Failing basic arithmethics issue+coping with such failure

[PerchloricAcid]

Had a test in mathematical physics today and didn't manage to finish it in time.
The idea was pretty basic (Gram Schmidt orthonormalization), and as soon as I had seen the problem, I knew how to solve it. Alas, I made a few calculation mistakes (addition and multiplication) during the process, and after locating the mistakes and correcting them, I was left with insufficient time to finish.

Unfortunately, this isn't the first time this kind of problem occurred to me. It seems to me that I have had this basic calculation problem since ever. Sometimes the trouble starts even before the calculation: while rewriting the problem to the piece of paper I calculate on, I make a mistake (e. g. instead of "solve 3x+5=2" I write "solve 3x-5=2"). Today I paid special attention attempting to prevent this, but I actually made that mistake! I did copy the values of a certain matrix correctly to my paper, but whilst using the matrix, I somehow "lost" the coefficient that was supposed to go along with it. Halfway during the process, I realized it and corrected it. Later, during work, I made several basic addition and multiplication mistakes.
So, all in all, I didn't make it.

I am tempted to say that we were given insufficient time, but there were students that were able to do it correctly in time. Therefore, I have a problem. I am aware of it, and I try to prevent these mistakes from happening every time, but too often I don't succeed. I would like to hear advice from fellow members of the community.

1) What to do to get rid of this problem permanently?

As a consequence of this failure, my self-esteem went kinda down. I mean, last year I was among the best students (avg grade 10.00 out of 10.00), this year it also seems that I have sufficient mental capabilities to grasp the concepts, but I keep making these stupid basic mistakes over and over. Will I ever be able to overcome this shit? What if I won't? What if I miss an opportunity somewhere someday because of a problem of this kind (e. g. some kind of application test)? ... Will I be a good [theoretical] physicist someday?

2) What to do to keep my self-esteem stable while I don't solve my problem?


Regarding 1), I figured that the cause of my problem might be lack of practice. Honestly, during a large part of my education, while doing problem solving at home, I made sure I know the concept and derivation of all formulae, but used wolframalpha.com or a calculator to execute calculation. So, I thought: "hmm, my skill of performing basic numerical calculations might increase if I did a simple problem on a daily basis, e. g. multiply two 4x4 matrices every morning". Does this make sense to you guys?
Regarding 2), this kind of failure doesn't make me feel this insecure every time it happens, but sometimes, such as today, it does. I tried to speak to myself rationally, explain to myself that I did know HOW to do it but failed to execute the calculation, and that that means nothing about my intelligence, that there is time to improve (how?), that this test may not affect my grade at all (I have another opportunity in a few months), etc... It didn't really help. I'm demotivated, I feel like a total noob, and I'm even thinking of not showing up on some other tests. I would really like to stop this stream of negative and counterproductive thoughts. It's stupid.

Thanks for reading and thanks in advance for sharing advice. I'm totally in need of consolation and even more in need of a way to solve this stupid problem. And yeah, a self-esteem boost might not be bad either

Cheers!

[Yakk]

May I note that you also failed in your test taking skills.

In particular, you should be willing to put down questions. If you discover a mistake, write down that you made a mistake, then go on to the next question rather than "not finish" the test. The goal is to avoid being "trapped" by an overly expensive fix caused by a minor error. In many contexts, the marks you'd get from trying gram-schmidt orthonomalization, making a mistake during it, pointing out where you made the mistake, then noting "don't have time to fix it" would be relatively high. And the marks you get from a blank answer to a question would be relatively low.

Prioritize heavily, and always. Note that this "skim over the test, answer easy questions first, halt if you run into a roadblock" also has the advantage of giving you more time to think about hard problems without sitting there chewing at your pencil.

Second, you could try structuring your work in a way that allows for easier later correction. Ie, suppose you have a matrix with a coefficient. Mark the point where you are trying to solve the matrix plus coefficient with a symbol. You are about to do a bunch of algebra on the matrix. Instead of doing it inline and losing the thread of your proof, create a "lemma" or "sub-calcuation" that occurs elsewhere. Refer to this sub-calculation by name, and insert the answer on the next line.

By branching off intense calculation to sub-problems, and keeping the main flow of your math clean, you can both error-correct the sub-problems (mostly) independently and check for logic errors in your main path separately. Plus the mathematics becomes easier for the marker to read (instead of being an unending stream of symbol manipulation), and your errors seem more minor if the structure is really clear and correct. This doesn't always work -- there are some cases where the manipulation at the highest level depends on really tiny details at the low level, but in many kinds of problems it should help with reliability and speed of error correction. Heck, you might already be doing this.

Third, the more mathematical education I got, the worse I got at multiplying and adding numbers and symbols reliably.

[PerchloricAcid]

In particular, you should be willing to put down questions. If you discover a mistake, write down that you made a mistake, then go on to the next question rather than "not finish" the test. The goal is to avoid being "trapped" by an overly expensive fix caused by a minor error. In many contexts, the marks you'd get from trying gram-schmidt orthonomalization, making a mistake during it, pointing out where you made the mistake, then noting "don't have time to fix it" would be relatively high. And the marks you get from a blank answer to a question would be relatively low.

Well, that wasn't really possible. We had only one problem, and 4 vectors in R^4. I did the first two correctly and messed the third one up, and when I figured there wasn't time to finish, I wrote the equation for the fourth with a blank space wherever something using the third vector was to be written (the form was e4=x4-____-(e2,x4)e2-(e1,x4)e1, because I messed up e3). So, I did this what you suggested as much as I see was possible, but the problem is that the teacher himself said that the calculation was the most important part.

I branched the calculation, e.g. calculated all the (ei,xj)ei 's elsewhere so I could refer to them in the main formula.

So, yes, I was already doing all that but apparently it's not enough
Thanks though

Btw, the results came out. I got 15/25. Better than expected, but that doesn't change that this problem of mine still exists.

[aoeu]

Regarding 1), I figured that the cause of my problem might be lack of practice.

Solve more of the problems and your error rate should go down and you become faster at them. If there are other ways to get better nobody told me about them.

[PerchloricAcid]

Yeah, basically that's what I intend to do. Hope it will be enough. Not sure, though.

[ConMan]

Making mistakes like that is horribly common, no matter what your mathematical skills are like - I did it a lot, although I usually caught the errors reasonably quickly, and my brother was known for losing a not-insignificant number of marks to similar errors. Practice will definitely help. Try practicing both with and without time limits - sometimes the stress of a limit is what causes you to make more mistakes, so it can help to feel more comfortable with the content first and then introduce more pressure.

[PerchloricAcid]

Try practicing both with and without time limits - sometimes the stress of a limit is what causes you to make more mistakes, so it can help to feel more comfortable with the content first and then introduce more pressure.

Thanks, this is a GREAT suggestion!
You're completely right, I tend to freak out when I have a time limit. This seems like a fine way to overcome it.

[Whizzkid1024]

Hello, a suggestion my math teacher in high school gave me to cope with stress, is doing 2 minutes of meditation/breathing exercise before starting te test (like, cleaning your head from stress, just channeling the stress out of your body) and I must say, that method works for me, stimulates improvisation in math and physics for example now i'm known as the least stressed out person during exams and still having sufficient grades (passed all subjects from the first go last year). I hope it helps...

[Dopefish]

It seems that basic arithmetic errors become far more common the further you go in math. (I'm pretty sure theres a PHDcomic to that effect too.)

I think theres two main reasons, the first being that you get so used with wrestling with the 'hard' concepts and just using wolfram for the grunt work (further fuelled by the fact that unlike high school, CAS's are pretty much fair game in later years) that you get rusty, and that can probably be fixed by spending time actually doing the 'easy' stuff more regularly.

The other thing I think is an issue is that people tend to sleep deprive themselves in the process of actually coming to grips with the hard stuff, and the amount of sleep I get seems to be strongly correlated with my ability to do basic math. I end up staying up way too late doing a 'hard' assignment, and end up tired. I'll then either do the basic math and fail at it, or not trust myself and use wolfram which just fuels the first issue. So again, sleep when tired. It's easy to lie awake at night pondering the details of an abstract proof, and that'll probably help with the proof, but you will end up tired and that's when the silly mistakes pour in.


As for coping...I just reassure myself that it is simply a matter of making stupid mistakes and I still am (as) smart (as I felt I was before seeing my mark). Having something like sleep dep to blame rather then my own stupidity works well, and also talking to classmates and getting a qualitative feel for where you stand in terms of relative ability can help too. I can think of at least one person who I'm quite confident I have a better understanding of the material then, however their numerical grades tend to be better on the basis of them making less sloppy mistakes. Grades aren't a big deal in the long run (within reason), and by talking people you can generally conclude that your mark wasn't representitive of your ability, on the basis of you getting lower than <inferior person>. (This of course works best if you're sufficiently arrogant as to make those judgements, but if you're used to 100%'s that doesn't seem like a huge leap.)

[jmorgan3]

It seems that basic arithmetic errors become far more common the further you go in math. (I'm pretty sure theres a PHDcomic to that effect too.)

Indeed.

[PerchloricAcid]

So, uh. It's been some time since I've complained about this issue.
I haven't actually been working on this problem on a daily basis, but, I did, in fact, do a lot of calculations in order to improve. I had my final exam in this subject two days ago. I've thought I'd done it perfectly.
However, I quite much fucked up one of the problems.
I saw the results and thought: "wait, wtf? I'd done this correctly!" Then I tried to solve the problem again, at home. I got the same result that I'd gotten on the test. I was thinking "like, wtf?" and felt pretty bad about it, so a friend suggested we compare the solution step-by-step. [May I also add that this problem was pretty easy when it comes to the idea, but there was indeed lots of calculating.]
My mistake was made while copying the problem from the paper I'd got to the paper I'd calculated on. I checked for that while working; for that, and everything else I could easily do wrong. I checked many times, really many times, say, ten times. As I'd made the exact same mishap tonight, while solving it at home, I'm now thinking to myself: how the hell does one keep oneself from failing due to such basic mistakes?
This time it wasn't even the calculation itself.

However, there was this other exam, too. Compared to this exam, it's more time consuming to prepare for, and you have to "think" much more. I had four small mistakes on the final exam: ALL of which are stupid mistakes, such as having a "-" in one row, and then accidentally leaving it out in the other. To be honest, I didn't have the time to check these results, so I can't say that "I checked 10x but still managed to fuck up" (as I can say with the previous).
Our teaching assistant gave me 75/100 points for this, and I felt devastated. I mean, c'mon, you don't take a quarter of somebody's points just because they lost concentration at some point. It was quite obvious that I did, in fact, know what to do - but the guy said something like: "you got this right here, then you got it wrong here, I can't tell whether you knew how to do this". How can I not know it if I had 10 rows of formulae correct, than obviously forgot to write a minus somewhere?! Sigh

Now I feel like shit even more than the last time I posted here. I feel as if no matter how hard I work, I'll keep making stupid mistakes.
I've got one more written exam left, and another one if I decide to do the mathematical physics one again (which I probably will do), and four oral exams yet. I feel as if I should give up on all of them, because hey, I'll probably fuck up again.

[Zcorp]

Our teaching assistant gave me 75/100 points for this...but the guy said something like: "you got this right here, then you got it wrong here, I can't tell whether you knew how to do this". How can I not know it if I had 10 rows of formulae correct, than obviously forgot to write a minus somewhere?!

Talk to him about this. Ask him to give you another problem or even demonstrate you have understanding of the concepts to him.

[PerchloricAcid]

Yep, talked to him. The conversation went something like:
- Well, what do you expect me to grade then, if not calculation?!
- Ideas perhaps? Isn't that more important?
- Those who didn't have ideas, got 0 pts.
- But, apart from having the ideas, my calculation doesn't really have much mistakes. *now I tried to remind/show him what were the exact mistakes*
- I really don't think that this deserves more than what you got.
However, he told me that I could pay the professor a visit (as he's just her assistant) if I really think that I deserve more, which I surely will (haven't had an opportunity yet).

[Our faculty doesn't really have the practice of giving bonus problems to people after the test, we just get to see our tests and how they're graded, and possibly increase the number of points if it turns out that the teacher made a mistake.]

The assistant is kind of a creep and douche btw, but still, I didn't expect such harsh grading from him. One thing is being creepy, and another is lunatic-style exam grading.
I'm having another semester of classes with him. Well, all I can do is try to improve my calculating even more.

Thanks for you reply

[Zcorp]

Unfortunate. Frustrating how people are put in to teaching positions that doesn't really understand the point of the job.

[Webzter]

I'm no expert, but I wouldn't discount some mild form of dyslexia. My wife and her sister both have a hard time with numbers (her sister far worse than her). This includes things like accidentally writing a wrong number down, writing a '-' instead of a '+', seeing a '+' and performing a subtraction anyway. If it's mild in your case, it might be unnoticed but significant enough to give you trouble...

[PerchloricAcid]

Webzter, that's exactly what keeps happening to me.
I haven't really thought of dyslexia though, I tend to attribute it to concentration problems and the like, even though I have the impression that I'm completely concentrated while working.
Were your wife and/or sister professionally diagnosed with dyslexia?
I don't want to find myself a stupid excuse for not being able to calculate or something, but I'm really becoming kinda desperate regarding this topic, so I don't want to rule any possible explanation out.

[Webzter]

Webzter, that's exactly what keeps happening to me.
I haven't really thought of dyslexia though, I tend to attribute it to concentration problems and the like, even though I have the impression that I'm completely concentrated while working.
Were your wife and/or sister professionally diagnosed with dyslexia?
I don't want to find myself a stupid excuse for not being able to calculate or something, but I'm really becoming kinda desperate regarding this topic, so I don't want to rule any possible explanation out.

Wife's sister was diagnosed. I'd encourage you to at least talk to someone who can rule it out or set you up to have some testing done. It doesn't mean you're stupid, lazy, not concentrating, or have poor study habits! It just means you see things differently (which, in many ways, is an asset). And, if it turns you you have dyslexia, then you know what you're up against.

[PerchloricAcid]

Thanks a lot, really.

Spoiler:

I'm seeing a therapist tomorrow, so I'll ask her about this, she'll probably know to whom to point me to.

[lucrezaborgia]

Wouldn't that be dyscalculia?

[Joren]

Wouldn't that be dyscalculia?

Yes it would.

Also in terms of stress, what really seems to help is to take 5 minuts to write about the upcoming tests, how you feel about it etc. Studies showed that on average grades where 0.5 points higher on a scale from 1-10. And I must say I surely did help for me.

[PerchloricAcid]

Studies showed that on average grades where 0.5 points higher on a scale from 1-10.

Have any links?

[Joren]

I'm afraid I don't. It was in a (trustworthy) magazine, that did post where they got their information from. But I doubt I still have it around here somwhere, and it was all in dutch to.

[PerchloricAcid]

Whoa, got 90/100 points on my mathematical physics test.
I definitely still have this problem with basic calculation, but at least this shit is over.
Thanks for your replies, guys.