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The Most Common Errors in Undergraduate Mathematics (2009)

math.vanderbilt.edu

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Re: The Most Common Errors in Undergraduate Mathematics (2009)

#31

Post by voxl »

tgb wrote: post #6

The "working backwards" one was what I always noticed students doing. It's super frustrating as a teacher since they're simultaneously so close to being right (when they manage to avoid an irreversible step) and yet also have completely misunderstood a basic idea in what it means to even attempt to prove something.

"Working backwards" is a completely valid method of proof, used all the time in automated reasoning. If a student successfully reasons backwards then there is no issue, it is a proof.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#32

Post by Jtsummers »

ARandomerDude wrote: post #23
konjin wrote: post #12

Earlier quoted context omitted.

Extra fine Japanese fountain pens are the solution to all your problems.

They're great...just not for math. Use a decent pencil instead, like a Graphgear 1000 and some HB lead.

Pens are fine for math. I often used a fine point gel pen in college. However, you have to have a high degree of confidence in what you're writing. If you make a lot of mistakes (either actual mistakes or just wrote down something incorrectly or with a misspelling), then pencils are definitely better.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#33

Post by MereInterest »

smabie wrote: post #11
whimsicalism wrote: post #8

Earlier quoted context omitted.

I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.

that seems like a ton of work, especially for problem sets

For the most part, just a matter of practice. One advantage that it has is that you have less incentive to make multiple simplifications in a single step. Copy a line, make a rearrangement. Copy a line, combine two like terms. Since you aren't re-writing everything that is unchanged, there isn't as much of a cost to showing your steps.

I did get a rather funny look from a professor in grad school when I turned in a fully typeset document on a timed take-home exam.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#34

Post by commandlinefan »

chapium wrote: post #28

Most of these appear to be errors caused by stress or tiredness.

That's what my (junior in high school) son keeps saying when he makes simple arithmetic errors that cost him points on tests. I disagree, actually - these mistakes are made by lack of practice. If you've practiced solving enough integrals, it doesn't really matter how tired you are, you're going to get the right answer just as you won't read words incorrectly if you're tired.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#35

Post by LanceH »

barrenko wrote: post #29
LanceH wrote: post #5

Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…

I went from something like 0.5 to 0.4 and then 0.2. Now I'm finding 0.3 pens ideal.

I have 0.28 and 0.38 and I probably choose based on the paper. If I choose one pen, it's the Uniball Signo DX 0.38. That seems enough for cheap paper and precise enough that everything is legible without extreme care.

If I were doing math I would prefer to use the 0.28 version and make sure my paper is good. Anything smaller and it feels like I'm drawing and not writing. I think the 0.2's are mostly used for art.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#36

Post by vulcan01 »

smabie wrote: post #11
whimsicalism wrote: post #8

Earlier quoted context omitted.

I stopped handwriting math to turn in my freshman year of college, LaTex was just too good looking.

that seems like a ton of work, especially for problem sets

I copied (most of) my method for taking live LaTeX notes from this guy.

https://castel.dev/post/lecture-notes-1/

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#37

Post by mattbk1 »

commandlinefan wrote: post #34
chapium wrote: post #28

Most of these appear to be errors caused by stress or tiredness.

That's what my (junior in high school) son keeps saying when he makes simple arithmetic errors that cost him points on tests. I disagree, actually - these mistakes are made by lack of practice. If you've practiced solving enough integrals, it doesn't really matter how tired you are, you're going to get the right answer just as you won't read words incorrectly if you're tired.

I read words incorrectly when I'm tired. Is this abnormal?

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#38

Post by whimsicalism »

vulcan01 wrote: post #36
smabie wrote: post #11

Earlier quoted context omitted.

that seems like a ton of work, especially for problem sets

I copied (most of) my method for taking live LaTeX notes from this guy. https://castel.dev/post/lecture-notes-1/

I love this setup! I mostly used Macdown in college (and now obsidian.md).

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#39

Post by cgriswald »

I’ve gone so far as to explain in my answer why a question is ambiguous and to give answers for the multiple interpretations.

I had one class that I dropped for many, many reasons, and one of the reasons was frequent ambiguous questions when the tests were all online and multiple choice. Some questions were ambiguous in a way that made the T/F answer invert depending on how you read the question. (To be clear, these were not trick questions that required precise reading. They were just bad questions.) Students never knew why they got the answer wrong unless they asked, which few did. A fair number of students started believing the opposite of the truth as a result of getting a question wrong on the test due to the ambiguity.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#40

Post by opnitro »

woliveirajr wrote: post #18
LanceH wrote: post #5

Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…

When I was 9 I failed some question about fractions because I saw one 6 and it was just a bad written 5. At that age it took me a while to understand where the problem was and too late to ask my teacher to reconsider it. Well, was so intense that I remember it until today, 30 and some years later.

Ever since I failed similarly I write my sevens with a line through them to prevent them being confused for ones
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