Is algebra necessary?

[Surlethe]

http://www.nytimes.com/2012/07/29/opini ... wanted=all

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

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

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

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

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

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, 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, 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. 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 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.

How about this: If you don't understand simple algebra by the time you're 18, you're either colossally lazy or a moron, and either way you don't deserve a high school diploma. Instead of watering down a nearly-meaningless high school diploma even more, let's try to make it mean something again. It should indicate basic numeracy (which includes algebra!), basic critical thinking skills, basic science (for which you need ... guess what ... algebra!), basic logic skills (guess what, math again!) ... and instead 33% of seniors simply can't even do some simple algebra.

[Sea Skimmer]

If we are going to try to force half the population into collage, and the other half have no option but burger flipping, teaching algebra as a mandatory thing in high school is kind of pointless. But then that also makes mandatory high school kind of pointless too, think of the money saved if we went back to a system that ended at 8th grade! High school after all once was purely seen as preparation for some kind of higher education while everyone else could work for GM.

Seriously though, so many people struggle with algebra in no small part because schools keep inventing new and ever more retarded ways to try to teach it, and in my case, they had the extra brilliant idea to switch between incompatible systems in the middle of our schooling too, instead of more rationally phasing in a new system with freshmen. Since my district generally ranked high in everything, I can't help but think the average American school is thirty times worse at handling it.

[Simon_Jester]

Could you be more specific, Skimmer? This is a matter of some personal concern to me.

[Zaune]

f we are going to try to force half the population into college, and the other half have no option but burger flipping, teaching algebra as a mandatory thing in high school is kind of pointless. But then that also makes mandatory high school kind of pointless too, think of the money saved if we went back to a system that ended at 8th grade! High school after all once was purely seen as preparation for some kind of higher education while everyone else could work for GM.

Please don't give the Republicans ideas!

That said, I think there's a valid argument for splitting the secondary-school maths curriculum into general maths -things everyone needs to know to function in modern society- and what you might call "vocational" maths, for students who've decided to pursue a career in science and engineering. That goes for some other subjects as well, actually.

[Mr Bean]

I was part of a class that was part of a one teacher experiment way back in the early 90s in North Carolina. Our teacher who'll I'll call Mr S noticed way back in 1985 that lots of elementary school text books were teaching algebra to 3rd and 4th graders but just not calling it that and removing things, specifically replacing X's with question marks. As in the publishing company had used the exact same set of first year algebra problems and had removed the X's and Y's and odd Z and replaced them with question marks of various kinds. The page numbers, the problems the number per page all added up they just yanked one or two problems and swapped out the standard algebra symbols for simplifications.

So this got him thinking what if I just taught my 4th graders Algebra, take them directly from multiplication tables and division in 2nd and 3rd grade directly into freshman year high school algebra. So he sat down and spent 1986 writing up this course for 4th graders. By the time I rolled around he had being doing this for almost four years at that point after spending a few years getting it approved by the administration of the school in North Carolina. Well Mr S taught our class Algebra and he went one better as after the success of the first year he had his students take the 11th grade state algebra proficiency test. And he was on his thread year with a 91% passing average for his 4th graders taking and passing the state test which only had an 87% state wide rate.

We were not gifted children or special in any way. Just had an unusually dedicated teacher who had a theory that said the best way to install good math skills was to start as early as possible rather than waste time which was his view of 4th-7th grade math was in essence one semester of math taught over three years and way to much time is spent on memorization of things like multiplication tables of things.

At the end of the year we passed all our standard 4th grade tests easily and our special did not count for anything test we all passed. We were not A students by any means the best score in the class was only a 90 out of a possible hundred (I remember getting a 70 something) with the lowest score being a 73 which was still passing (70 and above was passing in North Carolina) with most of our scores being in the low 80s. So we were not magically good but taking the test that your expected to take after three years of algebra with only one year of classroom instruction was impressive enough that three years later when the new Superintendent came on board they forced Mr S to stop his program despite his results and Mr S quit his job and went to work for one of the private school academies in the area.

[Solauren]

That said, I think there's a valid argument for splitting the secondary-school maths curriculum into general maths -things everyone needs to know to function in modern society- and what you might call "vocational" maths, for students who've decided to pursue a career in science and engineering. That goes for some other subjects as well, actually.

Like how it's set up in Ontario (at least in the 90s)?

Grade 9 - Math (covers all subjects)
Grade 10 - Math (covers all Subjects) Grade 9 + 10 were mandatory
Grade 11 - Algerbra or Business
Grade 12/Grade 13 - Algerbra II, Business II, Calculus

[Broomstick]

I have mixed feelings about math as it is currently taught in schools.

Despite not having a STEM career, I have occasionally found uses for algebra in my life. Not the really complicated/high end algebra, but it can certainly be useful even for the non-mathematical. What I didn't remember exactly (as it has been over 30 years since I took math in school) I could look up.

However, it still remains that a lot of people really don't need math beyond the basics. Certainly, this drive to push people into more and more math isn't necessarily a good use of time and resources. Calculus isn't necessary for most, and I don't see a necessity in requiring it outside of professions that actually need it. By all means, leave it as an option for everyone, but only require it where it truly is a requirement.

Let me put it this way: if calculus had been required to graduate from high school I would never have graduated. After literal years of struggle, three years to be precise, extra help, one-on-one tutoring, and failure I finally gave up on it. I can't learn it. I just can't. I realize to those that find math simple this is mind-boggling and the inclination is to regard me as stupid or lazy or something of the sort and there is probably nothing I can do to convince you I'm not mentally deficient. I certainly empathize with dyslexics who go through the same thing in regards to reading. I had the opposite problem - reading and comprehending text at a college level when 8 years old, but struggling with math. I got punished a lot in school because there was no way someone as smart as me could possibly be having a problem with math, I just had an attitude problem, right?

So, I am never going to be an engineer or a doctor because I can't do the math. I gave up my early ambitions to be a scientist because I can't do the math. There are a lot of other things I can do instead, and do well. But throughout high school I was told I was a failure and would never amount to anything because I couldn't, no matter how I tried, master calculus. There was nothing for me in the work world, I was a useless human being. The wonder is that I didn't drop out. I managed to get to college anyway, and get a degree anyway, and I now realize there are a LOT of professions out there that don't require high end math.

Some people find math easy, some don't. Definitely, everyone needs a certain amount of arithmetic and algebra type stuff but we shouldn't discard human beings because they can't master the higher mathematics.

Somewhere in algebra is where the dividing line exists. Where, exactly, that is I'm not sure but while I sympathize and understand the frustration of those who find math difficult or irrelevant I think failure to require algebra at all is not a good thing. Certainly, I think elementary algebra as defined in this wiki is useful and should be required. I also think the concepts in algebra should be taught in conjunction with the uses of the all the math on the paper for maximum understanding. What good does it do you to be able to solve an equation if you don't know what the equation is used for? Trigonometry invariably makes more sense when taught in conjunction with the uses of trig.

Given that I managed to (eventually) pass algebra despite a long history of problems with math, I'm inclined to think it's not so much a problem with the subject as much as how it is taught. As I said, elementary algebra should be required, but I'm not clear from the editorial what the author means by "algebra". Does it include the elementary replacement of numbers with variables in equations? Or does he refer to the more complex, more abstract, and more complicated "higher" algebras?

[Broomstick]

Grade 9 - Math (covers all subjects)
Grade 10 - Math (covers all Subjects) Grade 9 + 10 were mandatory
Grade 11 - Algerbra or Business
Grade 12/Grade 13 - Algerbra II, Business II, Calculus

Really?

30 years ago in my district algebra was required starting in grade 8. The sequence was supposed to be

Grade 8 - Algebra I
Grade 9 - Algebra II/Geometry
Grade 10 - Precalculus/Trigonometry
Grade 11 - Calculus
Grade 12 - Calculus II

That was considered the slow track. Smart kids started the sequence a year earlier. They let us dummies graduate with passing grades in algebra II and trig, but let us know we were mental defectives.

[Zaune]

Like how it's set up in Ontario (at least in the 90s)?

Grade 9 - Math (covers all subjects)
Grade 10 - Math (covers all Subjects) Grade 9 + 10 were mandatory
Grade 11 - Algerbra or Business
Grade 12/Grade 13 - Algerbra II, Business II, Calculus

Something along those lines, yes. I'd also argue for something similar with English Literature as distinct from English Language, though the former subject as taught to my generation has plenty of other problems besides limited practical applications outside a fairly narrow range of careers.

[Formless]

How about this: If you don't understand simple algebra by the time you're 18, you're either colossally lazy or a moron, and either way you don't deserve a high school diploma.

Question, Surlethe: given the dropout rate cited, how is this attitude at all useful? It sounds very much like part of the problem, not actually an accurate assessment of people's intelligence. From where I am sitting that statement sounds like a way of trying to shift or outright deny responsibility for the state of the academic environment. Passing a class isn't just about raw intelligence, after all, and failing in a class has repercussions besides just your GPA. Its emotionally taxing and exhausting motivation-wise. Take it from someone who has an academic disability and an IQ high enough above the bell curve to be statistically significant. I've known failure, yet at the same time I have empirical evidence I am no goddamn idiot (which makes it more frustrating when you have to retake a class and you knew the fucking material).

Algebra wasn't hard for me or anyone I knew (in fact, I started it before highschool, much like Bean. Gifted and Talented program you see), and has been fairly useful since then. But what the fuck am I supposed to do with all this useless geometry knowledge they wanted to hammer into my skull during freshmen year? A lot (not all, but a lot) of that stuff seems to be holdovers from an age where Plato was still a relevant part of the general curriculum. Or did you not notice that the article was about math as a whole, with algebra merely being focused on because of its exceptionally high failure rate? I do not understand why it must be considered must-have knowledge for everyone, no matter what. Academic masturbation is still masturbation. Reconsidering parts of the curriculum should at least be considered, rather than smugly dismissed.

Instead of watering down a nearly-meaningless high school diploma even more, let's try to make it mean something again. It should indicate basic numeracy (which includes algebra!), basic critical thinking skills, basic science (for which you need ... guess what ... algebra!), basic logic skills (guess what, math again!) ... and instead 33% of seniors simply can't even do some simple algebra.

I agree with the sentiment... except one thing. Logic and math are not one in the same. A lot of math people want to believe they are, but after having taken dedicated logic and philosophy classes, I must question this belief. Logic can be applied to whole areas where math doesn't apply. You use logic in math, and proofs are an element of both disciplines. However, logic is worth studying in its own right, so you know how to apply it to real life situations and arguments... even when no math is present. I suspect many people (some of whom I've met, others I've read) who excel at math (or math class) fail at basic logic or argumentation because they have never studied logic in other contexts but the one, very formal, very abstract application of it.

[mr friendly guy]

I must say most of what will be required for doctors would be arguably the mathematics involving statistics, as we had to learn the formulas for p-values and all these statistical analysis, which I have forgotten. Mostly when I was involved in some studies they just plugged the information into a computer which does the calculations anyway.

Algebra may be useful for med school though, as they taught us stuff involving physics, like the physics of blood flow, electricity (in defibrillators etc), so it was a useful skill to have to answer those questions as they involved calculations and equations.

I must say though, algebra has been useful for me in a non professional sense, just a few things of interest to me required algebra to work out etc. To my mind it would be sad in a way if people did not understand basic maths. I remember some idiot on youtube (yeah hold off the youtube has idiots rant please ) telling me I couldn't do maths when I pointed out that a country's GDP will double in 8 years if they grow by 9%, and 9 years if they grow by 8%. I then shoved his face in with equations and mockery. Strangely he didn't reply. Maybe he didn't understand enough algebra and logarithms. I guess it brought back those scary memories of high school.

[Melchior]

Algebra may be useful for med school though, as they taught us stuff involving physics, like the physics of blood flow, electricity (in defibrillators etc), so it was a useful skill to have to answer those questions as they involved calculations and equations.

Do you remember if you had to integrate, etc. for your physics exam? IIRC my physics exam in med school barely featured limits.

Math literacy is very important to society; I don't see how a voter could rationally form an opinion on most relevant policy issues without the ability to understand (simple) mathematical models. I recall reading a study that reported how most people can't grasp the concept of exponential progression (so, for example, surely they don't understand anything concerning demographics).

[Pint0 Xtreme]

Grade 9 - Math (covers all subjects)
Grade 10 - Math (covers all Subjects) Grade 9 + 10 were mandatory
Grade 11 - Algerbra or Business
Grade 12/Grade 13 - Algerbra II, Business II, Calculus

Really?

30 years ago in my district algebra was required starting in grade 8. The sequence was supposed to be

Grade 8 - Algebra I
Grade 9 - Algebra II/Geometry
Grade 10 - Precalculus/Trigonometry
Grade 11 - Calculus
Grade 12 - Calculus II

That was considered the slow track. Smart kids started the sequence a year earlier. They let us dummies graduate with passing grades in algebra II and trig, but let us know we were mental defectives.

That sounds crazy advanced for today's standards in US High Schools. My experience was:

Grade 9 - Algebra I
Grade 10 - Geometry
Grade 11 - Algebra II
Grade 12 - Trigonometry (Calculus available for advanced students)

[Melchior]

What good does it do you to be able to solve an equation if you don't know what the equation is used for? Trigonometry invariably makes more sense when taught in conjunction with the uses of trig.

Sadly it's impossible to contextualize everything while it's being taught - similarly one can need quite a bit of mechanical practice with limits, derivatives, etc. to be able to follow proofs that make use of them.

Given that I managed to (eventually) pass algebra despite a long history of problems with math, I'm inclined to think it's not so much a problem with the subject as much as how it is taught.

As far as I know (not much, but my mother is a math teacher and she keeps up to date on developments in the field), actual neurological adversity that especially limits the learning of maths is exceedingly rare; it's definitely something in the learning process - possibly bad teachers, a suboptimal didactic approach, cultural and psychological blocks, bad studying habits, etc.

[JLTucker]

Broomstick: Are you sure the problem wasn't the algebra? Employing calculus techniques is easy, it's just the algebra that can mess you up. Do you happen to recall any specifics about what you had a hard time with?

[Terralthra]

Grade 9 - Math (covers all subjects)
Grade 10 - Math (covers all Subjects) Grade 9 + 10 were mandatory
Grade 11 - Algerbra or Business
Grade 12/Grade 13 - Algerbra II, Business II, Calculus

Really?

30 years ago in my district algebra was required starting in grade 8. The sequence was supposed to be

Grade 8 - Algebra I
Grade 9 - Algebra II/Geometry
Grade 10 - Precalculus/Trigonometry
Grade 11 - Calculus
Grade 12 - Calculus II

That was considered the slow track. Smart kids started the sequence a year earlier. They let us dummies graduate with passing grades in algebra II and trig, but let us know we were mental defectives.

That sounds crazy advanced for today's standards in US High Schools. My experience was:

Grade 9 - Algebra I
Grade 10 - Geometry
Grade 11 - Algebra II
Grade 12 - Trigonometry (Calculus available for advanced students)

While the plural of anecdotes and so on, my experience (ten+ years ago) was:

7th grade: Algebra I (1+ year ahead, this was typically offered to advanced 8th graders only)
8th grade: bicycle to the high school for Geometry
9th grade: Algebra II
10th grade: Pre-Calc (worthless class, learned very little, as the curriculum was mostly trig review and a toe dipped into integral and differential calculus)
11th grade: Calculus BC
12th grade: drive over to the community college for Math 7, Introduction to Linear Algebra.

I was 1-2 years younger than most students in each of these classes, and by senior year, I'd run out of math and science courses to take at the high school.

Once I entered university proper, I was taking Calculus 3 and DiffEq as a freshman.

As for the OP...it's ridiculous on its face. I use algebra on an hourly basis just in basic living (adjusting recipes, calculating calories, calculating gas mileage, estimating the lifetime cost of a compound-interest loan), let alone for work and academia.

The poster of the original article seems to be treating "graduating high school" as some sort of intrinsic good which society should facilitate at all costs. The reasons that high school diplomas are correlated with higher socioeconomic status and income potential is the education you receive on your way to earning the piece of paper. Removing the "harder" education bits so that more people get the piece of paper would quickly destroy the value of the piece of paper.

And I agree with Surlethe - if you can not do basic algebra by the age of 18, you are either mentally deficient in a quantifiable way or have had a series of math teachers that are objectively unqualified to be doing their jobs.

[Sea Skimmer]

Could you be more specific, Skimmer? This is a matter of some personal concern to me.

Been a while now, but basically they switched from the class Algebra/Geometry ect... way of teaching, though they had a funky way of doing that too (didn't call it this), into an 'integrated system' called Imp or something, that tried to teach everything jumbled together in a hopelessly confusing manner that was supposed to give you complete math education in four years. End result was we switch into this and get classes which are half redundant and half pure draw a blank, because the integrated system assumed you already knew a random jumble of stuff, and so threw another random jumble of stuff at you which either you'd already learned, plus other stuff that was too advanced because you had not learned the enabling parts yet. And they just expected teachers to 'adapt' to this and adjust lesson plans, which never worked nor was going to work well even ideally since not everyone took the same damn classes before.

Last I heard after about seven-eight years they concluded the super integrated system was a complete failure even for kids who went through the whole thing, no idea what the replacement was.

[Lonestar]

What's great is that the author of the OP article also wrote a column supporting liberal arts.

In our own teaching, we've found that students arrive at college interested in the economy, their society and its culture. They are not incurious, as many academics complain. Nor do we agree with Charles Murray, who argues we are sending too many young people to college. On the contrary, we believe that every undergraduate, even those now basically majoring in beer, would benefit from giving a seminar paper on Jane Austen's "Persuasion."

Jane Austen trumps algebra.

[Enigma]

Something along those lines, yes. I'd also argue for something similar with English Literature as distinct from English Language, though the former subject as taught to my generation has plenty of other problems besides limited practical applications outside a fairly narrow range of careers.

That is already done in Ontario. English and English Lit.

[Simon_Jester]

Could you be more specific, Skimmer? This is a matter of some personal concern to me.

Been a while now, but basically they switched from the class Algebra/Geometry ect... way of teaching, though they had a funky way of doing that too (didn't call it this), into an 'integrated system' called Imp or something, that tried to teach everything jumbled together in a hopelessly confusing manner that was supposed to give you complete math education in four years. End result was we switch into this and get classes which are half redundant and half pure draw a blank, because the integrated system assumed you already knew a random jumble of stuff, and so threw another random jumble of stuff at you which either you'd already learned, plus other stuff that was too advanced because you had not learned the enabling parts yet. And they just expected teachers to 'adapt' to this and adjust lesson plans, which never worked nor was going to work well even ideally since not everyone took the same damn classes before.

Last I heard after about seven-eight years they concluded the super integrated system was a complete failure even for kids who went through the whole thing, no idea what the replacement was.

The present trend is toward the Common Core standards, which bypass the problem of Republicans hating federally mandated curriculum by just getting every damn state to sign onto the program, at least for math and reading. So far it's 40/50, including Pennsylvania.

Common Core is compatible with 'traditional' math course progression.

I was part of a class that was part of a one teacher experiment way back in the early 90s in North Carolina. Our teacher who'll I'll call Mr S noticed way back in 1985 that lots of elementary school text books were teaching algebra to 3rd and 4th graders but just not calling it that and removing things, specifically replacing X's with question marks. As in the publishing company had used the exact same set of first year algebra problems and had removed the X's and Y's and odd Z and replaced them with question marks of various kinds. The page numbers, the problems the number per page all added up they just yanked one or two problems and swapped out the standard algebra symbols for simplifications.

So this got him thinking what if I just taught my 4th graders Algebra, take them directly from multiplication tables and division in 2nd and 3rd grade directly into freshman year high school algebra. So he sat down and spent 1986 writing up this course for 4th graders. By the time I rolled around he had being doing this for almost four years at that point after spending a few years getting it approved by the administration of the school in North Carolina. Well Mr S taught our class Algebra and he went one better as after the success of the first year he had his students take the 11th grade state algebra proficiency test. And he was on his thread year with a 91% passing average for his 4th graders taking and passing the state test which only had an 87% state wide rate.

We were not gifted children or special in any way. Just had an unusually dedicated teacher who had a theory that said the best way to install good math skills was to start as early as possible rather than waste time which was his view of 4th-7th grade math was in essence one semester of math taught over three years and way to much time is spent on memorization of things like multiplication tables of things.

This is totally possible- frankly, a lot of kids get exposure to algebra in elementary and middle school.

The big things that you drill into kids in late elementary school are, hm... well, common core emphasizes basic geometry (calculating areas and so on), getting comfortable with fractions (many kids still have trouble with this in fourth grade), use of ratio and proportion...

Yeah, you could compress it, and probably condition kids to solve algebra problems faster too. The main problem would be manpower. This comes up a lot and I'll go into it more below, but there are big areas of the country where it is not easy to fill a school with good teachers.

I have mixed feelings about math as it is currently taught in schools.

Despite not having a STEM career, I have occasionally found uses for algebra in my life. Not the really complicated/high end algebra, but it can certainly be useful even for the non-mathematical. What I didn't remember exactly (as it has been over 30 years since I took math in school) I could look up.

However, it still remains that a lot of people really don't need math beyond the basics. Certainly, this drive to push people into more and more math isn't necessarily a good use of time and resources. Calculus isn't necessary for most, and I don't see a necessity in requiring it outside of professions that actually need it. By all means, leave it as an option for everyone, but only require it where it truly is a requirement.

I doubt more than a handful of school systems in the country seriously expect all students to take calculus. My science and tech magnet program didn't require it ten years ago, and my county doesn't require it now either.

The one thing that bugs me, they're falling in love with school uniforms again. Ugh.

I got punished a lot in school because there was no way someone as smart as me could possibly be having a problem with math, I just had an attitude problem, right?

Hm. I think the modern answer would be... yes, and no. The attitude problem isn't something you could punish out of mini-Broomstick, that would be grossly stupid; it's likely to be at least partly an imposed mental block though. You're certainly good enough at abstract thought otherwise.

Learned inadequacy and learned helplessness are the bane of a math teacher's existence- the kid who freezes up and insists they can't do it, for reasons that you wish you could go back in time five years and punch out of whoever put them into that frame of mind.

Algebra wasn't hard for me or anyone I knew (in fact, I started it before highschool, much like Bean. Gifted and Talented program you see), and has been fairly useful since then. But what the fuck am I supposed to do with all this useless geometry knowledge they wanted to hammer into my skull during freshmen year? A lot (not all, but a lot) of that stuff seems to be holdovers from an age where Plato was still a relevant part of the general curriculum. Or did you not notice that the article was about math as a whole, with algebra merely being focused on because of its exceptionally high failure rate? I do not understand why it must be considered must-have knowledge for everyone, no matter what. Academic masturbation is still masturbation. Reconsidering parts of the curriculum should at least be considered, rather than smugly dismissed.

Geometry covers a lot of stuff that's practical if you have a job involving shapes, which isn't exactly rare- construction and interior design come to mind. It's also a big part of the secondary purpose of high school math, which is teaching abstract thought.

School systems simply don't have the time or the manpower to teach dedicated logic and philosophy classes to all students. If they did, they'd be the first things hauled to the chopping block in the next round of clamor for "high stakes testing." So along with teaching raw computational skill, math class really is intended to promote abstract thinking about practical subjects.

It's not all there is to logic; it's just the best high schools can do without tripling the number of teachers and keeping kids in school ten or twelve hours a day.

What good does it do you to be able to solve an equation if you don't know what the equation is used for? Trigonometry invariably makes more sense when taught in conjunction with the uses of trig.

Sadly it's impossible to contextualize everything while it's being taught - similarly one can need quite a bit of mechanical practice with limits, derivatives, etc. to be able to follow proofs that make use of them.

The ideal is to break down instruction into units, each of which starts with brute comprehension of some concept (Spanish grammar, the causes of the American Revolution, limits) and then rising through basic applications of it toward advanced ones that require some serious brain-sweat.

7th grade: Algebra I (1+ year ahead, this was typically offered to advanced 8th graders only)
8th grade: bicycle to the high school for Geometry
9th grade: Algebra II
10th grade: Pre-Calc (worthless class, learned very little, as the curriculum was mostly trig review and a toe dipped into integral and differential calculus)
11th grade: Calculus BC...

There is a reason for a degree of redundancy in the math curriculum. Some teachers are just bad, some students have a bad year. Teaching everything once might get kids doing calculus by ninth grade or whatever... but unless you had a good teacher in every one of the previous nine years, you'd hopelessly screw up the progression. Because the next year the teacher starts on the assumption that everyone can do quadratic equations or whatever... and they can't.

"Fuuuuu-"

So you get years that sum up the content of previous years, while adding a modest amount of sophistication to it, because you can't be sure that the kids caught all that handwaving about complex exponents in Algebra 2 Trig and so it's desirable to cover it again in Precalc because they'll damn sure need it in calculus. To take an example that happened to me.

The poster of the original article seems to be treating "graduating high school" as some sort of intrinsic good which society should facilitate at all costs. The reasons that high school diplomas are correlated with higher socioeconomic status and income potential is the education you receive on your way to earning the piece of paper. Removing the "harder" education bits so that more people get the piece of paper would quickly destroy the value of the piece of paper.

To a large extent this has happened- while at the same time, making the piece of paper more common by educating more people in a thorough way also reduces its value. These days, being able to do algebra doesn't make you special the way it did in 1930.

And I agree with Surlethe - if you can not do basic algebra by the age of 18, you are either mentally deficient in a quantifiable way or have had a series of math teachers that are objectively unqualified to be doing their jobs.

You have NO IDEA how common this is. It only takes two or three in a row to totally burn out a student on math- sometimes even one if they're bad enough. And it's such a pain for large swathes of the country to keep good math teachers while removing bad ones. Payscales for teachers aren't stellar, and they vary a lot, and some districts can promise a more rewarding experience in terms of "we have quieter students who had bedtime stories read to them and don't think math is something that happens to other people."

So there's a powerful incentive to migrate to greener pastures, and a lot of teachers with mouths to feed or a condition of being chronically fed up with the people they deal with do. Meanwhile, the only way to get rid of lots of bad teachers in a hurry is to abolish the tenure system. Which sounds great... yeah. Who's evaluating teacher competence?

If it's standardized tests, a lot of people get fired because of a year or two of students having bad luck on the tests, or because they're in bad neighborhoods where the scores are almost automatically lower, which means high turnover in troubled schools. Which is really bad, because long-service teachers with ties to the local area are one of the things that helps keep kids functional in those environments. Meanwhile, the best schools in the district get to keep their teachers almost indefinitely because half their kids will learn in spite of themselves and get tutoring if they don't... which is good for those schools and keeps them strong.

If it's personnel- well. You've just made every teacher's job dependent on regular sit-in reviews by the school's administrative staff. Remember what your high school's vice principals were like? How some of them were jerks, or power-tripping? Yeah. Teachers don't like being vulnerable to that any more than you do.

In either case, you'll get a lot of good teachers who decide they're sick of dealing with 120 unruly children AND the endless circular firing squads of the review board. Nobody wants to put up with having Vice-Principal Bone trying to vet them for whether they're fit to do their job every damn year. So they pack up and leave, which puts you right back where you started, only now you've got this really intense review system that demoralizes your rookie teachers and causes lots of them to burn out and quit. And your retention rate is even worse, for both good and bad teachers.

It's a mess, and the solutions that play well with posturing state governors and city mayors don't necessarily work at ground level.

[Zaune]

That is already done in Ontario. English and English Lit.

It's done here in the UK as well, but only after the age of sixteen, when everyone who really doesn't want to be in the class has probably left school. I'd like to see English Lit and most of the more specialist maths stuff split off into electives a couple of years earlier.

[aerius]

Yeah, if we taught people algebra they might just figure out that a credit card at 20% APR will bankrupt them so fast that it ain't funny if they carry a balance, or that their $90k college loans will never get paid off until they retire (by which time they've probably paid in $300k for that loan to cover interest), or that the extra money they'll make with a degree is far outweighed by the cost of education. Or that a $500k mortgage with a $40k income does not work, even if the bank is giving you one. Cause if people started figuring these things out, it would be harder to make them into debt/wage slaves for the benefit of rich assholes who already have way too much money.

Or maybe you just want to bake some magic muffins and need to know how much special ingredients you need.

[Sea Skimmer]

The present trend is toward the Common Core standards, which bypass the problem of Republicans hating federally mandated curriculum by just getting every damn state to sign onto the program, at least for math and reading. So far it's 40/50, including Pennsylvania.

Common Core is compatible with 'traditional' math course progression.

Yeah well that would just be the thing, Common Core just says what you should learn, not how it is taught. Its somewhat specific for elementary and middle school grades in dictating certain subjects per grade, but high school is left wide open. The rest is still left up to the specific districts, and even specific schools. Not that I completely think one system should be imposed, but I just have very little faith in the ability of educators to sort out buzzwords from rational methods on such a distributed basis, and plenty of nations do fine with vastly more centralized school systems.

[Rogue 9]

What kind of goddamn idiot can't grasp basic algebra? When I was in high school it wasn't difficult; it was boring. Not because math is boring, but because the coursework was easy and the curriculum kept repeating stuff it had already taught us.

[PainRack]

I don't know....

The problems I had with algebra was that I just couldn't see the use of it in life during school. It was always just some abstract problem where I was supposed to show what is x or balance out some abstract equations. It ultimately became a form of cramming, and I can clearly say that I have utterly discarded 6 years worth of cramming, being stuck in school until 5-7pm each day and the countless hours of work involved, to the extent that I once gave the answer to my math teacher before I worked out the question because I memorised the question beforehand........

It was a pain in the arse and it literally took 4-5 years before I began to partially understand what algebra was for in science.....


Although I will echo Mr Bean comments about the possibility of teaching algebra early. I once took up my brother ten year old mathbook for tutoring purposes and realised that I could solve the problems inside using algebric equations..... much faster than using the modelling techiniques expected, which was just a half assed form of algebra anyway.

But then again, Singapore math exams are crazy. Our year 12 math exams routinely included a couple of advanced questions, and when I tutored someone, I realised I was actually dealing with a question that involved expotentials and expression........