Teachers, leave them kids alone


On my home planet, everyone learns basic algebra. Earth seems to be different.

People are actually discussing whether to remove algebra requirements from community college curricula. They don’t seem to be discussing the elimination of basic reading and writing skills, at least not yet. It seems to me, though, that passing algebra ought to be a really low hurdle to leap, but apparently it isn’t.

Algebra is one of the biggest hurdles to getting a high school or college degree — particularly for students of color and first-generation undergrads.

It is also the single most failed course in community colleges across the country. So if you’re not a STEM major (science, technology, engineering, math), why even study algebra?

I was a first generation undergrad. I didn’t take algebra in college…because I took it in high school. If you were on the college track, you took it early, because in your junior or senior year you’d take trigonometry/pre-calc. If you were an advanced math student (I wasn’t), you got calculus done right there in public school. 16 year olds can learn algebra. It really isn’t that daunting.

“Why even study algebra?” is a stupid question. If you’re not a history major, why study history? If you’re not an English major, why do you need to learn to write good? If you’re an American, why bother learning a foreign language? Algebra is a kind of minimum standard for elementary numeracy.

This interview with Eloy Ortiz Oakley is appalling in many ways.

You are facing pressure to increase graduation rates — only 48 percent graduate from California community colleges with an associate’s degree or transfer to a four-year institution within six years. As we’ve said, passing college algebra is a major barrier to graduation. But is this the easy way out? Just strike the algebra requirement to increase graduation rates instead of teaching math more effectively?

I hear that a lot and unfortunately nothing could be farther from the truth. Somewhere along the lines, since the 1950s, we decided that the only measure of a student’s ability to reason or to do some sort of quantitative measure is algebra. What we’re saying is we want as rigorous a course as possible to determine a student’s ability to succeed, but it should be relevant to their course of study. There are other math courses that we could introduce that tell us a lot more about our students.

No one decided that it was the only measure. People looked at the progression of math concepts that were taught — algebra, geometry, trigonometry, calculus — and set the standard on the most introductory of the math skills. Students who come into college not knowing algebra are totally screwed if they want to enter any STEM field, but even if they’re doing a non-STEM major, I’d argue that everyone ought to have that minimal level of math literacy.

I don’t see the problem here. If “relevance to their course of study” is the standard, I could see biology majors insisting that they don’t need to know psychology or literature (they’d be wrong). A college degree should not be a narrow certificate that says you’ve been exposed to a thin slice of knowledge, but here we are, arguing that it’s all about getting a job.

A lot of students in California community colleges are hoping to prepare for a four-year college. What are you hearing from the four-year institutions? Are they at ease with you dropping the requirement? Or would they then make the students take the same algebra course they’re not taking at community college?

This question is being raised at all levels of higher education — the university level as well as the community college level. There’s a great body of research that’s informing this discussion, much of it coming from some of our top universities, like the Dana Center at the University of Texas, or the Carnegie Foundation. So there’s a lot of research behind this and I think more and more of our public and private university partners are delving into this question of what is the right level of math depending on which major a student is pursuing.

Look. We get transfer students from community colleges at my university all the time. They do not and should not get a free pass on courses that our full four year students have to take — we don’t set standards arbitrarily. They need to take certain lower level courses because they’ll need those skills in upper level courses. If the community colleges set lower standards, it just means that they’ll have wasted two years as the four year colleges tell all those students entering in their third year that sorry, you have to go back and take all these courses your CC decided were unnecessary.

In a perfect world, students would learn algebra in high school; students who struggled or were not mature enough to engage in disciplined learning (which is a real problem) would attend a CC to get the prep they missed in high school, and the four year colleges would be able to assume a basic skill set on all entering students. If CCs are going to punt, what next? Do we just get unprepared students who enter college with 60 credits of unchallenging courses that do not prepare them all for the major curriculum?

And there are people writing about concepts of numeracy that may be different from what people have been teaching all this time. Do you have in mind a curriculum that would be more useful than intermediate algebra?

We are piloting different math pathways within our community colleges. We’re working with our university partners at CSU and the UC, trying to ensure that we can align these courses to best prepare our students to succeed in majors. And if you think about it, you think about the use of statistics not only for a social science major but for every U.S. citizen. This is a skill that we should have all of our students have with them because this affects them in their daily life.

I kind of agree with this — I would like to see more statistics-literacy in the general public. But this is a proposal to increase the amount of math students should know, and I don’t know how you teach statistics to students who can’t comprehend algebra. Again, there seems to be a relevance argument lurking here — if statistics awareness is good for every U.S. citizen, how can you suggest that art majors have no need of algebra? I want to see some minimal expectations for numeracy and literacy, and we don’t get there by trying to second-guess whether a student will ever find a particular fundamental skill “useful”. You just don’t know.

Comments

  1. thirdmill says

    Algebra teaches people to think logically, that objective reality exists, that there are some questions for which there really is only one right answer, and that sometimes, just showing up and participating isn’t good enough. I learned far more about life in math classes than I did just about anywhere else.

  2. A Masked Avenger says

    Good comments, PZ. I would offer a counterpoint to this one, though:

    In a perfect world, students would learn algebra in high school; students who struggled or were not mature enough to engage in disciplined learning (which is a real problem) would attend a CC to get the prep they missed in high school, and the four year colleges would be able to assume a basic skill set on all entering students.

    CCs aren’t just remedial high schools. I attended a CC, and transferred from it into an Ivy as a junior. 100% of my transfer credits were accepted, and I needed only 4 semesters to complete my ScB. But in addition, the CC gave 500% more damns about me than the university did: my transfer coordinator checked in with me 3-6 times per semester, and got me into an Ivy. My University advisor met with me about 3 times in 2 years, at my insistence, and gave me absolutely shitty advice every step of the way — starting with being so ignorant of her own university’s graduation requirements that she gave me advice which, if followed, would have delayed my graduation.

    At my CC I was employed as a tutor, and I basically served as a TA in remedial English and Math courses that taught the bare basics of grammar and arithmetic. So it’s true that CC’s serve everyone, regardless of their preparation level — and it’s true that if you’re starting with Math 100, you probably need more than 8 semesters to complete a bachelor’s. But it’s equally possible to get a top-notch education there, and show up at university well prepared for your final two years. I’m steering my son that route, now that he’s approaching college age.

  3. timberwoof says

    A scary number of people think that despite not having taken or passed high school geometry they can determine the shape of the Earth (to be flat). The same people are bewildered by simple measurements and calculations people can do themselves, either with friends far away or with a sufficiently long road trip. They say that algebra is all made-up mumbo-jumbo based on false assumptions. And these people want to set policy. This is why the aliens don’t talk to us.

  4. devnll says

    You’ve touched on it, but I want to hammer it again, because… well because it’s a favorite soapbox of mine, and _somebody’s_ got to stand on it ranting. What’re you going to do? Start leaving soapboxes unstood-on?

    Lowering the requirements at earlier stages of education based on relevancy to their intended focus doesn’t just mean that people continuing their education will have to play catchup. It means that people have to make the decision of what to study sooner. If the standard is that everyone leaving high school can do algebra, then all high school graduates can at least potentially study whatever they want at college (from a math requirements point-of-view), including things that would require algebra as a pre-req. Your grasp of the subject and/or your grades in it might hint at how _wise_ that decision would be, but at least you’ve been exposed to it. If it’s available but not required, then you’re essentially asking 14-16 year-olds to make the decision about their future career. Oh sure, they could always take the classes later, but that’s harder than it simply being the required path, and they’ll be behind their classmates.

    Speaking of which, the blase assumption that they could _afford_ to play catch-up later is pretty classist. University is stupidly expensive in this country these days; an extra semester or year to fill in the basics that your high school or community college didn’t feel the need to enforce is going to be the difference between “able to afford university” and “not” for a lot of people.

  5. A Masked Avenger says

    People looked at the progression of math concepts that were taught — algebra, geometry, trigonometry, calculus — and set the standard on the most introductory of the math skills.

    QFMFT.

    The transition between arithmetic and algebra is precisely about grappling with abstraction. Learning how to ask about “the number which, when I double it and add three, equals 15.” As well as a notational framework that makes a huge class of such problems easy to solve. Without coming to terms with abstraction, all other mathematics is impossible. Including statistics. A mean is an abstraction — but the difference between a sample mean and a population mean is doubly abstract.

    The alternative is to go with Euclidean geometry. Except for the little problem that people have a way harder time with Euclidean geometry than algebra. Geometry is taught in order to introduce the concept of proofs, which are again a meta-abstraction. Almost everyone who has suffered through high-school geometry has come away with the misconception that for some reason educators actually give a fuck about triangles (we don’t).

  6. slithey tove (twas brillig (stevem)) says

    My high school maths teacher advocating going straight to calculus, in elementary school, even before straight arithmetic. Teaching calculus involves “re-teaching” previous “methods” (ie algebra, arithmetic, geometry, etc) he argued it might be better to cause calculus to teach the earlier subjects, rather than try to “expand” for small. Ie. “start big, and fill in the details; rather than teach all the details and leter try to integrate (no pun) them into a bigger subject.
    IDK
    sounds good to me. I’ve tried to perform similarly in other areas. Start big and fill in details rather than learn all the details first.
    IDK
    ?

  7. sebloom says

    “If you’re not an English major, why do you need to learn to write good?”

    You’re not an English major so you don’t need to write well [sic]! :)

  8. nathanieltagg says

    It is in fact useful and relevant. Consider a recent story described to me: someone in our development office was told that there were matching funds available: an institution would provide matching funds of 40% on any project up to a match of $10k.

    The person was unable to figure out how much money the total project would cost us if we got the maximum match, without trial and error.

    It’s true! The problem (I’m misremembering it a bit) required one line of algebra to solve!

  9. Betsy McCall says

    History suggests something quite different than some of the things you are claiming, PZ. You often complain about physicists treading stupidly on bio turf. Shall we say the same caution is warranted when treading on mathematics, and math education?

    I have taught at various community colleges for 15 years now. The level of abstraction required in algebra is quite difficult for many students. And yes, the community colleges get more of those students than the universities. But let’s look at some facts:

    1) The entire algebra curriculum is designed to support the algebra one uses in differential equations. It was developed in the late 50s and early 60s not to merely develop “logic”, but to make more rocket scientists, all of whom will need differential equations. I often remind my DE students about the algebra they learned in beginning algebra or intermediate algebra or college algebra and haven’t used since then, like factoring sums of cubes. You need this in DE to solve higher-order equations, but you really don’t need it many other places.

    2) Factoring is one of the biggest hurdles students have in beginning algebra and really all kinds of algebra. It’s not used in statistics AT ALL. Algebra is not a monolith. It would be impossible to give up all algebraic topics and still do stats, but algebra-based stats courses could do with a lot less algebra than what students get now, and they would still be okay. Of course, just like physics, to really know where all the equations come from requires calculus, but I’ll settle for being able to interpret answers even if they can’t derive the equation from first principles.

    3) This discussion was not started by community colleges. The Dana Center is working out of the University of Texas, and are one of the biggest proponents of getting students a more targeted algebra experience. Students going into statistics would be much better served by understanding scientific notation and proportions, than using the quadratic formula or conic sections. Community colleges are not looking merely to pass more students. It’s possible to believe a strong math foundation is extremely valuable, and still come away believing that there is a better way to prepare students for the kind of critical thinking they will do in the real world, not just do algebra because that’s what we’ve been doing for 50 years.

    4) An alternative to changing the curriculum could be to change the way math is taught. This is also an option being explored. But change is hard either way. Faculty who came up under lectures and did fine with it, don’t know how else to teach math. Changing content is actually easier for them. Training faculty to do something besides lecture (or some version of lecturing) meets with strong resistance. And the time students would need for most of these other methods would have to increase. Yet many states now mandate only a certain number of credit hours can be used for various degree programs. So using more time for math, requires programs to remove other things their students need. No one is happy about that.

    Math education is undergoing a very serious, and much needed rethink. This kind of hand-wringing isn’t really helpful.

  10. cartomancer says

    I am not familiar with the US education system, but the way you describe it suggests that “algebra” is one course of study, done all at once, in one year. Likewise other elements of mathematics – geometry, trigonometry, etc.

    This is not how we do it here in the UK. Here we just have “mathematics” up to the age of 16, and each year you get taught a bit more of everything with the complexity increasing year on year. So in year 7 (11-12 years old) you would start off with basic algebraic terms and their use in linear equations. Then in year 8 (12-13) you would do quadratic equations (and begin trigonometry, building on the basics from year 7). In year 9 you get things like vectors, matrices, plotting algebraic formulas as graphs and so forth, leading eventually to some work on cubic equations and (at the very end of year 11, for the upper sets, if there is time) to calculus. I’m not really sure what post-16 mathematics is like here, because it is not compulsory and I never did any myself, though I do vaguely remember my fellows who did having to choose between doing statistics and doing mechanics as part of their A-level course.

    Perhaps, rather than trying to jam it all in at once, better results could be achieved if algebra were threaded throughout the High School experience? That might also help to dispel popular myths about it being difficult, which no doubt contribute to disengagement among some who take it.

  11. zibble says

    @9 Betsy McCall
    Any change or improvement in education should not be made without the steadfast acknowledgement that algebra is really fucking important.

    I find it incredible that anyone in the age of computers would actually think statistics were more essential than understanding functions and variables.

  12. zibble says

    @10 cartomancer
    That’s how it is in America, too. People are only talking about algebra as if it’s a one year course because that’s the Algebra 1 course that teaches the very very basic fundamentals. We have subsequent years of Algebra 2, Geometry, Trig, Calculus 1 and 2, but I think the problem is a lot of people don’t make it past the basic course, or they sleepwalk their way through it without actually learning anything.

  13. rgmani says

    Reading the interview, it seems to me that they are planning to get rid of intermediate algebra (which would correspond to Algebra 2 in my daughter’s school) and not elementary algebra (which would be Algebra 1). I might be in the minority here that is not totally opposed to this at the high school level. Algebra 1 and Geometry are high school graduation requirements in California and a lot of schools insist on Algebra 2 as well because it is an entrance requirement for both to UC as well as Cal State system.

    Somehow, I’ve never been sold on the choice of Algebra 1, Geometry and Algebra 2 as the essential courses needed for college admission – particularly for non-STEM students. No arguments about Algebra 1. That is essential to pretty much anything remotely mathematical that students might do in college. Instead of Geometry or Algebra 2, I’d probably have an elementary Probability/Statistics course. Perhaps a third required course could cover parts of Algebra 2 and Geometry.

    Something like that would be a lot more useful to students who are not going to be studying STEM subjects. I’m not sure it would be any easier than what we currently have, though.

    – RM

  14. colinday says

    Is there a specific topic in algebra that is difficult for students? Maybe the introduction of variables?

  15. brucej says

    Betsy McCall just said everything I came here to say only better.

    Blaming the student for not learning things that are poorly taught is not a constructive path for education, and I’m staggered by the level of ‘blame the victim’ here. I mean seriously, this is ‘If you didn’t want to flunk algebra, you shouldn’t have been dressed like that!’ level victim-blaming.

    Math, for all the ‘new math’ hoopla (dating myself here!) is still largely taught by rote. TO THIS DAY I have no fucking clue WHY I ever needed to learn how to solve a binomial equation other than to ‘pass Algebra 1’.

    It’s as if we taught reading by making student memorize random lists of words and sentence fragments, then complain that ‘these lazy-ass kidz these days can’t comprehend Huck Finn’

  16. naturalcynic says

    Perhaps Eloy Ortiz Oakley should change the first name to Eloi to signify a movement in that direction.

  17. says

    I’m a math faculty member in the system that Oakley is chancellor of. There are a lot of ignorant people pontificating on the issue of algebra as a community college requirement. First of all, it’s not “college algebra” that is being discussed. The minimum math requirement for graduation with an associate’s degree from a California community college was the same as the minimum math requirement for a high school diploma: intermediate algebra, that is, good old Algebra 2. There’s since been a roll-back to elementary algebra as the minimum graduation requirement for high school, and this noise is about doing the same in the community colleges. So we aren’t talking about college-level classes at all—just about giving up on holding the line on the remediation of high school deficiencies that has become too great a part of our colleges’ responsibilities. (That’s a related, but separate, complaint; the high schools say la-la-la when we comment on it.) So watch out when people say “college algebra” or (worse!) “abstract algebra” when prattling about this issue. They’re either being sloppy or they just plain don’t know. As for the bright notion that statistics is a better option, guess what the prerequisite for statistics is (throughout the greater part of the known universe). Algebra 2.

    I think I’ll wait for a pause in the debate and then offer my brilliant plan for a guaranteed 100% graduation rate. It’s genius, I tell you!

  18. Nerd of Redhead, Dances OM Trolls says

    Reading this thread, reminds me of a comment the Redhead said about her mother. Her mother didn’t “do algebra”, but according to her daughter, her mother set up the problems similar to algebra and essentially used the same techniques to solve the problem. Her mother had herself psyched out against the name of the mathematical process, not the process.

  19. zibble says

    @15 brucej
    Um, what? Learning *how* to do something is the exact opposite of rote memorization. Ime, the fact that algebra is antithetical to rote memorization is the problem kids have with it – all their other subjects have taught them to just stay up late the night before a test and memorize a bunch of answers they can regurgitate, so they resent that the same strategy doesn’t work in a subject that necessitates actual thought and understanding of the material.

  20. says

    sebloom @7, you just corrected PZ’s joke, thus eliminating the joke. Using “write good” was an intentional mistake. Now I bet you feel like a moran.

  21. anat says

    zibble, there are some things students learn to memorize in algebra instead of learning why they work from first principles. My kid was taught to memorize the formula for solving quadratic equations. I showed him in one evening why it worked and how the formula can be developed by simple algebraic steps but I doubt he cared. In my day we started with simple quadratics that we could all solve on our own and progressed gradually so each of us discovered the quadratic formula on our own, but these days they don’t have time because they needed to prepare for both end-of-year state tests and the 8th grade NCLB test or whatever currently replaces it. Similarly in trigonometry they memorized some of the identities rather than demonstrate them. And skipped much of analytical trigonometry – pretty much anything not needed for calculus. OTOH my kid got more calculus than I did (though they again relied more on memorization than proofs).

  22. says

    I’m not categorically opposed to trying “alternate pathways” to math education, but Eloy Ortiz Oakley said so little about what that actually means! It was all a bunch of “we want to look at this” and “there’s a lot of research on this” but zero hint of what the research actually says. Which part of algebra is being left out? What math do they teach instead? It’s only after a lot of coaxing from the interviewer that Oakley even mentions statistics, and there’s no elaboration on that matter.

  23. says

    #7 sebloom

    “If you’re not an English major, why do you need to learn to write good?”
    You’re not an English major so you don’t need to write well [sic]! :)

    That was a brilliant use of enallage by PZ, wasn’t it?

  24. inflection says

    I am a math professor at a Tech university, so I am fortunate that mathematical aptitude and enthusiasm is basically a given among the students I teach. A student who hasn’t had four years of math in high school didn’t walk in our front door, most likely. In the course of professional discussions, where I generally hear statistics being promoted as a replacement course sequence, it is a replacement for *calculus*, not algebra, and that substitution seems reasonable.

    Algebra is basic for quantitative literacy. Knowing the difference between linear and exponential growth is necessary for understanding financial matters. Even if you never write down “x equals,” you have to have the concept “plug a number into this blank here” in order to mentally calculate. It can’t be discarded from a post-secondary education.

    Last year I listened to one of our U.S. Congressional candidates maunder on about replacing math in the high school curriculum with civics or social studies. Go ahead, guess his party. Guess whether he won. *sigh*

  25. Vivec says

    Honestly I’d have been way more into mathematics and STEM fields as a whole if they’d been taught to me in anything but the most dry, boring, “learn the three things you need for the test” way possible.

    I couldn’t tell you a single equation or specific concept I learned in calculus or geometry because the class was literally just “okay heres the function for parabolas, do 10 of these problems, okay now here’s the function for elipses…” There was zero engagement, and if you had a hard time abstracting from an equation to an S-curve on a graph, fuck off and pay 500$ for a tutor. Mathematics classes in high school very nearly motivated me to drop out and just go for a GED.

    Like, until people can figure out a way to teach it that isn’t damn near painful to trudge through, I don’t think there’ll be much of a shift in opinion on the matter.

  26. Vivec says

    I’d also argue that, at least in my experience of someone that went to a fairly highly-rated high school, mathematics classes were absolute garbage for anyone with any sort of learning/attention disorder. The class boiled down to nothing but “get the test questions right or fail, and I won’t help you pass if you don’t get it.”

  27. zibble says

    @21 anat
    Well, yeah, those are definitely examples of ways that math teaching can be improved. I guess memorization of formulae did once have a point, but with the easy ability to look up that information through the internet, it’s become much more important to understand core concepts. You could even make that case for mental arithmetic – maybe even some people here might remember being told by their math teachers “you won’t have a calculator with you everywhere you go!” Turns out they were wrong about that, lol

    I think it’s really a damn shame when math teachers don’t bother to teach WHY the quad formula is the way it is. But you also need a class full of kids who actually care. I don’t know how you fix that in the anti-intellectual swamp our culture is currently mired in

  28. whheydt says

    I got funny looks in high school when I took wood shop, as I was clearly college bound, (and, indeed, went to UC Berkeley as an EECS major). One thing that really annoyed the shop teacher was the idea that kids that weren’t good at academic subjects should be “good with their hands” and got shunted into shop classes. He tended to get irate with kids that couldn’t complete a “bill of materials” for a project they wanted to do and couldn’t calculate board feet for the wood.

    On the flip side… In the late 1960s when I was at Cal, one of the ways one could satisfy the “2 quarter sequence humanities breadth requirement” was one quarter of physical anthopology and one quarter of archaeology. Some years later, I was really glad I’d taken those courses. If I hadn’t, I wouldn’t have seen the film that was shown of Francois Bordes doing flint knapping and therefore wouldn’t have gotten a change to meet him and see him do a demonstration up close and personal. There were three people there… Bordes, Karen Anderson (he stayed with the Andersons when he visited the Bay Area), and me.

  29. whheydt says

    Re: brucej @ #15…
    Ah, yes…the New Math. I ran into that in high school (yeah, that dates me, too). Hit it and more or less bounced because the assumption built into the courses was that you’d been getting it ever since early grade school. In the end, I must have absorbed some of it–or I got what it was based on later in some Engineering course or other–so what it really was was set theory. Totally useless to me until I got an “Aha!” reaction when I realized 20-odd years later that SQL statements dealing with relational databases are just…set theory. After that, SQL made sense.

    Or as Tom Lehrer put it.. So simple, so very simple, that ONLY a child can do it!

  30. robnyny says

    When I was in MBA school, students howled that the syllabus did not require calculus or even algebra. In finance, accounting, and statistics.

    In law school, students howled that the syllabus did not require calculus or even algebra, in finance, banking, and taxation.

    In practice, I dealt with a finance lawyer who could not multiply or divide by 10 without a calculator. That would make sense if he were from a planet that used Base 12, but he was from U Penn.

  31. emergence says

    Putting aside any issues about more complex algebraic equations, basic algebra – as in using symbols to represent variables in equations and knowing how to solve for their values – is a fundamental mathematical skill. You can’t even express or understand descriptive mathematical equations without understanding basic algebra. I don’t even really get how you could understand statistics without it.

    That said, I think that both ends of the student-teacher relationship need some improvement. A lot of teachers could probably stand to explain the concepts to students better than they do. Running through what a particular type of equation or expression represents in detail would be helpful, as would giving in-depth examples of how these equations are applied in real world situations. However, I’ve personally experienced as a student the kind of apathy toward learning that professors accuse students of. The mistakes that I’ve made as a student make it hard for me to think that asking students to adjust their attitude toward math is victim blaming. Maybe other students really have worked as hard as they can to understand math and still had trouble, but I can’t say that for myself.

  32. VolcanoMan says

    The intermediate algebra that they’re talking about making optional: I taught in a school in Canada where 9th graders learned that. Quadratic equations, both simpler, and multi-variable factoring, etc., and most of them handled it like champs. But they had a solid mathematics foundation to build upon.

    Now I’m not saying that all people should (or will) be able to handle that at 14, but by 17? By 19 (in community college)? But to shift the blame onto THEM for not getting it is also wrong. It is the schools that failed to set up the solid foundation which are causing them to fail algebra. Incidentally, this is where I start to argue for streaming (a dirty word in some circles here). By recognizing where a student is at, what they’re good at, you can design your curriculum to better serve their needs and teach the same things at different rates, and in different ways. Nobody chooses their genetic gifts, or the environs in which they grow up. Nobody should be stigmatized for being in a lower stream, or lauded for landing in a higher one. Anti-streaming dogma has made teachers’ lives much more difficult, because they now have to integrate multiple lesson plans into the same class, to achieve diverse goals amongst the students all sitting in the same room at the same time. This puts more strain on the teacher and leads to lots of teachers giving up and changing careers before they even get established. Streaming solves more problems than it creates because, although socialization goals are important in school (as the anti-streaming people argue), “school is for learning” (Buffybot, BTVS S06E01). Learning is better done when your peers are at your level, where everyone has a similar zone of proximal development (the difference between what a learner can do without help, and with help). In such a case, the teacher is providing one lesson that will benefit ALL learners in her class, not juggling three or four, and wasting most of her students’ time when she’s presenting too difficult, or too easy information and methods to a sub-group within the class (incidentally, this is also why I think mixed-grade classes are shitty).

    Algebra is important precisely BECAUSE it requires abstract thinking. Making it optional because it is expedient to the cause of upping graduation rates is accepting a society in which some college-graduated adults don’t have those kinds of abilities. Western society is already stratifying because of divergent educational achievement, and adults who don’t have certain skills are already looking at a future of underemployment. The value of going to a college such as these will diminish (for EVERYONE) if the standards are lowered. Employers almost never look at transcripts to see what classes you took, after all.

    And for those people who say algebra is not used in statistics, that may be true, but abstract thinking skills are paramount to stats. You have to understand what the formulas are doing, you have to predict sufficient sample size for a certain p-value, you have to understand why bigger random sample size better approximates the whole of society. Without abstract thinking, how can you even comprehend what a normal distribution is? These complexities are far-removed from the everyday, and they’ll be scary for someone who doesn’t have at least moderate familiarity with things like algebra.

  33. chrislawson says

    With due respect to Betsy McCall and others defending Oakley, remember that in the interview he says some ridiculous things, e.g.:

    “So if you’re not a STEM major (science, technology, engineering, math), why even study algebra?”

    “Somewhere along the lines, since the 1950s, we decided that the only measure of a student’s ability to reason or to do some sort of quantitative measure is algebra.”

    So, sure, it’s perfectly reasonable to discuss what level of maths should be required at various educational levels, but it’s hard to take policy suggestions seriously from someone who makes statements like that. I’d also point out that one of the things I agree with (statistics “is a skill that we should have all of our students have with them because this affects them in their daily life”) is also true of algebra. Anyone who thinks algebra is irrelevant to their life is leaving themselves wide open to exploitation if they ever apply for a bank loan, or order carpet, or choose a petrol based on efficiency, or try work out how many serves of a food they can eat to stay within a calorie-controlled diet.

  34. says

    Because major chunks of algebra can be “learned” by rote — just plug these numbers into this formula! — there has been a dangerous tendency to default to this mode too often. This is particularly true in school districts where algebra is taught by PE coaches who are just rounding out their schedules and have no personal engagement with the material. I’m fortunate to teach at a large school where we are able to offer instruction in lots of different formats, which shifts a substantial portion of the burden to proper placement, putting the student where he or she will do best. We even blend algebra with statistics in one of the more innovative approaches. But a big problem continues to be how poisoned the math well was in our students’ elementary school and high school experiences.

  35. says

    AnthonyBarcellos @17,
    LOL, I just saw that the NPR article refers to “abstract algebra”. I don’t think it means what they think it means.

    I took abstract algebra as part of my math minor, and it was the toughest math course I ever took. It was mostly useless, but I wish I remembered more of it, because it turns out group theory is useful in origami.

  36. consciousness razor says

    chrislawson:

    Continuing with that quote, for a taste of more ridiculous garbage:

    What we’re saying is we want as rigorous a course as possible to determine a student’s ability to succeed, but it should be relevant to their course of study. There are other math courses that we could introduce that tell us a lot more about our students.

    Uh…. we have some sort of math course which is apparently done “to determine a student’s ability to succeed” and tell “us” things about them. We have those things for educators, so that educators may make measurements of students and conjure up some determinations about success or potential success … or fuck, this bullshit doesn’t mean anything, does it? That’s a really fucking weird way to describe a course and the job of an educator. I mean, sure, you do evaluate their performance and so forth, but that’s not why you have a course in the first place. And you don’t design the whole curriculum around the goal of “measuring” students in different situations, like they’re lab rats running through a maze or something.

    If you can somehow make it out of a “higher” (or even secondary) education with no clear grasp of some very basic math, then I think you lost the opportunity to get a decent education, which is awfully sad. Forget about graduating — Plato would not have let you begin studying at his academy without knowing some geometry, because until then you weren’t ready for what that dude was cooking. And, well, a few things have happened since then, like algebra for instance…. Perhaps students ought to be exposed to such information, rather than being told by everyone that they need jobs/money/success or some such bullshit.

    The whole argument about stats being more useful for humanists (as if that mattered) is also just plain weird. I don’t get how that could be taken seriously. Maybe it’s worth mentioning anyway that stats is totally useless for almost everything in a music program. Of course, there are tons of other totally indispensable applications of math, from freshman year on, which had better come from somewhere or even more would struggle with the material. It’s not even anything terribly fancy most of the time (not by my standards at least), but it’s also definitely not statistics.

  37. Ichthyic says

    I rather think the argument about statistics courses being valuable to EVERYBODY, is not whether you can do a ChiSquare or understand what an analysis of variance is, but rather a good grasp of probability.

    understanding basic probability benefits everyone in a democracy. really.

    if you don’t understand that… then you should take a basic probability course!

  38. consciousness razor says

    Ichthyic, I totally agree about all of that. (And I enjoyed my stats class in college, but I like math in general.) It’s still extra suspicious to claim it’s more useful/valuable than algebra. And as PZ and anthonybarcellos pointed out, you need algebra for that anyway.

  39. says

    Mathematics teaches people how to break large problems down into smaller ones, how to solve the smaller problems, then put the smaller answers back together to get a solution to the large problem.

    This is a vitally necessary skill, and one that MUST be taught if we are to survive as a technology-based society.

  40. Holms says

    Question:

    What are you hearing from the four-year institutions? Are they at ease with you dropping the requirement? Or would they then make the students take the same algebra course they’re not taking at community college?

    Answer:

    This question is being raised at all levels of higher education — the university level as well as the community college level. There’s a great body of research that’s informing this discussion, much of it coming from some of our top universities, like the Dana Center at the University of Texas, or the Carnegie Foundation. So there’s a lot of research behind this and I think more and more of our public and private university partners are delving into this question of what is the right level of math depending on which major a student is pursuing.

    100% evasion. “there’s a great body of reasearch informing this discussion [from universities]” but no word on what they actually say. And we can lay some pretty safe bets as to what they do think of it all: it’s a terrible idea, and they absolutely will have to take up the burden of teaching algebra that the CCs are skipping out on.

  41. vytautasjanaauskas says

    As a non-american, what does algebra even mean? Linear algebra, abstract algebra or just being able to add numbers together?

  42. says

    I teach math at a French university, and must give you fellow Americans a dire warning.

    During the last few years, the French high school curriculum has undergone a couple of awful reforms, largely imposed to schools from above with little or no feedback by the actual teachers. In particular, the maths and physics programs have been “improved” in order to be more adapted to the needs of a modern society: Euclidean geometry and algebra were largely dropped to leave room for more statistics and probability, that kind of thing. Physics is taught in a more qualitative (i.e. hand waving) way and without the use of equations. That kind of stuff.

    It’s a disaster. Most reasoning and deduction has vanished from maths classes, substituted by small numerical calculations and rote learning of meaningless recipes. Physics and maths teachers have a hard time teaching this nonsensical program, with only the better ones managing to smuggle into class a little thinking and a basic set of skills.

    I routinely find 18 year old students in my university classes who don’t know how to solve a first order equation (2.x + 3 = 5), and occasionally can’t even sum two fractions, but somehow think that they will become engineers within a couple of years. After concluding a “scientific” high school specialisation, many still have absolutely no idea of what maths is or what it is good for. I have students complaining openly in class about all the “useless abstract stuff” I teach them, when all they want is to become middle school maths teachers — the “useless abstract stuff” in question being: reasoning by induction, the binomial formula, sets and functions…

    As a result, French university curricula in scientific subjects has now been steadily declining for at least a decade. The whole first bachelor year has become a big remedial class. This has dragged down the level of all subsequent years. Rigorous proofs are not even properly introduced until the second year. Subjects that only a few years ago were taught in the first year to all engineers are now unthinkable even for second or third year maths students. Exchange students from other European countries like Italy or Germany are amazed at how little is required of them here. Good students don’t want to do their Master’s in France anymore, and PhD students are becoming harder to lure in as well. The morale is low.

    Of course there are many other factors in play here, but, up to a certain point, I see the current situation as a real-life experiment showing what happens when you forcibly sterilise the teaching of maths in middle- and high school, to the point where it brings little or no understanding to students. And yes, school algebra lies the very heart of this.

    (Note: virtually all French universities are public, financed by the central government, essentially free of charge, and open to all students. There is a small set of elite schools with a very tough entrance exam, requiring years of preparation to pass. The latter don’t really suffer from the above-mentioned problems; they get the best students and produce the best engineers, but we’re talking about a small fraction of the engineers who get injected into society.)

  43. handsomemrtoad says

    RE: “I could see biology majors insisting that they don’t need to know psychology or literature (they’d be wrong).”

    I remember hanging out with some friends who were MIT undergrads, and hearing one of them, a brilliant electrical-engineering major, say that Frank Herbert (author of DUNE) was an important philosophical writer, because he had invented the concept of racial/genetic memory.

  44. says

    The transition between arithmetic and algebra is precisely about grappling with abstraction. Learning how to ask about “the number which, when I double it and add three, equals 15.”

    The problem is that math “is” the abstraction in the first place. Algebra is, or should be, merely the explanation of how the F we created this abstraction. Numbers are not “things” they are placeholders for things and using as letter, instead of a rock, for example, or beads on an abacus, etc., is just a different version of the same bloody thing. Yet, somehow we can’t manage to get this concept across to clowns like the one trying to remove it from college requirements? Yeah, pretty sure we are doing a damn poor job at this “teaching” thing, or something…

  45. drst says

    I gotta be honest. I suffered my way through algebra in high school and have never in my entire life, including a BA, two Master’s degrees and a PhD, and 20+ years both teaching and in the non-educational work force, needed to know more than that. Granted, while I work heavily with computers and digital tech, I’m not in a STEM field.

    I get teaching a basic level of understanding to high school students, but I didn’t take a single math course after high school. Requiring algebra (specifically) of everyone in college makes no sense to me. My undergrad college required a “science and math” block of courses, which I filled with 3 science classes. Two of them were taught for “non-science majors” like me (one of them was a bio class that was mostly the professor telling us how to poison people with different plants as I recall). They gave me some more info and a chance to geek out over rocks, which was fine by me and all I needed.

  46. felicis says

    One thing I have been disturbed about for a while – I took the SAT (and ACT) back in ’83. I took the GRE in 1995. I noticed that the math section on the GRE seemed identical (or at least fairly close to what I remembered) on the SAT. That is – the default assumption is that students will learn no additional mathematics at all in college.

    This is not a new problem.

  47. Mobius says

    Oklahoma State used to have a requirement that all students had to pass College Algebra, a step higher than Intermediate Algebra and just shy of Trigonometry. There were a lot of complaints and the university changed the requirements to include alternative courses to College Algebra. These courses still included algebra, but didn’t have that scary word in their title and were geared toward “practical” math.

  48. eidolon says

    Illiteracy is properly condemned and fought against. Innumeracy is somehow o.k. “It’s o.k. Donny John, I was never good at math either.”

    There is the concept of learning readiness – students do not reach a formal, operational stage at the same time. Still, by the time thy are 18, they should be there. The danger of the “when will you ever need this?” lies in the fact that goals and needs evolve throughout your life. As a teacher – and a student – I have learned that nothing limits your options more than poor math skills. Lowering the bar does not make for better high jumpers. Improving and changing how the fundamentals of Algebra and precursor courses are taught will enable more to clear the bar.

  49. consciousness razor says

    drst:

    I get teaching a basic level of understanding to high school students, but I didn’t take a single math course after high school. Requiring algebra (specifically) of everyone in college makes no sense to me.

    Maybe you skipped over anthonybarcellos’ comment #17. As part of the math faculty in the system at issue, I’m sure he knows what he’s talking about. This is about algebra 2, the class you presumably passed (and suffered through), the basic stuff you think high school students should learn, not a college-level course beyond that.

    eidolon:

    The danger of the “when will you ever need this?” lies in the fact that goals and needs evolve throughout your life.

    Definitely. I get that some people may want to complain that they were never properly taught how to use algebra. That’s unfortunate, but I would understand complaints like that. Saying it isn’t useful … that’s something else.

  50. says

    In 1892, there was an NEA task force which proposed that compulsory education should be as broad and all-encompassing as possible. They made this proposition because students were unlikely to be exposed to concepts outside of their profession after graduation, they should be exposed to as many as possible before graduation. This task force was made up mostly of teachers, and mostly of teachers of higher education.

    In 1914, there was another task force, made up largely of the sort of worker who is associated with education, but is not a teacher. (Principles, guidance counselors, etc.) This task force decided that any subject taught in compulsory education must be justified by being applicable to employment. Ever since then, that has been the prevailing attitude.

    It’s a difference in outlook which cannot be surmounted, comparable to how the right and the left look at government-provided services. (The left wants services to serve as many people who need them as possible, even if this means serving people who don’t actually need the service. The right wants to exclude as many people who do not need the service as possible, even if this means people who need the service are excluded. These two views cannot reasonably be reconciled.)

    @#9, Betsy McCall, @15, brucej
    Oh, so since students “won’t need” factoring, we should leave it out?

    Well, heck, on that principle, we can cut out all of English classes except for composition. No more literature — I haven’t needed to read any literature since college, and then only because my school required us to take classes outside our majors, which is obviously an inefficient method because we don’t need them. I haven’t needed a damn poem or play, ever, since the last one I had to read to pass a high school class.

    And history and geography; all that time spent memorizing who fought who in which war, and what sort of terrain is found in different areas? Forget it. It never comes up in job interviews.

    Heck, on your principle, education should be reduced to: learning to read phonetically, from index cards, learning to count (actual arithmetic can be handled by calculators now), and learning to type (why teach people to write when we have keyboards?). We can have the little bastards in and out of school in a year, maybe less.

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