A VERY STUPID ARGUMENT GETS THE FJM TREATMENT

Rarely am I moved to revive the FJM Treatment these days, as it tends to be very labor-intensive to write and it's not often that I have the time. But when Mike Konczal – Those of you who have been around forever remember him, and those who haven't probably know his current work – shared this article with the baiting tagline, "Algebra II Has To Go", I felt the urge stirring inside me. Understand two things: One is that I realize I am falling for Outrage Bait here; sites like Slate push this stuff purporting to be "edgy" mostly in the hopes of getting people to share it socially and vent about how dumb it is. The second is that Mike approached this from the perspective of someone who has taken a lot of very high level math in his academic life and no doubt accurately points out that much of it has never been useful beyond college.

The problem is that this article isn't about high level math. It's about algebra, and its author Dana Goldstein has fallen hook, line, and sinker for the arguments of one person with an agenda to sell books about "curriculum reform" that only excite administrators looking to boost retention by identifying and then justifying the elimination of whatever courses are too difficult for students to pass. As a faculty member, I see this very differently because the motives are very transparent to me. I read a noble proposition like "What's wrong with improving the curriculum to include more useful math?" as a stalking horse that quickly ends up pressed into service of the least noble motives. Are you ready? It has been a while, but hopefully you'll agree that it's time. Some of this is excised for length and irrelevance.

In his new book The Math Myth: And Other STEM Delusions, political scientist Andrew Hacker proposes replacing algebra II and calculus in the high school and college curriculum with a practical course in statistics for citizenship (more on that later). Only mathematicians and some engineers actually use advanced math in their day-to-day work, Hacker argues — even the doctors, accountants, and coders of the future shouldn’t have to master abstract math that they’ll never need.

*RECORD SCRATCH SOUND*

Algebra II is "advanced math"? Nobody needs to know Algebra unless they're designing a rocket engine or mapping the human genome? Isn't a sequence in Algebra, like, a rather basic component of math education? Gee I'd hate to think the authors are using an argument – a valid argument – against taking advanced calculus as a red herring here.

I showed the book to my husband, Andrei, a computer programmer who loved math in school. He scrunched up his face. “People don’t use Shakespeare in their jobs, but it’s still important for them to read it,” he said.

I like Andrei. Andrei seems to understand the educational system and its purpose.

“It’s not the same,” I told him. “Reading fiction builds empathy.”

“Math helps us understand the world around us!” Andrei replied. “Like how derivatives demonstrate change over time.” He smiled, and I could tell that for him, it was all clear and beautiful.

But I had no idea what he was talking about. In high school, I found math so indecipherable that I would sometimes cry over my homework. I don’t think I ever understood what a derivative signified 15 years ago, when I was struggling my way to a low B in calculus—a class I was convinced I had to take to pad my college applications.

Oh good. I'm glad we're establishing from the outset that the basis of this article is "I don't get it, so it's not necessary."

*EXAGGERATED FOREHEAD WIPE*

So Hacker’s book is deeply comforting. I’m not alone, it tells me—lots of smart people hate math. The reason I hated math, was mediocre at it, and still managed to earn a bachelor’s degree was because I had upper-middle-class parents who paid for tutoring and eventually enrolled me in a college that doesn’t require math credits in order to graduate.

This is impressive self-awareness. The author recognizes that she finds this argument appealing not because it has merit but because she hates math and thought math was hard. Glad we're all on the same page now.

For low-income students, math is often an impenetrable barrier to academic success. Algebra II, which includes polynomials and logarithms, and is required by the new Common Core curriculum standards used by 47 states and territories, drives dropouts at both the high school and college levels. The situation is most dire at public colleges, which are the most likely to require abstract algebra as a precondition for a degree in every field, including art and theater.

*CAR CAREENS OVER CLIFF*

How many colleges require anything beyond the most basic type of two-course math sequence, one or both of which can be satisfied by having taken "college level" math courses of dubious rigidity in high school? I guess Slate doesn't make its writers look up numbers on these things. My experience has been that what college level math is required is often required with some kind of massive loophole such as the ability to fulfill the obligation with specially created, easy to pass "Math for Poets" type classes designed to keep the tuition dollars students enrolled.

“We are really destroying a tremendous amount of talent—people who could be talented in sports writing or being an emergency medical technician, but can’t even get a community college degree,” Hacker told me in an interview. “I regard this math requirement as highly irrational.”

Community college math classes are too difficult? Hmm. That would point to getting very little math in high school, not too much, Mr. Iconoclast. This literally differs not one bit from arguing that someone would make a great EMT if only they didn't have to take some stupid class they can't pass about Shakespeare or psychology or hey this is fun you could put the name of any course in here and the appropriately-surnamed Hacker's argument works!

Unlike most professors who publicly opine about the education system, Hacker, though an eminent scholar, teaches at a low-prestige institution, Queens College, part of the City University of New York system. Most CUNY students come from low-income families, and a 2009 faculty report found that 57 percent fail the system’s required algebra course. A subsequent study showed that when students were allowed to take a statistics class instead, only 44 percent failed.

"When these students had to take a basic math course, slightly over half failed. When we let them take another course that for all anyone knows was designed to be easier to pass so we could keep our retention rates up…slightly under half failed." Sounds like Hacker is an "eminent scholar" in some field that isn't statistics. Oh wait, he's a political scientist. So he should be well aware of how stupid this argument is. And he has taught at the university level for quite some time, so he also knows how deceptive it is. And that he's basically just arguing "We should let them take statistics because apparently it's easier for them to pass," which is the worst possible argument for why they should take statistics instead of math.

Math in this case, just to remind you, is algebra.

Such findings inspired Hacker, in 2013, to create a curriculum to test the ideas he presents in The Math Myth. For two years, he taught what is essentially a course in civic numeracy. Hacker asked students to investigate the gerrymandering of Pennsylvania congressional districts by calculating the number of actual votes Democrats and Republicans received in 2012. The students discovered that it took an average of 181,474 votes to win a Republican seat, but 271,970 votes to win a Democratic seat. In another lesson, Hacker distributed two Schedule C forms, which businesses use to declare their tax-deductible expenses, and asked students to figure out which form was fabricated. Then he introduced Benford’s Law, which holds that in any set of real-world numbers, ones, twos, and threes are more frequent initial digits than fours, fives, sixes, sevens, eights, and nines. By applying this rule, the students could identify the fake Schedule C. (The IRS uses the same technique.)

In his 19-person numeracy seminar, the lowest grade was a C, Hacker says.

Wow. Where to start. OK, so this "civic numeracy" course, designed by Hacker himself and which based on the examples he chose to give involves nothing beyond addition, subtraction, division, and the ability to read English and numbers, produced 19 passing grades when Andrew Hacker taught said class (and awarded the grades, so you know it was super objective because he certainly had no motivation to prove his point, right?). Does anyone know if 19 is a sufficient sample size? I guess they didn't cover "sample size" in "civic numeracy."

Look, I'll be the first one to agree that a class where students learn how to read and interpret statistics is valuable. I teach this very material in a Political Science Research Methods course. It's important. And it is in no way an argument against the value of taking actual math. The sole motivation behind requiring it instead of math is that too many students now are failing math.

Or are they? Who knows, neither the author of this article nor apparently the shittiest social scientist on Earth bothered telling us if students are failing math more regularly today than in the past. That would be important to establish, right? Or else he/she have no argument, right?

Hacker’s previous book, Higher Education? How Universities Are Wasting Our Money and Failing Our Kids, took a dim view of the tenured professoriate, and he extends that perspective in The Math Myth. Math professors, consumed by their esoteric, super-specialized research, simply don’t care very much about the typical undergraduate, Hacker contends.

Ahh, OK. Finally we've established that Hacker makes his living publishing (presumably not without compensation) books pissing on academia. I know this type well. Bet he's real popular with his colleagues between his open minded approach to curriculum and his outstanding argumentation skills.

Math professors, consumed by their esoteric, super-specialized research, simply don’t care very much about the typical undergraduate, Hacker contends. At universities with graduate programs, tenure-track faculty members teach only 10 percent of introductory math classes. At undergraduate colleges, tenure-track professors handle 42 percent of introductory classes. Graduate students and adjuncts shoulder the vast majority of the load, and they aren’t inspiring many students to continue their math education. In 2013, only 1 percent of all bachelor’s degrees awarded were in math.

None of this is remotely relevant to the value of making students take basic algebra. Not even a little. These numbers are here to distract you. I thought we were making a "should" argument about the value of stats-as-math-alternative? Now we've progressed to simply grousing about academia.

“In a way, math departments throughout the country don’t worry,” Hacker says. “They have big budgets because their classes are required, so they keep on going.”

This is the least true thing anyone has written today, and today was the day after Donald Trump all but secured the GOP nomination. What's actually happening, not that Hacker would bother to do any research here, is that math departments are piling more courses on tenured or tenure track faculty (not necessarily introductory courses – note the key adjective he uses) to save money, and also hiring more adjuncts to teach the less demanding courses to save money.

What an excellent example of how to deceive with numbers. Is this in the "civic numeracy" book?

After Hacker previewed the ideas in The Math Myth in a 2012 New York Times op-ed, the Internet lit up with responses accusing him of anti-intellectualism. At book length, it’s harder to dismiss his ideas.

I'm dubious.

He has a deep respect for what he calls the “truth and beauty” of math; his discussion of the discovery and immutability of pi taught me more about the meaning of 3.14 than any class I’ve ever taken.

I bet he does, and I'm sure it did. That's not saying much, per the author's opening comments.

As a longtime education reporter, I know that American teachers, especially those in the elementary grades, have taken few math courses themselves, and often actively dislike the subject. Maybe I would have found abstract math more enjoyable if my teachers had been able to explain it better, perhaps by connecting it somehow to the real world. And if that happened in every school, maybe lots more American kids, even low-income ones, would be able to make the leap from arithmetic to the conceptual mathematics of algebra II and beyond.

Well, a decent social scientist could tell you that since K-12 teachers are so regularly and viciously shit on, not to mention underpaid and regularly threatened by state legislatures with further reductions in benefits and pay, nobody really wants to major in Education. So Education gets the students – Sorry, but if we're going to generalize here, this is accurate… – who can't succeed in any other major. And it gives them a 4.0 in courses specifically designed to be passed by students who are not very academically capable.

Search your heart. You know it to be true.

Of course, if math teachers are to help students understand how abstract concepts (EDIT: Examples omitted) function in the real world, they will have to understand those abstractions themselves. So it’s not reassuring that American teachers are a product of the same sub-par math education system they work in, or that we hire 100,000 to 200,000 new teachers each year at a time when less than 20,000 people are majoring in math annually.

OK so, to recap: Math is too hard because most K-12 students get a bad math education because teachers don't take much math in college, so let's require even less math in college.

Goddamn brilliance.

Could better teachers help more students pass algebra II? Given high student debt, low teacher pay, and the historically low status of the American teaching profession, it would be a tough road. In the meantime, it’s probably a good idea to give students multiple math pathways toward high school and college graduation—some less challenging than others. If we don’t, we’ll be punishing kids for the failures of an entire system.

Wait, what? So this isn't about offering a better alternative at all, then. It's explicitly about offering something easier. Easier and Better are very different, just FYI. "Poor kids have a disadvantage, so let's teach them less and lower the bar for them because the system failed them." Because the system failed them, obviously the system must fail for them. Makes sense.

Make no mistake about this whole trainwreck of an argument, folks: This is about retention rates and tuition dollars. The vast majority of postsecondary institutions in this country are under enrollment and financial stress right now and they are desperate to both attract and retain students. The internal pressure to lower subtly and sometimes not-so-subtly the bar to keep another paying customer in the fold is consistent and nearly universal outside of the top 0.01% of elite institutions. We need bodies and we need revenue. That fact doesn't make higher education Evil. The bad part would be pretending we're changing the curriculum for the students' benefit when in reality we are doing it to extract more revenue out of them. This is nothing but marketing speak for lowering the standards while pretending that we're not doing exactly that.

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80 Responses to “A VERY STUPID ARGUMENT GETS THE FJM TREATMENT”

  1. wmd Says:

    What got me was "abstract algebra" – this is usually a upper level course in the undergraduate curriculum, delving into subjects such as groups, rings and fields. It is about abstract mappings between sets – homomorphisms and isomorphisms. He's talking about something very different and is too pig ignorant to know better.

  2. Isaac Says:

    I'm 36 and shifting career-wise from a task doer to a task planner and manager. So now I'm starting to be brought in to the project planning meetings and conference calls where we have to decide things like HOW THE FUCK ARE WE GOING TO DO THIS DIFFICULT THING AND ALSO MAKE MONEY AND NOT GO BROKE OR GET SUED. Tough decisions that require the ability to collect all kinds of data, impressions, thoughts, and knowledge, jam them together, and come up with estimates so we can budget time, resources, and money. Often there's hundreds of thousands or even millions of dollars worth of stuff on the line. There's several approaches. At my last job, we just went with whatever was easiest and came first into the owner's mind. He's recently laid off most of the staff and is moving the factory into a shed behind his house. At my current job, they use math. And we're hiring people this month. Because math.

  3. Noskilz Says:

    I hope the institutions considering upping enrollment at any cost also consider that the reputations of their programs are probably much easier to damage than they are to fix. Producing graduates employers don't particularly want and who may not be well-equipped to strike out on their own will also probably hurt that bottom line in time.

  4. moderateindy Says:

    Sorry, but he has a point. From an overall curriculum standpoint, advanced Algebra should be replaced with a math class that would be more pertinent to everyday life. There is very little purpose in making it part of a requirement for the large majority of majors, much less high schoolers.
    That doesn't mean eliminating it. There are tons of disciplines for which advanced math is essential. But what do you supose the stats are for people that do poorly, or dislike advanced math, ending up in a vocation that requires it? basically zero. So from an overall educational standpoint why bother requiring a course with marginal overall benefit to most of those that are required to take it?
    I enjoyed math for the most part, but what I think one gets from advanced math, problem solving skills, and logic, can probably be taught as well, or better, via courses that aren't so math intensive.
    And if it is a barrier for people being able to pursue further education, then why not do a cost benefit analysis. What are the actual benefits from an education standpoint as compared to the cost of how many people it deters from getting an education. And are there other alternatives that can teach the same core principles, that have better academic outcomes?

  5. Talisker Says:

    Bravo, Ed.

    I have a PhD in applied mathematics and my job involves analysing the human genome. So I have a different perspective from most on what constitutes "advanced" mathematics. That said, introductory algebra is not advanced. In particular, two lines from the Slate article amused me:

    … even the doctors, accountants, and coders of the future shouldn’t have to master abstract math that they’ll never need.

    Later on, we have:

    Algebra II, which includes polynomials and logarithms […] drives dropouts at both the high school and college levels.

    OH NOES NOT THE POLYNOMIALS!!!!!

    I'm pretty sure Goldstein wouldn't know coding if it bit her in the ass. I speak with some authority when I say, if you can't handle the concept of variable substitution (polynomials) or functions (logarithms), you will be incapable of coding. Not mediocre or poor. Incapable.

    Moving on:

    “In a way, math departments throughout the country don’t worry,” Hacker says. “They have big budgets because their classes are required, so they keep on going.”

    This reminds me of an old academic joke. The Dean says to the Head of Physics, "I don't know why you want a budget for all this expensive equipment. Mathematics only wants pencils, paper, and wastepaper baskets. Sociology doesn't even want wastepaper baskets."

    Pure mathematics, a big-budget department? Please. PhD students to teach those required introductory classes are not terribly expensive.

  6. Talisker Says:

    The full Slate article has this gem of a quote from Hacker:

    More controversially, he points out that many of the nations with excellent math performance, such as China, Russia, and North Korea, are repressive. “So what can we conclude about mathematics, when its brand of brilliance can thrive amid onerous oppression?” he writes. “One response may be that the subject, by its very nature, is so aloof from political and social reality that its discoveries give rulers no causes for concern. If mathematics had the power to move minds toward controversial terrain, it would be viewed as a threat by wary states.”

    Hacker is a very, very stupid person. Not every activity should be judged by its capacity to overthrow oppressive regimes.

    By a similar argument, the government of the USSR was happy with ballet and classical music; therefore teaching children to dance or play an instrument is bad. It badly wanted to win gold at Olympic hockey, therefore playing team sports is bad. And so on.

  7. Lars Macomb Says:

    I am a professor of the human sciences. (I prefer that term, for myself, to "social sciences" which, though its research has proven essential to life in modernity, tends toward econometric language and methodology.) I got to the human sciences by way of philosophy. I got to philosophy by way of mathematics. Mathematics taught me how to think through multivariable problems. It, for me, was an indispensable exercise of mind. Had I gone to law school (as my father demanded), that educational exercise would have been indispensable for me there as well.

    Learning pre-calc and calc was not naturally "easy" for me. (Neither of my parents were educated.) I did benefit from having amazing teachers. The classes were often the highlight of my day. (And, yes, I had friends in college whose instruction was abysmal—professors who stood at the front of the room working out homework problems and talking to the blackboards.)

    In any case, I cite my personal narrative to make a case for keeping the bar high and seeing to it that pedagogy be funded that enables students to have experiences like mine–not only in math, but in languages, philosophy, history, composition, and so forth. But, alas, that's not where we are headed.

    The "consumer mentality" of the new corporate university model is only one facet of a much deeper narrative of cultural neglect. Yes, it's true, there is a growing legion of students who want to be personally flattered and affirmed by the discourse and curriculum of the contemporary university, even if this means that they will undergo four years of entertainment rather than four years of enlightenment.

    But, at the same time, this mentality did not grow itself. It is a product of an epistemology that has increasingly come to suggest that real answers are fully within reach, are in fact "downloadable," and should not require day after day of classroom drudgery and mental masturbation set up as a mere bourgeois affectation of arbitrary cultural hierarchy. Epistemology? Methodology? These are just barriers set up to inhibit students from "telling it like it is."

    In some respects, the mathematics issue taken up in this post represents (at least for me) a watershed moment. If what we want to do is release students on the world, after taking their money for four years of dorm-catered info-tainment, then their possession of intellectual competence at college-level mathematics ought to be a matter of consumer preference. If he/she does not want to study a foreign language, well, he/she should not have to. If he/she does not like math beyond what he/she needs to pay bills, then he/she should be free to take other courses instead.

    In the words of Kurt Cobain: "With the lights out, it's less dangerous/ Here we are now, entertain us/ I feel stupid and contagious/ Here we are now, entertain us."

  8. HoosierPoli Says:

    I was waiting for you to bring up the fact that it would be practically impossible to teach any statistics at all without algebra. Calculus, you can work around. But algebra…

    Teacher: Our statistical model will estimate the effect of various other variables on our dependant variable.

    Student: What's that?

    Teacher: Good question. The dependent variable is the number we're interested in studying. It could be lifespan, income, educational achievement…

    Student: (Interrupting) No, I mean, what's a variable?

  9. HoosierPoli Says:

    moderateindy said, "I enjoyed math for the most part, but what I think one gets from advanced math, problem solving skills, and logic, can probably be taught as well, or better, via courses that aren't so math intensive."

    Having taken a symbolic logic class in college (as a requirement, mind you), I can firmly attest that logic is a lot easier WITH numbers than without. A plus sign beats the hell out of modus ponens.

  10. Tim H. Says:

    I think this could be taken as an indictment of existing textbooks more than algebra itself. I remember reading an Asimov book on math, so much more comprehensible than actual textbooks.

  11. Katydid Says:

    As a military brat, I moved around a lot growing up. I had Algebra 1 in the 8th grade in Hawaii, then started 9th with Geometry, 10th with Algebra II, and 11th with Trigonometry, with the expectation to take Calculus my senior year. Hawaii is not known for its rigorous education, and I was just an average math student. In the 11th grade I moved to a southern state when my father was stationed there. To my dismay, that high school only required 2 years of math to graduate, and didn't require even Algebra 1: "9th grade math" (fractions) and "10th grade math" (???) would have sufficed. Out of a graduating class of nearly 2,000, I was one of 3 Calculus students my senior year.

    In college at the state university, I had to take 2 math classes to graduate, but computer science classes would have counted as math. As a Comp Sci major, I had to take 3 semesters of Calc plus some other math classes, but my roommates who didn't major in a STEM field got by with Algebra 1 and II.

    Do I have a math mind? No, I absolutely suck at math and hated every minute of it. Do I use any of it as a software engineer? Nope. Am I glad I took so much? Absolutely. I was exposed to concepts I never would have pursued on my own.

    P.S. Ed, I think it's brilliant you teach math as part of your classes, and I wish every professor did.

  12. Peggy Says:

    As a high school English teacher, I want to put in my two cents about students failing out of high school because they can't do math. While it is true in my experience that students struggle with math, because of poor numeracy skills or poor study habits, I can only think of one or two students in my 10 year career who failed out of high school or dropped out strictly due to their inability to pass math. We had a student drop out recently after 5 years of high school, having earned 0 math credits in five years, so she might seem to be the student they were talking about… But I was her English teacher during three of those five years, and she failed a lot of English classes, too.

    Her problem might have been an undiagnosed learning disability, or Stubbornness and lack of intelligence, or having been failed by poor teaching at the K-five level when she should have been developing numeracy. But she received significant help and attention for many years from many teachers. (I was her academic advisor for of the five years, so I assure you much was done to try to help her. We are an urban high poverty school, but we are very small and work very hard to prevent students from dropping out.)

    For my students, the barriers tend to be more about home environment and study skills. My students also often lack college role models, while many of them make it to college, a very high percentage dropped out after one or two semesters. All of this is typical for a high priority urban high school students.

    The thing is, I can assure you that even that student would say math was important and necessary. My students who want to find a way out of poverty are interested in feels like STEM. Our robotics club, in its second year, has won the local Championship twice and is on its way to winning state this year. As somebody who works with his students every day, I feel very strongly that math is important, study skills are important, and learning how to think logically given a set of rules is very important. That's all high school math is.

    Tl;dr: what an asinine article. Even the dropouts who can't do math would disagree.

  13. Jestbill Says:

    Education is a shuck.

    You teach people to read and–what do they read? Ayn Rand? All it does is make them uppity.

  14. Peggy Says:

    As a high school English teacher, I want to put in my two cents about students failing out of high school because they can't do math. While it is true in my experience that students struggle with math, because of poor numeracy skills or poor study habits, I can only think of one or two students in my 10 year career who failed out of high school or dropped out strictly due to their inability to pass math. We had a student drop out recently after 5 years of high school, having earned 0 math credits in five years, so she might seem to be the student they were talking about… But I was her English teacher during three of those five years, and she failed a lot of English classes, too.

    Her problem might have been an undiagnosed learning disability, or Stubbornness and lack of intelligence, or having been failed by poor teaching at the K-five level when she should have been developing numeracy. But she received significant help and attention for many years from many teachers. (I was her academic advisor four of the five years, so I assure you much was done to try to help her. We are an urban high poverty school, but we are very small and work very hard to prevent students from dropping out.)

    For my students, the barriers tend to be more about home environment and study skills. My students also often lack college role models, while many of them make it to college, a very high percentage dropped out after one or two semesters. All of this is typical for a high poverty urban high school students. None of it is based on their ability to do math. It's lack of support, and lack of money.

    The thing is, I can assure you that even that student I talked about above would say math was important and necessary. Many of my students who want to find a way out of poverty are interested in fields like STEM, because they're very focused on paying jobs pay off the absurdly high school loans they will have to incur.

    Our robotics club, in its second year, has won the local Championship twice and is on its way to winning state this year. They may be poor urban students, but that doesn't mean they don't kick ass at math. Math skill is not correlated with socioeconomic status.

    As somebody who works with these students every day, I feel very strongly that math is important, study skills are important, and learning how to think logically given a set of rules is very important. That's all high school math is.

    Tl;dr: what an asinine article. Even the dropouts who can't do math would disagree.

  15. Peggy Says:

    Whoops, sorry for double post. Ed, can you delete the first one?

  16. Phil Koop Says:

    I know I'm being trolled by this steaming pile of stupid, but I just can't help myself. Like wmd, I was particularly wound up by the conflation of polynomials and logarithms with "abstract" algebra, which compresses an amazing quantity of wrong into a tiny space.

    Polynomials and logarithms are not algebra, they are functions. I don't know what's in "Algebra II", but I'm pretty sure that in that course they would be functions of numbers. You know, the elementary subject of "numeracy." Polynomials are among the simplest functions; as a practical matter, it would be difficult to explain the concept of a function without mentioning them. And you can't get far in any mathematical subject, such as statistics, without the concept of functions. Logarithms are arguably a more advanced example of function, but they are important in the real world to understand things like growth rates, or the log-scale graphs that are displayed even in mass media.

    When the arguments or values of functions like polynomials are symbols, then sure, that's algebra. But when these symbols are numbers, that is not "abstract" algebra; I guess you could call it "concrete algebra." This use of symbols to represent numbers is very old, older than the world algebra itself, which is derived from an Arabic word and dates only to the middle ages. But this sort of algebra was used in antiquity.

    Gradually, in the 19th century, the realization dawned that the little symbols used in algebra don't have to stand for numbers – in fact, they don't have to stand for anything at all. What really defines an algebra is just the cardinality of a set of symbols and the rules used to manipulate them.

    This, admittedly, really is a pretty abstract idea. However, it is also a very beautiful and powerful one. If you find this idea dull or abstruse, then I have no quarrel with you. But please don't try to infect it with stupid.

  17. RosiesDad Says:

    1. Jaime Escalante (of Stand and Deliver fame) taught AP Calculus to underprivileged Hispanic students in the LA school district and his and their success propelled many of them to college.

    2. The CUNY system may be low prestige but the education you CAN get there is world class. I did my pre-veterinary studies at Hunter College and my biochem at Queens College (where my lab prof, James Hogg, had done his post-doc in Hans Krebs' lab at Oxford. Yeah, that Hans Krebs.) and five of us at Hunter went on to veterinary school at Cornell. So I guess CUNY was prestigious enough for the Ivy League.

    3. Kids don't need to be sold short, they need to be taught well and motivated to learn.

  18. Wim Says:

    I signed up for a remedial course of algebra in college. I didn't have to: it was entirely my choice and idea. Every other individual in the class was compelled to take it, due mostly to having failed that portion of their entrance exams. The instructor told me that I was the only volunteer she had ever encountered in a remedial class and she struggled to understand my purpose in being there. I told her I just wanted to see if I could do it, if I tried, and of course I discovered my high school teachers were right, I simply hadn't been paying attention or applying myself.

  19. Katydid Says:

    @Rosie's Dad; I especially agree with your #3. That's been my job as a parent; to have exposed my kids to as much as I possibly could, and encouraged them to try everything, even if it's hard. So much of the blithering ignorance surrounding us comes from people who have never seen what's outside their little bubble of comfort.

    I also agree with #1, and as for #2, that's fantastic!

  20. Totoro Says:

    While I agree with much that has been said I do get a sense that "practical numeracy" is getting short shrift in our educational system. Critical things like compound interest and credit card rates and payday loans should be a part of the curriculum. This is not to replace any of the concepts of Algebra ! and 2 but as a way to personalize the incredible usefulness of math in everyone's daily lives. Getting from y=x^2 to A=P(1+r)^t just isn't that big a leap and graphing that function can be a real eye-opener for many students.

  21. Isaac Says:

    Also, the idea that some people won't ever need real math and they'll know that when they are 19. I did two enlistments in the military, spent time as a carpenter, a farmer laborer, worked in mind-numbing manufacturing jobs, now I'm a software developer. Along the way, on 3 different campuses and over a 15 year span, I managed to finish my bachelors in (shudder) social sciences. It took me 3 tries to pass Calculus, but I'm sure glad I took it along with Algebra II, Trig, and whatever else was back in those hazy days. Also, college campuses are filled with STEM resources these days. Having trouble with some math or Chem? There's usually a free tutorial session every night of the week, and team discussions, and office hours, and you can pay a grad student three dollars and a pack of ramen and they'll meet you in the library to help you with it.

  22. Matt Says:

    I wanna see Hacker teach statistics without logarithms and exponentials. Is he just going to tell students the Gaussian is defined by Jeebus?

  23. pathman Says:

    I'm a physician and the highest level math class I took was "College Algebra" at a community college. I just don't need higher level math to do my job. I don't have any argument against higher math I'm just sharing my story. Take it for what it's worth.

  24. Phil Koop Says:

    RosiesDad is exactly right. I would just add that a constructive response to the "problem" of math would start with not intimidating kids about math. There are two sides to this. The first is that the sort of math taught in high school is not actually as hard as Hacker suggests. The second is that to the extent that math actually is hard – and after all, it does require a lot of effort and concentration – it's hard for all of us! (Unless you are Terry Tao or something.) Odds are that kid next to you who always does better than you is just more self-confident and therefore doesn't give up as quickly.

  25. verbal Says:

    I agree with you that math is important, but I don't know about the profitability of boosting retention. Most colleges lose money on each student they educate. If they were only interested in the tuition dollars, they'd love to have courses that lead students to drop out halfway through, because they have the full semester's tuition and then don't have to educate them the whole year.

    I think the motivations for lowering the bar are actually noble. People have hoped, as I-forget-who said, that "college would make us all middle-class." So, get everyone to college. Then they realize you have to graduate. So, a diploma! Everyone needs a diploma!

  26. John Danley Says:

    As someone who generally is known as Count Dyscalculia during Halloween, I can still spot a Hacker on the x-axis.

  27. Amanda Says:

    *Friend who teaches algebra 2 waves*

    Research is there to support your claim about the present day teaching force. No offense taken here. I'm surrounded by idiots and there is nothing I can do about it.

    There are solutions to this out there, but everything is such a clusterfuck at this point that I get too tired to even begin. 16 years of standards and testing and curriculum and EVERYONE GO TO COLLEGE and funding structures and school choice and…

    *sobbing intensifies*

  28. Pee Cee Says:

    Here's a course description for Algebra II from a local school:

    "This course includes the study of linear systems and applications; quadratic
    expressions, equations, functions and graphs; and rational and radical expressions and functions."

    *This* is the "advanced" math that we should purge from the high school curriculum?

  29. Ron POp Says:

    "Only mathematicians and some engineers actually use advanced math in their day-to-day work,"

    Yeah, we wouldn't want more of THOSE kinds of people in this country.

  30. Pee Cee Says:

    "16 years of standards and testing and curriculum and EVERYONE GO TO COLLEGE and funding structures and school choice and…"

    Not only that, the push is now for students to graduate high school with two full years of college credit given for courses taken at the high school – without even the small filter of having to pass the AP exam for the topic.

  31. Pee Cee Says:

    "Most colleges lose money on each student they educate."

    Got a source for that? I'm curious as to what sort of colleges this might be true for. (Private four-year colleges?) I suspect it's *completely* wrong for two-year colleges, at least.

  32. Robert M. Says:

    I wanted to post on this earlier, but I couldn't stop banging my head on my desk.

    Let's set aside the very important issue others have mentioned: either Hacker or Goldstein–it's not clear who originated the error–thinks a high-school algebra class qualifies as "abstract". Let's even set aside the issue of retention rates.

    Because what's driving me nuts is the Shakespeare analogy in Slate. The analogy itself is a really good one: Shakespeare is perceived by a lot of high school students as difficult and irrelevant. Undoubtedly we'd see a higher rate of success in classes that teach English if Shakespeare's work were removed from the curriculum and never referenced in college.

    But we keep it in the curriculum anyway! And we keep it despite occasional academic arguments that literally parallel Hacker's. We keep it because the task of embracing Shakespeare requires a sustained exercise in grasping for the unfamiliar. We keep it because it's a valuable tool for understanding the world around us–because art does indeed teach empathy. And we also keep it because we trust the people who teach the subject–the people who are experts in both the content and the pedagogy of language–when they tell us it's important.

    But sure, let's toss it aside. After all, what kind of consequences could possibly devolve from embracing innumeracy except for a small elite?

  33. Greg Says:

    I'm seriously disappointed by Goldstein, who, contrary to your assumptions, wrote an excellent book about teachers and why "reform" is horseshit. It's called the War on Teachers, and apparently consumed the greater part of her higher reasoning functions for some unknowable amount of time. Wonder if she'll ever get it back.

  34. Dave Dell Says:

    Robert M. – Shakespeare. Just a bunch of famous quotes strung together. What a hack.

    I recall (1960's) my local State University (Nebraska) admitting any graduate of a Nebraska accredited High School. Then, Freshman English was used to wash out a full 25% plus. Freshman English was a testing ground to see if you could concentrate enough and study hard enough to learn what might not be of any interest to you personally. If you couldn't do that then the rest of the college curriculum, including many other subjects that would require those aspects of concentration and good study habits, would be a waste of your time and the State's money.

    Of course, in the 60's there were many employment options that didn't require an advanced degree or even a HS diploma.

  35. Talisker Says:

    @Pee Cee: AIUI it's largely true in the UK, where student tuition fees do not match up with costs, and universities typically make up the difference from research funding. But I very much doubt it applies widely in the USA.

  36. Michael Says:

    As a person who runs a household and a small business owner, I literally use algebra on a straight-up daily basis.

    This is a sick man saying sick things.

  37. Robert Says:

    Math, like music, is one of the aspects of human knowledge that have consistently escaped my grasp. I have long regretted this, as science was my first intellectual love, and you can't get far in the sciences if you can't get past trigonometry.

    I did have one magic moment at work, though. A colleague needed to find out the optimal amount of reagent to order to go with the polymer resin he had on hand. He asked me, I turned it into an algebra equation and solved for x. He looked at me as if I'd done a card trick.

    Regarding the OP, I believe students should certainly learn algebra and geometry. If they can go farther, they should be encouraged to do so. I certainly encourage my sons.

  38. Delta Says:

    Wonderful, thanks for writing this; I'm a math lecturer at CUNY, wrote about the same subject today myself, and agree 100% with every word you wrote here. Additional thanks because what Hacker says make me so angry I'm almost shaking and can't read all of them — never mind a detailed take-down like you've so nicely done here. CUNY administration is at the forefront of wanting to eliminate even the most basic math so as to show higher retention/graduation rates, and Hacker gives them political cover for that project.

    Side comment to Dana Goldstein at Slate: PI IS NOT 3.14, FOR CHRISSAKE. The fact that journalists writing math/education hit-pieces are so willing to run our noses in own ignorance on the topic they're addressing is really infuriating.

  39. Tim Says:

    Ed, you and Professor Bruce Fleming at the US Naval Academy would probably get along well. He has published some controversial articles over the years about how USNA has dumbed down their academics over the years to enforce gender, race, and divsion 1 athlete quotas handed down by their source of funding, the highly efficient and cost-effective Department of Defense.

  40. Jim Says:

    So the idea here is "if something is too hard to get right the first time, it probably isn't worth doing at all"? That sounds like a terrific message to send to students.

    *eye roll*

  41. anotherbozo Says:

    Too bad about Mr. Hacker. He wrote one of the all-time best analyses of racism in America:
    http://www.amazon.com/Two-Nations-Separate-Hostile-Unequal/dp/0743238249/ref=tmm_pap_swatch_0?_encoding=UTF8&qid=1457022209&sr=8-1

    And now is peddling a far less compelling set of assumptions. Still, read his book if you're at all inclined. All white Americans are de facto racists, a point he supports brilliantly.

    Our algebra teacher in high school was one of the Slow Talkers of America:
    https://www.youtube.com/watch?v=Qvrh73BVraE
    This worked out well for me. Nothing beats an explanation to the less facile like one slowly delivered. He even wrote on the blackboard in large letters.

  42. SeaTea Says:

    I hate to break it to this entire country, but Universities are NOT, explicitly NOT, about teaching you practical skills that you will then put to use in your profession. They are about expanding your mind, introducing you to new concepts, and most importantly, about teaching you HOW TO LEARN so that when you graduate you have the tools to think critically, research, and acquire the knowledge you will need for the rest of your life, whatever the challenges you will face.

    I am a software engineer. I was a computer science major. Did ANY of the multitudinous computer science classes that I took in college teach me to be a software engineer? Not one. Not a single one. That was NOT the point.

  43. cackalacka Says:

    Much as pursuing a university education is not for everyone, having everyone wearing paper hats saying 'You want fries with that?' no a viable goal, either.

  44. Professor Fate Says:

    What math did for me personally was teach me a way to think about problems and solve them – really if you don't develop or use the logical part of your mind well you don't have one and you get things like, well the current political mess.
    And might I add I follow base ball – and as anybody can tell youu, ou use math a lot there – especially now with things like WHIP.

  45. Dave Dell Says:

    There's math and then there's math for rich people. Time Value of Money is a largely mathematical concept that is understood by rich people (or the people who handle their money) but not so much by the – for lack of a better word and I'm sure there must be a better word – masses.

    I recall a conversation with my nephew. $10,000 today or $900 on the first of every month for a year. $10,000 then? OK how about $950 a month for a year? $10,000? OK how about $1,000 a month for a year? Still $10,000? He needs the money NOW! This math works very well for the lending/renting/investor classes but not so much for the borrowing, renting, non-investing young lad that needs his construction business pickup repaired yesterday.

    Speaking of which… If the above nephew has a good year his taxes paid combining Federal Income, Social Security, Medicare, State Income, Property Taxes, Sales Taxes, Gasoline Taxes, and other fees will approach 45% even after saving some income taxes through business deductions of some of the above taxes and fees.

    My nephew doesn't really grasp this although he is good at practical construction math.

    I know this because I worked with numbers and money most of my adult life and thanks to all my math teachers that made this possible.

  46. Mia Says:

    The Shakespeare argument is a terrible one. Sure, reading fiction builds empathy, but that means you could build empathy by reading almost any fiction, right? (Down with Shakespeare, let's put Harry Potter into the high-school English curriculum! /sarc)

    In reality, the argument for reading Shakespeare is pretty similar to the one for teaching Teh Hard Maths: yeah, maybe it's a little difficult at first, but what you get out of it — i.e., cultural literacy or mathematical literacy — is valuable, even if you don't use it in your eventual career. In other words, Andrei was right. :)

  47. Major Kong Says:

    That fancy book-lernin' is just for elitists anyhow. None of you college types have any common sense.

    (my redneck relatives)

  48. Jesse Says:

    Thank you for posting this. Ugh this shit boiled my blood when I read it.

    As an engineer who had to take 7 semesters of college math and retained very little of it, I think there is value in being exposed and forced to learn something even if you don't retain a working knowledge of it. There are many times I've come across a problem in my work and said, "I can figure this out with calculus." I guarantee you I couldn't actually set up the integral and solve it off the top of my head. But I have enough vague awareness of what it is to pull out my textbook, Google it, or ask someone else for help, and I know that if I figured it out once in my life I could probably figure it out again.

    I find it possible that part of the reason people say "you'll never use that in real life" is that they don't know enough about it to know that they could be using it in their real lives.

  49. IU Sucks Says:

    Lol you think so much of yourself. Have you looked in a mirror? Have you made a substantive relationship work? Have you read your CV? You don't deserve to be intellectually outraged; you're basically just a waste of thousands of dollars in educational waste.

  50. Freecookies Says:

    HEY HEY HO HO, WESTERN CIV HAS GOT TO GO.

    (fast forward a few decades)

    HEY HEY HO HO, ALGEBRA 2 HAS GOT TO GO.

    (fast forward a few decades)

    ?

  51. mojrim Says:

    While Hacker's argument is indeed terrible that's less than half a story. What's lacking here is an argument for Algebra II as a general education requirement. You seem quite distant from and dismissive of many people's experience – Dana Goldstein is far from alone.

  52. democommie Says:

    i cannot do any sort of "math" beyond arithmetic. When I look at even the simplest algebraic "stuff", I am completely lost. It is frustrating, to say the least, that I can do carpentry (applied solid geometry?) without understanding the basics of geometry. I was finally diagnosed with ADD and several learning disabiltiies when I was in my mid 40's, math was one of the things that was flagged.

    I love chemistry, enginnering, architecture, astrophysics and the like and I am completely unable to understand what is being demonstrated, mathematically, in any of those disciplines.

    To me, the idea that math, of any sort, is not a course worth teaching is fucking nonsense.

  53. glenn93454 Says:

    Matheism it is then.

    Without math, we 9/11 wouldn't have happened, nor would it have been called 9/11.

    A life without math would be a life without greed.

    Everything would be infinitely divisible without math. No more food shortages. No more food surpluses. We all could just infinitely divide what food we have. Proportions wouldn't even matter to us. Life without greed, remember?

    Become Matheist. At least, become Mathnostic.

  54. vegymper Says:

    where are the previous 50 comments? WordPress and #$%"#$#!!!

  55. Rich Says:

    Goldstein is an idiot. For years, she mostly admonished the rest of the world for not emulating the Ossining, NY schools she attended. She otherwise seemed easily attracted to the faddish nonsense that has always attracted people interested in "reforming education". If she knew anything about education, she'd know that the history of the field is one of picking up and then discarding often obviously frivolous ideas. Moreover, most concepts useful or otherwise are ineptly implemented–progressive education reproduced as chaos or "basics" reduced to mindnumbing drills.

  56. Pee Cee Says:

    @vegymper

    Try http://www.ginandtacos.com/2016/03/03/a-very-stupid-argument-gets-the-fjm-treatment/comment-page-1/

  57. Poultine Says:

    I do think many people miss the opportunity to use basic (NOT abstract) algebra in their daily lives; I end up solving simple equations when cooking (I don't have enough of X, so good do I adjust the recipe?), brewing (the AA content of hopps is different every time, so you have to adjust), estimating arrival times, trying to figure out if it's worthwhile to refinance a loan. So, while it's helpful to dumb-down the lesson and say "here's an equation to solve this surviving problem," you lose the ability to apply the abstract concepts to any area of your life. Which, I would think, would be the ideal.

    My experience with people who struggle with math has been that they can't be bothered to learn the abstract, and just want a recipe for solving problems of a specific structure. And then get lost when the structure changes slightly. I've tried to help several people with math, and, while I'll readily admit that I'm a crap teacher, not a single one of them was willing to step back and learn the fundamentals they were missing.

    Also, I write software for a living, and you can goddamn be assured that I use algebra and polynomials on a regular basis. One of the core CS fundamentals is plotting the growth rate of computation sizes as datasets change. It's important, and not knowing this often makes coders do terrible things.

  58. frosty Says:

    I am a flunked-out math major who became an engineer*. Abstract Algebra was the only class I got a higher grade than a D in. It has nothing to do with Algebra II. F'r instance, once past calculus, you're no longer dealing with numbers and calculations, but proofs.

    These people are idjits.

    * Real Analysis was the course that broke me and made me change my major to the Dumb Jocks of STEM.

  59. Schmitt trigger Says:

    Indeed, where are the previous responses?

  60. Gary Thompson Says:

    I did my duty with algebra in high school. Then I got to college in the 70's still working it"s hippie curriculum. Statistics was taught as a pass/fail course. You were taught not the math of statistics but how it works. You studied the workings of it and you took tests to actually test your knowledge of it. If you failed a test you were re-educated on what you didn't understand and you took the test until you got it. To this day this mathophobic certifiable (Stanford/Binet) genius gets mean/median/mode. I know what they mean by sample. I understand standard deviation. In 2012 I was the guy calming my friends with the belief that Barack Obama would have another term. Why? Nate Silver. Statistics can lie if you feed in bad data. But, if you do the proper work it is rare when they don't predict the outcome. Of course, if your sample lies you're screwed.

  61. Math path | Technology as Nature Says:

    […] mostly agree with Hacker, contra […]

  62. Lori Says:

    Where do people get the idea that statistics is a more accessible subject than algebra? It certainly hasn't been for me. For me, statistics is deeply counterintuitive. I'm over 50 and still haven't managed to wrap my head around basic statistical concepts (but like a pit bull I keep trying). It's not for lack of general math understanding as I did manage to earn a BS degree with a concentration in math.

  63. Really? Says:

    I have been reading about this for a couple of days and it still seems like the stupidest thing I have heard in a long time.

    First, HOW DO YOU DO PROB AND STAT WITHOUT ALGEBRA? What is this nonsense they are peddling?

    Now, I am an engineer so I know a lot more math than most people, and math came easier to me than a lot of people. I do agree that this is certainly a cutoff where the math a person knows is unlikely to be used in their their life. Most people probably don't need calculus of any sort.

    However, how do you balance your checkbook, maintain/repair a home, drive and park, or put any of the various things together or take apart all the things we buy that come in boxes?

    There is a value in being numerate even if you write analysis of Shakespeare for a living. And speaking of that, the idea that english/literature/history have any more intrinsic value than low-mid level mathmatics is complete BS. Both are really most useful in providing a well rounded education that lets a person function within our society. However, you can easily get by without either of them, its just you won't be "in" on why things are the way they are (Please note I am not saying at all that literature/history are LESS important than math either, the whole idea of a deeply "focused" secondary education seems very problematic and actually stupid to me).

  64. c u n d gulag Says:

    Brilliant and hysterical as always!

    As for me, I believed in a God, until I had Algebra in JHS.

    What kind of of a "God" mixes pure numbers, with letters?
    Feh, say I!

    Still, we need math classes!

    What cracked me up, was that on my SAT and NY State Regents exams, I scored much higher in the math parts, than the ones on English.
    I actually got a very nice NY State scholarship for college, based on the results.

    When my teacher's saw my really high scores on those tests in both math and English, they asked me how I did it?
    I said I guess I had the "apptitude."
    What I didn't say, was that maybe you weren't such great teacher's!

    So, we really do need a wide spectrum of classes, including classes in "Civic's", and music.

    But, we can't afford these, can we?
    No!
    Because we need missiles and tanks, and chumps who'll join the military to get a degree, and be cannon-fodder, and not well-rounded citizens…

  65. Brutus Says:

    Before my comment, kudos to Lars Macomb for his comment — especially noting the transition of the higher education enterprise to “four years of dorm-catered info-tainment.” I would add that it now typically takes students more than four years to graduate.

    http://www.nytimes.com/2014/12/02/education/most-college-students-dont-earn-degree-in-4-years-study-finds.html?_r=0

    Colleges and universities have already discovered that a high school diploma fails as a reliable indicator of readiness to undertake college-level study of many subjects. Government agencies and private businesses are in the process of discovering in turn that a college degree fails as a reliable indicator of readiness to undertake the responsibilities of many entry-level jobs. Qualified students do indeed graduate from high school and college, but the trend is to dress up failures as successes by lowering standards and changing requirements. This starts in the early grades and often passes students through the system with lockstep predictability until they are no longer sources of revenue. As a result, the educated, informed public/electorate that in theory makes democracy possible is tainted at the source, and periodic elections held to choose our leaders turn into follies, where choices run either toward those least objectionable or those guaranteed to be the most destructive (because it’s fun to watch thing blow up — even our own government)! My assessment is that the barbarians are inside the gate and we (as a people) approach the United States’ fascist period with great anticipation.

  66. Major Kong Says:

    @c u n d gulag

    "and chumps who'll join the military to get a degree, and be cannon-fodder, and not well-rounded citizens"

    Ahem!

  67. F Says:

    Real analysis was the hardest class I ever took.

    I worry that some subset of the population is simply incapable of the kind of symbolic abstraction required for math.

    However, it really doesn't matter. Math is one of the skills that makes our society a better place. It's not about whether any one individual "needs" it. It's about whether our society functions better if more people can do it and math and Shakespeare both unequivocally qualify. Whether it's hard or not is completely irrelevant.

  68. c u n d gulag Says:

    Sorry, Major Kong!

    It's just that I worked and lived in Fayatteville, NC which I know you are aware is the home of Fort Bragg.
    I met too many young people who couln't otherwise have gone to college, without joining the military.
    Some came back home, solid of body and mind. Others I met, didn't, and we're physically and/or emotionally damaged. And obviously, those who lost their lives in that stupid and needless war and occupation in Iraq.

    I'm in these courageous folks debt.

  69. GeoX Says:

    I took honors algebra II in ninth grade ("honors" mainly because, let's face it, I came from a certain socioeconomic background). I had, and have, NO aptitude for math. Later on, I was only barely able to scrape by in trigonometry. But come ON, even a dope like me was able to maintain a B average in Algebra II. It wasn't that hard (and note that if it HAD been, I could've moved down to regular or basic level). The argument against it seems to boil down to "no one should ever have to take any course that anyone could find even a tiny bit difficult ever."

    I didn't like math because I wasn't naturally good at it, but in retrospect, I regret that I didn't try harder with it; it seems like fascinating stuff.

  70. fredpa Says:

    Without geometry, life would have no point.

  71. Kaleberg Says:

    This reminds me of the bilingual education people who argued that Hispanic immigrants didn't need to learn English in school. They could learn just enough to understand things like "clean the bathroom" or "mow the lawn" instead.

    Mathematics, including Algebra II, is the common language of the sciences. If you don't get at least to A2, you have cut the number of fields you are ready for in college in half. Worse, a lot of those fields you can't major in are the better paying ones.

    Granted, the way mathematics is taught in our state high schools is appalling. They are constantly interrupting the course to discuss applications and relevance. They go down side paths interminably. The whole point of taking geometry is to understand how a handful of simple rules and your brain can build an amazing logical structure that describes the real world. You'd have to hunt for that in a modern HS geometry text book.

    It's like diagramming sentences. Back when kids were taught this, they could reason about whether a sentence was complete and grammatical. Now, they aren't even taught the parts of speech, so they have to bang on their text and pray. It isn't exactly dumbing down. It's the elimination of any real educational content that bothers me. It's like the change after the fall of Rome. A Roman member of the ruling class was expected to have read Horace. A Carolingian member of the ruling class was expected to eat a lot of meat. It was not a clear change for the better.

  72. Delta Says:

    I fully agree with what Kaleberg just said. The junior-high school grammar class is directly comparable to the junior-high grammar class. Understanding the structure of a natural-language sentence is directly comparable to understanding the structure of an equation. Furthermore, the two buttress each other; you can assist algebra students by leveraging their understanding of sentence structure in the translations and conversions. Once one of those supports goes (like diagramming sentences), then it's no wonder that the other one can no longer bear the load.

  73. Delta Says:

    Edit: "The junior-high school grammar class is directly comparable to the junior-high algebra class."

  74. GeoX Says:

    It's like diagramming sentences. Back when kids were taught this, they could reason about whether a sentence was complete and grammatical. Now, they aren't even taught the parts of speech, so they have to bang on their text and pray.

    Is this true? I was taught parts of speech in elementary school (late eighties-early nineties). As for diagramming sentences (which I had to do in graduate school, oddly enough), no one will ever convince me that that's not a bizarre waste of time, albeit an oddly beguiling one.

  75. Anonymous Prof Says:

    If you're an academic, then you have to hear this crap ALL THE TIME. I constantly have people telling me-sometimes screaming at me- that I'm an incompetent teacher because I actually want students to learn things.

    Why do kids need algebra? Let me tell you a story. Last year, my pre-med seniors were rolling their eyes at the striking fast food workers. "Duh- if we pay them $15 an hour, then the cost of a Big Mac will be astronomical!"

    So, I told them to calculate what the actual change in the cost of a Big Mac would be. (Something like 5 cents.)

    Why are people so eager to eliminate math education? Because you need math to understand numbers, and economics is how they use numbers to screw people. My students- seniors, mind you!- just believe whatever the talking heads say, instead of doing the math themselves.

    Re: diagramming sentences, if you don't think diagramming sentences was important, then you aren't making your living with a keyboard. If you want to write clearly, then your writing needs to flow. That means it needs to be structured. So, you need to be able to use techniques like parallelism, which you learn by diagramming sentences.

    My seniors have so little understanding of the structure of writing that they are, quite literally, functionally illiterate. They can't do algebra, because they can't read well enough to understand the word problems. I decided, as an experiment, to give them a magazine article to read. None of them could tell me what the author was trying to say, because none of them can read. (Naturally, I found myself in the office of My Racist Dean, being screamed at for an HOUR. "What the hell are you doing? This isn't English class! You aren't supposed to be teaching them reading- you're supposed to be teaching them science!")

  76. Lori Says:

    With mathematical platonism, whether life has a point is in no way contingent on the person living it being mathematically literate.

  77. GeoX Says:

    Re: diagramming sentences, if you don't think diagramming sentences was important, then you aren't making your living with a keyboard. If you want to write clearly, then your writing needs to flow. That means it needs to be structured. So, you need to be able to use techniques like parallelism, which you learn by diagramming sentences.

    Well…I have a graduate degree in professional writing, and I teach English. Does that count? Again, I learned basic grammar and syntax in elementary school; I never learned anything from diagramming sentences.

  78. mate wierdl Says:

    The problem with Algebra is that most of what they teach are nothing more than useless technology, which has nothing to do with general human culture. The books are unnecessarily long, containing self serving problems and formulas that are used nowhere outside those books—not even by mathematicians.

    It's possible to blame the professors for putting up with these books, but the main motivation for writing these books is coming from publishers like Pearson or McGraw-Hill.

    Mentioning Algebra, as it is taught today in most schools, on the same page with Hamlet is an insult.

  79. Anonymous Prof Says:

    @GeoX: I guess my perspective is more limited than I realized, then. I will certainly admit that I *hated* diagramming sentences at the time.

    @mate wierdl: could you provide some examples?

  80. Bitter Scribe Says:

    Personally I got lucky because when I went to school, if you weren't in a STEM program, you only had to take a couple of techie-ish courses. I went for analytical algebra which, as frosty says above, is entirely about theorems and proofs and barely even uses numbers.

    The school had "rocks for jocks" classes for the kids who couldn't handle math. My own thinking is that if you're exposed to something in a meaningful way, you may find a use and purpose for it even if you're never really good at it. Better to offer a student something like that than throw something at her that she can't handle or has no interest in.