- #1

ProfuselyQuarky

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Being a teacher of a higher level class only to discover that those you are teaching can't even do basic work sounds extremely disheartening.

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- Thread starter ProfuselyQuarky
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- #1

ProfuselyQuarky

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Being a teacher of a higher level class only to discover that those you are teaching can't even do basic work sounds extremely disheartening.

- #2

fresh_42

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The very first phrase of our constitution is: The dignity of man is untouchable. (We have a gender neutral word for man, though.)~~whole lot of~~too many mistakes, but while occasionally helping my fellow peers, I’ve seen really--it hurts to say it--awful mistakes that shouldn’t even be mistakes. Like, a 16-year-old not knowing how to use FOIL, or being unable to graph a parabola or circle. One time, I even saw this: ##(5\log)x=5(\log x)## … what does that even mean?? What makes it worse is that it’s not coming from students who plan to just get out of school as soon as possible--these mistakes come from people saying they want to go to a good university and pursue all these highly credited careers. I find it really sad. So I was wondering, for all you teachers/professors/academics … is that really how it is everywhere? Or am I just stuck with a “special” batch of people? If the former, do you just get frustrated and upset and let the student know? Do you ignore the mistakes and just not care?

Being a teacher of a higher level class only to discover that those you are teaching can't even do basic work sounds extremely disheartening.

One of my favorite bumper stickers I ever saw was: The stupidity of man is untouchable.

It's a truth and as you see right now on every news channel: stupidity doesn't prevent people from getting famous, successful or rich.

The first year at our universities is usually the toughest one because the difference to school is quite big. There has been a favorite path for students: signed up in macroeconomic → found too much math → changed to microeconomic → still math, ... → finally registered to study laws.

However, you may not forget that even good students have bad days or just make mistakes on carelessness or due to time pressure. There are some mentors here I really admire for their patience with my mistakes or those of others. I guess one has to get more experienced than a 16 year old can be to handle it with calm. For now: get a laugh at (by yourself, not to others). This way they are at least good for something.

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- #3

ProfuselyQuarky

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That's a comicThere has been a favorite path for students: signed up in macroeconomic → found too much math → changed to microeconomic → still math ... → finally registered to study laws.

(in a ... really sad way ...)

Oh, of course, I’m not denying that! Just the other day I found myself plotting a graph of lab data with the independent variable on the y-axis … and then I started analyzing the daft-looking data and completing the report (explaining all the possible errors affecting the conclusion) without the slightest idea on where I went wrong.However, you may not forget that even good students have bad days or just make mistakes on carelessness or due to time pressure.

*sigh* I don’t find funny. Forgetting how to find the slope of a line in 11th grade is not funny. Sure, I can playfully tease and you get a laugh from the others, but it’s still sadFor now: get a laugh at (by yourself, not to others). This way they are at least good for something.

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- #4

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So when the time of the test came, sure enough, a lot of them solved ##(x+2)^2 = x^2 + 4x + 4## correctly. I was happy. But then most of them also said ##(x+y)^3= x^3 + y^3##. Sigh

- #5

ProfuselyQuarky

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Do you find it depressing or do you simply ignore it? Are you one of those teachers who will yell in front of class telling everyone how disappointed you are or do you smile and make fun of it?So when the time of the test came, sure enough,a lot of themsolved ##(x+2)2=x2+4x+4(x+2)^2 = x^2 + 4x + 4## correctly. I was happy. But then most of them also said ##(x+y)3=x3+y3(x+y)^3= x^3 + y^3##. Sigh

There was once this person who was trying to solve a system of equations and he was supposed to use Gaussian elimination. I told him to make an augmented matrix to derive something in row-echelon form and then … he asked what a matrix was.

Doesn’t something like that bother you?

- #6

Astronuc

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Perhaps you mean or perhaps less concussivelySo when the time of the test came, sure enough, a lot of them solved (x+2)2=x2+4x+4(x+2)2=x2+4x+4(x+2)^2 = x^2 + 4x + 4 correctly. I was happy. But then most of them also said (x+y)3=x3+y3(x+y)3=x3+y3(x+y)^3= x^3 + y^3. Sigh

It didn't occur so some that ##(x+y)^3 = (x+y)^2(x+y)##

- #7

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As an old professor of mine used to say, if you're in a history class and you didn't do well in the 1500s, you can still do well in the 1600s. That's not the case with math, though. Students need to have it stressed that, yes, they do need to remember all this stuff. It's not something you can forget right after the test, because math is cumulative.

A lot of it, I think, occurs because many teachers teach math as a set of arbitrary rules for manipulating formulas into particular forms that look completely uninteresting to the layman. And, don't get me wrong, we do need to have those rules drilled into our heads until we get it right. But oh, how much more beautifully math could be taught.

- #8

blue_leaf77

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$$\frac{d\,f(x)}{dx} = \frac{f(x)}{x}$$

Strangely though, she demonstrated that unintended joke in front of the class but only a (very) few of us noticed that that was laughable. The majority of the class seemed to either agree with her work or didn't know themself what to be done with that problem. I thought if she had been given other non-trivial mathematical expressions and was asked to simplify it, she might set up a new trend of math meme.

Such people are basically lacking in the information needed to properly tackle the problem they are given, at the same time they use "intuition" based on what they already have learned - a misuse of concept.

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She nearly cried when informed of her mistake a few days later.

- #10

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She nearly cried when informed of her mistake a few days later.

To be fair, degrees are stupid.

- #11

cnh1995

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My maths professor once carelessly stroke out variables and messed up the entire solution. While simplifying an expression, he stroke out the x's in log(x)/(x) and wrote it as log(x)/x=log(1)=0. Coincidently, the expected final answer was also 0, so he didn't realize his mistake until one of us brought it to his notice. He still does such things. He's famous among the students for doing such silly things and has earned a nickname too!I don't remember the particular form of f(x)f(x)f(x). Then she nonchalantly stroke out the ddd's in the numerator and denominator as if it acts like a multiplication, and ended up with a meme-type equation

- #12

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[tex]\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0[/tex]

From: http://www.math.vanderbilt.edu/~schectex/commerrs/

- #13

collinsmark

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What in the... .. That's just <loss for words>. I don't even know where to begin.Some student actually turned this in on an exam, and expected partial credit because he had the right answer:

[tex]\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0[/tex]

- #14

fresh_42

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I can't help but admire the artistic creativity. I love modern art.[tex]\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0[/tex]

I mean, NASA once crashed a Mars probe because Lockheed and them used different systems of unities ...

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- #16

fresh_42

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... or why multiplication points not always should be omitted, resp. conventions about notation has to be clearly defined.

- #17

ProfuselyQuarky

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It's hard to believe that that is a real mistake some one made ...

To be fair, the use of radians in daily measurements is stupid.To be fair, degrees are stupid.

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It's hard to believe that that is a real mistake some one made ...

I don't know that anyone's ever actually done that (though you never know...) but it's more of an example of how just because a method gives the correct result does not mean that method will always work.

- #19

fresh_42

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Why? ##\require{cancel} \frac{64}{16} = \frac{6 \cdot 4}{1 \cdot 6} = \frac{\cancel{6} \cdot 4}{1 \cdot \cancel{6}} = \frac{4}{1} = 4##It's hard to believe that that is a real mistake someone made ...

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To be fair, the use of radians in daily measurements is stupid.

Burn the heretic!

- #21

ProfuselyQuarky

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Haha. Let's see ...Why? ##\require{cancel} \frac{64}{16} = \frac{6 \cdot 4}{1 \cdot 6} = \frac{\cancel{6} \cdot 4}{1 \cdot \cancel{6}} = \frac{4}{1} = 4##

##\frac {63}{9}=\frac {6\cdot3}{3\cdot3}=\frac {\cancel{3}\cdot\cancel{3}\cdot2}{\cancel {3}\cdot\cancel{3}}=2##

Ah, accuracy.

I'm willing to die a martyr for what I believeBurn the heretic!

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- #22

fresh_42

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Exactly. Don't mess with Leonhard!Burn the heretic!

- #23

fresh_42

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##\frac{63}{9} ≡ \frac{3}{4} ≡ 3 \cdot 4 ≡ 12 ≡ 2 \mod 5 ## - Only a matter of perspectiveHaha. Let's see ...

##\frac {63}{9}=\frac {6\cdot3}{3\cdot3}=\frac {\cancel{3}\cdot\cancel{3}\cdot2}{\cancel {3}\cdot\cancel{3}}=2##

Ah, accuracy.

- #24

vela

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I can believe the part of the student wanting partial credit. I find it hard to believe anyone would actually turn that in! How did they end up in a calculus class?

[tex]\int_0^{2\pi}\cos x dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin(2\pi)}{2\pi} - \frac{\sin(0)}{0} = \sin - \sin = 0[/tex]

From: http://www.math.vanderbilt.edu/~schectex/commerrs/

- #25

DrGreg

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To solve: $$

\frac{dy}{dx} = y

$$Integrate:$$

y = \int y + C

$$Rearrange:$$

y - \int y = C

$$Factorise:$$

\left(1 - \int \right) y = C

$$Divide:$$

y = \frac{C}{1 - \int}

$$Expand the geometric series:$$

\begin{align*}

y &= C + \int C + \int^2 C + \int^3 C + \dots \\

&= C + \int C + \iint C + \iiint C + \dots \\

&= C + Cx + \frac{Cx^2}{2} + \frac{Cx^3}{3!} + \dots \\

&= Ce^x

\end{align*}

$$which is the correct answer.

Of course the method is nonsense for a 15-year old, but years later when I studied functional analysis and operator theory, I realised the method is essentially correct (if you rewrite it with more appropriate symbols, terminology and apply the correct terms and conditions). I don't know if my maths teacher had known this or not.

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