Gum is an erotic symbol, so dreaming of it signals repressed desires that need to be satisfied. Stepping on someone else's gum evidences your dependence on that person; and if someone else steps on yours, you will not likely receive help from others because you continually bother them with your demands.
Dreams reflect our actions that we have already performed. Most of us have dreams activities relating to our past life. One of the common dreams that every individual has gone through is their experiences during the school life, where you would get images of teacher hitting you, making you feel numb and shameful.
Reading in dream
Sometimes you will not be able to differentiate lucid dream. If you want to be sure, try reading a simple sentence, if you are able to read then you are in wakeful stage if not you are in lucid dreaming. Studies show that you cannot read while dreaming or you will not find the repeated sentences one more time.