a. My favorite hobby is dance.
b. My favorite hobby is dancing
1. a special set of movements
2. a social event that...
3. an act of damcing
4. piece of music
5. the art of music
There is a difference to me between the two sentences above (a;b):
a. I like the art of dancing. (It is possible that the referrent of 'I' never dances; I do not know)
b. I like to dance ( and I dance in my free time for enjoyment)
c. dancing teacher -- one that is dancing
d. dance teacher -- one that helds dance classes
"dance" seems to restrict the meaning of teacher: not just any teacher, but a dance teacher. Does it mean nouns can have adjectival function? Yes.
e. dancing class -- one that is dancing
f. dance class -- a group of people that is learning to dance or practising dance
Does this help you?