Is it worthwhile to redo problems where an arithmetic mistake has been made? When learning new concepts in math, is it worth my time to redo problems if my mistakes were purely arithmetic mistakes (or very simple algebra mistakes)? If I made sign errors, or added fractions incorrectly, would it be better for me to go back and redo the problem correctly, or to move on to a new problem?
Thanks for the help.
 A: It depends on the length of the problem.  If the problem splits up into stages, just redo the stage where the error occurred.  But it is important to get problems "all the way right."  Because sometimes an important insight or misunderstanding is still lurking in that "trivial" detail you haven't quite examined closely enough yet.
One reason I focus on easy problems when tutoring is because I tell my students, "You want to establish the habit of getting things right."
A: 
When learning new concepts in math, is it worth my time to redo
problems if my mistakes were purely arithmetic mistakes (or very
simple algebra mistakes)? If I made sign errors, or added fractions
incorrectly, would it be better for me to go back and redo the problem
correctly, or to move on to a new problem?

Disclaimer: this is my personal opinion, having tutored many students at A-Level and below.
Sorry to inform you that there are no short cuts to this process in maths. You need to go back and correct every single error you make. This is one of the ways you will become a grandmaster at arithmetic and algebra, the two most important fundamental aspects of elementary maths.
When you get to a certain level in maths, you care less about making these "silly mistakes" because a) you don't necessarily care about these mistakes, as you are focusing on other, more important aspects of the question, and trying to improve these parts, b) you don't make silly mistakes very often, c) when you do make mistakes, you already have built-in error-checking methods into your answering process so that you can correct your own mistakes.
If you are not at this level yet, then you need to re-do every question that you got wrong. You also need to be thinking about error-checking methods and making them a routine part of your answering process.
I have seen students time and time again not learning the fundamentals to grandmaster level, and those are the students who do not succeed in maths [or if they do succeed, they put in a needlessly large amount of effort due to going about things in a roundabout way].
If you don't know the rules of the game well and from the start, you're not going to get very far in the game [or if you do, it's going to take you a needlessly long time].
