Thing is, I'm starting to think that you've got a responsibility to the youth of America to see if you can flunk her. It's not that a fourth-grade math teacher needs to know Calc II, but anyone who's making that class of error is going to do weird, bad things to even fourth graders in terms of their understanding of math.
Also I hate HTML formatting. Is it even readable?
Also I'm infuriated by all her past teachers that contributed to her getting to this class with this deep a level of mathematical misunderstanding.
I don't know why I've declared private war on this student
Maybe her mathematical shortcomings are directed at you personally, heebie.
For some reason, at the end of her test, it said "DEATH TO APOSTROPHER." I didn't think anything of it at the time.
2: It is hard to see the operators between the fractions, which made it hard for me to see how the student was being stupid.
The small characters are x, =, =, and =, right? They are failing to simplify the equation properly because they once again failed to multiple exponents properly, right?
7: Right. Let me try to make those bigger.
2 - I can't really see what the signs are between the fractions: first one is multiply, but what are the others? = ?
it said "DEATH TO APOSTROPHER."
Weird. That's been at the end of all my Father's Day cards as well. I wonder what it means?
Instead of having "answers" on a math test, they should just call them "impressions," and if you got a different "impression," so what, can't we all be brothers?
What a sexist bastard.
Maybe a bunch of parentheses and brackets and "/" signs for division would be easier to read than the equations as written? I'm having trouble. Regardless, it looks to me like she got the last step completely right. So, partial credit.
Damn, pwned by rob whilst making a cup of tea.
Where did the quote in 11 come from?
This woman can't do algebra. I think a fourth grade math teacher should be able to do algebra.
7, 9, better?
The "preview" doesn't end up looking much like the actual post because the fonts are different. Also Unfogged looks different at school than at home. Let me know if I should keep tinkering with it.
12 - hey Brock, did you see the book protector I made C take photos of for you? If not.
Regardless, it looks to me like she got the last step completely right. So, partial credit.
This is sarcasm, right?
It's very creatively wrong though. I'm thinking the thought train is, "The rest of the problem would be easier if this simplified to 1; how can I make it come out to 1?"
It's a game like Word Golf; get to 1 from this expression with plausible-looking intermediate expressions.
Regardless, it looks to me like she got the last step completely right. So, partial credit.
She was within an order of magnitude!
Please tell me the answer to this is 2/7. Your math stuff is making me appalled at the amount of math I have forgotten. I need to go audit remedial math or something.
The rest of the problem would be easier if this simplified to 1; how can I make it come out to 1?"
Ironically, if you get = 1 to this particular test, the test is inconclusive.
23: You get full credit!
Please tell me the answer to this is 2/7.
I also had a moment of incomprehension until I realized that I needed to ignore everything she wrote and just take another look at the original problem (2/7 is correct, isn't it).
Don't let her teach 4th graders.
1 is absolutely right. I had an introductory physics t.a. (in college!) who completely misunderstood several basic concepts, and she taught us all sorts of unbelievably screwy shit. And it wasn't like she just sort of accidentally said the wrong thing in front of the class but really understood--which is a bad but completely understandable mistake. There were several bright students who would understood the material and would question her--"that doesn't make any sense, don't you mean [complete opposite of whatever she just said]?" And she'd stand her ground, often of the course of long drawn out arguments. And these were VERY BASIC concepts. To most mystifying thing to me about the whole thing was how on earth she could possibly be managing as a grad student in physics.
Anyway, the point being: Heebie's student has the same sort of issues. You not only must fail her, you must write a letter to the dean seeking retroactive failure in all her past math classes.
19: well, she did get that part right.
You not only must fail her, you must write a letter to the dean seeking retroactive failure in all her past math classes make sure all her children and children's children and children's children's children, lo unto the seventh generation, receive failing marks. Thus sayeth the Lord thy God, amen.
I must admit I have no idea how to solve this problem. I'm sure I used to, though.
You not only must fail her, you must write a letter to the dean seeking retroactive failure in all her past math classes.
The frustrating thing is that she'll retake Calc II with someone who allows calculators, and she'll pass, because you can completely avoid algebraic simplification with the fancy-pants things they've got available these days.
And yet she wants to teach math/science at grades 4-8!
27: you must write a letter to the dean seeking retroactive failure in all her past math classes.
Laying the groundwork for a productive well-adjusted adult.
30: Just look at the first expression, everything after that is complete nonsense.
There's one more 2 on top than on bottom, and one more 7 on bottom than on top, so everything cancels except these extra terms and you're left with 2/7.
(I swear I'm not being patronizing - it is very easy to be out of practice on these things.)
s/b lo unto the two-to-the-seventh generation
Bave, there's one more 2 in the numerator than in the denominator (n-1 versus n-2) and one more 7 in the denominator than in the numerator (n+2 versus n+1), thereby canceling out everything but the one 2 and one 7.
Huh, at the bottom of this test it says "PWN THE APOSTROPHER!"
Whatever.
That doesn't count as pwnage since heebie wrote the test.
1 is absolutely right. I had an introductory physics t.a. (in college!) who completely misunderstood several basic concepts, and she taught us all sorts of unbelievably screwy shit.
This gives me an excuse to tell an old story.
When I was a freshman in college, I was part of an unusually large freshman class -- for some reason the percentage of students who were admitted who chose to attend was higher than usual. So the college was scrambling a bit to find people to teach intro classes.
I took an econ class with someone who had been out of teaching, and working the state capital as an economist (I don't actually know if he'd ever taught, but I assume he had).
He was incredibly funny because he was so clearly struggling to remember back to how to present the basic Econ 101 arguments.
The worst part of it was that he couldn't quite remember how to draw the graphs. He'd put a graph up on the board that was correct, look at it, shake his head, erase it, write something incorrect, then erase that and go back to what he had originally, while vaguely muttering under his breath the whole time as he worked it out in his head.
I knew enough of the material already that I could tell what was happening and be entertained by it, but I'm sure half the class was lost.
He also had a nasty (to him) habit of pacing in front of the board and smacking his head into the TV installed in the corner of the room. After the first 4-5 weeks you could see him pace and get to that corner and just reach out a bit with his head to feel for the TV so he wouldn't run into it.
This is what I couldn't remember. Obviously I don't do algebra at all these days.
Um, excuse me, but I was told that there would be no math requirement for this blog.
Also, shouldn't this post be google-proofed, in case OFS searches for an answer to the problem?
I failed a student for plagiarizing last week (she did the whole "substitute every third word from a website with a synonym" thing, which made it a bitch to Google) and she pulled this stupid shit about how she doesn't remember where her notes came from but she must have taken another class in 16th-century sonnets (ha!) and so like, how are you even supposed to learn how to cite sources and is there somewhere on this earth where a student can go for help in learning how to properly attribute sources???
I said:
(a) Enotes.com is not a reasonable place to do research.
(b) Quotations from sources usually have, like, quotation marks around them, in addition to footnotes or parenthetical citations and a works cited section.
(c) Plagiarizing constitutes academic dishonesty and can get you expelled.
"Where can a person possibly learn all of that?" she asked.
How about freshman composition? Or high school? Or, Jesus Christ, thinking for two fucking seconds?
This is one of those "you should retroactively fail every English class you've ever taken" situations.
42: There's not. You don't have to get all the hilarious in-jokes.
JRoth, the only algebra you need to remember is A=A.
40: For Econ 101, couldn't they get pretty much any asshole on any non-lefty website to teach it?
Also, shouldn't this post be google-proofed, in case OFS searches for an answer to the problem?
There's nothing here that resembles the problem as phrased on the test. I can't imagine what could bring her here.
For Econ 101, couldn't they get pretty much any asshole on any non-lefty website to teach it?
It was a good example of the fact that teaching is a separate skill from subject matter knowledge.
He knew the material, he just couldn't think through a mistake (or even something that looked wrong) and talk to the class at the same time, so he'd swap back and forth between the two tasks.
48: I can't imagine what could bring her here.
What if she's searching for ejaculation jokes?
Q: When should you use d'Alembert's ratio test to determine if a series is convergent?
A: Come again?
27 is a good comment.
My fifth grade math teacher explained the system of grading, early in the year. There would be like fifteen 10-point quizzes, one per week, each taking up about 10 minutes of class. There would be four 100-point tests, each of which would take up a whole class period. There would be a bunch of homeworks. And each of these would count for 1/3 of your grade.
"Doesn't that mean the quizzes are actually worth a lot more than the tests?" I said. "I mean...shouldn't the tests be worth more, because there's more points on them, and they take longer to do?"
The answer was no, because obviously, the points on the tests add up to 400, and the points on the quizzes add up to only 150, and she didn't really know why I was confused about this.
48: Joke, heebs.
Does OFS really seem the type to go home after an exam and google mathematical expressions?
Even with Apo and Heebie's explanations I still don't understand the problem or the solution. Jesus. And I used to be okay at math, too.
54: Try turning the "n+1"s into actual numbers, to get examples of what this is abstractly modeling.
Take, say, (2 to the 5)/(2 to the 4). That's obviously just (2 to the 1). Or (2).
And (7 to the 6)/(7 to the 7). That's (7 to the -1). Or 1/7.
Even with Apo and Heebie's explanations I still don't understand the problem or the solution. Jesus. And I used to be okay at math, too.
Take a specific case of n=2.
you get
2/2401 * 343/1
That turns into
(2 * 343)/2401
Which turnn into
2/7
Now that looks trickier because it isn't obvious that 2401 = 343 * 7.
But if you think of it as
(2 * 7 ^3)/7^4 then it's obvious.
54: Either of the above, or there's some notation detail that you've forgotten, like Bave above with the exponents. I have zero doubt that it would take 2 seconds to clarify whatever is in your way.
46: Apo, I always felt that you got the shaft from that publicity whore Stan Lee.
I find the problem is actually much more difficult to work through when I try to follow the student's steps than when I just start from the beginning on my own. Her steps are very confusing.
I know this has been said already, but.
B, the fraction has a bunch of 2s and 7s on top, all multiplied, and a bunch of 2s and sevens underneath, all multiplied
in the form
(2 x 2 x 2 x ... x 2) (7 x 7 x 7 x ... x 7)/(2 x 2 x 2 x ... x 2) (7 x 7 x 7 x ... x 7)
it's asking how the 2s on top cancel with the 2s underneath, and the 7s on top cancel with 7s underneath
number of 2s on top = n-1
number of 2s below = n-2
number of 7s on top = n+1
number of 7s below = n+2
so there is one more 2 on top than below, and one more 7 below than on top
so when all the 2s cancel out, and all the 7s cancel out, yr left with 2/7
I can't imagine what could bring her here.
MAYBE I JUST LIKE COCK JOKES!
I find the problem is actually much more difficult to work through when I try to follow the student's steps than when I just start from the beginning on my own. Her steps are very confusing.
Her steps are total complete nonsense. All she's doing is writing mathy-looking gibberish.
I was extremely confused because I thought the term 2^(n-1) x 7^(n+1) was the entire term to be simplified, with the whole second line coming from the students manipulations, and I was, like, that's hard to simplify, and I certainly don't see how it's 2/7! Then I was debating with myself whether I would ruin my Unfogged credibility by admitting everyone else here was better at math than me.
Now I get that they're fractions, that makes it easy.
53: See, at times I'm gullible.
The thing is, even if you don't know what you're talking about, it's likely that the answer is either 2/7, 7/2, or 1. So you have (percent of likelihood x .33) of a right answer, which is better than zero.
49: that was the entire story of my first year teaching. God, that sucked.
If this sort of post keeps up,
mathy-looking gibberish
will have to be the new mouseover.
OFS is clearly not cut out to be a mathematician. But you should go out to lunch or dinner with her and the rest of your class and at the end of the meal hand her the bill and ask her to determine how much everyone owes. She might be good at that.
For Econ 101, couldn't they get pretty much any asshole on any non-lefty website to teach it?
ha. Yeah, the guy at your corner bar who bitches about taxes and government, he qualifies as an economist.
I'm a little frustrated because I can't seem to remember many of the stories from the class I mentioned in 27. And they were hilarious. For some reason, the only one I can remember right now (which was not at all one of the more hilarious, nor one of the more egregious), was her insistence that the equation for torque explains why, if you have a screw that's difficult to unscrew, you should get a screwdriver with a longer handle (so you'll apply more torque). Several students said, "wait, don't you mean a handle with a wider grip?" There was literally about a 30 minute argument about this, in which the t.a. refused to budge and dismissed the students' questions as simply misunderstanding how the equation worked.
But I really am a bit bummed to realize I've forgotten all the best stories. I wonder if I still have my class notes stored in a box somewhere. There are some gems in there.
68: Of course, you would probably need to consult with an arithmetician in order to check her work.
Maybe they make screwdrivers differently where she comes from.
He was incredibly funny because he was so clearly struggling to remember back to how to present the basic Econ 101 arguments. The worst part of it was that he couldn't quite remember how to draw the graphs.
Econ's convention of putting Q on the x-axis and P on the y-axis used to drive me fucking nuts.
mathy
This seems like a potentially useful Colbert-style coinage.
But you should go out to lunch or dinner with her and the rest of your class and at the end of the meal hand her the bill and ask her to determine how much everyone owes.
Any time they have to deal with fractions, I resort to gas tank examples. "Which do you want, 1/2 a tank of gas or 1/3 a tank of gas?"
"1/2!!"
"So if the denominator is bigger, the fraction is...."
"Smaller!!"
Or: "Wait, you're saying 1/3 of a tank of gas and another 1/3 of a tank of gas gives you 1/6 of a tank of gas?"
I just don't get why they don't ask themselves these questions after hearing me model them again and again and again.
Calculators have completely fucked our nation out of it's ability to deal with fractions.
Econ's convention of putting Q on the x-axis and P on the y-axis used to drive me fucking nuts.
Then what happened?
Which do you want, 1/2 a tank of gas or 1/3 a tank of gas?
Is this going to be on the test?
Then what happened?
Then I BURNED SHIT DOWN.
Which do you want, 1/2 a tank of gas or 1/3 a tank of gas?
Do I have a big gas tank or a small tank?
This is calculus, Gonerill. You have a hybrid.
mathy-looking gibberish
There's a piece which I've repeated failed to track down where someone takes a sciency-looking, mathy-looking equation by Samuel "Mad Dog" Huntington and does routine algebraic manipulations on it until you get something like "Social solidarity equals the square root of social equality divided by half of social mobility times the reciprocal of economic growth."
The real thing is much funnier than my parody, because it actually is a transformation of what Huntington actually wrote.
Or to put it in a nutshell, your student should go into international relations and help decide whether we should attack N. Korea or Iran first. They will welcome her math skills.
"Teacher, I don't ever expect to be filling a tank from the top while it's being drained from the bottom by a pipe with a different diameter than the one I'm filling it with".
Yes, a bunch of 2s times one 7 will give you a bunch of 14s.
The really amazing thing is that the same number of sevens times one two gets you the same number of fourteens!
Math!
||
I am meant to be writing a letter of condolence, on behalf of [beloved parent with advanced motor disease] to [surviving partner of parent's acqaintance who just died] in an accident that [acqaintance] almost certainly caused. My problem is that neither [beloved parent] nor I were specially close to [acquaintance], while [surviving spouse] is a total horrorshow, in all kinds of ways. The circumstances are sad, but beyond the basic semi-impersonal formulae of regret I can't think of anything to say that's true, or even particularly plausible.
|>
75.last, 81: Fortunately there does not yet appear to be the mathematical/physical science equivalent of the Regent University School of Law. "I have a degree in Calculatornomics."
Her steps are total complete nonsense. All she's doing is writing mathy-looking gibberish.
That's what makes them hard to follow.
"Which do you want, 1/2 a tank of gas or 1/3 a tank of gas?"
Doesn't this depend on whether I'm (a) trying to drive somewhere or (b) locked in a garage with a running car?
Calculators have completely fucked our nation out of it's ability to deal with fractions.
What was the culprit with possessive pronouns?
My most amazing fraction-related experience.
88: You know, I actually noticed that error after hitting post. But I assumed nobody else had as canny an eye for grammar as I. Well done!
44: I suggest: "I can think of a number of places you should have learned what you did was wrong. But you obviously did know it was wrong -- you changed the words to hide what you were doing. Why don't you tell me where you learned that?"
My most amazing fraction-related experience.
I never thought it would happen to 1/9 of me, but ...
I never thought it would happen to 1/9 of my butt...
I just don't get why they don't ask themselves these questions after hearing me model them again and again and again.
Maybe this would have more resonance:
The first part of the word "denominator" looks like the word "demon", which is why it's down at the bottom in fraction hell and not on the top in fraction heaven. So if there are more demons, then God's happiness is . . .
I like working in rigorous fields where apostrophes are important and orders of magnitude aren't.
My Calculus I teacher in college was in the beginning stages of early-onset Alzheimer's. And he'd forget to wear his hearing aid. Nobody in the class could figure out what was going on; but none of us knew enough to know that our confusion was the teacher's fault, not our own.
There was one whole class where he was proving some theorem or other, and at the end of the class he got to the "QED" moment. At this point, several students pointed out that he had proved something other than what he set out to prove.
It's my understanding that the college, who ultimately figured out what was going on, gave everyone in the class an A; I had a C at midterm, and I certainly didn't deserve the A I received. But everyone who needed to take more mathematics had to audit Calc I the next semester to catch up.
haha we kept score how often my calculus teacher said "99 times out of ten", or tripped over the rubber doorstop -- these were not reassuring signs, but actually his rather tiresome rote method worked quite well
You can trip over things with the best of them now?
actually his rather tiresome rote method worked quite well
That part was true of my HS trig teacher. He would start every class with a 5-min "rapid recall test" with 5 questions that just required remembering trig identities or basic values like sin(π/2).
It was annoying but it really helped.
97 is funny, that would be a particularly painful rote instruction.
Calculators have completely fucked our nation out of it's ability to deal with fractions.
I'm very sympathetic to this, but I do sometimes wonder how closely it resembles "word processors have completely fucked our nation's penmanship." Maybe the fucking of our ability to deal with fraction isn't such a big deal, since we have cheap and omnipresent calculators that can do that sort of thing for us? Does a loss of ability to deal with fractions necessarily imply a loss of any thinking skills that remain important for us? (Again, I'm predisposed to answer that last question "yes", but I don't really believe I have a good basis for doing so.)
it was my doctorate -- "falling down, fvcking up: normative and transgressive social spatialisations of performative
kinetic verticality as a vernacular phatic emphaticism"
Shorter 100: Heebie is teaching dinosaur math. Her Calc I arch-nemesis is teaching the math of the future.
Hasn't the joke been that 5 out of 4 Americans have trouble with fractions? I think that joke predates calculators.
Does a loss of ability to deal with fractions necessarily imply a loss of any thinking skills that remain important for us?
I think it's a key skill for having a basic ability to estimate and recognize order-of-magnitude errors.
I was talking with someone recently who was saying just that about people who grew up slide rules, vs those who used calculators. The latter are far more likely to not catch something like 5343 * 63 = 12000000
But then the Communists will bug all of our calculators, and they'll all fail at test time.
Except the calculators made for the Chinese market.
Maybe it's already happened. Who do you see in advanced science classes everywhere? Chinese, that's who. And Hindus.
The Clenis is to blame.
And I never did grok the dy/dx notation. I understood the concept of taking a derivative, and a second derivative, but what was the point of those pseudo-fractions you were supposed to append to your answer?
I understand I have Leibniz to blame for that notation.
People keep saying that orders of magnitude are a big deal, but they really don't have to be. You just need to have a good attitude about things.
60 did the trick for me. Thanks!
In gratitude, my advice on 84 is to say something to the effect of how maybe acquaintance was trying to commit suicide after all, so really, this is an occasion for congratulations on his/her success you can only imagine that horrorshow survivor must be beside him/herself, and how deeply awful the whole thing is, and that he/she has all the sympathy you can muster on the occasion.
In other words, the standard formula, but tarted up with a lot of adjectives.
LEIBNITZ WAS NOT EVEN WRONG
If I remember the story right, that notation is what suggested the operator calculus, which has proven its worth!
Your math stuff is making me appalled at the amount of math I have forgotten. I need to go audit remedial math or something.
If you're serious, buy a GRE prep book for the math section. The test covers exactly this sort of math, along with basic geometry.
What I've completely forgotten is logs and trig. I never found them intuitive to begin with, and I've haven't had to deal with them since high school.
60 did the trick for me.
Even prostitution is outsourced these days.
You realize, btw, Heebie, that this anti-calculator attitude of yours is deeply at odds with the "I'm a mathematician, not an arithmatician" thing.
Speaking of kids being taught dumb things, PK came home from school SO angry a couple of weeks ago, because one of the parent helpers told the kids that the earth was one light year away from the sun.
My children's teachers have generally been pretty competent, but a student math teacher at an Open House once made a very similar error to Heebie's student (reported in some other thread) while demonstrating some gizmo that could project a calculator onto a screen (We ain't one-at-a-timin' here. We're MASS miseducating!). She brushed of the .9999 as "That's the exact answer." I kept my mouth shut, but told my son when I got home not to listen to X. He replied with something like, "Don't worry, we know."
My worst was a high school physics teacher who opined that there was no exact value for pi "other than 22/7ths". He was manager at a swimming pool where I worked several summers, and when I would suggest I might be interested in teaching he'd shoot back with, "You're too smart to be a teacher."
You realize, btw, Heebie, that this anti-calculator attitude of yours is deeply at odds with the "I'm a mathematician, not an arithmatician" thing.
Um, I don't think so. How do you figure?
How do you figure?
With a calculator, of course.
there was no exact value for pi "other than 22/7ths"
I'm surprised by how often I've heard this. (And even its corollary: "Therefore 22/7ths is an irrational number.")
116: brushed of s/b brushed off. She could spell real good though.
thx B, yes, I think something like that will work -- yr strikethru idea actually kinda makes sense given the situation (the incident being quite odd), tho i doubt we will ever know
Comment 122 was brought to you by the good people at ExxonMobil.
By the way, Heebie, I want explicit confirmation: this student is getting an "F" in your class, right?
You've graded her final exam now, so there should be no wiggle-room in your answer.
Only vaguely related, but you know how when you get change from a cashier for a purchase, they will often hand your change back while counting up from the cost to the amount you gave them? E.g., if something costs $13.60 and you give them a $20 bill, they'll say something like, "13.60. And 40 makes 14 and this makes 15 and 20," while handing you, respectively, the coins, then a $1 bill, and then a $5 bill.
With modern cash registers, however, most cashiers will just say "your change is $6.40" and hand it to you all at once. But it amuses me when a cashier sort of feigns the old-fashioned procedure by counting up to the total change amount, i.e. "Here's 5 and 6 and 40 and that makes $6.40." It's like they're trying to show off that they know how to make change without actually showing that they know how to make change.
Some of these problems are fun for warming up the old algebra skills.
I do sometimes wonder how closely it resembles "word processors have completely fucked our nation's penmanship."
btock iz tollty rite hebee iz gnu worl w/o needz for teh bar thingy china just multiply o and o aginz til rite! w/ calc evenz!
m
iz summer plan!
I have to do my taxes this weekend, so I'll need a serious refresher on negative and imaginary numbers.
*rimshot*
My father was in the slide rule club at Lane Tech in Chicago in the late 50s.
117: I was joking, first of all. But second of all, bc presumably the reason many teachers allow calculators is so that students can be tested on their grasp of the concepts at hand, rather than on whether they make simple mistakes in arithmetic. (I completely agree with Heebie about both calculators and the arithmetician/mathemetician distinction, fwiw, and was, again, just teasing.)
121: I sort of inferred from your description of the situation. Glad to know that my inferences weren't horribly offensive, and that my suggestion will be helpful.
125: OMG, AB & I once ate at a pizza place where the HS age cashier couldn't make change for us. I can't recall the details, but it was not especially complex (not that subtraction ever is), and she could neither work the register nor do the math in her head. When we pass that place, we refer to it as Bad Math Pizza.
I never had a bad math/science teacher (one cranky old bat, but she was competent), but I did have an HS English teacher who, among her many flaws, thought that the well-known New England college was pronounced buh-DOYN.
I was joking, first of all.
Sure. But unless you were going for simple absurdism, I figured you had an actual point behind the joke, and I wasn't sure what that point was. I was only asking, after all.
Basically, my point was that since Heebie said calculators had destroyed the ability to understand fractions, replying "but they help with arithmetic!" doesn't really make much sense.
All of which serves as further proof, as if any were needed, that women are indeed bad at both math and humor. I'll bet OFS couldn't tell a joke if her degree depended on it.
I did have an HS English teacher who, among her many flaws, thought that the well-known New England college was pronounced buh-DOYN.
I had one who was extremely smart, had read everything and was a good teacher but just mispronounced everything that could be mispronounced. The only one that's stuck with me was pronouncing Khalil Gibran's first name "Cay-hill".
Slide rules rule! This will probably start a series of "I learned math using rocks!" comments.
131.first: Not to actually start this discussion in earnest, but I think that the situation at hand reveals the flaw in the "allow calculators is so that students can be tested on their grasp of the concepts at hand, rather than on whether they make simple mistakes in arithmetic" concept - understanding mathematics is a gradual, accretive process, and shortcutting on the foundations leads to structural weaknesses up above. Like college-age students who are utterly unfamiliar with manipulating fractions and exponents.
Of course, $0.99 calculators only address the most basic arithmetic, and so theoretically don't contribute much.
Do kids still learn times tables?
buh-DOYN
Ha. My high school roommate got his first job (teaching math, even!) there. "Rhymes with snowed in, and for good reason," he said.
132: No, I think she's trying to figure out the odds of you writing her Dean a letter if she answers 124 "incorrectly". "... and furthermore, she should return all her back pay."
when i studied maths they hadn't even invented zero yet!
I can't recall the details, but it was not especially complex (not that subtraction ever is), and she could neither work the register nor do the math in her head.
The nice thing about the old way of counting change is that it takes a subtraction problem and turns it into an addition problem. I'm not sure why but for most people, including me, addition is much easier to perform than subtraction.
thought that the well-known New England college was pronounced buh-DOYN.
Weird. Where'd she ever get the idea that "Boston" would be pronounced like that?
46: A does not = A
But I should have been pwnd
131.2: FWIW, another vote for just rolling out the usual platitudes. Best case, it's the expression of concern that will be valued, not any particular wording. Worst case, she'll obsessively and unpredicatably overanalyze whatever expressions of sympathy she receives, in which case safety lies in the platitudinous.
when i studied maths
When I studied math, there was only one of them.
"Here's 5 and 6 and 40 and that makes $6.40." It's like they're trying to show off that they know how to make change without actually showing that they know how to make change.
I, benevolent and well-minded woman that I am, have always assumed that they do that not to show off fake chops, but rather to show the customer, in a kindly fashion, that they are indeed getting the correct change.
Have I mentioned that Iris has a lot of evident math skillz? Makes me so happy - we really haven't focused on it (math is a distraction from learning about every minor goddess and hero, plus whatever the hell AB does with her), but she just counts and adds things for her own edification, and takes really readily when we show her new concepts (like that the 18 baby food jars she's just counted stack into 3 columns of 6). As 130 would indicate, lots of family pride on this point.
Plus, you know, patriarchy.
Do kids still learn times tables?
Yes, or at least mine did. Timed tests and everything. Made my little heart glad.
I don't know why I've declared private war on this student, except she is so persistently earnest in asking questions that belie gigantic misunderstandings of math, and so determined to tune me out when I give her a straight answer about how much background she's lacking.
The tuning out is probably the part that infuriates. Someone who doesn't know what they don't know - to the extent they're not even holding the end of the rope that leads into the darkness - isn't much fun to work with. I had a coworker like this recently. We have a building project that involves tiling a surface with glass quadrilaterals. As it happens, we want the quads to be planar, or at least nearly so, because we don't want to bend the tile material overmuch. But our problem coworker - self-styled as skilled in parametric modelling - just didn't get the concept of planar v. non-planar, or for that matter the difference between planar and parallel. I tried to explain that even if a couple of lines happen to look as though they're going the same way, it's not necessarily the case that you can make something flat out of them.
146: But she can't tell a joke, right?
Q: Why can't JRoth's six-year-old daughter drive?
In the post: "belie" s/b "broadcast," maybe?
145: Often that is the case, but there's a particular showy way of doing it that, at least to me, indicates that they've seen and are mimicing the old-fashioned way of counting change, but without actually understanding it.
"6 year old girls drive like THIS . . . ."
my point was that since Heebie said calculators had destroyed the ability to understand fractions
Right, I wasn't talking about the fraction thing specifically as much as the "no calculators on exams" generalization. You're *totally* overanalyzing my offhand half-assed teasing.
Men. So obsessive.
My sixth grade math teacher pronounced "Afghanistan" as "Afghafistan". (This was during the Soviet invasion.)
She was a terrible math teacher, too. I remember her teaching us some shortcut for calculating something-or-other to do with decimals, and I recognized that it would get the right answer in some cases, but not in others. One of those cases where it didn't work on the test, and I did it correctly. She asked me why I got the problem "wrong", and I tried to explain it to her, but she didn't understand.
My mother, who also taught sixth grade at the time, but didn't teach math, had to explain reciprocals to her, as well as telling her not to pronounce it "receptacle". (My mother would tell me lots of things that probably should have been confidential.)
156: Actually, in 117 I merely asked you a simple question. You're the one that wrote, like, a whole essay in response, you humorless humor-impaired person. And furthermore, I find your assertion that calculators caused the destruction of the Icelandic economy baffling.
I have come back around to thinking that memorization is a key component to learning, but I don't call in memorization, I call it internalization, which gives a better sense of what this sort of learning was about to begin with.
I tell my students "I want you internalize this concept. When you encounter situations like these, I want you to apply this concept without even thinking. You'll be doing just that later in the semester."
calculators caused the destruction of the Icelandic economy
It was those fancy graphing calculators. If they'd stuck with the $.99 solar-powered thingies, everything would have been okay.
||
Our more bookish and German-speaking fellows may enjoy this map of Bücherlandes.
|>
In the post: "belie" s/b "broadcast," maybe?
Yeah, but everyone knows blogging is really just a matter of writing down a bunch of crap that just looks like the right words.
146: The most mathematically-oriented of my three kids made that aspect of his personality evident when at a quite early age he asked at breakfast if forty-two was six sevens. "Yes! Why do you ask?" I calmly* asked. Turned out he had counted the letters on a hidden-word grid on the back of a cereal box (OK, so not so much on the verbal side).
*"He just recapitulated the invention of fucking multiplication!" was how I calmly described it to my wife when she didn't seem to be matching my enthusiasm.
When you encounter situations like these, I want you to apply this concept without even thinking.
150: She's only 5.
But, you know, a goal for next year.
If they'd stuck with the $.99 solar-powered thingies
"solar" s/b "geothermal"
We're talking about Iceland, after all.
146: But she can't tell a joke, right?
She has recently discovered "interrupting cow," and gets no end of amusement from "interrupting duck" and like variations.
I do wonder now that I've replaced the long forgotten algebraic simplification with spreading everything over the sheet in a stream-of-consciousness fashion: at what point do the excess calculations cause significant rounding errors?
158: It may help to remind them that athletes learn through rote repetition as well - not that these are schoolkids who wanna be like Mike, but it shows that this is how we learn, not just old-fashioned rote-is-rot nonsense.
Aside from mispronunciations due to bizarro transpositions/not being able to read, e.g. "Afghafistan" and "receptacle," mispronouncing a word can mean that you've never had an opportunity to use it in conversation, often due to class issues (such as a poor kid who reads a lot but doesn't have any peers to discuss the books with).
My calculus teacher didn't know how to pump her own gas, which probably explains the lack of handy gas-tank examples in her class. It made me feel better for getting Bs in calc, though.
When Caroline was five she figured out that 3 X 5 = 15. I was doing yardwork, and taking a break every so often to give her five pushes on the swing. She said she wanted me to do that three times, and then immediately pointed out that this would be 15 total.
166: Ah, I love the interrupting ______ joke. Truly a classic.
I'll need a serious refresher on negative and imaginary numbers.
That reminds me: I think we all need to pitch in and get heebie one of these t-shirts, once she's returned to her pre-pregnancy shape.
171.1 Yes, sniffing at someone when they reveal that a word is only in their "reading vocabulary" has a long tradition.
171: "Unique" was a word I heard a lot as a kid, but I never associated it with "you-ni-cue," as I read it in the pages of Peanuts.
Is "unique" supposed to be associated with "you-ni-cue"? (Or was that a joke?)
When one reads the word "unique", one might imagine that it's pronounced "you-ni-cue", Brock.
Maybe the most common example of the word where people think the spoken word and the written word are two different things is "misled".
177: I was like that with "horizon," which I read as "hor-uh-zon."
176: On my sojourns in the UK I concluded that there were an awful lot of Brits who suffered from that affliction. A nation of readers but not talkers, apparently. If you've never heard it pronounced properly, I can totally understand concluding that "controversy" is pronounced "con-TROV-versy " and "schedule" is pronounced "shedjuhl".
182: and in the reverse scenario, people who have only seen "Strawberry" written down may think it is a composite of "straw" and "berry", rather than being pronounced "strorbry".
Peanuts was a great builder of cultural literacy for me. I remember asking my mom what a "Van Gog" was, when Snoopy's Van Gogh was destroyed in a doghouse fire.
180: right, but that's the opposite of what JRoth said.
161: everyone knows blogging is really just a matter of writing down a bunch of crap that just looks like the right words
Otto flunking Heebie?
177: There was thread on these at Crooked Timber, where I found out that I was not alone in my mispronunciation (actually a misread) of "misled" as the past tense of "misle". And searching for it just now, I discovered that in a thread there 3 years earlier someone name Cryptic Ned owned up to the same confusion.
[Written before I saw CN's 180. Honest. The Internet is just so, ... so ... connecting.]
185: The point was that I was both reading it and hearing it, but never connecting the two (until I was at least 9).
I believe that I've told my spelling bee story about ennui, when I had just learned ennuiment in French class. Again, no connection.
Peanuts was a great builder of cultural literacy for me.
Last night at dinner my MIL was telling (in excruciating detail) about the book Beethoven's Hair, leading us to explain to Iris that Beethoven was a famous composer, etc. She gave us her best proto-teenage, "Duh, I already know all about Beethoven from A Snoopy Christmas, when he's playing music for Lucy." We gently explained that Schroeder is not, himself, Beethoven.
Kai's exersaucer has a ladybug that, when pressed, plays "Für Elise" in a manner that would probably drive Beethoven mad.
I remember as a kid reading about short TV series like Roots and in my head I would pronounce the term that referred to the genre as mihNIZurries. I think I also thought that it was etymologically related to the word "misery", because they were usually full of drama and depicted bad stuff like slavery.
183: My parents corrected my pronunciation of strawberry, but I could never figure out what they were correcting. I think it was just that my initial s was aspirated, rather than sibilant, but it sounded pretty close to my young ears.
Let me rephrase 179 and see if it works better: JRoth, you pronounce the word "unique" as "you-ni-cue"?
And Heebie's definitely in labor.
Otto flunking Heebie?
It was an attempt at good-natured ribbing. But it is now clear that my nature is not good.
181. When I was little, there was quay-awss, which is what my mother called my bedroom, and then there was see aitch hey yo ass, a word I occasionally saw in books. Just as I finally sorted that out, Mel Brooks brought me KAOS (and Barbara Feldon!).
Kai's exersaucer has a ladybug that, when pressed, plays "Für Elise" in a manner that would probably drive Beethoven mad.
Why, does it have a lot of annoying flashing lights or something?
166: Interrupting cow is one of those things that makes me think the next generation is better and smarter than my generation. We didn't have that joke when I was a kid, and I have a hard time telling it - I always wait too long to deliver the punchline.
Peanuts was a great builder of cultural literacy for me.
These days it's Calvin and Hobbes.
These days it's Calvin and Hobbes.
I hate to be the one to tell you this, but it's been almost 15 years since C&H was a syndicated strip.
Well, I realized this as I was typing the post. But PK's learned a lot of stuff from C&H, and I haven't seen anything more recent that's half as good, so it's all the kids today have.
192: Well not anymore.
198: But C&H rarely trod pop-culture ground. Off the top of my head I could name a dozen figures from high culture and from the 50s who get name-checked in early Peanuts; I can think of exactly one C&H that names names, and those are just McDonald's and Wal-Mart.
Why, does it have a lot of annoying flashing lights or something?
It does have flashing lights, but I was thinking more in terms of the high-pitched electronics, which I bet could pierce his near-deafness. And make him wish for total deafness.
201: Wait, so what is he learning? That we need to Get Rid Of Slimy girlS?
202: Um, JR, every single C&H strip mentioned both Calvin and Hobbes.
calvin and hobbes names two philosophers right there in the title
Also, M/tch is mean.
Um, I don't think so. How do you figure?
207: He pwns mercilessly.
How do you figure?
With an abacus.
*sob* I thought Brock would love my elegant solution to his book problem. [imagine me getting increasingly hysterical here] I think of you all the time Brock, and you won't even acknowledge me!
Not a speaking thing, but for years and years I read (and I only ever read it in American books, it's not a word that comes up much in English conversation) Episcopalian as Episcolopian. Like Nealopitan.
See, Brock is mean. I'm just honest.
From C+H I learned that the sun sets in Flagstaff, Arizona. Also, that bats aren't bugs.
209: asilon, sorry--I somehow missed comment 17 earlier. Is that packing material? That's a beautiful and elegant solution indeed, but it might take up a lot of space in my bag. And also, I'm not sure about long-term durability. And also, I'm not sure I could bear how nerdy it would make me. (Or rather, bear to acknowledge how nerdy I am, which I'm worried it would force me to do.) But it's a good idea.
Also, I've read your name probably several thousand times, and yet somehow I just now realized it wasn't "alison". Weird.
Now that I think about it, there's an entire world of mid-20th century cultural references that I only know because of Looney Tunes (also, very nearly 100% of the opera that I know).
176: When I talked about the ann-hill-ee-ation of matter and anti-matter in a very early science class, no one else in the class knew any better.
The teacher did. Lots of giggles.
The D.E. is always correcting my pronunciations. I respond by kicking her knees.
PK learning from Calvin and Hobbes. Bite me.
213: I would dearly enjoy annotated versions of some of their Hollywood-themed pieces. I'd probably do better now than I did as a kid, but not much.
211: Most importantly, you learned that you go to Pittsburgh when you die.
Still not clear whether this is for being good or bad.
215: Ooh, good example. There's also the parody of Masterpiece Theatre-style pretentious dialogue, which causes Calvin to say, "Holy shla-moley, isn't there a cop show on where people talk normal?" Without which I doubt I would say, "holy shlamoley."
Wait, never mind, that's the same one. I just finished recreating it in my head.
There's also the one where he's home from school watching TV and sees scandalous soap operas goings-on.
I can't remember when I finally learned that Looney Toons and the like weren't originally made as Saturday morning kids fare, but were shown to adults in cinemas before feature-length films. It suddenly made a lot of things about them make much more sense.
Looney Tunes made much more sense to me once I learned that they stopped making them like fifty years ago. But as a result of watching them, I have all of this cultural knowledge -- magnets are shaped like horseshoes, bombs look like bowling balls on a string, convict uniforms are striped pyjamas -- that doesn't match up to real-life facts in any age I've lived in.
they stopped making them like fifty years ago
And yet Noah will watch the DVDs of them over and over and over and laugh hysterically all the way through. Some of my very fondest memories of my father are of us watching LT together on Saturday mornings.
Comity!
When Iris was little, she would call him "Bugs Rabbit," no matter how many times she heard "Bugs Bunny." We didn't try too hard to correct her 'cos, you know, cute!
just to be clear here - that was a question on the "final exam" of a very introductory course, not the final exam of a three year mathematics degree? You can never tell with American education.
Here is the WARNER BROTHERS CARTOON COMPANION
A lot of the catchphrases were borrowed from popular comedians of the time:
225: Final exam for the second class in a three class calculus sequence. Well after she should have been able to simplify a fraction.
that was a question on the "final exam" of a very introductory course
and, just to be clear, it was one element of the question.
School teaches kids to swallow answers with no questions attached for decades. Then some teacher becomes frustrated that the students never ask questions, or don't know how to do so effectively.
I sympathize with the original gripe, but with distance it's hard to stay mad at them. Russia and China are even more unfriendly to students, something one can forget here, seeing only the top 2%, after defence skimming of the very best.
School teaches kids to swallow answers with no questions attached for decades. Then some teacher becomes frustrated that the students never ask questions, or don't know how to do so effectively.
Is this in reference to heebie's situation? Because it doesn't really match anything she's said about this particular student or in general about her classes.
I sympathize with the original gripe, but with distance it's hard to stay mad at them. Russia and China are even more unfriendly to students, something one can forget here, seeing only the top 2%, after defence skimming of the very best.
Huh?
No, no, wait, this">http://www.youtube.com/watch?v=zsgRCRlf77U>this is the link I wanted.
You, know, I think Karen designs her own outfits.
I guess this means I should go to bed, but I am strangely not tired.
I feel bad for the kid in the post.
238: Maybe you can save her, Sifu!
"substitute every third word from a website with a synonym"
This is reasonably clever. I think AWB should suggest the kid take cryptography.
239: there's no saving people. Math gets us all, in the end.
240: It was pretty poor encryption. Y'all have made my google-fu undergrad-proof.
When you're sad and when you're lonely and you haven't got a friend,
Just remember, math is not the end.
225, I was hoping this was from a 4th grade factoring quiz.
Anyway, the general rule is n/2 +7.
I've solved it! She thinks "equals" means "alternately, multiply the previous term by a/b and b/a where a is the base of the original numerator and b is the original denominator, but with the exponent of the original numerator, until you have a term with the same numerator as denominator, in which case you multiply the term by itself an infinite number of times and then simplify." Anybody could make that mistake.
My eighth grade math/physics teacher went down with something around Christmastime and we got a rush substitute for the rest of the year, a M. Buhrer. Sometime that winter he made a boneheaded arithmetic error in a fraction problem on the board, no big deal, can happen to anyone. Smartalec me promptly pointed it out, he disagreed immediately. I piped down for a minute, going over the calculation carefully, then piped up again, sorry Monsieur, mais j'avais raison. At which point he not only held his ground but told me if I don't take it back and apologize for misleading the class he'll give me an F for the quarter. I got pissed and didn't back down.
A few hours later during a break he came up to me and said that of course I was right on the math, but that I didn't understand that the most important lesson in schools is to learn to know one's place in the hierarchy and the need for unquestioning submission to authority. I wasn't surprised to find out a little later that M. Buhrer was the deputy leader of 'Vigilance', the local fascist party (He split from them the following year for their excessive moderation). Later on that year he made some comments about the eternal truths of racial hierarchy - in a class which was one third Arab. A parent principal conference soon followed. M. Buhrer was informed that he would be leaving at the end of the schoolyear.
246: yes, yes, but what was your grade?
I told my parents, they told the principal, and M. Buhrer got his own lesson in hierarchy and submission to authority - I did fine.
I have a math question which is either really dumb and reflects how much math I've lost or kind of important?
Why is x^-n equal to 1/x^n?
249: When you multiply two expressions that are the same base with exponents, you add the exponents. x^4 * x^5 = x^9. When you divide two expressions of the same type, you subtract the exponents: x^5/x^4=x. When you think about it, that means that 1/(x^3) has to equal x^-3.
249: I like moments like that in math, where you have a seemingly arbitrary decision about how to extend a concept, but it turns out there's only one way to make the puzzle pieces fit correctly.
Other interesting questions I'm not going to research right now: who decided that x^-3 would be 1/x^-3? Were alternative systems played with that just didn't work?
[This always happens.]
249: it's 'by definition'/'by convention'. Said convention adopted (per LB) to keep operations with exponents consistent.
Essentially x-n = (xn)-1 = 1/(xn) [Parenthesis unneccessary here, but nice.]
22 · 2-3 = 2-1 could have some other meaning than = 1/2 but it's a bit difficult to think of what that should be.
Also: that form (and meaning?) of notation seems to have been created by Newton, so if you want to complain, you'll have to bitch to him.
max
['Or Nicolas Chuquet, your call.']
It's the extension of the rule xa+b = xaxb. Let b = -a, and you get a+(-a)=0, and since x0 = 1, you have to make x-a = 1/xa to preserve the rule.
Apparently the law of exponents were explored as early as the 12th century by an Islamic physician/mathematician in Baghdad, Al-Samaw'al (born Jewish converted to Islam based on a dream) building on work of Abu Bakr al-Karaji a century or so earlier. Short version in the second item here, more detail in the book at this link, where you can appreciate the extent to which coming up with an efficient notational system is the crux of the mathematical biscuit (so to speak).
my grasp of mathematics was always very spatial when i was studying it, which meant i found some types of algebras much harder to grasp than others -- for an (easy) problem like this, i really do picture the fraction as a little (wall-less) house with an upstairs and a downstairs, and all the 2s and 7s as something like little bags of amount stacked above ands below, and you "cancel" by throwing out the same kind of bag upstairs and downstairs
this physicalisation served me well for non-euclidean geometry; less well in galois theory -- definitely i prefer notations which help you think you are moving bags upstairs and downstairs
magnets are shaped like horseshoes, bombs look like bowling balls on a string, convict uniforms are striped pyjamas
Actually, in our county they do make them wear the stripey black and white pajamas, as some sort of throwback humiliation, I presume. How awesome would it be if they attached a little styrafoam fake-ball-and-chain to the inmates?
255: I'm the opposite. I can't picture anything more complicated than a sphere, so I prefer to translate everything into a form where I can just manipulate symbols.
you can appreciate the extent to which coming up with an efficient notational system is the crux of the mathematical biscuit
Boy is this the whole deal when it comes to math for computer science. If only we had another three subscripts, then we'd be set!
more detail in the book at this link
Episodes in the Mathematics of Medieval Islam by J.L. Berggren
OO! WANT!
Earliest Uses of Symbols of Operation:
Negative integers as exponents were used by Nicolas Chuquet (1445?-1500?) in 1484 in Le Triparty en la Science des Nombres. Chuquet wrote 121‾m to indicate 12x-1 (Cajori vol. 1, page 102).
Negative integers as exponents were first used with the modern notation by Isaac Newton in June 1676 in a letter to Henry Oldenburg, secretary of the Royal Society, in which he described his discovery of the general binomial theorem twelve years earlier (Cajori 1919, page 178).
Before Newton, John Wallis suggested the use of negative exponents but did not actually use them (Cajori vol. 1, page 216).
max
['It's that guy, or the other guy, unless it's this... or if it's someone else.']
257:255: I'm the opposite. I can't picture anything more complicated than a sphere
Just so many spherical cows then.
255:definitely i prefer notations which help you think you are moving bags upstairs and downstairs
{blinkity} I don't use that part of my brain for math. I use the math part of my brain. How tautological of me. I can, say, look at an engine (or a map or whatever) and see how the parts all fit together, but that part of my brain doesn't do math. That part of my brain uses graphs, directly. That part of my brain looks at the World Trade Center (image: 757 impacting steel latticework with all windows removed; image: 50,000 gallons of high test jet fuel burbling all over everything - elevators, desks, papers as rapid ignition spreads) and says, well, what the hell do you expect to happen (image: closeup main vertical building supports, many feet thick, covered in jet fuel, plus extra graph of time versus total heat absorbed; image: small steel beam being slowly cut by blowtorch; image: steel cube covered entirely in asbestos dropped into vat of liquid steel), you truther nuts?
That is the source of a great many fistfights between the symbol driven part of my brain and the visual part, which does most the heavy lifting.
max
['Oh, well.']
That part of my brain uses graphs, directly.
Graphs is math.
in the uk the plural of graph is graph
259: Thanks for the link to that great resource. A good reminder that for many developments in math (and science) that the pioneers were navigating a notational and terminological wilderness as well as trying to nail down the new concept at hand. Also why so much historical primary material is nearly unreadable*. Math is often taught as such a "pat", given thing that the struggle is obscured.
*Different subject area, but is there any seminal work in Math and Science that has remained as readable as Darwin's On the Origin of Species? None that I know of, probably the result of pwning everyone so badly that you have several decades to organize your thoughts and words but then need to rush out a version in the face of events.
256
Actually, in our county they do make them wear the stripey black and white pajamas, as some sort of throwback humiliation, I presume. ...
Isn't the real reason to make escape more difficult?
A good reminder that for many developments in math (and science) that the pioneers were navigating a notational and terminological wilderness as well as trying to nail down the new concept at hand.
I again recommend Number as a book that is very good in writing about that dynamic. He is quite clear and convincing that he thinks certain notational advancements rank among the greatest accomplishments of human creativity.
Isn't the real reason to make escape more difficult?
They just end up hiding amongst the zebras and bar codes.
Q: What's black and white and red all over?
A: An escaped convict brought to terminal justice by vigilante students on a Texas college campus.
OFE failed the final but passed the class with a D.
Okay, so I know that X0=1, but why is that? How do you prove it?
It follows from the rule x^a * x^b = x^(a+b). Since x^0 * x^b = x^(0+b) = x^b, we must have just multiplied by the identity element, and so x^0 = 1.
The multiplicative identity is the lonliest number.
Just as zero is the additive identity.
Think of it like this! (NB not an argument.) Multiplication is repeated addition, and you don't find it puzzling why 0x = 0 (preusmably). After all, (n+1)x = nx+x, 1 = 0+1, (0+1)x = 0x+x, 1x = x, so 0x = 0.
Exponentiation is repeated multiplication and xn+1=xnx; x0+1=x0x, so...
"e" is the additive identity, according to heebie.
269: One way. To go from x^n to x^(n-1) you always divide by x. So x^1=x, x^0=1, and x^-1=1/x.
Oops, never mind.
"e" is the additive identity, according to heebie.
It is?
"lonliest"
You see, it ranks a zero with you. Except when it doesn't.
I usually put e somewhere in between 2nd or 3rd lonliest.
THE WORD IS SPELLED "LONELIEST" ARGGG
There is no exact representation of e except 6-23/7.
280: My God, a self-incrementing comment. Death of 'net imminent!
279: Leave out the techniquese, please? I feel like you're trying to tell me somthing.
Graphs is math.
Not whens I lack ze equation, O Banninator. That's where the fistfights come from.
THE WORD IS SPELLED "LONELIEST"
But Heebie was saying Lonliest, a descriptor of that which is most like Lon Chaney.
There is no exact representation of e except 6-23/7.
I like 24-7/π.
max
['Well, ♥π, I guess.']
Not whens I lack ze equation, O Banninator.
Equation?
Graphs are just a set of nodes and a set of sets of nodes.
JPS: 259: Thanks for the link to that great resource.
No problem. Thanks for the linke to the Islamic book. Must acquire.
A good reminder that for many developments in math (and science) that the pioneers were navigating a notational and terminological wilderness as well as trying to nail down the new concept at hand.
It has been in the back of my head all that that they could have decided that 2-1=1√2 =2. And thus 2-2=√2 =1.44xxx. (And maybe 21/2 is (1/2)2?) And then people would have used it that way for hundreds of years, because it would have been good enough. Which suggests why alphabets stay the same for a real long damn time.
max
['Why switch?']
268 is terrible news. There's really nothing you can do, Heebie?
287: Yes, it's very unfortunate that One Fat Englishman got such a low grade.
What grade did Our Favorite Student get?
It should be said that, just like tons of students look for patterns in the multiple-choice bubbles, they also look for cutesy answers to apparently-complicated expressions, because the person writing the test always makes the math convenient. Like, if you've got a test with some arbitrary complex quantity like (e^(pi*i)), you're probably best off just assuming that it's 1 or -1 or something like that.
