolli and how much carrots shoudl you put in to get 100g of vegetables?

2*x + 5 * x =(2+5)*x = 7 * x = 100

Solve for x. Then the amount of brocolli you need is 5*x grams and the amount of carrots is 2 *x grams.

Thanks dad.

Suppose you are making a meal, and the only thing your guests care about is taste. And you're a competent cook who can eyeball measurements without resorting to algebraic formulas, like every other cook in the world. What then?

Or suppose you run a restaurant. You use your chef to make a tasty dish, a commodity, then calculate the proportion of each ingredient in the dish and price it out, based on the wholesale prices you can negotiate with your suppliers. If you want to reduce the price a bit, you buy a cheaper ingredient. What the fuck does that have to do with algebraic formulas? You can produce the formulas after the fact, but nobody is using them.


When was the last time you requested 100g of vegetables in your dish? You ate the dish because it tasted good. You may have checked the nutrition label because you were curious what you were consuming, which the restaurant may have prepared after they had already made the dish based on taste.

What is the formula for me wanting a vegetable-laden diet one day and carb-heavy the next? What is the formula for wanting to eat at a restaurant but not being able to afford it? What is the formula for not being able to afford restaurants and not having time to go shopping and cook?

[Kenco Smooth]

Math is not logic. I think that more logic is needed in real life situations in solving problems and stuff like that. In math you just need to remember the rules of how a particular task is solved and just keep doing it with different numbers. Math doesn't increase logic or intelligence like people say it does. The majority of people i know like math have some really stupid ideas and beliefs.

Math isn't logic but neither is what you're talking about which sounds like a cross between common sense and having the same personal beliefs as you do. In which case you're right, there's no proof that teaching people maths will make them believe the same things as you. :rolleyes:

[MarxSchmarx]

Suppose you are making a meal, and the only thing your guests care about is taste. And you're a competent cook who can eyeball measurements without resorting to algebraic formulas, like every other cook in the world. What then?


actually the example that my dad used originally was with bags of frozen vegetables, where this kind of calculation makes more sense. But still, a lot of cooks make diligent use of scales (instead of "eyeballing it") particularly when starting out or trying a new recipe. if you're preparing lots of meals e.g. for an airplane, or your restaurant serves very few items, this kind of calculation is helpful.



Or suppose you run a restaurant. You use your chef to make a tasty dish, a commodity, then calculate the proportion of each ingredient in the dish and price it out, based on the wholesale prices you can negotiate with your suppliers. If you want to reduce the price a bit, you buy a cheaper ingredient. What the fuck does that have to do with algebraic formulas? You can produce the formulas after the fact, but nobody is using them.


"nobody is using them" is a strong statement - in fact a lot of restaurants, particularly chains use quite a bit of sophisticated math to figure out the best combination of all this. It's well known how places like McDonald's have their production system "down to a science". I don't understand what you mean by formulas after the fact? so how do you figure out the optimal combination then without using formulas?




When was the last time you requested 100g of vegetables in your dish? You ate the dish because it tasted good. You may have checked the nutrition label because you were curious what you were consuming, which the restaurant may have prepared after they had already made the dish based on taste.


I don't think you should be getting hung up on the 100g - the units are kind of arbitrary.



What is the formula for me wanting a vegetable-laden diet one day and carb-heavy the next? What is the formula for wanting to eat at a restaurant but not being able to afford it? What is the formula for not being able to afford restaurants and not having time to go shopping and cook?

Some of the most successful restaurants in the world figure this kind of stuff out and have computer programs simulating consumer behavior.

[The Jay]

Math is not logic. I think that more logic is needed in real life situations in solving problems and stuff like that. In math you just need to remember the rules of how a particular task is solved and just keep doing it with different numbers. Math doesn't increase logic or intelligence like people say it does. The majority of people i know like math have some really stupid ideas and beliefs.


Logic is following rules you dunce. I doubt that you know anything about formal logic, mathematics, or philosophy.

EDIT: That was rude of me. Sorry about that. You are grossly mistaken though.

[Quail]

I'm doing a maths degree and while most of the stuff I study isn't directly useful in my day to day life, I do think it's a worthwhile thing to study. It's good to understand logic (although I think I have a tendency to set out arguments like mathematical proofs when I'm debating instead of writing in a more persuasive style), and also I think that the methods for solving problems are valuable. Sometimes you have to be quite creative and you're forced to think outside the box. It teaches you valuable ways of thinking. (Not to mention, it's really interesting and kind of beautiful.) I don't think you should dismiss something as being totally useless just because you can't see a direct benefit from doing it.

Having said that though, I don't think it should be mandatory, but there should always be an opportunity to study it.

[Jazzratt]

Math is not logic. I think that more logic is needed in real life situations in solving problems and stuff like that. In math you just need to remember the rules of how a particular task is solved and just keep doing it with different numbers. Math doesn't increase logic or intelligence like people say it does. The majority of people i know like math have some really stupid ideas and beliefs. I'm pretty sure it would be quite difficult to understand, say, modal logic without first understanding mathematics.

[maskerade]

I always loved math even though I wasn't the best at it - there is something extremely satisfying about solving a complex problem, something which unfortunately cannot be replicated for social sciences.

Whether or not algebra is necessary is a bit of a strange question. It is the form of education that needs to be changed - no grading system, no division of classes based on perceived competence (such as standardized testing), restructuring of school classes (a school is not a factory...well, at least it shouldn't be), more input in school management from students and teachers - not the subjects themselves.

i don't think algebra should be removed. when i was in high school i had no idea what I wanted to do after, so i chose mostly soft subjects like philosophy, literature, languages, and now i lack the requirements to pursue things that i could see myself being interested in. if everyone was given/exposed to the required degree of competence in a given subject before they chose something more specific there would be much more freedom in pursuing something one wants to, rather than being stuck doing stupid fucking political science and anthropology. for example.

[Devrim]

You don't get it man. Im gonna spend over 100 hours in that classroom doing stuff i will never need and never want to. Im just pointing out an injustice of the educational system here.

I spend well more than 100 hours a month in my work doing things I don't want to. When you add on the travelling time, It is probably twice that. I don't think that you have actually got it that bad at the moment.

Devrim

[ÑóẊîöʼn]

Thing is, when I was at school, I don't remember having any inkling of things like set theory, which I don't think is an area of mathematics any more intrinsically hard to understand than algebra. Instead I familiarised myself with set theory through my own reading and things like videos on YouTube. But I'm pretty sure I would have been fascinated to learn about things like how some infinities can be bigger than other infinities, for example the set of all decimals is larger than the set of all whole numbers. That strikes me as a basic and important fact about mathematics, and it's the sort of thing which might strike a student as ludicrous or improbable, and I think that kind of reaction represents a teaching opportunity as it's the sort of thing a good teacher can demonstrate on a blackboard. Doubtless set theory says all sort of other things, but the important thing is that like algebra, it can be employed in a manner that goes beyond numbers.

[Ostrinski]

I have to do a million dumb people math classes before i take one thats worth anything because Im dumb at math. FML

The fuck does math hace to do with a history degree anyway

[∞]

The question is not stupid at all. He is talking about advanced algebra. In my country in gymnasiums which are supposed to be general schools all students regardless of what direction they choose have to study algebra which is advanced and unnecessary for someone that chose to study philosophy or sociology. I agree totally that forcing all students to study advanced algebra that won't have any use to them in their everyday life unless they choose to be scientists or something is stupid. I admit that i hate mathematics even tho i understand it and all i just don't find it interesting. So i chose to study social sciences but according to our education i have to study algebra till the end of my education.

Math can be very philosphical more "philosophers" should study it. I really grow weary of everyone thinking theyre a special snowflake and should exempt from something as important as math. I had an extremely difficult time in English but I hustled through it and passed. English by the way, some people write awesome essays and have a knack all you gotta do in gen ed. Math is pay some fucking attention. I have no complaints for that class because its always good to know things. Good you guys are such fucking babies. To graduate in my school you need to pass geometry, which I did as a FRESHMAN. And I struggled through 4 years trying to figure wtf Shakespeare was talking about. If anything the problem is the other way around in the US but Im glad I got that experience of doing something I dont like, it toughened me mentally. Thats life. You gotta do things you do t want to, grow the fuck up.

[∞]

Thing is, when I was at school, I don't remember having any inkling of things like set theory, which I don't think is an area of mathematics any more intrinsically hard to understand than algebra. Instead I familiarised myself with set theory through my own reading and things like videos on YouTube. But I'm pretty sure I would have been fascinated to learn about things like how some infinities can be bigger than other infinities, for example the set of all decimals is larger than the set of all whole numbers. That strikes me as a basic and important fact about mathematics, and it's the sort of thing which might strike a student as ludicrous or improbable, and I think that kind of reaction represents a teaching opportunity as it's the sort of thing a good teacher can demonstrate on a blackboard. Doubtless set theory says all sort of other things, but the important thing is that like algebra, it can be employed in a manner that goes beyond numbers.

They should teach kids the concepts behind the numbers and all these things in a sort of philozophical way and Im sure it would spark i terest in some students.

[Silvr]

I don't know how to do algebra. There is a giant hole in my life. :crying:

[∞]

I don't know how to do algebra. There is a giant hole in my life. :crying:

Khanacademy.org

Seriously though algebra is some pretty important shit.

[Silvr]

Khanacademy.org

Seriously though algebra is some pretty important shit.

I can't say I see any way that knowing algebra would be of use to me in my life right now.

[Yuppie Grinder]

algebra is cool

[Regicollis]

In many languages there is a distinction between such as in German 'Bildung' vs. 'Ausbildung' - general education vs. specialised education. I think it is important to remember that distinction. While specialised education supplies the students with the skills they need to perform specific tasks, for instance as engineers or plumbers - general education goes beyond vocations and provides skills for being human.

Algebra and mathematics is an important part of general education. You might not need it for the vocation you choose but by learning it you both learn to learn as well as learn to think in an abstract, logical and structured way - which is imperative for being able to do critical thinking. Learning literature, history or music is equally important. The general education broadens our horizon and helps us expand our imagination beyond our own current situation.

I think scrapping general education is a dangerous thing to do. It is a process that has been long under way and I think it is part of the explanation for the apathy and selfishness we see today. When people only learn about themselves they loose the ability to take a step away from everyday life and see the greater schemes in things. Instead they become nerds, specialists who know everything about their own field and nothing about anything else. It is the dream scenario for the capitalist class - they get highly skilled workers who lack the knowledge and solidarity to see that they are more than their job and that they share interests with other workers and not with their employer and workplace.

Historically it has also been an important goal for the workers' movement to broaden the access to education in the working class. Not to make them better at doing their jobs but to make them more aware about society as a whole.

I wholly agree that today's schools are leaving a lot of students behind but the solution is not just giving up. The solution is to make schools better at what they do for instance by removing mindless bureaucracy like standardised tests and by making sure teachers actually have the time and motivation to teach all students instead of just those who fit into the ideal of the standardised student.

[Yuppie Grinder]

Math is not logic. I think that more logic is needed in real life situations in solving problems and stuff like that. In math you just need to remember the rules of how a particular task is solved and just keep doing it with different numbers. Math doesn't increase logic or intelligence like people say it does. The majority of people i know like math have some really stupid ideas and beliefs.

Math is applied logic. You don't know what you're talking about.

[black magick hustla]

math makes $$$$$$

[Questionable]

Math bores the living hell out of me but I understand it's importance. I'd just rather be thinking about complex social issues than what figuring out what an abstract equation equals.

[Os Cangaceiros]

I didn't enjoy math at all when I was a student. I got C's in math class all the time...I was the classic example of someone who tried just hard enough to get an almost-decent grade, then immediately forget everything you just learned. I probably couldn't even do a sixth grader's math homework right now.

[Psy]

I wholly agree that today's schools are leaving a lot of students behind but the solution is not just giving up. The solution is to make schools better at what they do for instance by removing mindless bureaucracy like standardised tests and by making sure teachers actually have the time and motivation to teach all students instead of just those who fit into the ideal of the standardised student.
The problem is schools teach math in a vacuum rather then a tool, the major militaries of WWII taught basic algebra with much greater success then today's schools as it was needed for navigation and to calculate firing solutions. The math training during WWII was tool base (look up tables and slide rulers) yet even pencil & paper is a tool (just a very crappy one for crunching numbers).

[Lynx]

I'm learning that spatial data analysis requires very little math. All the geometry is handled by the software. Nice :)

[Psy]

I'm learning that spatial data analysis requires very little math. All the geometry is handled by the software. Nice :)
You still have to understand the math even with tool based training especially for slide rulers.

[Lynx]

You still have to understand the math even with tool based training especially for slide rulers.
With slide rulers or an abacus I might learn something of the process, but software is just a black box. The role of the person who operates the software is to accomplish the tasks that the software cannot yet do. Which, in this case, appears to be interpretation of output data.

[Psy]

With slide rulers or an abacus I might learn something of the process, but software is just a black box. The role of the person who operates the software is to accomplish the tasks that the software cannot yet do. Which, in this case, appears to be interpretation of output data.
Yet schools focus on memorization, while militaries during WWII didn't care about memorization they just wanted soldiers that can do math for the tasks that required math, for example navigators didn't have to memorize formulas during training they were actually given formula sheets during training by the time they deployed they did the calculations so many times in training they memorized it by associating it with the task thus didn't need to have the formulas written down.

[Lynx]

Yet schools focus on memorization, while militaries during WWII didn't care about memorization they just wanted soldiers that can do math for the tasks that required math, for example navigators didn't have to memorize formulas during training they were actually given formula sheets during training by the time they deployed they did the calculations so many times in training they memorized it by associating it with the task thus didn't need to have the formulas written down.
That pretty much summarizes the advantages of actual experience over theoretical training. Employers know this, our educators seem not to.

[Ele'ill]

I didn't enjoy math at all when I was a student. I got C's in math class all the time...I was the classic example of someone who tried just hard enough to get an almost-decent grade, then immediately forget everything you just learned. I probably couldn't even do a sixth grader's math homework right now.

I forgot everything before I got a decent grade : |

[blake 3:17]

I'd written a whole other post about some particular challenges in doing math and fossilized errors, but just remembered that the US hasn't gone metric.

WTF? Imperial has its own sense, but for doing anything counter intuitive, of course you're going to be messed up. Students practical experience will be some weird mishmash -- conversion of units is one of the single most difficult in thinking mathematically.

What do you expect from a country where the use of contraception is considered a cause of pregnancy?

[Lynx]

Navigation has not gone metric. You have polar coordinates, NS azimuths, quadrant bearings, UTM, etc.
(Scroll down to see simplified formulas (https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system))
I'm grateful that software can do the conversions!