requiring algebra is nice and should be done, but in stages. how the LA school system fails all....

[acroyear]

From this LATimes article(reg required)

[Math teacher] Seidel did not appear to make a difference with Gabriela Ocampo. She failed his class in the fall of 2004, her sixth and final semester of Fs in algebra.

But Gabriela didn't give Seidel much of a chance; she skipped 62 of 93 days that semester.

but earlier in the article, the systems own flaws revealed themselves

Birmingham High in Van Nuys, where Gabriela Ocampo struggled to grasp algebra, has a failure rate that's about average for the district. Nearly half the ninth-grade class flunked beginning algebra last year.

In the spring semester alone, more freshmen failed than passed. The tally: 367 Fs and 355 passes, nearly one-third of them Ds.

and

Like other schools in the nation's second-largest district, Birmingham High deals with failing students by shuttling them back into algebra, often with the same teachers.

Last fall, the school scheduled 17 classes of up to 40 students each for those repeating first-semester algebra.

Educational psychologists say reenrolling such students in algebra decreases their chances of graduating.

"Repeated failure makes kids think they can't do the work. And when they can't do the work, they say, 'I'm out of here,' " said Andrew Porter, director of the Learning Sciences Institute at Vanderbilt University in Nashville.

The strategy has also failed to provide students with what they need most: a review of basic math.

Teachers complain that they have no time for remediation, that the rapid pace mandated by the district leaves behind students like Tina Norwood, 15, who is failing beginning algebra for the third time.

Tina, who says math has mystified her since she first saw fractions in elementary school, spends class time writing in her journal, chatting with friends or snapping pictures of herself with her cellphone.

Her teacher wasn't surprised when Tina bombed a recent test that asked her, among other things, to graph the equations 4x + y = 9 and 2x -- 3y = -- 6. She left most of the answers blank, writing a desperate message at the top of the page: "Still don't get it, not gonna get it, guess i'm seeing this next year!"

In short, the system set itself up for utter failure. Rather than create a gradual improvement system where preparation for high school algebra was improved in the earlier grades, so that when the mandetory requirement was enacted, they had students ready for it; the system simply shoved this arbitrary requirement on a totally unprepared student body and simply let the failures fail. In short, I am disgusted with the school system far more than the students.

In fact, the guy responsible for this disaster used Cohen's own "i have one example, therefore i'm right everywhere" reasoning:

Former board President Jose Huizar introduced this latest round of requirements, which the board approved in a 6-1 vote last June.

Huizar said he was motivated by personal experience: He was a marginal student growing up in Boyle Heights but excelled in high school once a counselor placed him in a demanding curriculum that propelled him to college and a law degree.

"I think there are thousands of kids like me, but we're losing them because we don't give them that opportunity," said Huizar, who left the school board after he was elected to the Los Angeles City Council last fall. "Yes, there will be dropouts. But I'm looking at the glass half full."

On the other hand, Post columnist Richard Cohen's reaction to this is utterly wrong in every way as well.

Comments

[fiona64.livejournal.com]

The one and only course I ever failed was 8th grade algebra ... which I had to repeat the next quarter. I took the course from a different teacher and passed with an A. Some kids respond to different teaching methods better than others.

(I also suspect I have a mild form of dyscalcula ... but that's another story entirely.)

[delinda13.livejournal.com]

I've had to deal with the Southern California School system. The one that couldn't/ wouldn't teach Hank to read. It was a fortuniate turn of events that we moved to small town Iowa in time to get him the reading help he needed otherwise he wouldn't be getting the grades he is now.

He's still having some problems but he's doing ok. Not good enough for George Mason next fall, but ok.

Scare me to think that the new head of education in Prince George is from SoCal

[eac.livejournal.com]

You know, Joe, when I read these articles I can't even grasp what they're telling me.

I'm typically weak in math, and I got the lowest grades I've ever received in geometry (Ds *shudder*) but how can it be possible that HALF of freshmen flunked algebra last year? I understand that students become demoralized, but what the hell are teachers doing to teach this material the first time through?

[eac.livejournal.com]

Of course, it's equally inconceivable to me that California is only now requiring algebra and geometry to graduate...

[sirblackfox.livejournal.com]

Exactly the same here but I was halfway through 9th grade before I was able to convince my GC to move me to a different teacher's class. . . made a world of difference in not just learning Algebra but retaining it.

I think you're dead on with kids responses to teaching methods. My best friend in HS could only learn by having it drummed into his head over and over again (old school learning). . .but it worked for him. I had to be creatively taught, m'thinks.

[dglenn.livejournal.com]

With the caveat that I have no idea whether this is the problem over there, I feel compelled to point out that in addition to some students simply doing better with different teaching styles, when I've been a math teacher or tutor, most of my work has been undoing damage from earlier math teachers my students had had, who didn't really understand the math they'd been trying to teach.

So while I can't draw conclusions about California schools from all the way over here without a lot more information, I nonetheless find myself wondering, based solely on a pattern of observations on this coast, whether the teachers were properly prepared to teach algebra.

Note that even if the algebra teachers were sufficiently prepared, poor math instruction (or even merely insufficiently deep math instruction) in the earlier grades would, as was pointed out above, be enough to sabotage the teaching of algebra to that cohort.

It's amazing how much more difficult math can be to learn from teachers who don't really "get it" themselves. A good teacher will know at least three different ways to teach any one piece and be able to answer all of the "why?" and "how do we know that?" questions that may arise in a math class (though the answer may be, "see me after class if you're interested because the answer is too long to give now"); but a teacher whose understanding of math is only at the "I know if I follow these steps I get the same answer as the calculator" level himself won't be able to tie concepts together for his students and probably won't be able to show the ones who need a different approach any other ways to reach understanding.

Most students (not all, admittedly) could be starting to learn algebra by the fifth grade, if the curriculum were reorganized and the early math teachers understood the underpinnings well enough. Even without making such a radical change to the curriculum, we could be teaching the arithmetic currently taught in elementary school, but in ways that prepare students for about a third of their first algebra course to be, "Oh yeah! Just like ______ but more [formalized|generalized|abstract]!" And oh, how that would take the mystery and fear out of algebra!

(Disclosure: I was a Montessori student (whose teacher ironically worried that she hadn't taught me enough math). When I got to algebra in my next school -- with a teacher who was, AFAIK, not familiar with Montessori -- most of the first year of it was, "Oh, just like I learned years ago, only with different names for it, and symbols instead of glass beads and wooden blocks!" I don't think Montessori intentionally teaches algebra, but the ways the concepts are presented bear some resemblance to how an alebraicist would present them. OT1H, this disclosure reveals that my opinions about math instruction may be shaped by what some might consider an "unfair advantage"; OTOH, it illustrates how mathematics is a fabric that can be explored by picking up any corner and working from there, not something that can only be taught in one specific order. You can derive arithmetic from set theory if you want.)

[eac.livejournal.com]

OT1H, this disclosure reveals that my opinions about math instruction may be shaped by what some might consider an "unfair advantage"

I think it's utterly worth considering how "unfair advantages" work to help students learn. :)

And I think your observations about teachers and depth of math understanding are probably also spot on.

[wilhelmina-d.livejournal.com]

Frankly, I agree with Richard Cohen. I think Algebra is a waste of most kids' time and should be an elective not a requirement. I think that the whole way we look at schooling should be revised. Instead of Algebra I think kids should be taught how to balance a check book. Instead of Geometry kids should be taught how to calculate compound interest.

OK - not really "instead of", but in addition to with a higher priority. Yes, the Algebras and Geometries of the world are important and can help provide a base for higher learning (even if you're not specializing in math or medicine, for example), but they do not help build a foundation for a life in the day to day world.

For full disclosure Geometry is the only class I ever failed. The only reason I got a "D" and not an "F" is that I came to an agreement with the teacher - I'd volunteer in the library during his class instead of ostentatiously reading in his class (because I'd given up trying to understand the class - I just couldn't get it). I hated Algebra, too, but passed it with a C-. I got A's in English, History, Social Studies, etc, and I know it wasn't a lack of trying.

[dglenn.livejournal.com]

When I was a classroom teacher, it seemed like: a third of the class would get my first explanation; then another third would get the second explanation while the first third went, "oh we were right"; and the final third would get the thirdexplanation while the first third went, "why are we still talking about this?" and the middle third went, "that does mean the same thing, right?"

And in one class there was one student who illustrated the difference between "slow" and "stupid". He'd sit there with a frown on his face, ignoring the second and third explanations while he bashed his brain against the first explanation for a while. And about the time the last of his classmates were finally seeing how the third explanation worked, he'd finally make sense of the first one and look up again, smiling. I think he may have worked twice as hard as anyone else in that class, and he never came up with answers quickly, but his test and homework scores were right up there in the B range and he never actually fell behind.

And that wasn't even "different teaching methods", just different ways of explaining things by one teacher with one "teaching method". For students who really do need different methods -- or even if they don't require a different teaching method but would do better with a different one -- the difference in results when they get what they need is much more dramatic.

Repeating a failed class with the same teacher ... Uh, I see a problem with having that as the default. (It can work, and there are circumstances where it even makes sense, but when this many are failing, it seems insane to just do it all over with no changes.)

[dglenn.livejournal.com]

Well there's also the possibility -- as fits my reputation in school -- that I'm just gifted at math (which would make my opinions about how math should be taught an example of what I think theferrett referred to as "the tyranny of the exceptional individual", or something like that. But although I acknowledge that I'm smart (in the sense that I score very well on so-called intelligence tests), I suspect that my apparent gift for math is a combination of a) exposure to a superior instructional method early on, b) exposure to instructional methods suited to me personally, c) exposure to an especially gifted teacher using classical methods later on, and d) finding math pretty enough to want to look at it more closely.

That is, I think that my "natural advantage" in math was acquired rather than innate. But there's no control subject for this experiment, so I don't really know.

But I do think that Montessori is a superior method for most children, and that we would do better to make that the norm and reserve currently conventional methods for the few students not well suited to Montessori. So yeah, considering "unfair advantages" that can be shared, and how to distribute them to more of the population, is worthwhile.

[faerydusted1.livejournal.com]

Oooh.. have to disagree with you there, hun. And this is coming from someone who also despised and struggled with Algebra in High School. First of all, I agree whole heartedly that young people need to learn to read maps and balance checkbooks. However, saying that Algebra and Geometry should go on the back burner because they are not practical to every day life is the same argument being used today to cut back on those classes you did love, as well as to attack Art and Music. "Children should be learning real-world skills, not what happened 600 years ago" or "My child needs to know how to survive in today's wold, not how to play an instrument".
What these folks don't understand (and I'm talking more about those extreme cases that want to rid our schools of the arts completely, although your comment was what initially sparked my thought), is that its the wide range of these classes that allow for broader thought and problem-solving. In the classes I taught I always heard 'Why do we have to learn this'? True, my students would probably never going to have to know about Social Studies or Science, but the skills they learned in the actual learning of those things was what I hoped they'd gain.
That having been said, I have, on occasion, cringed to have found myself using Algebra and Geometry in my every-day, simple life. It happens.

I also agree that there are teachers who don't know the material well and there are students and teachers whose stles don't mesh. What I hate to see in addition to those issues are school systems where the pressure is put on the teachers to pass kids who don't learn the material and are therefore unprepared for future classes. Its all very messy.. :(

[wilhelmina-d.livejournal.com]

You have a very good point there, which is why I amended what I said to "in addition to" instead of "instead of", but you still have a really good point. Education in and of itself is a Good Thing because it teaches you how to learn and how to broaden your horizons and can come in handy.

However, if half of the freshmen are failing algebra (and I am basing that on the above article, not any hard data) there's obviously something more than teaching styles not meshing. There's gotta be a larger issue at hand. What it is - eh, I'm not the person to answer that.

I still do agree with the gist of the opinion article, though. If she expects to fail high school because she can't get this class (assuming all things being ideal that she's actually trying) maybe she shouldn't have to take it to graduate. Maybe they need to look at the individual situation instead of just running her through the same system over and over. And I can't think of a time when Algebra has come in handy and I work with math all the time for my job, maybe not "higher" math, but it is math. :)

[fiona64.livejournal.com]

Oooh.. have to disagree with you there, hun.

Likewise. I used algebra as a newspaper editor ... calculating photograph conversions and layout designs.

[acroyear70.livejournal.com]

However, if half of the freshmen are failing algebra (and I am basing that on the above article, not any hard data) there's obviously something more than teaching styles not meshing. There's gotta be a larger issue at hand. What it is - eh, I'm not the person to answer that.

I pointed out the larger issue. The larger issue is that they lower grades were not in any way preparing the student body for such a requirement. The idea that you could just "require" some mid-level math to graduate and everybody is magically "more prepared" is total bull. The truth is that you have to start *young* if you want to raise the levels.

This is why, much as it generally sucks, "No Child Left Behind" focussed on the elementary and middle school grades, not on high school students, and didn't require current high school students (well, current as of the time the law went into effect) to conform to the same minimum standards that future students will have to meet. You scale it up - to raise the standard of older students means to start looking at your younger students and raising their levels up so they'll meet that higher standard.

And as I also noted, the only justification for this guy saying "it'll work, it worked on me!" is that one example. no studies, no debates, no reading the real literature written by real educators on this issue (my mother would have had a fit over this)...just "hey it worked on me, so it'll be great!" and everybody bought the b.s..

some more comments i made in other blogs

[acroyear70.livejournal.com]

in reply to

Basic algebra -- used to balance a check book, calculate recipe amount, resize photos, figure out postage. Yeah, this girl won't need to know how to do any of that.

I wrote

I think this girl probably *does* know how to do all of those things and doesn't realize its algebra she's doing. again, a failure of most math classes is to try to teach it too much in the abstract first (rules and derivations) and THEN use the word-problem to try to apply that knowledge. This is even more the case in geometry.

I feel it should go the other way around (as that's how we discovered it in the first place) -- give the problem, the application that needs new knowledge you don't already have, and then show where the new lesson or "rule" answers the question in the way that what you already know doesn't. and last, show the derivation of it (if it applies) to "prove" that it works in all cases, not just the original example.

at least, that's how i'd try teaching for those not mathematically inclined. for those going into a math field, the derivation approach is more important because it forces the student to learn to create new algorithms and rule out logical directions that while accurate, don't go anywhere. this is all essential in applying higher maths to physics, chemistry, and computer science.

To a "software developer" who says he never uses algebra, much less calculus, I told him he was full of it:

in software you are doing *nothing but algebra*. you don't take calculus to use calculus (although it helps as background understanding for big-O notation and algorithm analysis and optimization). you take calculus so that by the time you get to *using* algebra and analitic geometry, it is so practiced and ingrained its natural and just happens.

just because you're using more functions than raw math, on strings more often than numbers, doesn't mean your not manipulating variables just as much as you would be in an algebra two class.

in fact, i would propose that real string manipulation (substrings, replacements, indexing, searching, regexps) is actually *harder* than most of content of an algebra one class and you couldn't do it without knowing those rules first.

and, of course, any visual graphics rendering requires knowing and using analytic geometry, even without going 3-D. a simple little map library i wrote, requiring java-2D, made me go back and re-learn (well, re-derive) 2 weeks worth of linear algebra to know what was going on to make sure the scrolling system worked, but because i knew it the code worked first time with no bug-fixing required.

[acroyear70.livejournal.com]

i address the "different methods" approach in a new comment at the bottom of this page.

[acroyear70.livejournal.com]

Repeating a failed class with the same teacher ... Uh, I see a problem with having that as the default. (It can work, and there are circumstances where it even makes sense, but when this many are failing, it seems insane to just do it all over with no changes.)

Well, in some cases its necessary (my dad's sister failed geometry in newfoundland, and had to take it again with the same guy simply because there wasn't another math teacher in the rather tiny school), but I don't see any high school in LA County as having that problem.

in fact, my aunt technically failed the class a second time, but the teacher gave her the 'C' because both recognized she'd never "get" it so why hold her back. into algebra 2 and she had no hassles at all. the "abstractions" and "proofs" stuff of geometry, with no numbers except "90", "180" and "360", basically meant nothing to her no matter how it was explained (my dad tried to tutor her as well, to no avail). but put in stuff that has real numbers and she can handle nearly anything (she's an executive assistant and has to do considerably accounting with no problem at all).

[acroyear70.livejournal.com]

heh, i was the opposite. i am grateful for still having the aptitude for math *in spite* of all the elementary school systems tried to do to destroy it. i could have (in the way they do now for math-inclined students, at least in MD) managed to get through to calculus by 10th grade and gone on to greater things (like actually had calculus-based AP-Physics mechanics in my senior year) if the school systems I was in for 4th and 5th grades actually supported the idea that kids could do that.

instead, i got 2 years of *exactly* the same thing (3 digit by 2 digit multiplication/division), which was something i'd already demonstrated i'd mastered in 3rd grade...and then *6th* grade "GT" level gives me exactly the same shit for yet another year!

4 years of rote arithmetic and its a miracle i managed to keep interested in it enough to make it effectively a career (software development IS algebra, and i really feel that string manipulation is more complex than most of what an algebra 2 class throws at one).

[fiona64.livejournal.com]

Interestingly enough, I too found geometry insanely easy. I could "see" how it all fit.

[cozit.livejournal.com]

Sometimes the problem is developmental. Algebra is where even some *very* bright students run into trouble, because it's abstract, rather than concrete. (Hey, it's what took me down from GT with the GT kids a grade ahead of me, all the way back down to a "regular class" in my own grade... yeah, I got it... quite well actually :-))

Intervention is the reason I've got a job. But just in case you think "oh, great.. that county's got people helping the students out... remember I was hired as a *half* time Math *Assistant*. Not actually required to have all the background I have... either in the maths or in teaching.

Hey, on the bright side, I'm not seeing about half the kids I had last year at all, and first half to second half of this year, I've got more than a 50% change in who I'm seeing. Two *have* ended up with IEPs (in other words they have a learning disability that has been diagnosed and they will receive assistance through that program)... but that's good, too... if they get the help they need to get past what holds them up.

Then again, I've got three *very* stubborn students in one grade level... who I had last year... had this fall... and have again. In part because they refused to even *try* on most of the evaluation test they were given... they don't want to go to the class that they do have, they'd rather be with me and drive me batty. I swear I'm not joking when I tell them that I've had it and they get no more than one warning before being sent to the office if they keep the other from learning and waste my time as well as theirs... but without a grade or anything else to "earn" from their time with me... they've little to no incentive.

Sigh.

*g* On the bright side, I get to throw different ways of looking at hings at them. This month's oddities include integer math with number lines and flipping line segments (hey, it works, and it's a visual they can take with them and re-try on the back of the test or scratch paper to remind them how to play with negatives) and my combining variables lesson... that includes llamas, ducks, badgers, mushrooms and snakes (yes, first two sub in for X and Y... second set of 3 for a different set :-)

[cozit.livejournal.com]

Some kids get into the "it's not cool to do the work" rut. Others aren't ready for it, developmentally. In some schools and school districts, that can add up.

I don't know about there at all... and I don't know if it's a state thing or a Howard County thing... but here you *cannot* teach an Algebra I or higher class unless you hold the state's Secondary Math certification. Mostly to keep those who haven't a clue from attempting to teach it. When I student taught in a 7th grade math class, I was not allowed to teach the GT students for that reason. *g* My cooperating teacher knew my background and capabilites... so I ended up tutoring occasionally during lunch, and when she had to be out of the class and had a sub come in, that was the period that *I* was supposed to teach, even before I reached the point where I was taking over the other classes. From her lesson plans, but I had the freedom to go ahead and make them mine, rather than follow specifially. It was fun... the kids also learned quickly that I *meant* it when I told them not to ask me how to solve any of the questions I hadn't either worked out before or had in the book in front of me before 10am. My brain just doesn't work that way very well until then. (fine after that... and I *do* understand it, so a reminder in front of me was all I needed to teach or review properly... just couldn't actually do the proper logical steps that early w/o the framework.)

[cozit.livejournal.com]

They're not completely able to teach the higher math kids. J's one of those. Poor kid has been (mostly) bored out of his skull with the math stuff since kindergarden. Even this year he's in 4th grade GT, being taught the 5th grade GT curriculm as well... which is the equivalent of 7th grade math, the year before pre-algebra, for the 'regular' tracks. They don't know what they will do with him next year (and his one friend who is being taught at the same level, but isn't quite as advanced as he is)... yet.

I'm seriously thinking of sending an e-mail to the coordinator who teaches the 6th graders who are at an equivalently advanced level... asking if there's any suggestions she might have.

Oh... and at home? He's actually playing with algebra I topics (so more than a grade above what he is being taught now). Yeah, we've glossed over most of the geometry stuff... but that's mostly because of a combination of lack of interest on his part, and lack of strength in it on ours (that was the class that started my downfall... since they'd had me skip alg. I that year to enter it, and I was trying to learn both at the same time... blech... I *might* have liked it, but the stress of that year was enough to kill that idea off for me).

At least math is fun for him... and he doesn't mind doing the "easy stuff" as they make sure that he doesn't have any glaring holes that need covered (like in the geometry direction).

[dglenn.livejournal.com]

The teachers whose damage I had to repair weren't algebra teachers; they were the elementary school teachers that had left their students at a huge disadvantage for understanding any later math. If those teachers had been required to really understand algebra (even though they aren't teaching it) and to grok number theory, that would do a lot of good.

The problem is that too many early math teachers are perfectly competent at elementary-school arithmetc (and presumable able to do algebra) but don't really understand why it all works. And that affects how they teach, and which questions from students they can or can't answer meaningfully (and correctly), and results in kids who find math harder and/or more confusing -- more arbitrary-seeming and mysterious -- than it ought to be. But we're not requiring them to be fluent in the topics they're not expected to teach directly ... *sigh*

So what I was dealing with as a tutor was usually algebra students that had a competent algebra teacher but a personal disadvantage because of their previous teachers (and occasionally I did have to help someone cope with a bad algebra teacher as well, of course, but that wasn't the usual case). And what I dealt with in my brief stint as a classroom teacher included a lot of back-filling concepts that hadn't been adequately taught by those who had come before me.

There was an awful lot of "it's not supposed to be that hard, really; let me show you why".

I'm extremely tired right now and possibly not communicating very well; I'll try to remember to come back to this after I've slept.

[cozit.livejournal.com]

Don't assume elementary school teachers know their math... not even *really* through the 6th/7th grade... before pre-algebra stuff.

I sat in the back of my "Mathmatics for Elementary School Teachers" class (yeah, a bit over 10 years ago, but I'm guessing it hasn't changed much) and crocheted in an attempt to keep my mouth shut when hearing the *dumbest* questions. I am forever grateful that my teacher went to bat for me and got me exempted from the second semester of that pair of required courses... Still have the text, and still use it occasionally... *that* much was useful for methods I hadn't come across yet... but...

Number lines

[dglenn.livejournal.com]

Side effect of teaching addition and subtraction on a number line: whoever teaches them two-dimensional or three-dimensional vector arithmetic later (whether it's a math teacher or a physics teacher) can start off by reminding them that they'd done something similar under a different name before, so it looks less OhMyGodTooNewAndConfusing.

[dglenn.livejournal.com]

In other words, the problem I identified is even worse than I'd imagined it was?

Scared now.

Dayum.

Re: Number lines

[cozit.livejournal.com]

*g* That's also why I point out to them that multiplying two unit measures together gives the a square unit measure... or a measure unit squared (to the 2) (gee, that's hard to type w/o superscripts).

Even if they think that's stupid or makes no sense now, in middle school... it might come back at them later on in physics or chem.

[cozit.livejournal.com]

Then there are the number of teachers literally scared by the very smart (thank goodness my kids' school has none of those that I know of... so far, knock on wood). Add in the teachers who are nervous of those with obvious disabilities (even those that impact learning very little)...

And you've also got a number of teachers who aren't up to the job of teaching anything other than the middle kids... some might be great at doing that, but others aren't... and the highs and the lows lose out in that situation anyway.

Frustrating. One of the reasons I'm going for School Library Media now, rather than sticking with Elementary Ed. or trying for a secondary (well, really I just don't really like dealing with HS much... middle's ok, elementary better :-)

I figure I might be able to hook some more kids on reading for fun and to learn something that way both... and maybe it'll pay off in other directions as well eventually. Like my sister who *hated* science in middle and HS... but ended up after she was almost finished her non-science degree going on to take a bunch of science classes and go to med school... as she said she wanted to do in HS. She's doing pretty good so far :-)

I've another sister who *never* liked reading until college... another developmental thing, that just took time... but inspiration to continue is good.