Via Physics and Physicists, a breathtaking blog at the Washington Post proudly proclaiming the author's ignorance of algebra:
I am told that algebra is everywhere - it's in my iPod, beneath the spreadsheet that calculates my car payments, in every corner of my building. This idea freaks me out because I just can't see it. I sent out a query on my blog last week asking, Who among us in the real world uses algebra? Can you explain how it works?
This is exactly the sort of intellectual innumeracy I have ranted about countless times. The whole concept of the blog (subtitled "A year reliving high school math") is a demonstration of the low esteem in which math and science are held. To someone who knows and uses math regularly, this whole project is analogous to someone going on tv and saying "Who among us in the real world uses reading? Can you explain how it works?"
Try to imagine a major national paper sponsoring someone to spend "A year reliving high school English"-- reading The Catcher in the Rye and The Scarlet Letter and taking vocabulary quizzes. It's a little hard to picture, isn't it? Functioning adults are simply expected to have the skills acquired in high school English classes, but somehow, it's acceptable to not only not know algebra-- which is really junior high math, not high school math-- it's perfectly ok to broadcast that fact to the entire world.
In this installment, she does manage to find some alegra in the Real World, via her brother, an entertainment rigger. Who knew that people hanging heavy beams supporting lights for rock concerts needed to use math?
Of course, the situation doesn't really improve with the discovery of her brother's use of math. She goes on to give a link to a pdf list of formulae used in the rigging business, and adds a note that betrays another, related, sort of ignorance:
UPDATE: My apologies. I had planned to run a list of diagrams that riggers use that would help put these formulas in context. In the end I could not get permission from the author of the book in which they are published. Sorry to throw this up there without more clues. I'm going to send this post to a few entertainment riggers to see if we can piece together how these formulas are used.
I looked at the list of formulae, which is just a collection of results from simple statics problems. The diagrams that ought to be there would be simple free-body diagrams showing the various tension and weight forces on the loads being suspended. Reverse engineering them would be a little tricky, but I could probably do it if I didn't need all this pseudoephedrine at the moment.
Here's my problem with the aside: these diagrams are just pictures. They're not the products of some secret black art, drawn in the blood of unbaptized infants under the dark of the moon. There's no reason beyond sheer laziness why any educated person should need to reproduce the exact page from some book. You could knock off a non-infringing copy of the diagrams in much less time than it takes to contact the publisher and be denied permission to reprint them.
But that would require somebody to understand what the diagrams mean. Which really requires a pretty minimal level of cluefulness, but evidently more than could be mustered before posting the article for the entire world to see.
So, not only is she proclaiming her ignorance of junior high school math, she's proclaiming an ignorance of high school physics. Which is entirely typical, but no less depressing for that.
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It's not just people like this blogger who seem to be (or maybe actually are?) ignorant about the importance of mathematics and science in life.
The husband of our local community college's president writes, with annoying regularity, position articles to our paper stating that the current emphasis on mathematics and science in public education is unfounded, since "an insignificant percentage" of adults actually use
any math at all, in private or in their work. I've always wondered how their dinner conversations go (or don't go) after publication of one of his letters.
I need to contact this blogger right away. I need to find out if I belong to the "real world" or not so I can stop paying income tax in it.
Consider "alternative energy" and "sustainable energy." How much of that would survive if the electorate were not seeking light at the end of the tunnel with its eyes wide closed?
Wow. And we wonder how we get into financial crises? Does this mean that people really don't balance their checkbooks? They don't plan budgets? I share your frustration Chad.
Yeesh. How many times do they have the Pythagorean Theorem listed there in one form or another? A half a dozen, at least.
And, no, we cannot help unless we know the damn context of the variables... although with fifteen minutes and a dusty, forgotten civil engineering text I could probably come up with some shrewd guesses.
Bah humbug!
Someone who has a blog "reliving high school math" is not holding math in low esteem- except perhaps in self defense. This is someone who recognizes that they should know more math. To treat them with distain simply aggrevates the problems.
Plus, I've seen a certain English grad student's angry bloging that would beg to differ with your characterization that functioning adults are expected to have acquired basic English skills (I think they'd settle for a lack of comma-splices; forget explication of The Scarlet Letter and advanced vocab for now).
Also, if you expect all junior high students to be able to effectively use that list of formulae, methinks you went to a very different junior high than I did.
Ultimately, it's a kind of snobbery (elitism + arrogance) to assume everyone had the same kind of access to education you did.
1) Math is hard for some people
2)People are poorly educated, and not just in math
3) Math being easy for you, and coming from a well-educated background, do not make you admirable. Indeed, they seem to be related to your condesending attitude, which is deplorable.
You know, it's interesting that this came up on my RSS aggregator at the same time as this Onion article, entitled "And If You Direct Your Attention To The X-Axis, You'll Find I Have No Idea What I'm Talking About."
No kidding, John, on the versions of PT. I like AA +BB and A2 +B2! But that way the guys don't actually have to understand the formulas, they just have to know what values to plug in.
My brother used algebra when he was selling surplus hardware. A guy needed him to figure out how much roofing tin he needed, based on the rise, run, and amount of overhang of the roof. Pat figured it for him and then got in trouble when the guy came back pissed that he'd bought too much (because he'd measured wrong). If you use it at a minimum wage, no skills necessary job, it isn't useless.
Becca,
I don't know maps and directions, and really, who in the real world uses maps and directions? I just don't get it. I asked my brother who is a florist if he knows, and lo and behold he uses maps and directions in his work! He gave me two documents. The first said:
"2 exits W on I-90, take exit for 590 south, get off at main"
But gee, what does that all mean? There are these numbers and things in there, but I can't make heads or tails of where this is supposed to lead me to. There is this map thing accompanying it, but I can't photocopy it to show it to you. So I guess its just all some kind of secret dark art, and we'll just never know what these direction things mean.
You missed the point of the article. Those questions you quoted were rethorical. They motivated the overall goal of the article, which was to show that it pays to understand algebra. This was an advertisement _for_ algebra.
@ Becca, #6
One problem here is that "math/science is hard" is still seen as an acceptable excuse to not take those classes, or do well in them. Some people find English to be hard, but that's not viewed as a reasonable excuse. I was still required to take 4 years of it in high school. Only one year each of math and science, if I recall correctly, and I went to a pretty decent high school (coincidentally, Niskayuna High)
----
The analogous argument of that blog isn't "Where is Shakespeare in my everyday life?" Rather, it's "Where is beginning composition in my everyday life?" (I hope that the answer to that need not be explicitly given) This is an issue of literacy, not literature.
That blog seems like a waste of inter-web space. How much do you thinks she gets paid to write about her illiteracy? Though I guess one must consider that it is the Washington Post. You have to assume that they picked her because she can provide her audience with content they will relate to... Sad.
Becca @6 & Tom @11
Tom: Exactly. I found english hard. I also found math hard in high school (it got easier once I hit calc, I'm weird)
The very statement "Math is hard" is offensive to me. Sure it's hard. History is hard. English is hard. PE was almost impossible.
Since when does something being "hard" make it avoidable?
Becca says "(I think they'd settle for a lack of comma-splices; forget explication of The Scarlet Letter and advanced vocab for now)" Ok, I have no idea what a comma splice is. I'm sure I could look it up, but that's not my point. If I were to say "Why do I have to take english classes to learn about 'comma splices' that I'll never use again? English is hard!" The education system would look at me and sigh.
But the other direction of this is perfectly acceptable. It's not the scientists who are being snobbish. We're just saying that this stuff is as important as that stuff.
As for whether or not JR High students understand all this: obviously they don't and this is a flaw in the education system that we're trying to FIX!
@Becca, #6
1) Math is hard for some people
Actually, it's been shown that the differences in the ability to learn mathematics are minimal. They tend, however, to be exaggerated by poor teachers, who assume that because a kid doesn't pick up a concept in the first explanation, the kid never will.
Math being generally cumulative - understanding of a concept depending on understanding the concept from which it is derived - as soon as a teacher does that to a kid, it becomes a self-fulfilling prophecy - the kid won't get succeeding concepts and everyone (including the kid) will assume that the kid "can't learn math".
I usually nod vigorously in agreement with almost everything you post. (We both studied physics at the U. of Maryland, so of course great minds think alike.) But I think Ms. Chandler's blog isn't a good example of the problem you want to address.
Read her 10/09/08 post titled "Math Reading List." She opens by saying "I'm hungry for some good books about math," and soon after says that John Allen Paulos's _A Mathematician Reads the Newspaper_ is on her "must read list." Is this blogger really THE ENEMY?
In the blog's first post, she describes her goal: "...a place where I aim to bridge the cultural divide between math people and the rest of us, to make the abstractions of algebra a little more lifelike. Visitors will find scenes from math classrooms, profiles of people who use math at work..."
In this context, consider the algebra-in-my-iPod passage that you quoted first. She's actually on to something: The usual response to a whiny teen bitchin' about algebra is indeed, "Hey, it was used to design that iPod you're so addicted to." But this is an extremely poor response because the iPod makes its internal algebra TOTALLY INVISIBLE. Our beloved iPod ploy gives the obnoxious teen a valid riposte - "Yeah, but I don't need algebra to use it."
And that's why the reading analogy misses the point. If the snotty little brat says "Why bother to learn reading?" you can physically grab the iPod instruction sheet and say "You have to read THESE instructions to work your goddamn iPod." But you can't pick up an iPod and angrily shake algebra in the kid's face - You can only lamely say "Trust me - it's deeply buried in there somewhere."
And that is what Ms. Chandler realizes - In most people's everyday life, reading is immediately and obviously necessary everywhere, but algebra is deliberately made invisible almost everywhere. Since it's so frequently hidden in most common living, why should _everybody_, not just specialists, learn it? That's a valid question that the iPod Ploy and the Reading Analogy both totally fail to answer
So, when Ms. Chandler asks "Who among us in the real world uses algebra?" she's not proudly trumpeting her ignorance because she believes the answer will be "Nobody but a tiny group of nerd-specialists, that's who!" Instead, I think she's saying "Quit giving that lame old answer about the invisible algebra that a few Ph.D. engineers deeply buried in my iPod - Let's instead find some obvious in-your-face examples of non-mathematicians using algebra."
That's very good advice, and that's why I think she's not the best target for your justifiable wrath.
Seems like the blog is only just beginning. The first post is here. In case anyone wants to know the motivation for writing about math in the first place.
I need to contact this blogger right away. I need to find out if I belong to the "real world" or not so I can stop paying income tax in it.
Hey, that's not a bad idea. :) And it brings up a good point. Without realizing it, most people do some very basic algebra every day. In fact studies have shown that even young babies have an innate sense of certain algebraic constructions (and I mean algebra and not arithmetic, though there is some innate sense of that as well). Most thinking that is a step above the most basic - anything that considers variables of any sort - is essentially algebra. In fact the earliest forms of the actual scholarly study of algebra were not even symbolic.
To be fair, most adults don't use mathematics beyond remedial addition/subtraction/multiplication/division. In my experience, mathematics is almost never taught as a practical skill beyond this level. Algebra, as I remember it, was a mess of useless formula-fondling exercises and bizarrely contrived "Brain teaser" word problem puzzles (Come to think of it, this also describes my experience with basic Physics education as well). A few people have a natural knack for working with the tautology that is mathematics, but the rest of us find ourselves expending a great deal of effort in what seems like a context-free philosophical exercise. This is probably the reason that even to this day, I occasionally find myself trying to solve a mathematics problem and somehow ending up simplifying the problem down to "x=x" or "1=1" or something equally useless - without context to guide the process, it's easy to get stuck in the Algebrea Tar Pits...)
Despite earning an "A" in "Intermediate Algebra", I didn't start to actually, really, "get" even basic algebra until I finally took chemistry the following semester and we went over "unit analysis"[1]. Once I was actually directly using the mathematics on actual "stuff", right there in my hands where I could directly see what the mathematics had to do with it, it got much more understandable.
(This is probably why introductory statistics, strangely enough, was probably my favorite math class ever - it was "practical" right from the start. The "Applied Calculus" class that included a bunch of homework problems based on actual real-world scientific studies was a close second.)
While I firmly agree that mental laziness and anti-intellectualism against math and science are a problem, automatically labelling an admission that one doesn't "get" the point of mathematics as "proud ignorance" doesn't help solve things. Neither does an example of engineering physics as "practical" mathematics when the majority of people's "engineering" experience involves jury-rigged fixes with no mathematics whatsoever. Might as well insist that Physical Chemistry is really important for everyone because the physics of intermolecular forces underlie the results of every burger-flipper's job...
[1] - I had taken phyics in high-school as well, where we must have previously done unit analysis...but again, see my comment above about how physics was taught to me...
The real problem is:
#1: At home. Mom or Dad tells the student, "Oh, I was never good at math either."
#2: At school: The other teachers (especially English and History) say, "Don't worry about it. I never liked that Math stuff either."
#3: Peer groups. "What class do you hate? Algebra, right? That teacher is like, you know, right?"
#4: Pop culture. Peggy Sue Got Married (1986):
[Peggy Sue hands in her algebra test]
Mr. Snelgrove: And what's the meaning of this, Peggy Sue?
Peggy Sue: Well, Mr Snelgrove, I happen to know that in the future I will not have the slightest use for algebra, and I speak from experience.
[JVP: At that point, I heard the audience in the theatre applaud]
I often see journalists using technical terms loosely. I do it myself when speaking metaphorically. I can see in certain circles or instances how this could render words and meanings meaningless.
Tom- I can appreciate the literature/literacy distinction, but I consider comma-slices and algebra as functioning as part of the bridge between minimum-to-get-by-literacy/nummeracy and able-to-go-onto-literature-if-desired-literacy/nummeracy.
Brian- I'm totally in agreement with you that "hard" isn't a good reason not to try, and that we need to do a better job teaching many things. As a scientist who would have immensely prefered to take fewer things like English, I totally empathize with your complaint re: course # required.
I just didn't think that was the point of Chad's post.
So, you can write basic English inteligibly without knowing what a "comma-splice" is.
Similarly, you can solve problems that require abstract reasoning without knowing the symbolic conventions that allow one to solve algebra problems.*
Kevin- there are many people who get where they need to go quite reasonably who think maps or directions are basically gobbly-gook. Moreover, the subset of people who can't use either well are now being rescued by the GPS based systems. Just because a skill is essential to you doesn't mean it's actually essential.
Lest I be missunderstood- just because some people can't/won't need to/don't like certain skills doesn't mean we shouldn't teach them. However, implying "you can't possibly function without this skill" to an (obviously) functioning adult is A)obvious false and B) demeening.
*At least, this is how I explain my nearly testing into pre-calculus at a time when my last formal math training was in division- i.e. I knew "X" was "an unknown" but I didn't know what a "variable" was, and the quadratic equation was more inscrutible than Chinese characters. Yet I could reason through simple algebra problems anyway.
In short, you don't need algebra training to do algebric-type thinking.
I think bashing people for finding equations and the "language" of algebra confusing is not only a weird kind of snobbery, but only serves to widen the gulf between people that "get" it and people that "don't".
Re #21: Becca, "I knew 'X' was 'an unknown' but I didn't know what a 'variable' was" -- I don't get that.
I don't know what you mean by "know" in the above.
I want to -- after all my years of teaching Math -- but I'm still not clear on what you mean. Would you be willing to explain?
Are you sure? There are an awful lot of atheist babies, but relatively few atheist adults. Something is happening ...
Jonathan Vons Post-
Oh, sure!
I remember encountering algebric expressions long before I had a defintion for the term "variable", or assoicated the idea of an unknown placeholder with the letters. One of my early thoughts about algebra was that I didn't see why they didn't use a question mark "?" or a blank "___" or an empty box instead of an "X" ("X", after all, has perfectly respectable xylophones to communicate).
After I realized "X" = "?", but before I learned the rules about manipulating equations, I could look at simple single-variable algebra problems and think about what would fit for the unknown and get the right answer. I knew what computation to do and mentally did it. In a weird way, I think this made learning the symbol manipulation harder (it was hard to see the point with the basic examples they kept giving).
Thnk you Becca. That clarifies. The most important task for the teacher is to deduce what is going on in the student's head.
What I'm getting from you now includes:
(1) you knew the IDEA of a variable, functionally, in use, but did not know the word nor formal definition;
(2) "The unknown placeholder" is, in some elementary textbooks, indicated with an empty square, or an iconic symbol such as a flower. It is a huge invention that a letter can be used to do that job. It is possible that the teacher never explained this to you.
(3) It is also bad teaching that the teacher insisted on "X" as in "X marks the spot" or "X as in xylem." The point is that different letters or symbols or words can be used in that way. It is useful to use words that abbreviate the concept in mind (E for energy, M for mass).
(4) You had a meta-mathematical question, which the teacher never realized.
(5) The examples were too "easy" -- perhaps the teacher did not want to scare students with complexity. Or perhaps the teacher did not know examples of equations which do not have solutions.
In my humble opinion, the primary cause of baffled math students is bad math teachers.
I'll be that none of your Math teachers EVER told you what Mathematics really WAS, or what its most essential key ideas were (quantity, structure, change; or stuff, structures of stuff, properties of structures of stuff), nor how those ideas fit together.
Odds are, your Math teachers had degrees in Education because they were not qualified to get degrees in Math or Science. They did not know what Math was. They spread their ignorance. By induction, this can continue for arbitrarily many generations in the USA, until China and India rule the geopolitical world -- and CAN "do the math."
(1) Exactly right on this part... as for the rest of it...
I had the IDEA of an unknown, and I already had placeholder for that (e.g. "?" and "___") so why on earth would I want to use another placeholder that was associated with other ideas? (by the way, "X as in Xylem" made me smile). I "got it" pretty quickly, but I was stubborn about adopting the conventions because they didn't strike me as the most intuitive.
I don't remember a teacher ever explaining it to me, but, in fairness, that was probably because I didn't have any teachers at the time.
I was in normal classrooms until halfway through fifth grade, then there was a four year gap in my formal education. The last math I remember from grade school was probably fractions (which I hated).
Then, I took a placement test and tested nearly at the college pre-calc level. In between I read some math textbooks, and argued about math with my father, but had no "teachers" per se.
When I went back to formal education at the local community college, I was taking intermediate algebra. I think there were a number of times I could solve problems through sound mathematical reasoning, and there were a number of times where ignorance of the conventions drove me nuts (or, as I've described, sometimes I knew the conventions perfectly well I just didn't think they were the best possible ones to use).
So anyway, it's possible I remember more of the process of figuring out algebra than an average person, since I had a lot more time to sit and stare at equations and wonder about what they meant without being taught how to solve them.