Professors shouldn't be allowed to do this

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lilturtle
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Professors shouldn't be allowed to do this

Postby lilturtle » Mon Jan 17, 2011 3:55 pm UTC

There are trick questions, and then there are these.

Question VII: Why would you expect Tungsten to be diamagnetic?

Correct Answer: You wouldn't.
My Answer: No.
98% of My Classmates Responded: You'd expect it to be diamagnetic because ... blah blah blah ... magnetic permeability ... d and p orbitals ... blah blah blah ...

Most of my class got the question wrong. I got half credit for not being specific enough (in retrospect, I don't know why I answered "No").

I mean, I can't complain since I did pretty well anyhow. But damn it this annoys me to no end.

It's almost like that finals question my English professor asked us on Crime and Punishment: Why did Raskalnikov go to Canada in the end? (Hint: He didn't. And only half the class got that right).

Why do they insist on doing these things? Bah!

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Re: Professors shouldn't be allowed to do this

Postby SlyReaper » Mon Jan 17, 2011 4:03 pm UTC

I think you've been very meta here because I think this is in itself a trick question. I have never heard of a teacher or professor pulling pranks like that.
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Re: Professors shouldn't be allowed to do this

Postby sikyon » Mon Jan 17, 2011 4:56 pm UTC

lilturtle wrote:There are trick questions, and then there are these.

Question VII: Why would you expect Tungsten to be diamagnetic?

Correct Answer: You wouldn't.
My Answer: No.
98% of My Classmates Responded: You'd expect it to be diamagnetic because ... blah blah blah ... magnetic permeability ... d and p orbitals ... blah blah blah ...

Most of my class got the question wrong. I got half credit for not being specific enough (in retrospect, I don't know why I answered "No").

I mean, I can't complain since I did pretty well anyhow. But damn it this annoys me to no end.


I think that's a fair question. Why isn't it? When you're out using the knowledge you've learned, you'll have to figure things out from scratch. Can't expect to be pointed at every correct answer...

lilturtle wrote:It's almost like that finals question my English professor asked us on Crime and Punishment: Why did Raskalnikov go to Canada in the end? (Hint: He didn't. And only half the class got that right).


Hahaha, this would have blown me out of the water. I remember reading that book in grade 12 class and I was soooo bored of it after the first 4/5th that I just didn't bother to read the conclusion of the story. I really, really didn't care what happened to anyone in that story at that point anymore. I could never figure out why it was such a highly regarded novel...

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Re: Professors shouldn't be allowed to do this

Postby Hope_ » Mon Jan 17, 2011 5:01 pm UTC

I think it's just a way of teaching you that in exams like that you have to be specific (Which is why I never did well at any exams, except english exams, I tend to waffle and go off on tangents, as is obvious here). Treat it as a learning experience and you'll probably remember it more now that it's annoyed you. :P
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Re: Professors shouldn't be allowed to do this

Postby Von Haus » Mon Jan 17, 2011 5:48 pm UTC

I feel wronged by that question even though I haven't had to answer it. If it was worded "Would you expect Tungsten to be diamagnetic? Explain your reasoning." It would have just worked so much better. Any student doubting their knowledge who may have thought tungsten wasn't diamagnetic but seeing that question could realistically panic someone and make them assume what they thought was wrong, thus penalising people for having self doubt which doesn't seem to me what an exam should be testing. Plus it seems anyone who just happend to know this fact gets an easy mark without actually having to show that they understand the theory behind it, which again seems to be missing the point of asking the question. It could be argued that the 98% showed a greater understanding of the theory and yet got penalised.

I think there's just a part of me thinking the professor set the question because he thought it was clever rather than because it was a good question to set. Which isn't a good policy to have when you have a responsibility to write papers that affect the futures of the students taking them.

lilturtle wrote:It's almost like that finals question my English professor asked us on Crime and Punishment: Why did Raskalnikov go to Canada in the end? (Hint: He didn't. And only half the class got that right).


That sort of thing would have been a big problem for me for my GCSE English Literature (quite a few years ago now), we did Pride and Prejudice and even though I managed to blag an A* I still haven't read it all the way though. (The fact that my girlfriend is probably the biggest P&P fan in the world makes this even worse.)
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Re: Professors shouldn't be allowed to do this

Postby Chandani » Mon Jan 17, 2011 6:13 pm UTC

We had a question on our math test (it was a team one so it wasn't that bad) which asked us to find a line parallel to two planes.
Easy, right?
The planes were perpendicular to each other.

...

I don't know if you can actually solve it or not, and since she hasn't graded the test yet. But on first glance, it really doesn't make much sense.

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Re: Professors shouldn't be allowed to do this

Postby mystictxe » Mon Jan 17, 2011 7:04 pm UTC

I find both of the questions to be perfectly valid. Self-doubt has nothing to do with it. If you know the material you know the material. Simple as that.

As to the poster above me, try the line that is their intersection.

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Re: Professors shouldn't be allowed to do this

Postby Chandani » Mon Jan 17, 2011 7:19 pm UTC

I don't think that would be rigth: a parallel line is one that doesn't intersect the planes, and the line of intersection is, well, the line of intersection.

My problem with the questions mentioned above (except my math question) is the implied expectations that go with the material. If it is a short answer or something which work needs to be shown, then you expect there to be something written down of substance. If I see a question like the above, when I am pretty sure that the answer is no, and no explanation is needed, then I always check with my teacher that there is no mistake. If they say no, then I address the question as written.

Of course, if I didn't know, I'm not sure how I would react.

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Re: Professors shouldn't be allowed to do this

Postby Angua » Mon Jan 17, 2011 7:23 pm UTC

Generally in my exams, it was always clear how many marks a question was for, that way you could judge the amount of detail required. Eg, if it was a question like the tungsten one, one mark would be yes or no, 2 marks would be yes/no and a sentence explaining, and more marks would require at least a couple of lines to answer.
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Re: Professors shouldn't be allowed to do this

Postby SlyReaper » Mon Jan 17, 2011 7:34 pm UTC

Chandani wrote:We had a question on our math test (it was a team one so it wasn't that bad) which asked us to find a line parallel to two planes.
Easy, right?
The planes were perpendicular to each other.

...

I don't know if you can actually solve it or not, and since she hasn't graded the test yet. But on first glance, it really doesn't make much sense.


Yeah, that's definitely solveable. You know the line where they intersect? Any line parallel to that intersection line (including the intersection line itself) will be parallel to both planes.
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Re: Professors shouldn't be allowed to do this

Postby Yakk » Mon Jan 17, 2011 7:46 pm UTC

The funny part is I'm having difficulty figuring out the mechanical technique in which it is harder to solve than any other case.

Now, the case where the two planes are parallel, the default mechanical technique (in 3 space) ends up having issues finding the line that is parallel to both, because it is expecting a solution space with fewer degrees of freedom, and responds to the extra degrees of freedom with a zero.
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Re: Professors shouldn't be allowed to do this

Postby Chandani » Mon Jan 17, 2011 7:58 pm UTC

Thanks for that. Obviously I should have practiced thinking in 3D more (or maybe the teacher should have addressed it a bit). Because I'm pretty sure you can't have a parallel line to two perpendicular lines in 2D. And when you're used to thinking like that, seeing the above problem is slightly offputting.

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Re: Professors shouldn't be allowed to do this

Postby achan1058 » Mon Jan 17, 2011 8:36 pm UTC

I do think that it's not a good way to pose a question. Intentionally misleading the students is almost never a good idea. It causes many problems, including but not limited to students who knows the answer but being mislead by your statement, students attempting to bring it up to the dean, etc.

Anyone who thinks self doubt doesn't matter should read upon the Milgram experiment or the Hofling hospital experiment. Authority can indeed make people override their (correct) judgment.

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Re: Professors shouldn't be allowed to do this

Postby Vaniver » Mon Jan 17, 2011 8:41 pm UTC

If those questions are effective at separating the students who understand the material from the students that don't, that is the only relevant measure of fairness. From your descriptions, that is the case- so not only should professors be allowed to do this, but they should do it more.

A set contains as much information as its complement- if you can explain everything, you can explain nothing. Knowledge is falsifiable.

Yakk wrote:The funny part is I'm having difficulty figuring out the mechanical technique in which it is harder to solve than any other case.

Now, the case where the two planes are parallel, the default mechanical technique (in 3 space) ends up having issues finding the line that is parallel to both, because it is expecting a solution space with fewer degrees of freedom, and responds to the extra degrees of freedom with a zero.
It seems to me if you do things the dumb way- i.e. start with the set of lines parallel to one plane, then subtract all the lines not parallel to the other plane- you come out of it fine. It's not as easy to write code for, but still doable (and if you're writing code, it's easy to put in a special case for when they're parallel).

achan1058 wrote:Authority can indeed make people override their (correct) judgment.
A characteristic for which students deserve to lose points.
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Re: Professors shouldn't be allowed to do this

Postby Yakk » Mon Jan 17, 2011 8:46 pm UTC

Of course self doubt matters, and authority can convince people to give into it.

It doesn't mean that a question that tests "how certain are you" is always bad.

Ie, imagine the question on a university math exam "Why would you expect, in the integers, that 1+1 is equal to three?"

Or "Why would you expect that the moon was made of green cheese?"

Nobody would expect to answer those "wrong". The difference is that this is a harder question -- but to someone who really knew the material, it would be just as "duh" as the above exam question.

One issue with the question is that it fails to describe very well what is expected. "You wouldn't" is the correct answer, and "becuase it isn't diamagnetic". A justification why it isn't diamagnetic isn't asked in the question. I guess a bunch of reasons saying why someone might expect it to be diamagnetic even though it isn't would be valid. Think of the "why would you expect 1+1 equals 3" -- what would be the right answer, and how would you embellish it? Beyond "it doesn't equal 3" the question is ambiguous.
Vaniver wrote:It seems to me if you do things the dumb way- i.e. start with the set of lines parallel to one plane, then subtract all the lines not parallel to the other plane- you come out of it fine. It's not as easy to write code for, but still doable (and if you're writing code, it's easy to put in a special case for when they're parallel).

You can write code that iterates over an uncountable set? :p That seems far from a dumb solution.

The obvious solution is to take the normals that define the orientation of the planes, and take their cross product. This (except when those two planes are parallel) gives you a direction vector for a line that is perpendicular to both planes.

If you do this with two parallel planes, you end up with zero as their cross product.
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Re: Professors shouldn't be allowed to do this

Postby Vaniver » Mon Jan 17, 2011 9:42 pm UTC

Yakk wrote:You can write code that iterates over an uncountable set? :p
Hey, I said it wasn't easy :P

It seems to me not difficult to compare two sets to see if they have any intersections given that the sets are both unit circles centered on the origin (but with arbitrary normal). It comes down to the same problem, but it knows what to do when the normals are identical.

Is there a reason you're not accepting something like the following, or are you just belaboring that you need to account for the special case, and its answer is a different type (that can still be collapsed to a satisfactory but non-unique answer)?

Code: Select all

def find_par_line(a, b)
  if ((c=a.cross_product(b)).length==0)
    return a.perp_line
  else
    return c
  end
end
(where you've written cross_product and perp_line to behave as expected)
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Re: Professors shouldn't be allowed to do this

Postby Yakk » Mon Jan 17, 2011 9:51 pm UTC

Sure. But you'll note that a student who learnt the mechanical "take the cross product of the two planes' normals to find a line perpendicular to both" would be stymied by two planes that are parallel.

When I saw the question, my brain hiccuped and said "well, maybe the posters problem is that the cross product came out zero, and thus the problem was insolvable by the known technique". But that didn't work. So I then tried to think up any mechanical technique that works with planes in general position[1] yet didn't work with two perpendicular planes, and couldn't find one.

I missed the "two perpendicular lines do not have one parallel to both" error the poster made. Clever on the part of the professor then -- checking to see if the students have managed to lose their 2d geometry rules.
Spoiler:
[1] I've been reading too much historical math recently, because I thought this was funny.
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Re: Professors shouldn't be allowed to do this

Postby Chandani » Mon Jan 17, 2011 10:08 pm UTC

On the other hand, my team eventually got to the correct solution (at least to the best of my memory), which makes me happy.

There was one other problem which bugged me, but I'm not going to bring it up here as to keep the thread a little bit more on topic.

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Re: Professors shouldn't be allowed to do this

Postby douglasm » Tue Jan 18, 2011 2:48 am UTC

Chandani wrote:Thanks for that. Obviously I should have practiced thinking in 3D more (or maybe the teacher should have addressed it a bit). Because I'm pretty sure you can't have a parallel line to two perpendicular lines in 2D. And when you're used to thinking like that, seeing the above problem is slightly offputting.

Ah, but the 3D analogy for that 2D impossibility is that you can't have a plane that is parallel to two other planes.

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Re: Professors shouldn't be allowed to do this

Postby Chandani » Tue Jan 18, 2011 2:53 am UTC

douglasm wrote:Ah, but the 3D analogy for that 2D impossibility is that you can't have a plane that is parallel to two perpendicular planes.

Made that a bit clearer. Since you can have three planes parallel to each other as long as the all the planes are parallel. As soon as two are penpendicular, then it doesn't work.

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Re: Professors shouldn't be allowed to do this

Postby douglasm » Tue Jan 18, 2011 1:23 pm UTC

It doesn't take the two planes being perpendicular to make parallel-to-both impossible. All you need is that they not be parallel.

In 3D space, a plane cannot be parallel to two other planes unless those two planes are themselves parallel to each other.

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Re: Professors shouldn't be allowed to do this

Postby ++$_ » Wed Jan 19, 2011 4:58 am UTC

I think this kind of question is really iffy. For example:
Why would you expect the chromatic number of a graph to be a bounded function of its girth?
Answer 1: Roughly speaking, all other things being equal, the colorings of a graph with higher girth are less restricted. So it is a reasonable hypothesis.

OR:

Answer 2: You wouldn't, because of Erdos's theorem on chromatic number and girth.

Either of these answers is reasonable. Answer 1 answers the question, and further explains why Erdos's theorem is a surprising result. Answer 2 demonstrates that you know about Erdos's theorem, but doesn't answer the question. How are you supposed to know which one the professor wants?

I think either answer is reasonable. If you aren't willing to accept both, then you shouldn't phrase the question that way.

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Re: Professors shouldn't be allowed to do this

Postby BurningLed » Wed Jan 19, 2011 9:50 pm UTC

That vaguely reminds me of http://xkcd.com/803/

On the test: "Planes fly because of _______"

"Newton's laws of physics, air pressure, and the angle of attack."

Whereas popular belief is that it's due to Bernoulli's principle.
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Re: Professors shouldn't be allowed to do this

Postby jmorgan3 » Wed Jan 19, 2011 10:06 pm UTC

To people
Vaniver wrote:If those questions are effective at separating the students who understand the material from the students that don't, that is the only relevant measure of fairness. From your descriptions, that is the case- so not only should professors be allowed to do this, but they should do it more.

Look at the actual wording of the question and the expected answer again:
lilturtle wrote:Question VII: Why would you expect Tungsten to be diamagnetic?

Correct Answer: You wouldn't.

If there truly is no reason to expect Tungsten to be diamagnetic, then the question does not have a correct answer. "You wouldn't" doesn't answer the question posed. "You wouldn't" is an answer to a different question, "Would you expect Tungsten to be diamagnetic?" . While a greater understanding of the material will help you realize what the professor is actually asking, it is still a case of http://xkcd.com/169/.
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Re: Professors shouldn't be allowed to do this

Postby torgos » Wed Jan 19, 2011 11:12 pm UTC

mystictxe wrote:I find both of the questions to be perfectly valid. Self-doubt has nothing to do with it. If you know the material you know the material. Simple as that.


While someone with a really deep understanding of the material would catch the trick question, the question is problematic in that it fails to distinguish between students who know absolutely nothing and students who would answer the question 'Would you expect Tungsten to be diamagnetic?' correctly. Even if I had been fairly confident that the answer to the latter question was 'no', I would probably have take the phrasing of the question to indicate that perhaps I was remembering incorrectly, and at best wasted a lot of time vainly trying to figure out why Tungsten would be diamagnetic.
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Re: Professors shouldn't be allowed to do this

Postby phlip » Thu Jan 20, 2011 12:43 am UTC

BurningLed wrote:That vaguely reminds me of http://xkcd.com/803/

On the test: "Planes fly because of _______"

"Newton's laws of physics, air pressure, and the angle of attack."

Whereas popular belief is that it's due to Bernoulli's principle.

It is due to Bernoulli's principle. Which is to say you can solve it with Bernoulli and get the same answer as if you solve it with Newton.

It's equal-transit-time that's the myth.

On topic: it's a standard trope of exams to have questions like "Given that thing A is true, solve question B." It is an unwritten rule in these situations that thing A is true, and the correct answer to question B follows from it. And that the expected answer only discusses question B, taking thing A as read... not questioning thing A at all. If I got this question in an exam, even if I was 100% sure that the assumption was false, I'd still assume the examiner made a mistake in the question, and try to answer the question I think they intended... with an answer starting "Tungsten is not a diamagnetic. However, for a material that is a diamagnetic, the signs are [etc]." and spend most of the answer in that second part. And if I wasn't 100% sure, I'd probably drop the first part, which is what the professor was apparently looking for.

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Re: Professors shouldn't be allowed to do this

Postby RebeccaRGB » Sat Jan 22, 2011 12:36 am UTC

I once had a professor who asked a multiple-choice question in which the first two answers were correct, the third was incorrect, and the last was "all of the above."

EVIL. EVIL. EVIL.

He was a douchebag in several other ways, as well. One of only two professors I've had that I didn't like.

I feel your pain, OP.

EDIT: At least he gave us the option of skipping the final and not having it count towards our grade. I had a B in that class, and naturally chose to skip the final because I just couldn't deal with that guy anymore.
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Re: Professors shouldn't be allowed to do this

Postby Ambermutt » Wed Feb 16, 2011 7:46 pm UTC

The main issue is that this is a trick question. It's kinda fuzzy because it does, technically, test your knowledge, even if it is phrased to force you to make a mistake. While I think it's cruel and misleading, it isn't unfair. It makes the students a little more likely to question these statements in the future, and with any luck, to have more confidence in their own knowledge.

On the other hand, some teachers take this "teaching the students to think" thing too far when they make students lose points over things completely unrelated to the subject. Example in the spoiler.

Spoiler:
One of my chemistry teachers gave us a multiple choice test. Normally, you mark the correct letter (A, B, C, D) with an X over it. That's what teachers have taught us since 1st grade. In the instructions, she specified that you had to mark it with an asterisk over the letter. Another time, it was a dot, another time by circling it. We (the students) reached the conclusion that if this went on long enough we would eventually get a test that said "Mark the appropriate choice with the Mona Lisa". Almost everyone messed it up the first time, and she really did mark down the points, even if the marked choice was correct.

Note: I don't mind if hidden in small print in the instructions it says "Add an asterisk next to your name for an extra point" (we got that one on a math test), because you can still get full credit for knowing the subject, it's when teachers decide that playing their dumb game is worth more than answering correctly that really annoys me.
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Re: Professors shouldn't be allowed to do this

Postby Kurushimi » Mon Feb 21, 2011 2:49 pm UTC

Yakk wrote:The funny part is I'm having difficulty figuring out the mechanical technique in which it is harder to solve than any other case.


This might be a weird method, but if the planes were given by equations like Ax + By + Cz = D, then we know that the vector (A, B, C) is perpendicular to that plane. Find the cross product of the two vectors perpendicular to the plane and you'll find a line parallel to both planes. And this method works as long as the planes aren't parallel.

I've been faced with questions like these before. When I find a question that seems to contradict what I know is true, I try to reason out why I know that thing is true. If I can't, I accept that I'm missing the question not because the question is tricky, but because I don't know all the material. If I can, I assume the test writer made some error, or maybe did it on purpose to trick me. Either way, if I have a logical explanation for the answer, I can't deny it.

Also, about those 98% of students that tried to explain why tungsten is diamagnetic, how exactly did they do this? How could they give any type of logical explanation to prove something that isn't true? Obviously their reasoning was faulty and they didn't catch this because they didn't understand the material.

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Re: Professors shouldn't be allowed to do this

Postby Yakk » Wed Feb 23, 2011 12:26 am UTC

Kurushimi wrote:
Yakk wrote:The funny part is I'm having difficulty figuring out the mechanical technique in which it is harder to solve than any other case.
This might be a weird method, but if the planes were given by equations like Ax + By + Cz = D, then we know that the vector (A, B, C) is perpendicular to that plane. Find the cross product of the two vectors perpendicular to the plane and you'll find a line parallel to both planes. And this method works as long as the planes aren't parallel.
My problem was finding a mechanical technique that didn't work when the two planes are perpendicular to each other.
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