Mastering mathematics
Category: Humor
Posted on: October 6, 2006 8:45 AM, by PZ Myers
I am very glad that I am not a math teacher.
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Comments
Tears in my eyes, this is so funny; especially the last one (#5), which is so inventive that I would have given an A for it.
I wonder if I would still be laughing about a possible biology equivalent of this...
Posted by: amphioxus | October 6, 2006 9:33 AM
I guess there are biology equivalents... a few years ago I granted a non-majors Human Biology class the opportunity to tell me about reflexes on a weekly quiz. This is a direct quote from a young lady on the women's basketball team:
"If you touch something "hot" (and yes, she put the word in quotation marks), you will start jerking off and there is not a single thing you can do to stop yourself"
Sort of a reflex, I guess...
Uncle Don
Posted by: Don Culberson | October 6, 2006 9:42 AM
What's kind of sad is that several people have left comments on that page to inform him that his actual solution number two can't be correct, because 1/0 isn't infinity.
Limits, man, limits.
Posted by: sammy | October 6, 2006 9:50 AM
Those are freaking hilarious. (and I'm an English major!)
Posted by: JM | October 6, 2006 9:57 AM
Oh man, I can't stop laughing at the (a+b)^n one.
Posted by: cooper | October 6, 2006 10:09 AM
I must be simple...#3 left me rolling on the floor. They're all pretty hysterical, though.
Posted by: Greg Baumbach | October 6, 2006 10:21 AM
I don't know, these didn't seem very funny to me. Items #1 and #3 show students who were deliberately trying to be cute, but I bet for teachers that gets old really quickly, especially considering how old, old, old those particular jokes are. For the other items it's not so clear, but is students' ignorance funny? Maybe the teacher did a crappy job explaining things? The limit notation in #2 is sloppy -- yes, depending on how you use the 'infinity' symbol this might be okay, but the way I've usually seen it used, in #2 the teacher is incorrect. Finally, there is not enough context to know for sure, but #5 appears to contain a sexist slur by whoever created the slide.
Posted by: Kurt | October 6, 2006 10:24 AM
Speaking of innumeracy, this popped up on yahoo today:
http://news.yahoo.com/s/space/20061005/sc_space/nasacompletessurveyofnearbysupermassiveblackholes
"...these black holes have masses of up to billions of tons compressed into a region about the size of our solar system"
Billions of tons, huh?
Posted by: Mikey | October 6, 2006 10:27 AM
These have been circling around the Internet by way of e-mail forwarding for a while now; I had already seen them. I agree that the lim shouldn't be infinity in #2.
Posted by: j | October 6, 2006 10:38 AM
#5, at least, I believe is apocryphal; there is no obvious right answer to the question. No good algebra question involves a question mark, there should be a variable there. The only reasonable answer would be
x = asin(n?)
which makes no sense.
Number 2 has the same feel; I think it's fake.
4 may have a facutal basis, may not... not terribly intersting.
1 and 3 are likely real (or at least have certainly been done by real students). Sad, though, that it's presented as failures by the students; when in fact they're giving clever (if trite) answers to questions that appear to be designed to squeeze any interest in mathematics out of the respondant.
Posted by: Evan Murdock | October 6, 2006 10:51 AM
Spidey sense says examples 2-5 are made up for humorous intent. Spidey sense is tingling for #1, but is undecided.
Posted by: Frumious B | October 6, 2006 10:51 AM
In any proper calculus class, number two would be incorrect -- the limit from one side is infinity, and the limit from the other is negative infinity. In that sense, 1/0 really isn't necessarily infinity -- it depends on where you get it from.
Of course, I don't think that's what the commenter had in mind. :)
Posted by: Davis | October 6, 2006 11:23 AM
Btw, Ig Nobels were announced last night:
http://www.improb.com/ig/ig-pastwinners.html#ig2006
Posted by: Peter Z. | October 6, 2006 11:54 AM
Faaaaaaaaaaaaaaake. :)
Now if you want to know what real students are thinking, have a look at this:
http://shrimpandgrits.rickandpatty.com/2006/10/06/classics-of-student-literature/
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Posted by: calisto | October 6, 2006 1:33 PM
I'm with Kurt, these are lame. But these are hysterical.
Posted by: Jeremy Henty | October 6, 2006 1:56 PM
For the other items it's not so clear, but is students' ignorance funny?
In the sense of "you have to laugh to keep from crying", yes.
It's the same thing that makes The Daily Show and The Colbert Report funny.
Posted by: Rick @ shrimp and grits | October 6, 2006 2:02 PM
This must be mostly faked up.
On #2 there is indeed a problem; limit is spelled lowercase. But the infinity is a convenient shorthand. While it is correct that the real line doesn't properly contain infinity, the point at infinity is usually added for convenience, for example here. Here there was also no definition declaring in which set x belonged, so it wasn't only a convenient shorthand but fully correct AFAIK.
The extended real line is analogous to adding the point at infinity to the complex plane (by mapping it on a sphere) to become the extended complex plane. As long as you remember which topology you work with, it is fine. Relax and enjoy the math!
Posted by: Torbjörn Larsson | October 6, 2006 2:15 PM
"in which set x belonged"
Duh! In which set the numbers belonged, of course!
Posted by: Torbjörn Larsson | October 6, 2006 2:17 PM
I don't know, the sloppy notation on #5 and the error in #2 are totally typical of some high school math teachers I've encountered. We certify teachers for high school math who don't understand why their zero-level remedial university math courses don't count toward their math credit requirement; why are we surprised?
Having seen real students in the field, none of those really surprise me--and they're certainly something it's bloody difficult to decide how to answer. I've certainly seen real students do things like #4 and #5. (I had a student try to cancel the "n" in "ln" once, truely.) The posters here who don't think these can possibly be real... well, I envy you your sheltered lives.
#2 I don't believe at all, however. I've never seen anyone *draw* an infinity that actually looked like an 8 on its side... and in speaking you would refer to it by name, and hopefully explain what that symbol is if the student didn't seem to know. If a teacher ever found themselves getting an answer like that, it might be time to look for a new job.
#3 is obviously someone trying to be cute, and #1 is probably the same. The reason #1 rings false is that by the time they're seeing the binomial theorem, students already have internalized the idea that words like "expand" don't necessarily mean the same in mathematics as they do in everyday life. In fact, by that point, the challenge is to get them to realize that sometimes they *do* mean the same.
Really, though, it's nice when students do things like 4 and 5. It means they're paying attention and thinking about things. Not only that, but you can clearly see what they don't understand--there's an articulate misconception to latch onto and explain. Simply being *wrong* is easy to correct; being vauge and disinterested (doing things like 1 and 3, where the students are just trying to be cute) is much worse, but even 1 and 3 are better than a blank page.
Posted by: lytefoot | October 6, 2006 3:14 PM
One can find a student to commit almost any atrocity against logic and reason. It may be easier to spot in a math problem, but it's not just math teachers who encounter truly bizarre answers.
This week I gave an exam that is worth (all by itself) about 15% of the semester grade. A student told me at the beginning of the period that she had forgotten to bring the homework that I was collecting before the exam, but she was going to go home and get it. The homework assignment is worth barely 1% of the semester grade, so I told her, "You should take the exam and turn the homework in later for half credit." She assured me she lived right next to the campus and quickly left the room! She returned one hour later, as I was collecting the exam, and calmly handed me her homework. "I'll just pass on the exam," she said.
Yeah, she'll pass on the exam, all right, but she won't pass the class. (She's the student who got 7% on Exam #1 and now she has a zero on Exam #2.) Criminy!
Posted by: Zeno | October 6, 2006 5:19 PM
I have seen an answer like #3 on a test I gave. He probably meant it as a joke, but the kid was so clueless I was not sure.
Of course nearly every math teacher has seen what we called "the Freshman Dream":
(a + b)^2 = a^2 + b^2
Posted by: Craig O. | October 6, 2006 5:40 PM
Those remind me of that Calvin and Hobbes cartoon where the teacher asks him to explain something (just exactly what has slipped my mind) "in your own words," and he writes down "Yakka foob mog. Grug pubbawup zink wattoom gazork. Chumble spuzz," and thinks, "I love loopholes."
Posted by: Interrobang | October 6, 2006 8:04 PM
When kids use jokes on teachers that are as bad as the jokes we force our (students) captive audience to listen to, there is real humor in that.
(As a first year Russian student, I was asked to decline "Karandash'." Of course I answered, "No, thank you." But I like the binomial expansion better!)
Posted by: Jonathan | October 7, 2006 9:54 AM
#5 appears to contain a sexist slur by whoever created the slide.
Yeah, I wondered what that "Blondie" was referring to as well.
I can imagine that this wouldn't be side-splitting if you were a math teacher and exposed to it all the time.
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Posted by: calisto | October 8, 2006 12:27 AM
That reminds me of a student who decided it would be great to (on a multiple choice question) write down all the letters. When grading it, I thought (as you might expect): "Cute, a wise-ass". But the same student actually wanted to argue that they should be given credit because they "put down the right one".
As funny as Calvin and Hobbes is, it still can't beat out real life.
Posted by: Rick @ shrimp and grits | October 9, 2006 4:59 PM