the difference between showing and checking

So we had a quiz in math a couple of days ago and I had gotten none of the questions wrong on the quiz. I was very angered to find out that I had been marked down 5 points for not checking my work and it bumped the grade from a 100 to an 83. I went on to say that I did check the answers in my head just to make sure that they were right. He then proceeded to tell me that I didn't have the work written down. I then said that checking and showing are to very different things and that checking means the way for you to make sure that the answer is right. He is still refusing to give me full credit on my quiz. Aren't I correct though on the difereence between checking and showing?

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Addendum: his definition of checking was writing the steps of your work on paper. Your version of checking is checking the answers in your head; these are not the same concepts, regardless of what meaning you attribute to the word. – Jason Polak Oct 17 '12 at 1:53
Can you give an example of one of the questions and what you actually wrote, so we can see whether there is in fact a gap? If they are questions of the type "Solve equation for $x$", and you have a whole lot of lines beginning with $\Rightarrow$ that finish with $x=2$ (for example); then you must still demonstrate that $x=2$ is in fact a solution to the original equation. Perhaps that is what your teacher is trying to enunciate. – user22805 Oct 17 '12 at 4:51