Uh...yeah.   Well, if you want to do well in math, that is.  There are two basic reasons why showing work--almost every step--is really vital in math.  More musing about it following the two reasons.    

1. To avoid little mistakes.  Too many times students do steps in their head, and such as subtracting 17 to both sides of an equation, but actually add instead of subtracting on one side---and if they had actually written the -17 on both sides, their brain would have realized that it was subtract, not add...and the student would not have lost 3 or 4 or 8 points on a test.  Just a few of these kinds of a mistake on a test and all of a sudden an A grade has turned in to a C, or a B grade has turned in to a D. 
   
2. Checking answers:
• When practicing at home, if students check an answer and sees it is wrong, how do they know where they went wrong?  How do they learn from their mistake if they don't see where their mistake was?  Therefore, it's vital to write down every step, to allow you to go back and analyze why you were wrong...either a small calculation error, misplaced decimal or negative sign, not doing a procedural step correctly, or not realizing you just didn't know how to do it.  When you compare your steps to the steps in the solution, then you will be able to learn from the correct steps, and focus on the one or two things you did not do correctly the first time.  Learning those one or two things will often mean a grade's difference on a test.  This happens a few times...that's the difference between C and A, or D and B...if you really learn from the mistakes, adding in good practice, study, and memorization. 
• When finished with a test, you are required to come to get the test back and make student corrections--meaning to analyze your errors, correct the problem by showing step-by-step how to get the correct answer, and writing a sentence saying what your error had been (all that is 5% of your monthly grade).  It's pretty hard to do this if you don't have the steps written out on the test from when you did it the first time.  Therefore, it's vital for you to write every step to every problem, so you can look back at it later to figure things out better, if needed. 
  

• As a corollary to number 1 above, writing out every step when taking a test really can help you keep focused on the procedures you have to do in order to get the question right.  In fact, sometimes you might not be completely sure of the next step in a problem--but if you see the previous step written down, that sometimes jogs your brain to remember the next step.  If you don't write down a step, or you skip a step, then you don't get this little reminder, and you probably look at the problem blankly, and give up or go in a weird direction rather than get it right. 

• Also, not writing down steps can lead to bad habits, such as misplacing decimal points in your mind, or other little things.  Remember that education is not just learning information. It is also about training your mind so you think well, and can figure things out.  Although you DO want to be able to do a lot of things in your head, you also want to get the test questions correct, and learn the material really well--and on long hard math problems, you should not be thinking about saving time or acting smart by doing things in your head...you should be thinking about getting an A, and doing whatever it takes.

• It is reasonable that not EVERYTHING be written down.  For students in middle school and above, you are expected to know your multiplication facts perfectly (though 12).  Thus, I don't expect you to have to write down 7•6=42.  That kind of stuff you should know in your head and should do quickly and easily.  It's writing down the steps in a problem that I'm talking about...the steps that lead you to an answer, and that you have a far better chance of getting correct if you write them down and see them on paper rather than trying to keep track of them in your head.