Keep making the same mistakes over and over

[Kalidor]

A recurrent problem I have when facing written examinations (I'm a math major) is calculation mistakes. They often have a devastating effect e.g. I just badly failed a quantum mechanics examination because I found the wrong eigenstates for a certain Hamiltonian which led to the rest of the questions of the test becoming trivial (vanishing expected value of energy ecc) which of course the instructor could not tolerate. The mistakes was a stupid wrong calculation of the eigenvectors of a 2 x 2 matrix. After realizing that something was wrong I looked for the error but it took me too long to find it...
It's really frustrating to perform poorly in written tests because of mistakes like these and it seemes to be happening too often lately. Has anyone here been in a similar spot sometime in his life/career? What am I doing wrong? Too little practice with exercises?

Thanks in advance

 

[Dead Boss]

Check your calculations before proceeding to next step. And be careful in the first place. It's easy to incorrectly read a number you wrote when writing fast, for example. Such mistakes are very common and all you need to do is pay more attention on what you are doing, instead of worrying about time left.

 

[zgozvrm]

I used to make stupid mistakes in math all the time. I finally started slowing down and double-checking my work. Eventually, I was able to speed up my work without making those mistakes.

Just like pianists; there are "naturals" that pick it up easily, and others who need to practice making the right finger movements to avoid accidentally hitting 2 keys at once.

So, basically, it comes down to practice, practice, practice.

 

[micromass]

Double check every thing you do! That's what I did every step, and I seldom made errors...

Also: make a list of things you tend to do wrong. And then check your test whether you did one of these things...

 

[AlephZero]

As well as checking step by step, check using common sense. It seems like you did that in the example you gave, because you realized the later parts of the question were too easy (or just pointless) if something was equal to 0.

In that situation, I would be inclined to write a comment like "I think this is wrong, because ecc should not be 0, but I can't find my mistake." At worst it will do you no harm, and if you have an intelligent professor/examiner who can see that you made a trivial copying error, it may gain you a mark or two.

 

[Outlined]

check what you wrote down on your own paper is the same as in the examination. Is matrix A the same as on your examination? Really? Check it again!

check results, found an eigenvector and eigenvalue? Check whether the computation Ax = lambda * x holds.

Use tests: a polynomial of degree 4 and just 2 zero points then they should have multiplicity 2! If not you missed another zero point

check -> check -> double check. Always! In the past years I never made a fundamental mathematical error. I could not solve every math problem but the ones I did were always (nearly) perfect, that is no fundamental error, only some details.

 

[Kalidor]

Thanks guys. As a result of my common calculation errors I am now pretty tense when I face a written test of some importance. I guess when I double check my way into a good mark I'll be more self confident.