Mother as a proper noun

I was helping my little next door neighbor with her 4th grade english paper, she had to correct grammer. I tolled her the the word mother needed to be capitilized when it was used as a proper noun. The sentence was something to the effect of "... then I waved good bye to Mother..." and not MY mother just Mother as if it was her name. I just want to make sure that I am not going to get her a bad mark for this paper, because it was used alot. If some one could let me know that would be cool. Thank you, Elenore

[Tdol]

That's right:

Here is a present I bought for Mother.
Did you buy a present for your mother?

Capital Letters - The OWL at Purdue