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# Why Learn Algebra? I'm Never Likely to Go There.

I didn't take algebra in 8th grade, but if I cipher $4.1 million into the State of California's entire budget for education, I'm pretty sure the result is number not large enough upon which to make policy decisions.

posted by three blind mice at 12:58 PM on July 10, 2008

No shit. You should be able to start with algebra in what, 3rd, 4th grade? As far as I can tell, most of the grade school math curriculum is just filler.

posted by mr_roboto at 1:03 PM on July 10, 2008

I don't see how you would do that, since geometry makes extensive use of algebraic formulas.

I took algebra in eight grade; this seems like a great idea.

posted by Pope Guilty at 1:20 PM on July 10, 2008

I believe that studies have shown that many 8th graders have difficulty conceptualizing geometry. Their brains are still developing and what not and it is often thought best to wait until high school. Obviously, this doesn't apply to everyone, as I have long been an adult with a (hopefully!) developed brain and yet have the weakest grasp on geometry.

posted by boubelium at 1:24 PM on July 10, 2008

I'm no developmentalist, but this smacks of bullshit to me. Let's see a citation.

posted by solipsophistocracy at 1:31 PM on July 10, 2008 [1 favorite]

I may not be the best writer in the world, but I still can learn how to improve my writing skills. Mathematics is a subject just like any other, but aside from a learning disability most individuals can at least gain a basic understanding of Algebra. The, "I don't get it" excuse is thrown around way too much, and I think it is one of the key reasons why there are fewer women in science and engineering. Often the people who "don't get math" are women, and it is okay because most women "don't get math."

posted by kscottz at 1:37 PM on July 10, 2008 [3 favorites]

Well it's a real debate, isn't it? Do we pick and choose kids and say "he isn't skilled enough, we'll give him easier work to do so he'll continue to get a good grade and feel confidant", or do we say "This is what we expect from students of age x, we'll try to teach them all and some will get worse grades than others. But they'll still learn."

Do we set kids up to fail, or do we assume some are failures to start with and never try to get them ahead? Both sound like somewhat shitty options.

A key factor may be the freedom and time individual teachers may have to concentrate and tutor individual students. That's pretty much how it worked when I was at school. Some kids tried hard but had problems, and they're the ones who had the teacher hanging around their desk helping them out. Depends highly on the teacher, the school, class size, I guess.

x million Chinese kids say that's probably bullshit. If 8th graders have difficulty conceptualizing geometry, you do your best to

posted by Jimbob at 1:49 PM on July 10, 2008 [3 favorites]

I've often thought the same thing. Of course, I have natural inclination for mathematics, so maybe I'm not the best person to make this observation, but you're right, I'm pretty much as bad as you can get when it comes to artistic ability, but that doesn't stop me from painting a picture; I'm just really bad and slow at it. Of course the irony is that art and math share so many things....

posted by gagglezoomer at 1:50 PM on July 10, 2008

- Because they'll all need it in real life.

- Because we have no way of knowing which of those children are the 25% who will go to college.

- Because ideally all of those children would go on to some sort of post-secondary education, and they need to be prepared for that.

I too am pretty sure that I took algebra in sixth grade. And that curriculum looks too easy to me for the eigth grade — and I stopped taking math after tenth grade.

posted by orange swan at 2:07 PM on July 10, 2008

Screw algebra. I would like to see our students learn to read, write and comprehend english. Should we somehow be successful in that ebdeavour I would move on to teaching a second language.

posted by notreally at 2:08 PM on July 10, 2008

I had geometry in 8th grade, and had a much easier time than I did in 7th grade algebra. We got to draw and build polygons, and that bit made everything make a lot more sense to me. However, there were only about 15 kids in that class, and we were the top math group in an 8th grade that was divided into three math groups. I have to wonder how good the average California public school math class is these days. A great school can teach kids just about anything. A crappy one, not so much. Personally, this seems a bit ass backwards to me, because I think spending money on kids in school and building a better educational system is the way to go.

posted by oneirodynia at 2:14 PM on July 10, 2008

I don't know that this is entirely true, I am

Still, algebra for 8th graders should be a given. Like all other classes, some will excel and some will struggle. Determining this earlier gives us the opportunity to give those that don't get it additional time and resources to figure it out.

posted by quin at 2:25 PM on July 10, 2008

It depends. What's the income rate below which someone is no longer a person?

posted by invitapriore at 2:29 PM on July 10, 2008 [16 favorites]

When was the last time you solved a quadratic equation or raised a number to a fractional degree?

posted by tkolar at 2:32 PM on July 10, 2008

OK, at the risk of being considered mentally retarded, I'll fess up. I didn't "get" algebra until I was in my mid30s. I tried, though, goddamn I tried.

In 8th grade, I took Algebra I. Flunked it. First time I had ever received less than a B+ in any subject, ever. 9th grade, I took Algebra 1a, which was essentially the first half of Algebra 1 spread out over a school year and my parents hired a private tutor. Flunked that and made the tutor despair. Repeated 1a in 10th, got a D more because I had a teacher who gave me a pity pass than any actual competency on my part. Scored an 800 on the SAT in verbal and a math score of which I'm too embarrassed to repeat here, graduated HS, entered college and promptly signed up for a remedial Algebra class (because at this point, it was a grudge match). Flunked it. Took it again. Flunked it. Took it yet again, and yep, flunked it. Gave up and switched to an art major. Graduated, entered the work force and never thought about formal algebra until I spotted an "Algebra for Dummies" book and thought I'd try again. For whatever reason, this time I got it but it took being within a year of going to my 20th HS reunion to be able to do it.

So, am I retarded? I really don't believe I am. But I wasn't ready to "get algebra" for a very long time.

Anyway, on topic: my son is entering 5th grade in public school (and as an aside to gagglezoomer: don't be an ass) and pre-algebra was included in his 4th grade study. Thankfully, he got it right away.

posted by jamaro at 2:49 PM on July 10, 2008 [1 favorite]

Jimbob, I'm not suggesting we give the less skilled math students easy work to boost their self-esteem, I'm suggesting we give them work that is challenging but within their level of comprehension so they can be better prepared to take Algebra at a later time (9th grade vs. 8th grade) as opposed to the current method of just throwing them to the wolves in 8th grade and hoping they come out the other side intact.

In the case of my stepson who I referenced earlier, the issue wasn't that he was getting bad grades but still learning, it was that he was getting bad grades and completely lost in a class that was well beyond his skill level. I fail to see the benefit in that.

posted by The Gooch at 3:04 PM on July 10, 2008 [1 favorite]

Ms Vegetable was a HS math teacher. A

posted by a robot made out of meat at 3:18 PM on July 10, 2008 [1 favorite]

So, K - 12 grade education should only have bearing on those who go onto higher education?

posted by ericb at 3:23 PM on July 10, 2008

Dude, was this supposed to be rhetorical? I'm going with around May, and yesterday, respectively. Unfortunately, I didn't get to use these mad algebra skills to boss anyone around. Yet. Maybe that comes in Algebra 2.

posted by whatzit at 3:35 PM on July 10, 2008

Took "eighth grade math" in 8th grade with some vague stab at Bonus Extra Pre-Algebra for some subset of the elect at my Catholic junior high. The pre-algebra went the way of the dodo because the rest of the kids didn't want extra homework and stopped doing it-- and since it wasn't on the curriculum and we were still expected to do 8th grade math too, it wasn't getting graded.

Got to 9th grade, placed into honors algebra. Teacher decided that she didn't want to teach Chapter 3 on polynomials because everyone should already know that, assigned the homework, and was out that day.

Cue massive downward spiral from there on out, as I had never seen these topics and had no idea how to cope. Ninth-grade teacher was no help at all, even though I spent about three hours or more a week staying after to get extra help. I made tutors from MIT go home in defeated tears by the time I hit Algebra 2 in 11th grade, and I was still staying after for hours. I got a C- in Algebra 2 and promptly stopped taking math classes.

(I did pretty well at geometry, actually. Much easier for me for some reason.)

I don't, as far as I know, have dyscalculia or any other learning disability that could have spawned that kind of academic nightmare. Apparently, not knowing anything about polynomials and having teachers who think you Ought To Be Smarter Than That will slaughter your forward progress.

posted by fairytale of los angeles at 3:39 PM on July 10, 2008

I have my doubts that pay scale is the biggest problem. Phillip Greenspun's on to something when he talks about how university science really doesn't pay well, yet competition for positions is fierce.

I think he's partly correct that some of the reason for this is that many people don't have the social skills to realize how much the rewards diminish for the inputs. But I also think that a lot of people either go into industry math/science or reach for the university community because they want to

And you know, one of the things about secondary ed? There's no time they really give you for that. But you know what's worse? Nobody really expects it from you. Nobody's gonna pat you on the head if you do it, you've got other things to worry about, other mundane things involved in just getting the school to work. Unless you're very lucky, there's no community of other people who want to build it, prove it, write about it, delight in puzzles, etc etc. Maybe one of your fellow faculty members, two if you're lucky, maybe a few of your students, but most of those will be having their own battles with alienation with the system.

I got high reviews from my cooperating teachers, my students, and my university evaluators when I did student teaching. The only negative they mentioned? The fact that I didn't seem committed. In fact, outright reluctant. And it wasn't because of concerns over how much money I was going to make. The biggest and most indelible doubt had to do were these very doubts about what day-to-day life in the public secondary education community were going to be like.

I'm projecting my own experience across the broad screen of the whole dilemma, and I recognize that's likely to lead to mistakes. So I say to myself sometimes that it's best to realize there's probably other ways -- maybe China's way, where culturally, being a teacher *is* an achievement, and being a hardworking student is also highly valued. Maybe something else.

But when it comes down to it, I think that the way best suited to the U.S. way is to build something in the secondary ed space where teachers are free and encouraged to

posted by weston at 4:05 PM on July 10, 2008 [2 favorites]

Some kind and degree of algebra is pretty much the foundation of everything else.

Calculus... yeah, probably somewhat overemphasized, given the breadth of useful Math out there, and I think one could reasonably argue that linear algebra and probability/basic statistics and some discrete math are all just as practical (possibly more, especially stats), but Calc is an essential part of any thorough study of natural sciences or engineering. In the context of the social push towards engineering for those with technical talent, it makes sense.

In a broader educational context? Calculus takes on this role as the quantitative equivalent of music appreciation, but instead of studying Mozart and Bach and Beethoven and Chopin and Tchaikovsky, you're studying Newton and Leibniz and Cauchy and Euler and Fourier and Gauss. Is the cross section of their selected works the ideal mix? Heck if I know. Sometimes I'd much rather be discussion Von Neumann and Nash and Conway and Knuth. But time's limited, and you could do a lot worse than the Calc school of Math Appreciation.

posted by weston at 4:21 PM on July 10, 2008

I actually did OK in math in middle school (all A's and B's), because I had the same teacher in a small prep school that was not only very good at making math interesting, she leaned on me when I needed it. When I went to public high school, the classes were large, the time was short, and somehow... I just wasn't getting it. Unlike nearly every other subject, math had nothing to do with my real life. I didn't go to math movies or read books about math, or visit the Math Academy or the Mathquarium. I passed college qualitative reasoning with the second highest score on the final when I was seventeen, so it wasn't a problem of not having a logical mind; I just had nothing to pin all that mathematics to in the real world.

posted by oneirodynia at 4:31 PM on July 10, 2008

Let's rephrase that more accurately: If for the most part only the children of reasonably well-off parents ever earns a college degree, and since we're talking about public schools were children of reasonably well-off people are rarely sent for schooling, why insist that those other (ie relatively poor) children learn something that may help them do better in high school, earn a scholarship, and thus compete for college space with the children of the reasonably well-off?

posted by davejay at 5:34 PM on July 10, 2008

Nope. I actually enjoyed the first semester of so of algebra--understanding that x=a given number, and that you can use that to extrapolate out, and using variables to solve equations, made sense to me.

Somewhere around matrices, (still don't understand the damn things; I remember sitting in class starting at those boxes and thinking, wait, what?), I just got lost, and never really found my footing again. Like others have commented, I had absorbed the idea that some people are just "good at" things, and since I was good at English and history, I assumed I was "bad at" math and didn't try to get over that hump. And because I was passing, and quiet, and one of 32 kids in a class, and maybe because I was a girl, no one paid attention. I regret that I didn't fight harder, and also that it was so easy to slip under the radar.

I think that the earliest we can teach kids mathematical concepts and reasoning, before the cultural conditioning messes with their heads, the better, frankly.

posted by emjaybee at 5:51 PM on July 10, 2008

Yep. I just finished a summer class (6 weeks) and this pretty much the same thing as I just went through.

I've always had a tough time with most math, and I'm pretty sure I'm not retarded. The reason? Having just gone through 6 intensive weeks of it, two things: the way it's taught and the way my brain seems to process information. For me, I need to to make a relationship between a concept and the real world. I had to translate the information into a "language" I could understand. The way I've been taught algebra pretty much simply states, "This is the way it is, now do it." That type of learning doesn't create knowledge, it creates mimicry. That's why so many people can do well in algebra in school, and 10 years later, barely remember a thing. Sure, it works for some people, but not for others. It's a shame those who can't adapt to that teaching style are thought to be less intelligent, and that they think that of themselves.

I went into the final exam with an average grade of 70. It was required that we get at least a 50 on the exam to pass the course no matter how high our average. I got a 48.

posted by sluglicker at 5:56 PM on July 10, 2008

*Anyways, can anyone who couldn't understand elementary algebra and later got it explain what it was that troubled them so? Lack of proficiency with fractions/negative numbers? Not understanding what it meant to solve an equation? Not understanding what a function was?*

The last one, precisely. I understood elementary algebra - which I'm defining as the basic turning-prose-into-equations and knowing how to balance them and solve for "x"... The kind that's on the Math SAT, and as far as that went I was in the 90s percentile-wise. I also loved geometry proofs. But every time they'd start graphing things (graphing what? what are we making a graph of? what's the graph for?) and talking about "f of x" (what's a function? why? what are we trying to figure out?) I was Absolutely And Completely unable to grasp what was going on. So I never went past Algebra II because there was no point in even attempting pre-calc - it would be like registering for "Pdjkrq".

posted by moxiedoll at 6:05 PM on July 10, 2008

The latest neuroscience says our brains can rewire themselves. I think the issue is that different brains need different approaches or differing amounts of practice to rewire properly. Unfortunately math classes tend to put everyone through the same cookie-cutter teaching methods. The result, students falling by the wayside, is not surprising.

Here's a great book on why *everyone* can learn math: The End of Ignorance. The author has put his words into action with the JUMP (Junior Undiscovered Math Prodigies) volunteer program which has had phenomenal success. www.jumpmath.org

posted by storybored at 6:18 PM on July 10, 2008 [2 favorites]

Even with a computer, you still need Algebra.

posted by delmoi at 6:41 PM on July 10, 2008

With Mathematica (or equivalent) you can avoid algebra and most of calculus just as easily as a calculator lets you avoid arithmetic; you still need to know what to do, but you don't need to know the details of how to do it.

posted by Pyry at 6:55 PM on July 10, 2008

I've held a variety of jobs in my life, and I can't think of any time where I've had to harken back to my sole algebra course. If I were an engineer, that would be different, but I'm not.

posted by jonmc at 7:05 PM on July 10, 2008

I hope you won't mind if I took it as a challenge to write the clearest brief explanation that I can.

Calculus is a set of techniques for doing math with infinitely small things. There are two sides to the subject: differentiation and integration.

Differentiation lets you calculate the rate at which something is changing. For example, consider driving a car. The rate at which your position is changing is your speed: so many feet per second. The rate at which your speed is changing is your acceleration: " (ft/sec) / sec " or just "ft / sec^2".

Using algebra you can calculate your average speed over some length of time. Say, you were at 0 ft at 0 sec and then, 10 seconds later, you were at 100 ft. So you went 100 ft in 10 sec, or 100/10 ft/sec, or 10 ft/sec... ON AVERAGE.

If you want to know your speed at an exact time, say at 5 seconds after you start, you'd naturally start shrinking the time gap over which you're measuring. So, may you measure from 4 sec to 6 sec, then from 4.9 to 5.1 sec, then 4.999 to 5.001 sec, and so on. You're getting very close, but you're still just computing your AVERAGE speed over that length of time. Eventually things fall apart because the time gap becomes essentially zero and the change in position becomes essentially zero and so you end up with something that looks like 0/0 ft/sec, and algebra just broke. Sorry, you need a new tool.

With differentiation calculus, you can shrink that gap to zero and know your speed EXACTLY at 5 sec.

Integration is a bit more abstract and I struggle to come up with an example that doesn't involve graphs of lines, but it is essentially the opposite of differentiation. Instead of doing division with infinitely small things you're now doing multiplication with infinitely small things.

Calculus was initially invented to solve problems involving the motion of the planets around the sun, but it turns out to be useful for a huge variety of problems in business and science.

One last thing that might cause a mind-expanding moment:

First we have things, like apples and toy blocks and jellybeans.

The answer to an arithmetic problem is a number, which is an abstraction of things.

The answer to an algebra problem is an arithmetic problem.

The answer to a calculus problem is an algebra problem.

The answer to a differential equation problem is a calculus problem.

posted by LastOfHisKind at 7:15 PM on July 10, 2008 [14 favorites]

In Singapore, Math is a separate, standalone subject - we don't have individual subjects for each area of mathematics. Each school year, everyone learns a bit of arithmetic, geometry, algebra, calculus, statistics (and whatever other topics possible) all the way to age 18. For anyone who's interested, the official primary (age 7-12) and secondary (age 13-16) maths syllabus is online (both pdf files).

In primary school many subjects end up being taught by a common teacher though, or at least until about age 9. I think this is mostly due to a shortage of teachers, and also, quite honestly, you don't need to be a mathematics grad to teach kids how to add up money or divide pizza.

Interestingly, I hardly remember anyone talking about "concepts" and "principles" and "logic" when referring to math. One just internalised the formulae, memorised what equations produced what kind of graphs, learnt methods of tackling different types of questions, and

posted by hellopanda at 7:48 PM on July 10, 2008

... that's a really good question.

posted by Durn Bronzefist at 8:08 PM on July 10, 2008

No room for standardized testing with that approach to pedagogy.

posted by Blazecock Pileon at 9:51 PM on July 10, 2008

If this were true, I'd largely consider it a feature instead of a bug. :)

But I don't think it's true. I think it just means you can't take a kitchen sink approach with mandated/tested curriculum under the setup I described.

posted by weston at 10:52 PM on July 10, 2008

Specifically, it is the clearly insane belief that if you add up an infinite number of infinitely small things you will get a finite number.

Like most religions, once you accept the completely whacked out premise everything flows pretty easily from there.

posted by tkolar at 1:07 AM on July 11, 2008 [2 favorites]

But generally you are actually tryign to Cut up a finite thing into a countably infinite number of pieces...

which does kinda make sense...

posted by mary8nne at 3:54 AM on July 11, 2008

I can haz agreement.

posted by inigo2 at 7:08 AM on July 11, 2008

My 11th grade physics teacher was named Mr. Wenis. True story!

posted by chugg at 9:20 AM on July 11, 2008

I thought basic calculus operated over the set of real numbers, which aren't countably infinite.

posted by Blazecock Pileon at 9:54 AM on July 11, 2008

One of my middleschool subs was named Richard Les, pronounced "lis." He went by Dick. It was very unfortunate.

posted by Solon and Thanks at 3:10 PM on July 11, 2008

The fucking wikipedia entry suffers from the same problem most math textbooks suffer from, which is that they don't explain things in common terms that everyone can understand. Every math class I've ever been in has carried this idea around that each class should build upon the lessons of the previous. Well that's all well and good if you did great in the previous class... but if you only barely scraped by, you're starting every new year already behind... it's like stepping up to bat with two strikes automatically against you.

The best explanation I've heard about calculus--and the one that finally made it

So, you know how to get the area of most basic shapes, right? A square:

OK, smarty pants, how do you get the area of a curved object? Ah. Well, maybe if you were smart you'd cut the curve into little rectangles, and then add all those areas up and get an approximation. Well, if you keep making smaller and smaller rectangles, you'll get closer and closer to the correct value. Anyway, there's a neat mathematical trick figured out by either Sir Isaac Newton or Gottfried Leibniz (depending who you ask) in around 1670 that can allow you to calculate the area of a curved shape. Leibniz is the bastard to blame for all the fucked up symbols in calculus (

The second half of calculus can be summed up pretty simply: a technique to get the slope on a curve. When you've got a straight line, figuring out the slope is easy Geometry I stuff...

And that's it. Slope on a curve, area of a curve. Calculus. If math classes just presented it like this, people would get it in no time. But instead, they start whipping out the

So unfortunately for all the poor souls taking math, you have to mess all the simplicity up with all the extra physics bullshit that just confuses people. Why does someone in math class give a fuck about acceleration? Stop trying to make every single goddamned math problem

posted by Civil_Disobedient at 11:29 PM on July 11, 2008 [3 favorites]

Post

# Why Learn Algebra? I'm Never Likely to Go There.

July 10, 2008 12:27 PM Subscribe

EducationFilter: California becomes the first state to mandate all 8th graders take Algebra; in part because U.S. students constantly trail their peers from other nations in mathematics. At least one person thinks it's a bad idea ("If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?"). Here's the algebra curriculum 8th graders will have to learn.

Here's a more in-depth story on it from the L.A. Times.

This post's title is a paraphrased quote from comedian Billy Connolly: "I don't know why I should have to learn Algebra. I'm never likely to go there."

Here's a more in-depth story on it from the L.A. Times.

This post's title is a paraphrased quote from comedian Billy Connolly: "I don't know why I should have to learn Algebra. I'm never likely to go there."

The idea that there's a two-tier curriculum that early on seems pretty terrible.

It's one thing to have remedial (extra easy) and honors (extra hard) courses in addition to a standard in-between, but to

Um, because, like, if they take algebra in the eighth grade, that 25 percent figure might, you know,

posted by Sys Rq at 12:44 PM on July 10, 2008

It's one thing to have remedial (extra easy) and honors (extra hard) courses in addition to a standard in-between, but to

*only*have remedial and honors classes--and to give students the rest-of-their-lives-affecting choice between an easy A and something they'd have to work for, well, that just seems more than a tad misguided.*If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?*Um, because, like, if they take algebra in the eighth grade, that 25 percent figure might, you know,

*go up?*Duh?posted by Sys Rq at 12:44 PM on July 10, 2008

Algebra isn't just for solving math problems, it's a basis for understanding how systems equate with one another. Most of human business or task-oriented communication is a form of algebra, in an oblique way. Saying that algebra applies exclusively to other forms of math is really short sighted.

posted by Burhanistan at 12:51 PM on July 10, 2008 [9 favorites]

posted by Burhanistan at 12:51 PM on July 10, 2008 [9 favorites]

I'm all for it - as long as anyone post-school-age caught doing algebra without a college degree gets a fine and long jail sentence.

Why make kids use their brains in school if they're not going to use them in "real life"?

posted by Benny Andajetz at 12:51 PM on July 10, 2008

Why make kids use their brains in school if they're not going to use them in "real life"?

posted by Benny Andajetz at 12:51 PM on July 10, 2008

I'd just like to point out that the proposed Algebra curriculum for 8th graders is roughly the same as an outline for the college-level Algebra class I'll be taking in the Fall.

I'm not sure exactly if that's good or bad, and for whom.

posted by Avenger at 12:51 PM on July 10, 2008 [2 favorites]

I'm not sure exactly if that's good or bad, and for whom.

posted by Avenger at 12:51 PM on July 10, 2008 [2 favorites]

Add me to those who think that

posted by rob paxon at 12:51 PM on July 10, 2008

*("If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?")*is ridiculous reasoning.posted by rob paxon at 12:51 PM on July 10, 2008

Here's a better link to the L.A. Times story. California State Supernintendo O'Connell: "let’s be honest: we’re just setting our schools up for failure."

The local NPR talked about it this morning, spouting stats that I can't verify (that 60% of students take algebra in the 8th grade now).

From memory, most kids were in pre-algebra in 8th grade when I was a kid.

posted by jabberjaw at 12:55 PM on July 10, 2008 [1 favorite]

The local NPR talked about it this morning, spouting stats that I can't verify (that 60% of students take algebra in the 8th grade now).

From memory, most kids were in pre-algebra in 8th grade when I was a kid.

posted by jabberjaw at 12:55 PM on July 10, 2008 [1 favorite]

I seem to recall that my Minnesota middle school required me to take Algebra, or some sort of Algebra-prep class. It wasn't a big deal at all. If you were a kid who hated math, then Algebra was no different than all the other math subjects you disliked (and for you math nerds, the inverse).

I guess I would question, if not algebra, what the hell are they teaching these kids? After 7 years of primary education, you would think multiplication tables and fractions would hvae run their course.

posted by boubelium at 12:56 PM on July 10, 2008

I guess I would question, if not algebra, what the hell are they teaching these kids? After 7 years of primary education, you would think multiplication tables and fractions would hvae run their course.

posted by boubelium at 12:56 PM on July 10, 2008

*The state was under pressure from the U.S. Department of Education to change its current eighth-grade math test by Aug. 1 or face losing up to $4.1 million in funding.*

I didn't take algebra in 8th grade, but if I cipher $4.1 million into the State of California's entire budget for education, I'm pretty sure the result is number not large enough upon which to make policy decisions.

posted by three blind mice at 12:58 PM on July 10, 2008

Jeez...I had algebra in 6th grade! That was 1980 though I think. Maybe algebra has become harder.

posted by spicynuts at 12:59 PM on July 10, 2008 [1 favorite]

posted by spicynuts at 12:59 PM on July 10, 2008 [1 favorite]

*I guess I would question, if not algebra, what the hell are they teaching these kids? After 7 years of primary education, you would think multiplication tables and fractions would hvae run their course.*

No shit. You should be able to start with algebra in what, 3rd, 4th grade? As far as I can tell, most of the grade school math curriculum is just filler.

posted by mr_roboto at 1:03 PM on July 10, 2008

Aren't the teaching geometry prior to algebra?

posted by spicynuts at 1:05 PM on July 10, 2008 [1 favorite]

posted by spicynuts at 1:05 PM on July 10, 2008 [1 favorite]

Rarely is the question asked, is our children learning?

posted by Nelson at 1:06 PM on July 10, 2008 [1 favorite]

posted by Nelson at 1:06 PM on July 10, 2008 [1 favorite]

I went to a relatively affluent public high school, and there were students as late as tenth grade who were still learning how to use fractions and negative numbers.

Of course, there were also a lot of them in pre-calculus.

I can understand objections to this requirement insofar as there may be a large number of their students who simply can't learn algebra, but that just points to bigger problems in their school systems.

posted by Target Practice at 1:10 PM on July 10, 2008

Of course, there were also a lot of them in pre-calculus.

I can understand objections to this requirement insofar as there may be a large number of their students who simply can't learn algebra, but that just points to bigger problems in their school systems.

posted by Target Practice at 1:10 PM on July 10, 2008

I think this is a fantastic idea. One of my regrets regarding my own education was the late start I had with mathematics. As a friend of mine says: the difference in having a job where you're the boss and having a job where others boss you, is knowing math.

posted by thatbrunette at 1:13 PM on July 10, 2008

posted by thatbrunette at 1:13 PM on July 10, 2008

No matter how much any administration large or small tries to improve any program/subject area, there will still be those that make it, and those that barely make it, and those who just wont get it. I personally hate methods of trying to 'improve' certain areas, because it will never achieve exactly the results expected or imagined...

Good Luck California.

posted by JoeXIII007 at 1:15 PM on July 10, 2008

Good Luck California.

posted by JoeXIII007 at 1:15 PM on July 10, 2008

People still send their kids to public schools?

posted by gagglezoomer at 1:16 PM on July 10, 2008 [1 favorite]

posted by gagglezoomer at 1:16 PM on July 10, 2008 [1 favorite]

I didn't have to take algebra until 9th grade (and then algebra II in 11th). I failed so hard on the algebra test at college that they were astounded. (Srsly, I'm horrific at math.) FTR, we had to take geometry in 10th grade and had choices senior year between: ap calculus, pre-calculus and consumer math. It was pretty obvious who would take what course. I took the first semester pre-calc and failed miserably and transferred to consumer math and barely passed. Ugh.

I think this could be a good thing. But then again, with most drastic changes, it seems like they tend to do more harm than good.

posted by sperose at 1:17 PM on July 10, 2008

I think this could be a good thing. But then again, with most drastic changes, it seems like they tend to do more harm than good.

posted by sperose at 1:17 PM on July 10, 2008

*Aren't the teaching geometry prior to algebra?*

I don't see how you would do that, since geometry makes extensive use of algebraic formulas.

I took algebra in eight grade; this seems like a great idea.

posted by Pope Guilty at 1:20 PM on July 10, 2008

*Aren't the teaching geometry prior to algebra?*

I believe that studies have shown that many 8th graders have difficulty conceptualizing geometry. Their brains are still developing and what not and it is often thought best to wait until high school. Obviously, this doesn't apply to everyone, as I have long been an adult with a (hopefully!) developed brain and yet have the weakest grasp on geometry.

posted by boubelium at 1:24 PM on July 10, 2008

Eighth grade is not too early to require algebra, as long as the students are properly prepped for it in seventh. The mandated curriculum appears pretty basic. However, some kids just take more time to grasp this stuff and would probably be better served by taking pre-algebra in eighth grade.

posted by caddis at 1:27 PM on July 10, 2008

posted by caddis at 1:27 PM on July 10, 2008

I can't remember what grade we started algebra in my Australian highschool, 8 or 9, but it was compulsory. And yes, some people got it, and some people didn't. But then, some people got

Now,

posted by Jimbob at 1:30 PM on July 10, 2008 [1 favorite]

*physical education*and some people didn't, some people got*home economics*and some people didn't, some people got*art*and some people didn't. That's school. Algebra is a scary sounding word, but it really covers some pretty basic and universal ideas.Now,

*calculus*, that's about where my brain said "No more!". But even with calculus, it's still something that's useful to*know*about as a concept, and what it does, even if you can't use it in practice.posted by Jimbob at 1:30 PM on July 10, 2008 [1 favorite]

*I believe that studies have shown that many 8th graders have difficulty conceptualizing geometry. Their brains are still developing and what not and it is often thought best to wait until high school*

I'm no developmentalist, but this smacks of bullshit to me. Let's see a citation.

posted by solipsophistocracy at 1:31 PM on July 10, 2008 [1 favorite]

*I can understand objections to this requirement insofar as there may be a large number of their students who*

**simply can't learn algebra**, but that just points to bigger problems in their school systems.I may not be the best writer in the world, but I still can learn how to improve my writing skills. Mathematics is a subject just like any other, but aside from a learning disability most individuals can at least gain a basic understanding of Algebra. The, "I don't get it" excuse is thrown around way too much, and I think it is one of the key reasons why there are fewer women in science and engineering. Often the people who "don't get math" are women, and it is okay because most women "don't get math."

posted by kscottz at 1:37 PM on July 10, 2008 [3 favorites]

Does anyone have an idea of when they stopped having "tiered" math in middle school? When I went to middle school in the mid-80s (in California, for reference), we were placed according to our ability (I tended to fall in the "middle" group, who took Pre-Algebra in 8th grade, Algebra in 9th). The obvious benefit to this was we were put in classes according to our skill level, so there was less chance of getting lost in a class that was way beyond your ability.

Since my stepsons (currently going into 8th and 9th grade respectively) have been in middle school, this "tiering" system has no longer been in effect - all students in the same grade take the same math class. So my soon-to-be 9th grader was put into Algebra in 8th grade despite clearly not being intellectually prepared for Algebra. And his grades reflected it. Even factoring in things like goofing around in class, not paying as close attention to the teacher as he should, rushing through homework, etc. it was clear that this kid was simply not ready for this level of mathematics.

I can understand to a point the arguments for this requirement - raising the level of education, not wanting US children to fall further behind their worldwide peers - but I fail to see the benefit of shoving kids into classes they are obviously not prepared for. If an 8th grader has the skills and ability to take Algebra I in 8th grade I'm all for it; I just think it's a mistake to assume all of them are. I'm confident in saying my stepson would have benefited far more from a math class more matching his current skill level, instead of putting him in a class that did little more than kill his confidence that he will ever perform well in math.

posted by The Gooch at 1:38 PM on July 10, 2008 [2 favorites]

Since my stepsons (currently going into 8th and 9th grade respectively) have been in middle school, this "tiering" system has no longer been in effect - all students in the same grade take the same math class. So my soon-to-be 9th grader was put into Algebra in 8th grade despite clearly not being intellectually prepared for Algebra. And his grades reflected it. Even factoring in things like goofing around in class, not paying as close attention to the teacher as he should, rushing through homework, etc. it was clear that this kid was simply not ready for this level of mathematics.

I can understand to a point the arguments for this requirement - raising the level of education, not wanting US children to fall further behind their worldwide peers - but I fail to see the benefit of shoving kids into classes they are obviously not prepared for. If an 8th grader has the skills and ability to take Algebra I in 8th grade I'm all for it; I just think it's a mistake to assume all of them are. I'm confident in saying my stepson would have benefited far more from a math class more matching his current skill level, instead of putting him in a class that did little more than kill his confidence that he will ever perform well in math.

posted by The Gooch at 1:38 PM on July 10, 2008 [2 favorites]

I think the idea that any kid with a fully functioning mind (as opposed to actual mental retardation) could "just not get" algebra is hard to imagine.

posted by delmoi at 1:45 PM on July 10, 2008

posted by delmoi at 1:45 PM on July 10, 2008

I graduated high school in 81 (barely). I had a genuine dislike for both of the lower level math teachers at my school, so I took the minimum requirement (Pre-Algebra) and didn't take any more math in high school. I did take it in college when I went and got A's in it, and enjoyed it because I some great teachers.

Shoe horning kids into remedial classes for stuff they either have no interest in or lack the ability to understand is pretty much doomed to failure. Having worked with some "at risk" kids, it's not a job I'd want as a teacher either.

posted by doctor_negative at 1:46 PM on July 10, 2008

Shoe horning kids into remedial classes for stuff they either have no interest in or lack the ability to understand is pretty much doomed to failure. Having worked with some "at risk" kids, it's not a job I'd want as a teacher either.

posted by doctor_negative at 1:46 PM on July 10, 2008

I started algebra at the UK equivalent of 6th grade, as did everyone else in my class. I don't recall anyone having a particular difficulty with it, and I went to a state school just as standard as any other.

posted by malusmoriendumest at 1:48 PM on July 10, 2008

posted by malusmoriendumest at 1:48 PM on July 10, 2008

*If an 8th grader has the skills and ability to take Algebra I in 8th grade I'm all for it; I just think it's a mistake to assume all of them are.*

Well it's a real debate, isn't it? Do we pick and choose kids and say "he isn't skilled enough, we'll give him easier work to do so he'll continue to get a good grade and feel confidant", or do we say "This is what we expect from students of age x, we'll try to teach them all and some will get worse grades than others. But they'll still learn."

Do we set kids up to fail, or do we assume some are failures to start with and never try to get them ahead? Both sound like somewhat shitty options.

A key factor may be the freedom and time individual teachers may have to concentrate and tutor individual students. That's pretty much how it worked when I was at school. Some kids tried hard but had problems, and they're the ones who had the teacher hanging around their desk helping them out. Depends highly on the teacher, the school, class size, I guess.

*I believe that studies have shown that many 8th graders have difficulty conceptualizing geometry.*

x million Chinese kids say that's probably bullshit. If 8th graders have difficulty conceptualizing geometry, you do your best to

*teach*them so they can better conceptualize geometry.

posted by Jimbob at 1:49 PM on July 10, 2008 [3 favorites]

*I think the idea that any kid with a fully functioning mind (as opposed to actual mental retardation) could "just not get" algebra is hard to imagine.*

I've often thought the same thing. Of course, I have natural inclination for mathematics, so maybe I'm not the best person to make this observation, but you're right, I'm pretty much as bad as you can get when it comes to artistic ability, but that doesn't stop me from painting a picture; I'm just really bad and slow at it. Of course the irony is that art and math share so many things....

posted by gagglezoomer at 1:50 PM on July 10, 2008

The U.S. really needs a public Trade School system. The ongoing folly of pretending that every child will be going to college is causing a tremendous amount of angst for the 75% of the population that won't be, and lowering the educational quality for the 25% who will.

posted by tkolar at 1:54 PM on July 10, 2008 [7 favorites]

posted by tkolar at 1:54 PM on July 10, 2008 [7 favorites]

Pope Guilty writes:

The math curriculum at my high school was organized around a progression of Algebra I in 9th grade, Geometry in 10th grade, Algebra II in 11th grade, and Trigonometry/Pre-Calculus in 12th grade. The accelerated math students would take Algebra I in 8th grade and have the option of taking Calculus for AP credit in their 12th grade year.

posted by anifinder at 1:56 PM on July 10, 2008

*I don't see how you would do that, since geometry makes extensive use of algebraic formulas.*

The math curriculum at my high school was organized around a progression of Algebra I in 9th grade, Geometry in 10th grade, Algebra II in 11th grade, and Trigonometry/Pre-Calculus in 12th grade. The accelerated math students would take Algebra I in 8th grade and have the option of taking Calculus for AP credit in their 12th grade year.

posted by anifinder at 1:56 PM on July 10, 2008

I grew to hate math around 5th grade (I had a harsh teacher who forced us to compete in long division speed contests), was held back from algebra, and sat in the basic math classes with all the burnouts. Looking back, algebra was the point at which everything started to make sense and the bigger picture started to emerge. I think I just have a naturally abstract mind, and can't cope with the long division bullshit we were put through. At this point, I love math, particularly the brain-melting stuff. I wish they'd taught me algebra back in 3rd or 4th grade, before I completely wrote off the entire subject.

posted by naju at 1:59 PM on July 10, 2008

posted by naju at 1:59 PM on July 10, 2008

*If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?*

- Because they'll all need it in real life.

- Because we have no way of knowing which of those children are the 25% who will go to college.

- Because ideally all of those children would go on to some sort of post-secondary education, and they need to be prepared for that.

I too am pretty sure that I took algebra in sixth grade. And that curriculum looks too easy to me for the eigth grade — and I stopped taking math after tenth grade.

posted by orange swan at 2:07 PM on July 10, 2008

Despite the elitist-sounding pull quote in the FPP, y'all really should read Ellison's column (third link). In it he mentions that 44 percent of ninth graders who take algebra in the L.A. district

Speaking as someone who would like to see every kid, college-bound or not, exposed to algebra and given a chance to succeed at it, I don't think these "high standards" will have that effect. They're the equivalent of an unfunded mandate, but rather than being under-funded with money, they're under-funded with real effort to acknowledge and address the causes of our failing schools.

posted by aws17576 at 2:07 PM on July 10, 2008 [3 favorites]

**fail**. Numbers like that indicate a defective product, so to speak, and it is not rational to order an increase in production levels and call the problem fixed.Speaking as someone who would like to see every kid, college-bound or not, exposed to algebra and given a chance to succeed at it, I don't think these "high standards" will have that effect. They're the equivalent of an unfunded mandate, but rather than being under-funded with money, they're under-funded with real effort to acknowledge and address the causes of our failing schools.

posted by aws17576 at 2:07 PM on July 10, 2008 [3 favorites]

Screw algebra. I would like to see our students learn to read, write and comprehend english. Should we somehow be successful in that ebdeavour I would move on to teaching a second language.

posted by notreally at 2:08 PM on July 10, 2008

solipsophistocracy writes:

It could very well not be entirely sound; this subject is well outside my expertise. Yet, I don't find it totally unbelievable. As I understand things, young preteens/teens are undergoing some rather dramatic development in the brain.

As far as a citation goes, I don't have a smoking gun for you. I think this article from The Walrus a few years back had an impression on my opinion. That article has a little sentence on geometry, but that's it. I swear I read an article about math and teen brains, though I can't place it at the moment.

posted by boubelium at 2:13 PM on July 10, 2008

*I'm no developmentalist, but this smacks of bullshit to me. Let's see a citation.*It could very well not be entirely sound; this subject is well outside my expertise. Yet, I don't find it totally unbelievable. As I understand things, young preteens/teens are undergoing some rather dramatic development in the brain.

As far as a citation goes, I don't have a smoking gun for you. I think this article from The Walrus a few years back had an impression on my opinion. That article has a little sentence on geometry, but that's it. I swear I read an article about math and teen brains, though I can't place it at the moment.

posted by boubelium at 2:13 PM on July 10, 2008

"If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?"

If, like, most adults never read books, why make kids learn how to do it?

posted by Artw at 2:13 PM on July 10, 2008

If, like, most adults never read books, why make kids learn how to do it?

posted by Artw at 2:13 PM on July 10, 2008

I went to college (where I did no math) but I do algebra all the time - don't these people ever have to figure stuff out with variables? How do they figure out what the gross salary would have to be to make it worth taking the job after you deduct the cost of the commute from the weekly net pay? It does seem weird for everyone to take it in eighth grade, though, but that's just because when I went to school only the AP kids did that.

posted by moxiedoll at 2:14 PM on July 10, 2008

*I was special, right?!?*posted by moxiedoll at 2:14 PM on July 10, 2008

*I believe that studies have shown that many 8th graders have difficulty conceptualizing geometry. Their brains are still developing and what not and it is often thought best to wait until high school*

I had geometry in 8th grade, and had a much easier time than I did in 7th grade algebra. We got to draw and build polygons, and that bit made everything make a lot more sense to me. However, there were only about 15 kids in that class, and we were the top math group in an 8th grade that was divided into three math groups. I have to wonder how good the average California public school math class is these days. A great school can teach kids just about anything. A crappy one, not so much. Personally, this seems a bit ass backwards to me, because I think spending money on kids in school and building a better educational system is the way to go.

posted by oneirodynia at 2:14 PM on July 10, 2008

I'd see this as a positive thing.

Here's some negative scarey stuff as balance.

posted by Artw at 2:15 PM on July 10, 2008

Here's some negative scarey stuff as balance.

posted by Artw at 2:15 PM on July 10, 2008

Is there a provision in this new mandate to ensure that 8th-grade algebra teachers aren't fucking assholes? No? Then there's something wrong with it.

I still hate you, Mrs. Moore, you bitch!

posted by goatdog at 2:20 PM on July 10, 2008 [4 favorites]

I still hate you, Mrs. Moore, you bitch!

posted by goatdog at 2:20 PM on July 10, 2008 [4 favorites]

*As a friend of mine says: the difference in having a job where you're the boss and having a job where others boss you, is knowing math.*

I don't know that this is entirely true, I am

*terrible*at math, and yet at every fricking job I've ever worked, they eventually want me in charge of other people. It's a pain in the ass, I tell ya.

Still, algebra for 8th graders should be a given. Like all other classes, some will excel and some will struggle. Determining this earlier gives us the opportunity to give those that don't get it additional time and resources to figure it out.

posted by quin at 2:25 PM on July 10, 2008

The curriculum, if I read it correctly, is for Grades 8 through 12 and covers the same ground as the curriculum we had for grades 7 though 10.

As I recollect about 10% of the students found it tough going and had extra coaching to make the grade while the rest of us stumbled through it one way or another.

Off course that was long, long ago in a country far, far away - but it doesn't seem like a particularly bad idea. At least I've used algebra from time to time - unlike Latin (five years of purgatory.)

posted by speug at 2:27 PM on July 10, 2008

As I recollect about 10% of the students found it tough going and had extra coaching to make the grade while the rest of us stumbled through it one way or another.

Off course that was long, long ago in a country far, far away - but it doesn't seem like a particularly bad idea. At least I've used algebra from time to time - unlike Latin (five years of purgatory.)

posted by speug at 2:27 PM on July 10, 2008

*People still send their kids to public schools?*

It depends. What's the income rate below which someone is no longer a person?

posted by invitapriore at 2:29 PM on July 10, 2008 [16 favorites]

*but I do algebra all the time*

When was the last time you solved a quadratic equation or raised a number to a fractional degree?

posted by tkolar at 2:32 PM on July 10, 2008

I took algebra in 8th grade here in California, but my mom, a native Rhode Islander, never got the chance; when meeting with her guidance counselor in 1970, he refused to let her enroll in the class, telling her that "you're just going to end up getting married, so you don't need it; I'll put you in business math instead." Yikes.

She has since told me that it pains her greatly to have not had the experience of being exposed to the subject, and that it was a major achievement, in her mind, that my brother and I both took it and passed and went on to do more math and science later.

Algebra made things like understanding genetics and chemistry and oceanography that much easier later; I can read pretty much any non-specialist scientifically-based work (say, Jared Diamond's

I can't imagine what it would have been like to have never taken more advanced science classes in school, or to know that I felt unable to make a budget to organize my finances, or that I couldn't figure out the costs and benefits of something over time that might not be apparent to me, like compounding interest. I'm glad I was given the chance, and I'm pretty happy that all the students in this state will have the opportunity I had and my mom didn't.

posted by mdonley at 2:38 PM on July 10, 2008 [4 favorites]

She has since told me that it pains her greatly to have not had the experience of being exposed to the subject, and that it was a major achievement, in her mind, that my brother and I both took it and passed and went on to do more math and science later.

Algebra made things like understanding genetics and chemistry and oceanography that much easier later; I can read pretty much any non-specialist scientifically-based work (say, Jared Diamond's

*The Third Chimpanzee*, which I'm reading now) and not have any problems understanding it or have any serious doubts about the methods used by scientists to produce the results. I use math often now, whether working out a grading scheme for my students or trying to figure out how good a job offer is. And I understand the scientific method, which makes planning how to solve a problem easier - and helps me evaluate the usefulness of the results of a controversial or disputed experiment: was the sample size too small? Was the test repeatable? And I don't have to*believe*in the theory of evolution, because I know it's true: not only do I understand that*gravity*is also a theory, but also because the evidence has been convincing time and time and time and time again, regardless of what comes out of the mouth of someone on a pulpit or on a school board, so the theory is, in my mind, proven. These kinds of things all came from the science classes I was able to take because I'd taken algebra.I can't imagine what it would have been like to have never taken more advanced science classes in school, or to know that I felt unable to make a budget to organize my finances, or that I couldn't figure out the costs and benefits of something over time that might not be apparent to me, like compounding interest. I'm glad I was given the chance, and I'm pretty happy that all the students in this state will have the opportunity I had and my mom didn't.

posted by mdonley at 2:38 PM on July 10, 2008 [4 favorites]

*I think the idea that any kid with a fully functioning mind (as opposed to actual mental retardation) could "just not get" algebra is hard to imagine.*

posted by delmoi at 1:45 PM on July 10

posted by delmoi at 1:45 PM on July 10

OK, at the risk of being considered mentally retarded, I'll fess up. I didn't "get" algebra until I was in my mid30s. I tried, though, goddamn I tried.

In 8th grade, I took Algebra I. Flunked it. First time I had ever received less than a B+ in any subject, ever. 9th grade, I took Algebra 1a, which was essentially the first half of Algebra 1 spread out over a school year and my parents hired a private tutor. Flunked that and made the tutor despair. Repeated 1a in 10th, got a D more because I had a teacher who gave me a pity pass than any actual competency on my part. Scored an 800 on the SAT in verbal and a math score of which I'm too embarrassed to repeat here, graduated HS, entered college and promptly signed up for a remedial Algebra class (because at this point, it was a grudge match). Flunked it. Took it again. Flunked it. Took it yet again, and yep, flunked it. Gave up and switched to an art major. Graduated, entered the work force and never thought about formal algebra until I spotted an "Algebra for Dummies" book and thought I'd try again. For whatever reason, this time I got it but it took being within a year of going to my 20th HS reunion to be able to do it.

So, am I retarded? I really don't believe I am. But I wasn't ready to "get algebra" for a very long time.

Anyway, on topic: my son is entering 5th grade in public school (and as an aside to gagglezoomer: don't be an ass) and pre-algebra was included in his 4th grade study. Thankfully, he got it right away.

posted by jamaro at 2:49 PM on July 10, 2008 [1 favorite]

*Well it's a real debate, isn't it? Do we pick and choose kids and say "he isn't skilled enough, we'll give him easier work to do so he'll continue to get a good grade and feel confidant", or do we say "This is what we expect from students of age x, we'll try to teach them all and some will get worse grades than others. But they'll still learn."*

Jimbob, I'm not suggesting we give the less skilled math students easy work to boost their self-esteem, I'm suggesting we give them work that is challenging but within their level of comprehension so they can be better prepared to take Algebra at a later time (9th grade vs. 8th grade) as opposed to the current method of just throwing them to the wolves in 8th grade and hoping they come out the other side intact.

In the case of my stepson who I referenced earlier, the issue wasn't that he was getting bad grades but still learning, it was that he was getting bad grades and completely lost in a class that was well beyond his skill level. I fail to see the benefit in that.

posted by The Gooch at 3:04 PM on July 10, 2008 [1 favorite]

Jimbob:

Harold Stevenson, who did cross-cultural studies of elementary school education, had some interesting comments on this. He noted that in the American families he studied, much more emphasis was placed on children's innate talents and abilities (e.g. whether they're "good at math" or not), whereas the Chinese and Japanese families emphasized hard work: they assumed that even an average or poor student could master the material if they worked hard enough.

The phrase I remember from my childhood is, "If so-and-so can do it, why can't you?"

posted by russilwvong at 3:06 PM on July 10, 2008

*x million Chinese kids say that's probably bullshit. If 8th graders have difficulty conceptualizing geometry, you do your best to teach them so they can better conceptualize geometry.*Harold Stevenson, who did cross-cultural studies of elementary school education, had some interesting comments on this. He noted that in the American families he studied, much more emphasis was placed on children's innate talents and abilities (e.g. whether they're "good at math" or not), whereas the Chinese and Japanese families emphasized hard work: they assumed that even an average or poor student could master the material if they worked hard enough.

The phrase I remember from my childhood is, "If so-and-so can do it, why can't you?"

posted by russilwvong at 3:06 PM on July 10, 2008

Along with delmoi, I've never been able to understand how someone even moderately intelligent could have serious problems with college/elementary algebra (so designated because algebra is the stuff with groups and rings). Then again, in about 10 minutes I'm going to go try (again) to read a paper about cohomology rings of partial flag varieties (which is in an area like college algebra's long lost great great uncle), so maybe I'm not the best judge of these things.

Anyways, can anyone who couldn't understand elementary algebra and later got it explain what it was that troubled them so? Lack of proficiency with fractions/negative numbers? Not understanding what it meant to solve an equation? Not understanding what a function was?

posted by TypographicalError at 3:10 PM on July 10, 2008

Anyways, can anyone who couldn't understand elementary algebra and later got it explain what it was that troubled them so? Lack of proficiency with fractions/negative numbers? Not understanding what it meant to solve an equation? Not understanding what a function was?

posted by TypographicalError at 3:10 PM on July 10, 2008

I am SOOOOO not a math person, and my school history shows it:

- Pre-algebra in 8th grade, I think I passed with a C?

- Bombed out of 1st-level Algebra halfway through my freshman year, and got downgraded to remedial math for the rest of the term

- Got a B- on my second attempt my sophomore year, a miracle considering I was out for a good chunk of second semester due to a broken ankle

- Took Geometry my junior year, barely passed with a C

- Took one semester of Algebra II my senior year, switched to Creative Writing and never looked back

I did what I could, of course (despite my mother shredding me on the stand for supposedly being lazy but that's another issue altogether), but it was very clear that I was just not very mathematically-inclined. Later in college, I cleared its equivalent of Algebra II and decided to stop there since 1) it was the minimum requirement for the general ed aspect of things and 2) I swear my head would implode if I tried to go further. Clearing with a B was enough of an achievement for me.

On that note, I second the sentiment that the U.S. needs a public trade school system. That would have been so much better for me as opposed to regular school.

posted by Yoshi Ayarane at 3:13 PM on July 10, 2008

- Pre-algebra in 8th grade, I think I passed with a C?

- Bombed out of 1st-level Algebra halfway through my freshman year, and got downgraded to remedial math for the rest of the term

- Got a B- on my second attempt my sophomore year, a miracle considering I was out for a good chunk of second semester due to a broken ankle

- Took Geometry my junior year, barely passed with a C

- Took one semester of Algebra II my senior year, switched to Creative Writing and never looked back

I did what I could, of course (despite my mother shredding me on the stand for supposedly being lazy but that's another issue altogether), but it was very clear that I was just not very mathematically-inclined. Later in college, I cleared its equivalent of Algebra II and decided to stop there since 1) it was the minimum requirement for the general ed aspect of things and 2) I swear my head would implode if I tried to go further. Clearing with a B was enough of an achievement for me.

On that note, I second the sentiment that the U.S. needs a public trade school system. That would have been so much better for me as opposed to regular school.

posted by Yoshi Ayarane at 3:13 PM on July 10, 2008

The fact is, you will never get enough qualified math teachers until you pay them enough to make teaching a viable alternative. I had one good math teacher before college, and she taught geometry, and I did well in it and enjoyed it. The former nun I had for algebra was god-awful (no pun intended).

I teach first and second grade, I love teaching math, and my students almost all say that math is their favorite subject.

-also-

When comparing similar 4th-grade students in private and public schools, the students in public schools performed better than those in private schools in this study. In 8th, they were about the same. So yes, people do send their children to public school, and for good reason.

posted by Huck500 at 3:15 PM on July 10, 2008 [2 favorites]

I teach first and second grade, I love teaching math, and my students almost all say that math is their favorite subject.

-also-

When comparing similar 4th-grade students in private and public schools, the students in public schools performed better than those in private schools in this study. In 8th, they were about the same. So yes, people do send their children to public school, and for good reason.

posted by Huck500 at 3:15 PM on July 10, 2008 [2 favorites]

*I guess I would question, if not algebra, what the hell are they teaching these kids? After 7 years of primary education, you would think multiplication tables and fractions would hvae run their course.*

Ms Vegetable was a HS math teacher. A

__majority__of her students (inner city 12th graders) couldn't function with fractions or negative numbers. Like, adding them. Calculators were required for tasks such as 3 + -2. She attributes this to a) years of cumulative deficits in effort b) years of cumulative deficits in instruction c) summers of complete regression in even basic topics. I like to add on d) fetal alcohol.

posted by a robot made out of meat at 3:18 PM on July 10, 2008 [1 favorite]

Algebra sure helps later on in life.

"The angle of the dangle is equal to the heat of the beat when the throb of the knob is constant."posted by ericb at 3:20 PM on July 10, 2008 [1 favorite]

That's trig, surely?

posted by Artw at 3:23 PM on July 10, 2008 [2 favorites]

posted by Artw at 3:23 PM on July 10, 2008 [2 favorites]

*"If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?".*

So, K - 12 grade education should only have bearing on those who go onto higher education?

posted by ericb at 3:23 PM on July 10, 2008

oops.

http://www.metafilter.com/70699/A-Mathematicians-Lament

posted by anoirmarie at 3:24 PM on July 10, 2008

http://www.metafilter.com/70699/A-Mathematicians-Lament

posted by anoirmarie at 3:24 PM on July 10, 2008

If they not be lurnin' algebra, they'll likely not be gettin' much more in there educamation.

Hey -- at least Jay Leno will have a 25% pool of future particpants for his 'Jaywalking' segments

posted by ericb at 3:30 PM on July 10, 2008

Hey -- at least Jay Leno will have a 25% pool of future particpants for his 'Jaywalking' segments

__right there in California__!posted by ericb at 3:30 PM on July 10, 2008

*When was the last time you solved a quadratic equation or raised a number to a fractional degree?*

Dude, was this supposed to be rhetorical? I'm going with around May, and yesterday, respectively. Unfortunately, I didn't get to use these mad algebra skills to boss anyone around. Yet. Maybe that comes in Algebra 2.

posted by whatzit at 3:35 PM on July 10, 2008

*Anyways, can anyone who couldn't understand elementary algebra and later got it explain what it was that troubled them so? Lack of proficiency with fractions/negative numbers? Not understanding what it meant to solve an equation? Not understanding what a function was?*

Took "eighth grade math" in 8th grade with some vague stab at Bonus Extra Pre-Algebra for some subset of the elect at my Catholic junior high. The pre-algebra went the way of the dodo because the rest of the kids didn't want extra homework and stopped doing it-- and since it wasn't on the curriculum and we were still expected to do 8th grade math too, it wasn't getting graded.

Got to 9th grade, placed into honors algebra. Teacher decided that she didn't want to teach Chapter 3 on polynomials because everyone should already know that, assigned the homework, and was out that day.

Cue massive downward spiral from there on out, as I had never seen these topics and had no idea how to cope. Ninth-grade teacher was no help at all, even though I spent about three hours or more a week staying after to get extra help. I made tutors from MIT go home in defeated tears by the time I hit Algebra 2 in 11th grade, and I was still staying after for hours. I got a C- in Algebra 2 and promptly stopped taking math classes.

(I did pretty well at geometry, actually. Much easier for me for some reason.)

I don't, as far as I know, have dyscalculia or any other learning disability that could have spawned that kind of academic nightmare. Apparently, not knowing anything about polynomials and having teachers who think you Ought To Be Smarter Than That will slaughter your forward progress.

posted by fairytale of los angeles at 3:39 PM on July 10, 2008

Math is something I truly suck at. I can remember struggling with it in Grade 1, and I can remember struggling with it all through my school career.

I somehow fought through math/algebra until about Grade 12 (just squeaking by in high school math); then my processor was just overloaded and I failed grade 12 algebra *twice*. I ended up taking a problem solving course in university, some statistics, some financial math, some logic - I find all these things more useful in solving mathematical or even day-to-day life problems than Algebra.

Can someone tell me why discussion of making-people-better-at-math instantly invokes Algebra and Calculus?

posted by Deep Dish at 3:56 PM on July 10, 2008 [1 favorite]

I somehow fought through math/algebra until about Grade 12 (just squeaking by in high school math); then my processor was just overloaded and I failed grade 12 algebra *twice*. I ended up taking a problem solving course in university, some statistics, some financial math, some logic - I find all these things more useful in solving mathematical or even day-to-day life problems than Algebra.

Can someone tell me why discussion of making-people-better-at-math instantly invokes Algebra and Calculus?

posted by Deep Dish at 3:56 PM on July 10, 2008 [1 favorite]

*The fact is, you will never get enough qualified math teachers until you pay them enough to make teaching a viable alternative.*

I have my doubts that pay scale is the biggest problem. Phillip Greenspun's on to something when he talks about how university science really doesn't pay well, yet competition for positions is fierce.

I think he's partly correct that some of the reason for this is that many people don't have the social skills to realize how much the rewards diminish for the inputs. But I also think that a lot of people either go into industry math/science or reach for the university community because they want to

**do something**. They want to build it, prove it, they want to achieve, they want to be in the thick of working in their subject.

And you know, one of the things about secondary ed? There's no time they really give you for that. But you know what's worse? Nobody really expects it from you. Nobody's gonna pat you on the head if you do it, you've got other things to worry about, other mundane things involved in just getting the school to work. Unless you're very lucky, there's no community of other people who want to build it, prove it, write about it, delight in puzzles, etc etc. Maybe one of your fellow faculty members, two if you're lucky, maybe a few of your students, but most of those will be having their own battles with alienation with the system.

I got high reviews from my cooperating teachers, my students, and my university evaluators when I did student teaching. The only negative they mentioned? The fact that I didn't seem committed. In fact, outright reluctant. And it wasn't because of concerns over how much money I was going to make. The biggest and most indelible doubt had to do were these very doubts about what day-to-day life in the public secondary education community were going to be like.

I'm projecting my own experience across the broad screen of the whole dilemma, and I recognize that's likely to lead to mistakes. So I say to myself sometimes that it's best to realize there's probably other ways -- maybe China's way, where culturally, being a teacher *is* an achievement, and being a hardworking student is also highly valued. Maybe something else.

But when it comes down to it, I think that the way best suited to the U.S. way is to build something in the secondary ed space where teachers are free and encouraged to

*practice*their subject as well as teach it. That's what I think is going to draw the teachers who're most likely to make a difference in our culture into the secondary ed game.

posted by weston at 4:05 PM on July 10, 2008 [2 favorites]

*Can someone tell me why discussion of making-people-better-at-math instantly invokes Algebra and Calculus?*

Some kind and degree of algebra is pretty much the foundation of everything else.

Calculus... yeah, probably somewhat overemphasized, given the breadth of useful Math out there, and I think one could reasonably argue that linear algebra and probability/basic statistics and some discrete math are all just as practical (possibly more, especially stats), but Calc is an essential part of any thorough study of natural sciences or engineering. In the context of the social push towards engineering for those with technical talent, it makes sense.

In a broader educational context? Calculus takes on this role as the quantitative equivalent of music appreciation, but instead of studying Mozart and Bach and Beethoven and Chopin and Tchaikovsky, you're studying Newton and Leibniz and Cauchy and Euler and Fourier and Gauss. Is the cross section of their selected works the ideal mix? Heck if I know. Sometimes I'd much rather be discussion Von Neumann and Nash and Conway and Knuth. But time's limited, and you could do a lot worse than the Calc school of Math Appreciation.

posted by weston at 4:21 PM on July 10, 2008

I had the tiered math system, taking pre-algebra (and bombing on the placement test, so so much for me) in seventh. Barely passed Algebra 1a and 1b. Did freaking daily tutoring on senior year algebra and barely passed that. Made damn sure I went to a college where if you had certain majors, you didn't have to take a math class. Whee, math learning disability!

If they'd forced me into algebra in 8th grade, I would never have graduated middle school. Modern-day schooling scares the shit out of me.

posted by jenfullmoon at 4:22 PM on July 10, 2008

If they'd forced me into algebra in 8th grade, I would never have graduated middle school. Modern-day schooling scares the shit out of me.

posted by jenfullmoon at 4:22 PM on July 10, 2008

If algebra is what some call a gatekeeper for academic success, then preparing students for it should be undertaken carefully and early on.

The National Council for Teachers of Mathematics provides standards as guideposts for mathematical development, incorporating algebraic thought as early as third grade, embedded in properties of multiplication. To me, as a prospective math teacher, the NCTM standards seem sound and reasonable, emphasizing the logic and reasoning that are at work alongside basic arithmetic when developing math skills.

Unfortunately, the feedback I've received from those in my upcoming profession (middle school math instruction) is that elementary teachers, as a general tendency, have more of a disposition or persuasion toward the other core subjects they're also teaching (Language arts, social science), and the mathematical concepts get short-changed either in time allotted, enthusiasm of approach, or accurate content knowledge for conveying -- sometimes all at once.

For that reason, it's no wonder to me that by middle school, students are already behind or else semi-skilled beyond superficial understanding of what's been taught -- inheriting this proportion of readiness-or-not among incoming students, my task becomes double-pronged in accelerating the abilities of kids who have already fallen behind!

I think many children who succeed in math are comfortable with it as are their parents (as are numerous posters on this thread expressing incredulity that anyone 'not get it? Horrors!') by 8th grade; and such children probably also get the verbal expression " 'x' amount of Chinese kids" and know what's referred to.

But increasingly the gap is widening between children who have added reinforcement both at home from parents comfortable with math and English language/who spend time talking to / exposing their kids to the 'everydayness' of math -- and the other end of the spectrum who, whether because their parents are limited English speakers or have their own phobias leftover from bad math instruction during their own childhoods, are not able to provide the reinforcing factor that enables their children in the same way as their math-savvy peers.

Incidentally, Cali is not the only place where students chronically under-perform in math at middle school level and beyond.

Also I'd be interested to learn whether those top-of-the-mark Chinese/Singapore students receive separate instruction in math at the primary grades, rather than lumping it in together with all core subjects under one teacher.

posted by skyper at 4:25 PM on July 10, 2008 [3 favorites]

The National Council for Teachers of Mathematics provides standards as guideposts for mathematical development, incorporating algebraic thought as early as third grade, embedded in properties of multiplication. To me, as a prospective math teacher, the NCTM standards seem sound and reasonable, emphasizing the logic and reasoning that are at work alongside basic arithmetic when developing math skills.

Unfortunately, the feedback I've received from those in my upcoming profession (middle school math instruction) is that elementary teachers, as a general tendency, have more of a disposition or persuasion toward the other core subjects they're also teaching (Language arts, social science), and the mathematical concepts get short-changed either in time allotted, enthusiasm of approach, or accurate content knowledge for conveying -- sometimes all at once.

For that reason, it's no wonder to me that by middle school, students are already behind or else semi-skilled beyond superficial understanding of what's been taught -- inheriting this proportion of readiness-or-not among incoming students, my task becomes double-pronged in accelerating the abilities of kids who have already fallen behind!

*x million Chinese kids say that's probably bullshit.***Jimbob**, how funny you used actual algebraic vernacular to make a point I've considered often during this debate -- which is alive and well in Virginia USA, as the 2nd-largest school system already implemented mandatory algebra for 8th grade some years ago. Yet during my student teaching of 7th graders last fall, merely getting students comfortable with mathematical*language*often stalled with getting them to distinguish such vocabulary as "variable" from "coefficient" etc. -- let alone the proportion of 7th graders still using fingers to manually skip-count because they hadn't mastered their tables. My point is that there are many levels on which children can miss the crux of math learning, especially with under-prepared instructors at early or mid-level schooling.I think many children who succeed in math are comfortable with it as are their parents (as are numerous posters on this thread expressing incredulity that anyone 'not get it? Horrors!') by 8th grade; and such children probably also get the verbal expression " 'x' amount of Chinese kids" and know what's referred to.

But increasingly the gap is widening between children who have added reinforcement both at home from parents comfortable with math and English language/who spend time talking to / exposing their kids to the 'everydayness' of math -- and the other end of the spectrum who, whether because their parents are limited English speakers or have their own phobias leftover from bad math instruction during their own childhoods, are not able to provide the reinforcing factor that enables their children in the same way as their math-savvy peers.

Incidentally, Cali is not the only place where students chronically under-perform in math at middle school level and beyond.

Also I'd be interested to learn whether those top-of-the-mark Chinese/Singapore students receive separate instruction in math at the primary grades, rather than lumping it in together with all core subjects under one teacher.

posted by skyper at 4:25 PM on July 10, 2008 [3 favorites]

Fuck Algebra. That's why computers were invented. Well, that and porn.

posted by jonmc at 4:27 PM on July 10, 2008

posted by jonmc at 4:27 PM on July 10, 2008

I think Weston is right on the money, but I'd also add that I think there's a prestige aspect to it as well. I bet that if you got a few hundred people together and asked them to rank the perceived intelligence of people in a bunch of different jobs, and included "Physics Postdoc" and "Elementary Educator" in there (provided your sample knew what both those things were), they'd rate the person doing Elementary Ed lower.

Consciously or not, I think people pick up on that when they're choosing occupations. There are lots of low-paying occupations that still manage to have stiff competition -- but they also tend to be the jobs that I suspect would score the highest on a perceived "prestige" scale.

People are willing to work for a lot less if it's a job that's held in high social regard by their peers; likewise people will turn down (in my experience) a job that has more pay if it's low-prestige.

Also see salaries for lawyers vs HVAC technicians. There are lots of people slaving away in law school even though they'll probably never make as much as the guy doing HVAC work (particularly when you factor in their debt and delayed-start load), yet there they are.

Never underestimate the value that people unconsciously place on ego-driven concerns. Just paying teachers more won't solve the problem and get the very best people into the field; there also needs to be a sea change in how people perceive the occupation. I think that kind of change can take a generation or two, personally.

I wonder how elementary education professionals are regarded in China, compared to the U.S.?

posted by Kadin2048 at 4:28 PM on July 10, 2008 [1 favorite]

Consciously or not, I think people pick up on that when they're choosing occupations. There are lots of low-paying occupations that still manage to have stiff competition -- but they also tend to be the jobs that I suspect would score the highest on a perceived "prestige" scale.

People are willing to work for a lot less if it's a job that's held in high social regard by their peers; likewise people will turn down (in my experience) a job that has more pay if it's low-prestige.

Also see salaries for lawyers vs HVAC technicians. There are lots of people slaving away in law school even though they'll probably never make as much as the guy doing HVAC work (particularly when you factor in their debt and delayed-start load), yet there they are.

Never underestimate the value that people unconsciously place on ego-driven concerns. Just paying teachers more won't solve the problem and get the very best people into the field; there also needs to be a sea change in how people perceive the occupation. I think that kind of change can take a generation or two, personally.

I wonder how elementary education professionals are regarded in China, compared to the U.S.?

posted by Kadin2048 at 4:28 PM on July 10, 2008 [1 favorite]

I really don't think school is getting tougher. Quite the opposite, it's getting easier. Introducing all children to algebra is not that radical an idea. Sometimes learning about something is valuable, even if you don't use it. (I am poor at math, have always been poor at math. I can't even blame my teachers or parents).

posted by gesamtkunstwerk at 4:30 PM on July 10, 2008

posted by gesamtkunstwerk at 4:30 PM on July 10, 2008

*Anyways, can anyone who couldn't understand elementary algebra and later got it explain what it was that troubled them so? Lack of proficiency with fractions/negative numbers? Not understanding what it meant to solve an equation? Not understanding what a function was?*

I actually did OK in math in middle school (all A's and B's), because I had the same teacher in a small prep school that was not only very good at making math interesting, she leaned on me when I needed it. When I went to public high school, the classes were large, the time was short, and somehow... I just wasn't getting it. Unlike nearly every other subject, math had nothing to do with my real life. I didn't go to math movies or read books about math, or visit the Math Academy or the Mathquarium. I passed college qualitative reasoning with the second highest score on the final when I was seventeen, so it wasn't a problem of not having a logical mind; I just had nothing to pin all that mathematics to in the real world.

posted by oneirodynia at 4:31 PM on July 10, 2008

Isn't 8th grade rather late? A smart kid could learn some programming like two years before that. So I'd imagine one should try algebra about the same time.

posted by jeffburdges at 4:54 PM on July 10, 2008

posted by jeffburdges at 4:54 PM on July 10, 2008

i looked at the requirements, and while i KNOW i could do them in middle school (when we had algebra; we had trig in 9th grade, which i rocked at), i couldn't do half of those tasks now. that is certainly because i haven't used my algebra skills since probably 11th grade. so, since i haven't used those skills, it might mean i mostly didn't need them for my particular life. but, it doesn't mean that five other kids in my class didn't need them or couldn't have used them if they had the skills. so, i think the requirement is a good one, but it could also fail as epicly as NCLB did.

posted by misanthropicsarah at 5:03 PM on July 10, 2008

posted by misanthropicsarah at 5:03 PM on July 10, 2008

I now teach college chemistry and invariably the first few weeks of instruction for my introductory level classes have to feature some degree of remedial math. How to plot a simple Cartesian graph. How to solve for X in a simple algebraic equation. What it means to add a negative number to another number. Things students should have learned in high school, without a doubt.

And for some students, no matter how many times you go over it with them or how many ways you try to approach it, they're still struggling with these fundamentals late in the semester.

I'd say half of the students that don't pass my class in a given semester fail because they just can't handle pretty basic algebra. And considering that my courses are required for students who want to go into the health care professions (nursing, nutrition, etc.), it's sad to see how many folks are culled from health care fields essentially because they can't solve for X, or (more critically) understand how a prose paragraph can be represented by an algebraic equation.

It is this latter part that seems to be the crux. Somehow, many students make it all the way through high school without being able to handle the dreaded "word problem". They simply don't make the connections between the practical scenario and the mathematic expression that fits or describes it.

posted by darkstar at 5:04 PM on July 10, 2008

And for some students, no matter how many times you go over it with them or how many ways you try to approach it, they're still struggling with these fundamentals late in the semester.

I'd say half of the students that don't pass my class in a given semester fail because they just can't handle pretty basic algebra. And considering that my courses are required for students who want to go into the health care professions (nursing, nutrition, etc.), it's sad to see how many folks are culled from health care fields essentially because they can't solve for X, or (more critically) understand how a prose paragraph can be represented by an algebraic equation.

It is this latter part that seems to be the crux. Somehow, many students make it all the way through high school without being able to handle the dreaded "word problem". They simply don't make the connections between the practical scenario and the mathematic expression that fits or describes it.

posted by darkstar at 5:04 PM on July 10, 2008

People learn to "hate" math in school. This is the real math crisis. The root problem is that there is a time limit as to how fast one must learn it. Once a student falls behind, persistent anxiety sets in. Algebra is retaught in college to most students because they were moved ahead prematurely into a snowball effect, perhaps cheating their way through, rendering any teaching talent useless. The evidence suggests the need for a major overhaul. The easiest, immediate and relatively "free" way to improve math performance is to let the students who can do math naturally move ahead in it, and then let them tutor their peers along the way. Since these tutors are still in the school system and possess a knowledge of math, it would be foolish to ignore their natural gifts as future math experts considering they are classmates to needy peers. This could be done without having any strict deadlines except as prerequisites to other classes. When a student masters their math on practice tests given by a professional teacher, they take a national test somewhere else as proof of passing. Problem solved.

posted by Brian B. at 5:22 PM on July 10, 2008 [1 favorite]

posted by Brian B. at 5:22 PM on July 10, 2008 [1 favorite]

It is worth noting that if someone isn't fairly competant at algebra, they have absolutely no chance at getting any further at math, as well as anywhere in chemistry, physics, astronomy, etc. It is pretty much an absolute prerequisite for any area of science. You won't even get that far in biology without it. It is probably also the math that is most helpful to learn for real-world applications - calculators can do arithmetic even if your own skills are terrible, but a person without algebra ability won't be able to set a problem up for the calculator to do, even if the calculator could handle it. Problems solvable with algebra turn up quite often in life.

Personally, I wonder if it shouldn't be taught even earlier, leaving other kinds of math for later. The kind of number-manipulation skills it uses are useful in every kind of math, and I wouldn't if people wouldn't be better at picking up long division, fractions, etc. if they had learned algebra already. A lot of classical arithmetic abilities are basically simple algorithms, and students might understand the concept of algorithms better if they had learned algebra already.

posted by Mitrovarr at 5:23 PM on July 10, 2008 [2 favorites]

Personally, I wonder if it shouldn't be taught even earlier, leaving other kinds of math for later. The kind of number-manipulation skills it uses are useful in every kind of math, and I wouldn't if people wouldn't be better at picking up long division, fractions, etc. if they had learned algebra already. A lot of classical arithmetic abilities are basically simple algorithms, and students might understand the concept of algorithms better if they had learned algebra already.

posted by Mitrovarr at 5:23 PM on July 10, 2008 [2 favorites]

How do I solve for e(x)pelled?

posted by ...possums at 5:27 PM on July 10, 2008 [1 favorite]

posted by ...possums at 5:27 PM on July 10, 2008 [1 favorite]

*If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?*

Let's rephrase that more accurately: If for the most part only the children of reasonably well-off parents ever earns a college degree, and since we're talking about public schools were children of reasonably well-off people are rarely sent for schooling, why insist that those other (ie relatively poor) children learn something that may help them do better in high school, earn a scholarship, and thus compete for college space with the children of the reasonably well-off?

posted by davejay at 5:34 PM on July 10, 2008

er...

Obviously I am not one of those children.

posted by davejay at 5:35 PM on July 10, 2008

*only the children...ever earns a college degree*Obviously I am not one of those children.

posted by davejay at 5:35 PM on July 10, 2008

Oh, and yeah, the earlier you teach mathematical concepts, OR the later you teach mathematical concepts, the more likely students are to get it; math requires a lot of translation between arbitrary notation system and conceptual thinking, and so requires a mind that is hungry for knowledge and/or driven to succeed. Kids in high school, for the most part, are quite preoccupied with their social status, the changes that come with puberty, and other such distractions, and so do not qualify.

So from that perspective, I say start teaching algebra in fifth grade, but stretch it over the course of a couple of years, starting with the basic concepts and eventually graduating to complex notation methods.

posted by davejay at 5:39 PM on July 10, 2008

So from that perspective, I say start teaching algebra in fifth grade, but stretch it over the course of a couple of years, starting with the basic concepts and eventually graduating to complex notation methods.

posted by davejay at 5:39 PM on July 10, 2008

I think part of the reason we fall behind in math is because it's kind of socially acceptable to be bad at math, or to be math-phobic. I think learning to speak, learning to read and learning to write are all harder than algebra; but everybody can do it because, dammit, if we don't then we are put very, very far down the social latter.

I know lots of people that describe themselves as "bad at math." And it's considered totally socially acceptable. A couple of them are teachers.

posted by jabberjaw at 5:46 PM on July 10, 2008 [1 favorite]

I know lots of people that describe themselves as "bad at math." And it's considered totally socially acceptable. A couple of them are teachers.

posted by jabberjaw at 5:46 PM on July 10, 2008 [1 favorite]

What if we taught English the same way we taught Math?

posted by anthill at 5:47 PM on July 10, 2008 [6 favorites]

posted by anthill at 5:47 PM on July 10, 2008 [6 favorites]

*Anyways, can anyone who couldn't understand elementary algebra and later got it explain what it was that troubled them so? Lack of proficiency with fractions/negative numbers? Not understanding what it meant to solve an equation? Not understanding what a function was?*

Nope. I actually enjoyed the first semester of so of algebra--understanding that x=a given number, and that you can use that to extrapolate out, and using variables to solve equations, made sense to me.

Somewhere around matrices, (still don't understand the damn things; I remember sitting in class starting at those boxes and thinking, wait, what?), I just got lost, and never really found my footing again. Like others have commented, I had absorbed the idea that some people are just "good at" things, and since I was good at English and history, I assumed I was "bad at" math and didn't try to get over that hump. And because I was passing, and quiet, and one of 32 kids in a class, and maybe because I was a girl, no one paid attention. I regret that I didn't fight harder, and also that it was so easy to slip under the radar.

I think that the earliest we can teach kids mathematical concepts and reasoning, before the cultural conditioning messes with their heads, the better, frankly.

posted by emjaybee at 5:51 PM on July 10, 2008

*I'd just like to point out that the proposed Algebra curriculum for 8th graders is roughly the same as an outline for the college-level Algebra class I'll be taking in the Fall.*

Yep. I just finished a summer class (6 weeks) and this pretty much the same thing as I just went through.

I've always had a tough time with most math, and I'm pretty sure I'm not retarded. The reason? Having just gone through 6 intensive weeks of it, two things: the way it's taught and the way my brain seems to process information. For me, I need to to make a relationship between a concept and the real world. I had to translate the information into a "language" I could understand. The way I've been taught algebra pretty much simply states, "This is the way it is, now do it." That type of learning doesn't create knowledge, it creates mimicry. That's why so many people can do well in algebra in school, and 10 years later, barely remember a thing. Sure, it works for some people, but not for others. It's a shame those who can't adapt to that teaching style are thought to be less intelligent, and that they think that of themselves.

I went into the final exam with an average grade of 70. It was required that we get at least a 50 on the exam to pass the course no matter how high our average. I got a 48.

posted by sluglicker at 5:56 PM on July 10, 2008

Whoever wrote the description of the 8th grade curriculum doesn't understand factoring. They could have factored the word "Students" out of the enumerated list to make it more readable.

posted by storybored at 6:02 PM on July 10, 2008 [1 favorite]

posted by storybored at 6:02 PM on July 10, 2008 [1 favorite]

The last one, precisely. I understood elementary algebra - which I'm defining as the basic turning-prose-into-equations and knowing how to balance them and solve for "x"... The kind that's on the Math SAT, and as far as that went I was in the 90s percentile-wise. I also loved geometry proofs. But every time they'd start graphing things (graphing what? what are we making a graph of? what's the graph for?) and talking about "f of x" (what's a function? why? what are we trying to figure out?) I was Absolutely And Completely unable to grasp what was going on. So I never went past Algebra II because there was no point in even attempting pre-calc - it would be like registering for "Pdjkrq".

*I still don't understand what calculus is*, and I've read the wikipedia entry and everything. I think... maybe it's the way math is taught and so forth... but maybe some of us are just wired differently? And by "some of us" I mean "most of us" and "differently" I mean "in a really linear, concrete way"?

posted by moxiedoll at 6:05 PM on July 10, 2008

I went to a Catholic high school, and for some reason, most of the kids who had gone to Catholic school previously had not taken algebra in 8th grade. Meanwhile, many of us who went to the far inferior public schools, urban public schools, even, had taken algebra.

I guess the reason is probably that the catholic schools usually only ever had one eighth grade math class, because there were not enough students to have different levels, as there were at most public schools. But you'd think maybe, since the Catholic schools always say how much better they are, with their smaller class sizes, better teachers, and God helping them out, they could have the one level of eighth grade math class, and use those smaller classes to focus on the students who are having trouble with it. And pray that they do better.

Oh, which reminds me of a fun story. You may have heard this one. It's pretty good.

There was a mother whose 3rd grade son was having quite a lot of difficulty in school, particularly in math class. She got his grade card one quarter and saw that he was doing quite poorly. She sat him down and asked him why? What was the problem?

"I dunno."

"That's not an answer. Is it that you just don't like math? Is it the teacher? Is it just too hard? Do you want me to help you out more with your homework. We need to do something to get you doing better at math."

"I dunno. I'm just bad at it"

She tried having him stay after class to work with his teacher a couple times a week. She tried private tutors. Positive reinforcement. Negative reinforcement. Everything. She phoned the teacher regularly to see if there had been any results. Nothing though.

Finally, she decided that perhaps switching schools would help. She figured the discipline of a Catholic school, and their smaller class sizes, better teachers, and God, was the best bet. Though as we all know, God does not play dice. Turns out his college did not require statistics classes for M. Div degrees.

As soon as the switch was made, she began seeing results. Every day, her son came home and immediately started working on his math homework, for as long as it took to get it right, before moving on to other subjects, and finally to playing with friends, television, and video games. Weeks later, he came home with his first report card from the new school sporting an A in math, and his usual respectable grades in all other subjects.

"Honey, so what was it that made you want to try so hard at math?"

"As soon as I saw the guy nailed to a plus sign, I knew they meant business!"

posted by gauchodaspampas at 6:12 PM on July 10, 2008 [5 favorites]

I guess the reason is probably that the catholic schools usually only ever had one eighth grade math class, because there were not enough students to have different levels, as there were at most public schools. But you'd think maybe, since the Catholic schools always say how much better they are, with their smaller class sizes, better teachers, and God helping them out, they could have the one level of eighth grade math class, and use those smaller classes to focus on the students who are having trouble with it. And pray that they do better.

Oh, which reminds me of a fun story. You may have heard this one. It's pretty good.

There was a mother whose 3rd grade son was having quite a lot of difficulty in school, particularly in math class. She got his grade card one quarter and saw that he was doing quite poorly. She sat him down and asked him why? What was the problem?

"I dunno."

"That's not an answer. Is it that you just don't like math? Is it the teacher? Is it just too hard? Do you want me to help you out more with your homework. We need to do something to get you doing better at math."

"I dunno. I'm just bad at it"

She tried having him stay after class to work with his teacher a couple times a week. She tried private tutors. Positive reinforcement. Negative reinforcement. Everything. She phoned the teacher regularly to see if there had been any results. Nothing though.

Finally, she decided that perhaps switching schools would help. She figured the discipline of a Catholic school, and their smaller class sizes, better teachers, and God, was the best bet. Though as we all know, God does not play dice. Turns out his college did not require statistics classes for M. Div degrees.

As soon as the switch was made, she began seeing results. Every day, her son came home and immediately started working on his math homework, for as long as it took to get it right, before moving on to other subjects, and finally to playing with friends, television, and video games. Weeks later, he came home with his first report card from the new school sporting an A in math, and his usual respectable grades in all other subjects.

"Honey, so what was it that made you want to try so hard at math?"

"As soon as I saw the guy nailed to a plus sign, I knew they meant business!"

posted by gauchodaspampas at 6:12 PM on July 10, 2008 [5 favorites]

I would also like to suggest that modern math education has far too much emphasis on memorization and not enough on understanding concepts and being able to derive them from principles. Most of the situations that convinced me I wasn't very good at math were due to calculus professors trying to teach a very difficult one-off formula or tool that was excessively difficult and unnecessary for understanding the concepts. While many in the class could successfully apply it and thus pass the test, I bet the vast majority of them couldn't explain it and not one of them could derive it.

You have to understand what you're doing in math, and hopefully be able to derive it, to make progress in any meaningful sense of the word. Teaching math without teaching understanding and derivation is like leading someone into the wilderness without giving them the skills to find their way - they might be able to follow you, if they're quick, but the minute you're gone they'll be completely mystified and helpless.

Oh, and another thing about teaching math - tests that require a curve for anyone to pass are confidence killers. Unless you have a class full of statistically outlying morons, the majority of the class should be getting the majority of the questions right. If they're not, you made the questions too hard, or people are getting into the class who shouldn't be there.

posted by Mitrovarr at 6:16 PM on July 10, 2008

You have to understand what you're doing in math, and hopefully be able to derive it, to make progress in any meaningful sense of the word. Teaching math without teaching understanding and derivation is like leading someone into the wilderness without giving them the skills to find their way - they might be able to follow you, if they're quick, but the minute you're gone they'll be completely mystified and helpless.

Oh, and another thing about teaching math - tests that require a curve for anyone to pass are confidence killers. Unless you have a class full of statistically outlying morons, the majority of the class should be getting the majority of the questions right. If they're not, you made the questions too hard, or people are getting into the class who shouldn't be there.

posted by Mitrovarr at 6:16 PM on July 10, 2008

*but maybe some of us are just wired differently?*

The latest neuroscience says our brains can rewire themselves. I think the issue is that different brains need different approaches or differing amounts of practice to rewire properly. Unfortunately math classes tend to put everyone through the same cookie-cutter teaching methods. The result, students falling by the wayside, is not surprising.

Here's a great book on why *everyone* can learn math: The End of Ignorance. The author has put his words into action with the JUMP (Junior Undiscovered Math Prodigies) volunteer program which has had phenomenal success. www.jumpmath.org

posted by storybored at 6:18 PM on July 10, 2008 [2 favorites]

*Fuck Algebra. That's why computers were invented. Well, that and porn.*

Even with a computer, you still need Algebra.

*Arithmetic*you can avoid.

posted by delmoi at 6:41 PM on July 10, 2008

*Even with a computer, you still need Algebra.*

With Mathematica (or equivalent) you can avoid algebra and most of calculus just as easily as a calculator lets you avoid arithmetic; you still need to know what to do, but you don't need to know the details of how to do it.

posted by Pyry at 6:55 PM on July 10, 2008

As a middle-school math teacher in California, I have a few comments on this.

1. At first glance, I wasn't sure why this was news. The state standards adopted in 1997 put Algebra 1 in the 8th grade. What IS news here is schools have been allowed to give a "general math" test to 8th-grade students not enrolled in Algebra 1. That was going to be codified this year as a state-adopted course called "Algebra Readiness" for the students who were, ahem, not ready for Algebra in 8th grade. At my school, we had piloted some of the trial materials for this course and were really excited to be start it. That's what has been shot down. It will be one-size-fits-all, NCLB-compliant.

2. Students are exposed to algebraic concepts waaaay before 8th-grade. The CA standards all the way from kindergarten through 7th grade include a strand (category) called "Algebra and Functions." For example, in 3rd grade, standard AF 1.5 reads: "Recognize and use the commutative and associative properties of multiplication (e.g., if 5 × 7 = 35, then what is 7 × 5? and if 5 × 7 × 3 = 105, then what is 7 × 3 × 5?)." Sure, that may seem obvious to most of you, whether or not you remember the terms "commutative" and "associative" properties. It is an incredibly important concept, though, that order or grouping doesn't matter with certain operations. It helps you solve difficult problems more easily by allowing you to change it around a little.

I think that's what is most important about "Algebra": training the brain to think about different ways to solve problems. The trouble with learning Algebra can be when a teacher does not validate equally sound, but conceptually different, methods of solving problems. That might be why goatdog hated Mrs. Moore.

3. Huck500 had some interesting comments.

(a) Maybe if pay for teachers was higher, it would compete with the other careers many math majors go into, but I also believe that there's a personality component to the shortage of math and science teachers.

4. My school currently offers tiered courses. About 60% take a regular, grade-level-standard class. 25% are in an "Honors" class and are studying material about 1 year above grade level. The remaining 15% need remedial, below-grade-level help. We want to be able to meet them where they are, not try to get them over a hurdle without the proper foundation to stand on. This is the group we want to offer "Algebra Readiness" to, in the belief that they will then have the proper foundation to take, and pass, Algebra in 9th grade. Instead, what will happen now is that 15% at my school will fail miserably in Algebra 1 in 8th grade. They will not be able to connect the instruction to previously understood concepts, they will space out in class, give up on doing homework and not be any better prepared to pass Algebra 1 in 9th grade. That is precisely what Jack O'Connell is worried about.

So am I.

posted by msacheson at 6:55 PM on July 10, 2008

1. At first glance, I wasn't sure why this was news. The state standards adopted in 1997 put Algebra 1 in the 8th grade. What IS news here is schools have been allowed to give a "general math" test to 8th-grade students not enrolled in Algebra 1. That was going to be codified this year as a state-adopted course called "Algebra Readiness" for the students who were, ahem, not ready for Algebra in 8th grade. At my school, we had piloted some of the trial materials for this course and were really excited to be start it. That's what has been shot down. It will be one-size-fits-all, NCLB-compliant.

2. Students are exposed to algebraic concepts waaaay before 8th-grade. The CA standards all the way from kindergarten through 7th grade include a strand (category) called "Algebra and Functions." For example, in 3rd grade, standard AF 1.5 reads: "Recognize and use the commutative and associative properties of multiplication (e.g., if 5 × 7 = 35, then what is 7 × 5? and if 5 × 7 × 3 = 105, then what is 7 × 3 × 5?)." Sure, that may seem obvious to most of you, whether or not you remember the terms "commutative" and "associative" properties. It is an incredibly important concept, though, that order or grouping doesn't matter with certain operations. It helps you solve difficult problems more easily by allowing you to change it around a little.

I think that's what is most important about "Algebra": training the brain to think about different ways to solve problems. The trouble with learning Algebra can be when a teacher does not validate equally sound, but conceptually different, methods of solving problems. That might be why goatdog hated Mrs. Moore.

3. Huck500 had some interesting comments.

(a) Maybe if pay for teachers was higher, it would compete with the other careers many math majors go into, but I also believe that there's a personality component to the shortage of math and science teachers.

*Disclaimer: wild generalizations ahead.*Many people who are liberal arts majors have the social disposition to be teachers, while many math and science majors often have a hard time communicating their knowledge in an accessible way. (b) Private schools do not have to follow standards and teachers do not have to be credentialed. In the lower grades, that may mean a wide variety of the quality of math instruction.4. My school currently offers tiered courses. About 60% take a regular, grade-level-standard class. 25% are in an "Honors" class and are studying material about 1 year above grade level. The remaining 15% need remedial, below-grade-level help. We want to be able to meet them where they are, not try to get them over a hurdle without the proper foundation to stand on. This is the group we want to offer "Algebra Readiness" to, in the belief that they will then have the proper foundation to take, and pass, Algebra in 9th grade. Instead, what will happen now is that 15% at my school will fail miserably in Algebra 1 in 8th grade. They will not be able to connect the instruction to previously understood concepts, they will space out in class, give up on doing homework and not be any better prepared to pass Algebra 1 in 9th grade. That is precisely what Jack O'Connell is worried about.

So am I.

posted by msacheson at 6:55 PM on July 10, 2008

I want to say thank god for algebra. I sucked so hard at arithmetic (I blame dyslexia) that it was such liberation to shuffle things around an equation till an answer was revealed. It was in seventh grade.

posted by pointilist at 7:00 PM on July 10, 2008

posted by pointilist at 7:00 PM on July 10, 2008

*Even with a computer, you still need Algebra.*

I've held a variety of jobs in my life, and I can't think of any time where I've had to harken back to my sole algebra course. If I were an engineer, that would be different, but I'm not.

posted by jonmc at 7:05 PM on July 10, 2008

*I still don't understand what calculus is, and I've read the wikipedia entry and everything.*

I hope you won't mind if I took it as a challenge to write the clearest brief explanation that I can.

Calculus is a set of techniques for doing math with infinitely small things. There are two sides to the subject: differentiation and integration.

Differentiation lets you calculate the rate at which something is changing. For example, consider driving a car. The rate at which your position is changing is your speed: so many feet per second. The rate at which your speed is changing is your acceleration: " (ft/sec) / sec " or just "ft / sec^2".

Using algebra you can calculate your average speed over some length of time. Say, you were at 0 ft at 0 sec and then, 10 seconds later, you were at 100 ft. So you went 100 ft in 10 sec, or 100/10 ft/sec, or 10 ft/sec... ON AVERAGE.

If you want to know your speed at an exact time, say at 5 seconds after you start, you'd naturally start shrinking the time gap over which you're measuring. So, may you measure from 4 sec to 6 sec, then from 4.9 to 5.1 sec, then 4.999 to 5.001 sec, and so on. You're getting very close, but you're still just computing your AVERAGE speed over that length of time. Eventually things fall apart because the time gap becomes essentially zero and the change in position becomes essentially zero and so you end up with something that looks like 0/0 ft/sec, and algebra just broke. Sorry, you need a new tool.

With differentiation calculus, you can shrink that gap to zero and know your speed EXACTLY at 5 sec.

Integration is a bit more abstract and I struggle to come up with an example that doesn't involve graphs of lines, but it is essentially the opposite of differentiation. Instead of doing division with infinitely small things you're now doing multiplication with infinitely small things.

Calculus was initially invented to solve problems involving the motion of the planets around the sun, but it turns out to be useful for a huge variety of problems in business and science.

One last thing that might cause a mind-expanding moment:

First we have things, like apples and toy blocks and jellybeans.

The answer to an arithmetic problem is a number, which is an abstraction of things.

The answer to an algebra problem is an arithmetic problem.

The answer to a calculus problem is an algebra problem.

The answer to a differential equation problem is a calculus problem.

posted by LastOfHisKind at 7:15 PM on July 10, 2008 [14 favorites]

My 8th grade algebra teacher was named Harry Peckart. Swear to God. It's tough enough teaching junior high algebra when you're Mr. Peckart. But Harry?

posted by jonp72 at 7:21 PM on July 10, 2008

posted by jonp72 at 7:21 PM on July 10, 2008

*Also I'd be interested to learn whether those top-of-the-mark Chinese/Singapore students receive separate instruction in math at the primary grades, rather than lumping it in together with all core subjects under one teacher.*

In Singapore, Math is a separate, standalone subject - we don't have individual subjects for each area of mathematics. Each school year, everyone learns a bit of arithmetic, geometry, algebra, calculus, statistics (and whatever other topics possible) all the way to age 18. For anyone who's interested, the official primary (age 7-12) and secondary (age 13-16) maths syllabus is online (both pdf files).

In primary school many subjects end up being taught by a common teacher though, or at least until about age 9. I think this is mostly due to a shortage of teachers, and also, quite honestly, you don't need to be a mathematics grad to teach kids how to add up money or divide pizza.

Interestingly, I hardly remember anyone talking about "concepts" and "principles" and "logic" when referring to math. One just internalised the formulae, memorised what equations produced what kind of graphs, learnt methods of tackling different types of questions, and

*just practised*. The response to anyone agonising over a particular area of the syllabus?

*Just practise*. Keep doing the same type of questions over and over again, and eventually you'll recognise it when it comes out in the exams, and you'll know which formula to apply and how to get the answer out.

posted by hellopanda at 7:48 PM on July 10, 2008

I never knew that grade 8's didn't learn Algebra. I learned it in grade 8 in Ontario in the late 70's.

posted by substrate at 8:00 PM on July 10, 2008

posted by substrate at 8:00 PM on July 10, 2008

Reading the syllabus ... I'm wondering what the fuss is. To me it seems pretty normal for a year 8 maths course (Australia, graduated high school 1998).

I work in software engineering. I've always been talented at maths - well, most maths. It took a while for me to get the hang of calculus (8 years, all up, actually), but number theory, logic, algebra, trigonometry, etc, was all pretty straightforward to me. I dislike statistics, because they're boring and annoying.

Sure, some kids in my class had issues with the maths we did, but *shrug*. No biggie. Someone's always going to fail something, after all. We can't all pass everything. We're not all geniuses.

I guess the only major shock I get from the article is that this wasn't compulsory already - what the hell do those kids do in maths anyway, if they weren't already doing this stuff?

posted by ysabet at 8:05 PM on July 10, 2008

I work in software engineering. I've always been talented at maths - well, most maths. It took a while for me to get the hang of calculus (8 years, all up, actually), but number theory, logic, algebra, trigonometry, etc, was all pretty straightforward to me. I dislike statistics, because they're boring and annoying.

Sure, some kids in my class had issues with the maths we did, but *shrug*. No biggie. Someone's always going to fail something, after all. We can't all pass everything. We're not all geniuses.

I guess the only major shock I get from the article is that this wasn't compulsory already - what the hell do those kids do in maths anyway, if they weren't already doing this stuff?

posted by ysabet at 8:05 PM on July 10, 2008

*what the hell do those kids do in maths anyway, if they weren't already doing this stuff?*

... that's a really good question.

posted by Durn Bronzefist at 8:08 PM on July 10, 2008

I have no idea what algebra is, and my job is to clean the bathrooms at a Jack in the Box in Modesto.

Don't let this happen to your child.

posted by Mr. President Dr. Steve Elvis America at 9:28 PM on July 10, 2008 [3 favorites]

Don't let this happen to your child.

posted by Mr. President Dr. Steve Elvis America at 9:28 PM on July 10, 2008 [3 favorites]

*But when it comes down to it, I think that the way best suited to the U.S. way is to build something in the secondary ed space where teachers are free and encouraged to practice their subject as well as teach it. That's what I think is going to draw the teachers who're most likely to make a difference in our culture into the secondary ed game.*

No room for standardized testing with that approach to pedagogy.

posted by Blazecock Pileon at 9:51 PM on July 10, 2008

LastOfHisKind writes:

The way I was introduced to integration was with area.

We all know that to get the area of a rectangle, we multiply the length of its base times its height. Now, let's say we want to calculate the surface area of a lake with a weird shape. There's no formula for that, so how do we do it?

Well, we cut up the lake into tiny rectangles, all the same width. Then we calculate the area of all those rectangles and sum them together. That'll give us a pretty good estimate for the area.

Now, if we pick a large number for the width of the rectangles, our area will probably be pretty far off of the true area, since a rectangle isn't really shaped like our lake.

So what we'll do is we'll pick a really small number for the width of our rectangles; that'll be a really good estimate for our lake and give us the most correct answer. But is it possible to get closer than an estimate? Can we get an "exact" answer?

In fact, with knowledge of a relatively straightforward proof (omitted here) in your toolbox, you can actually "pick zero" for the width of your rectangles and get a meaningful, exact answer.

Cutting up your lake into rectangles of equal width (a fixed interval) and then summing the areas

posted by anifinder at 10:21 PM on July 10, 2008 [1 favorite]

*Integration is a bit more abstract and I struggle to come up with an example that doesn't involve graphs of lines, but it is essentially the opposite of differentiation. Instead of doing division with infinitely small things you're now doing multiplication with infinitely small things.*

The way I was introduced to integration was with area.

We all know that to get the area of a rectangle, we multiply the length of its base times its height. Now, let's say we want to calculate the surface area of a lake with a weird shape. There's no formula for that, so how do we do it?

Well, we cut up the lake into tiny rectangles, all the same width. Then we calculate the area of all those rectangles and sum them together. That'll give us a pretty good estimate for the area.

Now, if we pick a large number for the width of the rectangles, our area will probably be pretty far off of the true area, since a rectangle isn't really shaped like our lake.

So what we'll do is we'll pick a really small number for the width of our rectangles; that'll be a really good estimate for our lake and give us the most correct answer. But is it possible to get closer than an estimate? Can we get an "exact" answer?

In fact, with knowledge of a relatively straightforward proof (omitted here) in your toolbox, you can actually "pick zero" for the width of your rectangles and get a meaningful, exact answer.

Cutting up your lake into rectangles of equal width (a fixed interval) and then summing the areas

*is*integration. The only difference is most of the time the "shape" of your lake is determined by the graph of a function.posted by anifinder at 10:21 PM on July 10, 2008 [1 favorite]

*No room for standardized testing with that approach*

If this were true, I'd largely consider it a feature instead of a bug. :)

But I don't think it's true. I think it just means you can't take a kitchen sink approach with mandated/tested curriculum under the setup I described.

posted by weston at 10:52 PM on July 10, 2008

I took Algebra in 7th grade. And 8th grade. And finally passed in 9th grade. Maybe I just had bad teachers for the first two years, but I really didn't get it at all.

posted by OverlappingElvis at 11:49 PM on July 10, 2008

posted by OverlappingElvis at 11:49 PM on July 10, 2008

*Calculus is a set of techniques for doing math with infinitely small things.*

Specifically, it is the clearly insane belief that if you add up an infinite number of infinitely small things you will get a finite number.

Like most religions, once you accept the completely whacked out premise everything flows pretty easily from there.

posted by tkolar at 1:07 AM on July 11, 2008 [2 favorites]

My math curriculum during the mid 90s in a good California public school district:

In high school, multivariate calculus was available to advanced grade 12 students. Students could take further courses at a nearby junior college, although this was very uncommon.

posted by ryanrs at 3:44 AM on July 11, 2008

7 AlgebraI was about two years ahead, so most students probably took algebra in grade 9. But a handful of students took algebra in eighth grade; enough to have a regular class.

8 Geometry

9 Pre-calc / Trigonometry ; AP Physics

10 Calculus

11 Multivariate Calculus

12 Differential Equations

In high school, multivariate calculus was available to advanced grade 12 students. Students could take further courses at a nearby junior college, although this was very uncommon.

posted by ryanrs at 3:44 AM on July 11, 2008

*Specifically, it is the clearly insane belief that if you add up an infinite number of infinitely small things you will get a finite number.*

But generally you are actually tryign to Cut up a finite thing into a countably infinite number of pieces...

which does kinda make sense...

posted by mary8nne at 3:54 AM on July 11, 2008

It does sound like a pretty basic maths course..

I did the highest level of maths in Australia and distinctly remember doing stuff like Complex Algebra, Differenential Equaltions, some basic Integral Calculuse techniques, gravity, acceleration and that kind of calculus stuff all in HighSchool.

Maybe even a little Matrix algebra. If someone can't undestand basic algebra at that age they are just not trying.

posted by mary8nne at 3:58 AM on July 11, 2008

I did the highest level of maths in Australia and distinctly remember doing stuff like Complex Algebra, Differenential Equaltions, some basic Integral Calculuse techniques, gravity, acceleration and that kind of calculus stuff all in HighSchool.

Maybe even a little Matrix algebra. If someone can't undestand basic algebra at that age they are just not trying.

posted by mary8nne at 3:58 AM on July 11, 2008

*Screw algebra. I would like to see our students learn to read, write and comprehend english. Should we somehow be successful in that ebdeavour I would move on to teaching a second language.*

I can haz agreement.

posted by inigo2 at 7:08 AM on July 11, 2008

*My 8th grade algebra teacher was named Harry Peckart*

My 11th grade physics teacher was named Mr. Wenis. True story!

posted by chugg at 9:20 AM on July 11, 2008

*But generally you are actually tryign to Cut up a finite thing into a countably infinite number of pieces...*

I thought basic calculus operated over the set of real numbers, which aren't countably infinite.

posted by Blazecock Pileon at 9:54 AM on July 11, 2008

My family had a rule that you could have as many helpings of dessert as you wanted, as long as each piece was half the size of the previous one.

It took me until Grade 12 to realize that I'd been had: if you integrate 1+1/2+1/4+1/8....infinity, you get two pieces of dessert.

posted by anthill at 10:19 AM on July 11, 2008 [3 favorites]

It took me until Grade 12 to realize that I'd been had: if you integrate 1+1/2+1/4+1/8....infinity, you get two pieces of dessert.

posted by anthill at 10:19 AM on July 11, 2008 [3 favorites]

I was wondering why I couldn't put my finger on when I studied algebra. Then I had a look at the Irish National Curriculum (huge pdf here, in case you're interested).

Like in Singapore, in Ireland, maths at school is just one big subject taught by your class teacher.

It turns out that there is an "algebra" component to maths classes

For the record, for 4 and 5 year olds learning how to "extend patterns" forms their introduction to algebra. At 5 and 6 they'll work on "exploring and using patterns". At ages 7-8 they'll work on "number patterns and number sentences", at 9-10 they'll be on to "directed numbers sequences, rules and properties, variables and equations". By the time they get into heavier stuff, in secondary school, they've never known maths

posted by tiny crocodile at 10:59 AM on July 11, 2008

Like in Singapore, in Ireland, maths at school is just one big subject taught by your class teacher.

It turns out that there is an "algebra" component to maths classes

*from**the very beginning*: even infants (4-6 year olds) meet algebraic concepts (though of course they won't be given that scary word to put on it).For the record, for 4 and 5 year olds learning how to "extend patterns" forms their introduction to algebra. At 5 and 6 they'll work on "exploring and using patterns". At ages 7-8 they'll work on "number patterns and number sentences", at 9-10 they'll be on to "directed numbers sequences, rules and properties, variables and equations". By the time they get into heavier stuff, in secondary school, they've never known maths

*without*algebra. That's got to help.posted by tiny crocodile at 10:59 AM on July 11, 2008

jonmc:

In terms of practical, everyday life, usually you'd use algebra when doing calculations involving money.

Suppose you drive a car. How much do you spend on gas every year? Say you drive a car that gets 25 miles per gallon, and you drive about 20,000 miles each year. Since the price of gas is fluctuating so much, let's say the price of gas is $p / gallon. If x is the total amount you spend each year, x = (20,000 miles / 25 miles per gallon) times $p / gallon. When p is 3, you spend $2400 each year. If p goes up to 4, you spend $3200.

When you're buying a car, how much extra will you spend on gas if you get a less fuel-efficient car? Let d1 be the miles per gallon for one car, and d2 be the mpg for a second, less fuel-efficient car. Then the extra cost each year is (20,000 / d2) times p - (20,000 / d1) times p. You can apply algebra and get 20,000 times p times (1 / d2 - 1 / d1). If d1 is 25 mpg and d2 is 15 mpg, and p is $3/gallon, you pay an additional $1600 each year. If p is $4/gallon, it goes up to $2100.

Of course you don't need algebra to figure out that when you buy a gas guzzler, you're going to be spending more on gas. But you can use algebra to figure out

(By the way, mpg ratings are misleading--it'd be better to use gallons per 100 miles.)

tkolar:

Not really. anthill's example is an excellent one: you have an infinite series of numbers that gets arbitrarily close to a finite number. So it's more like saying that if something gets smaller and smaller, eventually you can ignore it.

posted by russilwvong at 11:45 AM on July 11, 2008

*I've held a variety of jobs in my life, and I can't think of any time where I've had to harken back to my sole algebra course.*In terms of practical, everyday life, usually you'd use algebra when doing calculations involving money.

Suppose you drive a car. How much do you spend on gas every year? Say you drive a car that gets 25 miles per gallon, and you drive about 20,000 miles each year. Since the price of gas is fluctuating so much, let's say the price of gas is $p / gallon. If x is the total amount you spend each year, x = (20,000 miles / 25 miles per gallon) times $p / gallon. When p is 3, you spend $2400 each year. If p goes up to 4, you spend $3200.

When you're buying a car, how much extra will you spend on gas if you get a less fuel-efficient car? Let d1 be the miles per gallon for one car, and d2 be the mpg for a second, less fuel-efficient car. Then the extra cost each year is (20,000 / d2) times p - (20,000 / d1) times p. You can apply algebra and get 20,000 times p times (1 / d2 - 1 / d1). If d1 is 25 mpg and d2 is 15 mpg, and p is $3/gallon, you pay an additional $1600 each year. If p is $4/gallon, it goes up to $2100.

Of course you don't need algebra to figure out that when you buy a gas guzzler, you're going to be spending more on gas. But you can use algebra to figure out

*how much*more you're going to be spending.(By the way, mpg ratings are misleading--it'd be better to use gallons per 100 miles.)

tkolar:

*Specifically, [calculus] is the clearly insane belief that if you add up an infinite number of infinitely small things you will get a finite number.*Not really. anthill's example is an excellent one: you have an infinite series of numbers that gets arbitrarily close to a finite number. So it's more like saying that if something gets smaller and smaller, eventually you can ignore it.

posted by russilwvong at 11:45 AM on July 11, 2008

Anthill, that essay is excellent. Should be required reading for math teachers.

posted by naju at 12:06 PM on July 11, 2008

posted by naju at 12:06 PM on July 11, 2008

*My 8th grade algebra teacher was named Harry Peckart*

My 11th grade physics teacher was named Mr. Wenis. True story!

My 11th grade physics teacher was named Mr. Wenis. True story!

One of my middleschool subs was named Richard Les, pronounced "lis." He went by Dick. It was very unfortunate.

posted by Solon and Thanks at 3:10 PM on July 11, 2008

The principal at the school I did the last 3/4 of sixth grade at was named Nancy Phenis.

The bathroom walls were entirely predictable.

posted by Pope Guilty at 4:55 PM on July 11, 2008

The bathroom walls were entirely predictable.

posted by Pope Guilty at 4:55 PM on July 11, 2008

lastofhiskind and anifinder - those explanations were just what I always wanted.

posted by moxiedoll at 5:21 PM on July 11, 2008

posted by moxiedoll at 5:21 PM on July 11, 2008

Pryry, Mathematica is useful only if you already know algebra quite well. It lets you avoid careless errors, process longer computations, etc., but no symbolic manipulator today can tell you what you are looking for.

posted by jeffburdges at 8:45 PM on July 11, 2008

posted by jeffburdges at 8:45 PM on July 11, 2008

Damn, to continue with the derail, my geography teacher was a Mr. Hore.

posted by Jimbob at 9:04 PM on July 11, 2008

posted by Jimbob at 9:04 PM on July 11, 2008

*I still don't understand what calculus is, and I've read the wikipedia entry and everything.*

The fucking wikipedia entry suffers from the same problem most math textbooks suffer from, which is that they don't explain things in common terms that everyone can understand. Every math class I've ever been in has carried this idea around that each class should build upon the lessons of the previous. Well that's all well and good if you did great in the previous class... but if you only barely scraped by, you're starting every new year already behind... it's like stepping up to bat with two strikes automatically against you.

The best explanation I've heard about calculus--and the one that finally made it

*"click"*for me went something like this... (sorry, it's not a one-liner... but if you actually take the time to read it, I think you'll find it pretty easy to understand):

So, you know how to get the area of most basic shapes, right? A square:

*length * width*; a cube:

*length * width * height*... etc. Basic stuff, right? Now, that's useful for all kinds of reasons that you're no doubt already aware of. You can calculate how many cardboard boxes could fit into a shipping container. Or how much oxygen is remaining in the shipping container if you were trapped in it. There's just all kinds of useful things you can do when you can calculate the area of something.

OK, smarty pants, how do you get the area of a curved object? Ah. Well, maybe if you were smart you'd cut the curve into little rectangles, and then add all those areas up and get an approximation. Well, if you keep making smaller and smaller rectangles, you'll get closer and closer to the correct value. Anyway, there's a neat mathematical trick figured out by either Sir Isaac Newton or Gottfried Leibniz (depending who you ask) in around 1670 that can allow you to calculate the area of a curved shape. Leibniz is the bastard to blame for all the fucked up symbols in calculus (

*dy / dx*-- why the hell don't you cancel out the

*d*s?

*aaah!*). Anyway, the technique is called

*integration*, and it's one-half of what calculus is.

The second half of calculus can be summed up pretty simply: a technique to get the slope on a curve. When you've got a straight line, figuring out the slope is easy Geometry I stuff...

*y*. But how do you find the slope when it's a curvy line? The standard solution is to take two points on the curve and connect them with a straight line. Then just use the ol' Geometry I equation to get the slope. The closer the points are to each other, the more accurate the answer. The second part of Calculus is a technique to get the

_{2}- y_{1}/ x_{2}- x_{1}*exact*slope--not an estimate like above--and it's called

*integration*.

And that's it. Slope on a curve, area of a curve. Calculus. If math classes just presented it like this, people would get it in no time. But instead, they start whipping out the

*Δx/Δy*and then the fucking

*cos θ*bullshit and you can watch as the eyes glaze over. You can blame Newton for that. It turns out that those two simple things--area of a curve, slope of a curve--are really useful at describing things that happen in physics.

^{2}So unfortunately for all the poor souls taking math, you have to mess all the simplicity up with all the extra physics bullshit that just confuses people. Why does someone in math class give a fuck about acceleration? Stop trying to make every single goddamned math problem

*"real"*, motherfuckers!

posted by Civil_Disobedient at 11:29 PM on July 11, 2008 [3 favorites]

Look at that, I already done screwed up.

Area of a curve:

Slope on a curve:

Post-flooding corrections because you were too lazy to proofread before hitting "POST"? Priceless.

posted by Civil_Disobedient at 11:38 PM on July 11, 2008

Area of a curve:

*integration*Slope on a curve:

*differentiation*Post-flooding corrections because you were too lazy to proofread before hitting "POST"? Priceless.

posted by Civil_Disobedient at 11:38 PM on July 11, 2008

@civil_disobedient: very nice explanation of calculus. For me, in high school, calculus was when mathematics suddenly started intersecting with the real, physical world: like your calculus teacher saying: how would you calculate the volume of that

But I ended up being a social sciences major in college, so high school calculus was the last time I thought much about math. Until last year when I built a small house with my brother as a summer project, more of a mountain cabin. And we realized we had both completely forgotten how to do trigonometry, and we had to dig up an old textbook and relearn it. Which is admittedly a lot easier the second time around: more of a re-membering than re-learning process.

And this is apropos of the question in the FPP: people who don't go to college

posted by jackbrown at 12:16 AM on July 12, 2008

**mountain**over there, and you suddenly realize that so far, everything you learned in math has been kind of abstracted and idealized for manageability, but there**is**a mathematics of the physical universe, and that's calculus. The first time, for me, that math seemed beautiful.But I ended up being a social sciences major in college, so high school calculus was the last time I thought much about math. Until last year when I built a small house with my brother as a summer project, more of a mountain cabin. And we realized we had both completely forgotten how to do trigonometry, and we had to dig up an old textbook and relearn it. Which is admittedly a lot easier the second time around: more of a re-membering than re-learning process.

And this is apropos of the question in the FPP: people who don't go to college

**do**need algebra, and a lot more, sometimes. To do any reasonably complicated construction, for example, you're going to have to know how to do trigonometry, there's no way around it. So learning algebra and geometry and all the rest is more than just good brain exercise and logical thinking when you're a kid. Its necessary.posted by jackbrown at 12:16 AM on July 12, 2008

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At least one person thinks it's a bad idea ("If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?").It's true, who cares if the remaining 4 out of 5 student have bad math skills?

posted by turaho at 12:37 PM on July 10, 2008 [14 favorites]