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Author Topic: Random Stuff  (Read 1116216 times)

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SirPeebles

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Re: Random Stuff
« Reply #3025 on: May 03, 2014, 07:39:21 pm »
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The example I gave here was just for illustration.  The problem I gave them asked them to show that a certain function is a solution to a given differential equation. 
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sudgy

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Re: Random Stuff
« Reply #3026 on: May 03, 2014, 07:44:49 pm »
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I think the problem is that they haven't done things like you think they have when they haven't.

The don't think it be like it is, but it do.

Oops, I messed up that sentence somewhat.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

SirPeebles

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Re: Random Stuff
« Reply #3027 on: May 03, 2014, 08:17:39 pm »
+9

Bah, enough of that math stuff.  Here are some jokes.  And to make them funnier some British guy interrupts to explain them.

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Voltaire

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Re: Random Stuff
« Reply #3028 on: May 03, 2014, 09:32:43 pm »
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I work at a board game store now!

Nice!
Please hide all of thier copies of Fluxx in a fire outside

Hey! I collect Fluxx!*

*by collect I mean, I drunkenly lost my girlfriend's base game**, with tons of rare promos and the original versions of many cards, back when they were promos first, and have dedicated myself to re-creating the lost deck with the original versions of these cards. Anybody have the promo version of Final Card Random from 3.0?

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Titandrake

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Re: Random Stuff
« Reply #3029 on: May 04, 2014, 02:13:44 am »
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I don't think any Twitch Plays Pokemon stuff needs its own thread anymore.

I checked in on the stream, and it seems like right now they're playing Platinum. However, there's also a side game of Pokemon Stadium 2. Everyone starts with $1000, it shows 2 teams of Pokemon, you place a bet, and then they randomly fight. Only restriction is that if you would go below $100, you stay at $100 instead.

This might be the only reason I watch the stream now.
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Re: Random Stuff
« Reply #3030 on: May 04, 2014, 03:25:41 am »
0

I don't think any Twitch Plays Pokemon stuff needs its own thread anymore.

I checked in on the stream, and it seems like right now they're playing Platinum. However, there's also a side game of Pokemon Stadium 2. Everyone starts with $1000, it shows 2 teams of Pokemon, you place a bet, and then they randomly fight. Only restriction is that if you would go below $100, you stay at $100 instead.

This might be the only reason I watch the stream now.
saltybet + tpp = ??
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Thisisnotasmile

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Re: Random Stuff
« Reply #3031 on: May 04, 2014, 05:53:34 am »
0

Bah, enough of that math stuff.  Here are some jokes.  And to make them funnier some British guy interrupts to explain them.

People from Australia are referred to as "British" now?
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Awaclus

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Re: Random Stuff
« Reply #3032 on: May 04, 2014, 06:33:02 am »
+7

Bah, enough of that math stuff.  Here are some jokes.  And to make them funnier some British guy interrupts to explain them.

People from Australia are referred to as "British" now?
He probably meant to type "brutish", it's an easy mistake to make since U and I are right next to each other on the keyboard. By the way, I just realized that the last part of my previous sentence sounds a lot more romantic than I intended when you read it out loud.
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Re: Random Stuff
« Reply #3033 on: May 04, 2014, 06:46:39 am »
0

Bah, enough of that math stuff.  Here are some jokes.  And to make them funnier some British guy interrupts to explain them.

People from Australia are referred to as "British" now?

Ruled by a British Queen!
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Ozle

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Re: Random Stuff
« Reply #3034 on: May 04, 2014, 06:47:37 am »
+2

I work at a board game store now!

Nice!
Please hide all of thier copies of Fluxx in a fire outside

Hey! I collect Fluxx!*

*by collect I mean, I drunkenly lost my girlfriend's base game**, with tons of rare promos and the original versions of many cards, back when they were promos first, and have dedicated myself to re-creating the lost deck with the original versions of these cards. Anybody have the promo version of Final Card Random from 3.0?

**she doesn't actually care that this happened

Oh dear.
I have removed the +1 I gave you and will be withholding future +1's until you learn the error of your ways.
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Polk5440

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Re: Random Stuff
« Reply #3035 on: May 04, 2014, 08:57:26 am »
0

It's definitely ugly, but lines 2, 3 and 4 are equivalent to each other, so they are demonstrating what you are asking.

If I really wanted to do it this way for some reason, I'd say "let's assume that 2 is a solution (line 2). Equivalently, we have (line 3). Which is equivalent to 2=2, which is always right. Hence, our assumption was right."

I guess you would rather see "x^2 - x - 4/x = ... = 0" ?

It's not just ugly.  They are not demonstrating what is asked, unless perhaps they were to explicitly indicate lines 2, 3, and 4 are equivalent.  Unless the student indicates otherwise, the convention is that they are indicating that line 1 implies line 2, line 2 implies line 3, and so forth.  One student even put a "therefore" symbol in the last line, which is especially egregious.

What I would like to see is

x^2 - x = 2^2 - 2 = 4 - 2 = 2
4/x = 4/2 = 2
Therefore x^2 - x = 4/x when x=2.

But what they have written is most certainly not correct, and I don't know where this habit comes from.

You have not been clear that you are expecting a higher level of formality when presenting answers. And you should be clear that the point of these stupid questions is to practice writing in a higher level of formality, not to review basic high school algebra.

What the students write down makes clear that they plugged in numbers and did enough calculations that they convinced themselves that 2 is a solution. They have not formally written out the verification process, though. It's scratch work, not proof. The "bad habit" comes from not having to write out formal proofs for stupid things.

But it really does matter.  Like for verifying trig identities

But this is what you have to teach. Why it matters. And convince them that the extra work it takes to formally write it out is sometimes needed. Because often, it's not.
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Polk5440

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Re: Random Stuff
« Reply #3036 on: May 04, 2014, 09:00:42 am »
+1

The example I gave here was just for illustration.  The problem I gave them asked them to show that a certain function is a solution to a given differential equation.

Then it makes even more sense why they write what they do. If it's not obvious, then they may simply be working from both sides of the equation until they get to a point in which they convince themselves the expressions are equal. They don't rewrite their scratch work formally.

Just like a programmer has to convince people of the necessity of cleaning and commenting code, a mathematician must convince people of the necessity of writing formal statements.
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SirPeebles

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Re: Random Stuff
« Reply #3037 on: May 04, 2014, 09:11:07 am »
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But this is what you have to teach. Why it matters. And convince them that the extra work it takes to formally write it out is sometimes needed. Because often, it's not.

There's a limit to what you can teach someone in one semester.  I did teach them what solutions to differential equations are.  I did numerous examples.  I taught them about solutions to linear systems of algebraic equations and to linear systems of differential equations.  I taught them about eigenvectors, eigenvalues, Laplace transforms and so on.  How much time am I supposed to devote to explain why circular arguments are not valid? They've already taken half a dozen other math classes at university in addition to years of math classes in high school.  Plus just everyday experience and logic, including in other courses.  If they don't already grasp that circular reasoning is flawed, what am I supposed to do about it?  Maybe I'm just an awful teacher.
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Polk5440

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Re: Random Stuff
« Reply #3038 on: May 04, 2014, 09:28:33 am »
0

Here's the thought process and the scratch they write down:

Here's my starting equation:
x^2 - x = 4/x
I am asked to verify 2 is a solution. Let's plug it in. Are the two sides equal?
2^2 - 2 ?=? 4/2
I don't know. It's not obvious. Let's simplify each side a little. Are the two sides equal?
4 - 2 ?=? 2
I don't know. It's not obvious. Let's simplify each side a little. Are the two sides equal?
2 ?=? 2
YES. It's obvious to me. I am convinced 2 is a solution. BIG CHECKMARK.

If they are doing it right, they are THINKING 2^2-2=4-2=2 and 4/2=2=2, but that is not what they are writing down. They are thinking, okay, I can go down the left hand side and up the right hand side.

For your other example, they are really unsure and start applying functions to both sides that might not be invertible, causing problems.

sqt(9) ?=? 3
Are they equal? I don't know. It's not obvious. Hmmm. I don't know how to take the square root of 9. Let's square both sides, instead. If the square is equal the square root must be equal, right?
9 ?=? 9
YES! So, I can start with 9 = 9 and go up the page to what we were asked to verify. BIG CHECKMARK.


If you can give them an example of where this informal scratch work actually leads "verifying" an incorrect answer, then that might be a good example to share.
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Polk5440

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Re: Random Stuff
« Reply #3039 on: May 04, 2014, 09:47:57 am »
+1

But this is what you have to teach. Why it matters. And convince them that the extra work it takes to formally write it out is sometimes needed. Because often, it's not.

There's a limit to what you can teach someone in one semester.  I did teach them what solutions to differential equations are.  I did numerous examples.  I taught them about solutions to linear systems of algebraic equations and to linear systems of differential equations.  I taught them about eigenvectors, eigenvalues, Laplace transforms and so on.  How much time am I supposed to devote to explain why circular arguments are not valid? They've already taken half a dozen other math classes at university in addition to years of math classes in high school.  Plus just everyday experience and logic, including in other courses.  If they don't already grasp that circular reasoning is flawed, what am I supposed to do about it? 

That's fair.

If you are doing examples, then maybe the only time you should have to take is the time to stop after doing an example and saying, "This is the level of formality I expect from you on your homework. If you write [stupid example] then this is how I read it [circular logic]. Please write it out like this [point to good example]." The problem then probably isn't they don't know, but that they choose not to spend the time to write down clean answers if they think they can get away with it. It saves them time. If they don't understand what you are asking, then, as you say, it's not part of your course, so to what extent should you spend time on it? They can ask in office hours, maybe.

It just seems like if the problem comes up year after year with a large number of students, there should be something easy and relatively time-cheap that you can do to head off the problems so you don't waste office hours or your evenings marking up all these incorrect assignments every year.

Have you voiced concern to your colleagues who teach the lower level courses?
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qmech

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Re: Random Stuff
« Reply #3040 on: May 04, 2014, 09:53:10 am »
0

sqt(9) ?=? 3
Are they equal? I don't know. It's not obvious. Hmmm. I don't know how to take the square root of 9. Let's square both sides, instead. If the square is equal the square root must be equal, right?
9 ?=? 9
YES! So, I can start with 9 = 9 and go up the page to what we were asked to verify. BIG CHECKMARK.

I agree with most of what you're saying, as I would certainly verify a solution by plugging it in and rearranging to get 0=0.  But this example of SirPeebles' is very different, as the squaring is irreversible.  I'd happily accept the first example, but wouldn't accept a "verification" that lost information by squaring.
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Polk5440

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Re: Random Stuff
« Reply #3041 on: May 04, 2014, 10:09:31 am »
0

sqt(9) ?=? 3
Are they equal? I don't know. It's not obvious. Hmmm. I don't know how to take the square root of 9. Let's square both sides, instead. If the square is equal the square root must be equal, right?
9 ?=? 9
YES! So, I can start with 9 = 9 and go up the page to what we were asked to verify. BIG CHECKMARK.

I agree with most of what you're saying, as I would certainly verify a solution by plugging it in and rearranging to get 0=0.  But this example of SirPeebles' is very different, as the squaring is irreversible.  I'd happily accept the first example, but wouldn't accept a "verification" that lost information by squaring.

Yes, this is a potential example of what can go wrong.

Edit: something like this makes your point even better:

does -3 ?=? 3
I don't know. Let's apply absolute value.
3 ?=? 3
YES! Solution verified! (Except not.... )
« Last Edit: May 04, 2014, 10:13:05 am by Polk5440 »
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sudgy

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Re: Random Stuff
« Reply #3042 on: May 04, 2014, 11:13:48 am »
0

But this is what you have to teach. Why it matters. And convince them that the extra work it takes to formally write it out is sometimes needed. Because often, it's not.

There's a limit to what you can teach someone in one semester.  I did teach them what solutions to differential equations are.  I did numerous examples.  I taught them about solutions to linear systems of algebraic equations and to linear systems of differential equations.  I taught them about eigenvectors, eigenvalues, Laplace transforms and so on.  How much time am I supposed to devote to explain why circular arguments are not valid? They've already taken half a dozen other math classes at university in addition to years of math classes in high school.  Plus just everyday experience and logic, including in other courses.  If they don't already grasp that circular reasoning is flawed, what am I supposed to do about it?  Maybe I'm just an awful teacher.

Not telling them the level of formality you want, then marking them wrong on it, is similar to not teaching them how to do all of these things you just mentioned, then marking them wrong on it because they didn't know how.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Ozle

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Re: Random Stuff
« Reply #3043 on: May 04, 2014, 11:25:40 am »
+2

TL:DR summary - Maths stuff
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SirPeebles

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Re: Random Stuff
« Reply #3044 on: May 04, 2014, 11:32:50 am »
+1

It isn't a level of formality thing though.  I'm not looking for anything particularly formal or precisely worded.  But the underlying logical structure of what they've written down is

"I want to prove P.  If P is true, then 2=2.  2=2 is true, therefore P is true."

Maybe that's not what the reasoning in their head is saying, but I'm not sure.  Maybe it is clear to you, but many students approach these things quite mechanically and are unable to articulate the reasoning when pressed.  All I can go by is what is written down.  Again, I am not looking for any fancy notation or style.  But the underlying structure of the written argument needs to be valid.  It's not a trick question or anything. Nor is about level of formality.

Honestly I'm rather taken aback by the resistance I've found here.
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heron

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Re: Random Stuff
« Reply #3045 on: May 04, 2014, 11:35:44 am »
0

If you just change that to:

P is true if and only if 2=2. 2=2 is true, therefore P is true.

Then it works fine. So I suppose the students need to clarify their argument a little more.
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Re: Random Stuff
« Reply #3046 on: May 04, 2014, 11:41:07 am »
0

I work at a board game store now!

Nice!
Please hide all of thier copies of Fluxx in a fire outside

Hey! I collect Fluxx!*

*by collect I mean, I drunkenly lost my girlfriend's base game**, with tons of rare promos and the original versions of many cards, back when they were promos first, and have dedicated myself to re-creating the lost deck with the original versions of these cards. Anybody have the promo version of Final Card Random from 3.0?

**she doesn't actually care that this happened

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sudgy

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Re: Random Stuff
« Reply #3047 on: May 04, 2014, 11:59:37 am »
0

I think (at least what I would think they are thinking) is "If P is true, and I use that in a situation, I should be able to get another statement which is obviously true."

[checking this]

"P is true because when you assume P is true you get another statement which is true."

If P wasn't true, then 2 != 2, or such nonsense.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

qmech

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Re: Random Stuff
« Reply #3048 on: May 04, 2014, 12:06:47 pm »
0

I think (at least what I would think they are thinking) is "If P is true, and I use that in a situation, I should be able to get another statement which is obviously true."

[checking this]

"P is true because when you assume P is true you get another statement which is true."

If P wasn't true, then 2 != 2, or such nonsense.

If this is the thought process then SirPeebles is right to be concerned.
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SirPeebles

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Re: Random Stuff
« Reply #3049 on: May 04, 2014, 12:13:53 pm »
+1

I think (at least what I would think they are thinking) is "If P is true, and I use that in a situation, I should be able to get another statement which is obviously true."

[checking this]

"P is true because when you assume P is true you get another statement which is true."

If P wasn't true, then 2 != 2, or such nonsense.

Exactly.  I'm afraid that some of them may be using the reasoning you've described.  It is important to correct this when it pops up, even if it is only resulting from sloppiness.

And by the way, I'm just marking them wrong on one problem.  It's not like I'm failing them and petitioning that they be expelled from the university or anything.  Sometimes a student needs the concreteness of their answer being marked wrong before they really start questioning what they think they already know.  I can go on in lecture as much as I want about the proper way of verifying solutions, but I find that students have this issue ingrained already and just zone out during such lectures, assuring themselves that they already know how to solve equations.
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