Hi B.!! Well, as a Mom who has been through 7 years of dance with two of my daughters I can say YES you should get your dance teachers a little something for Christmas. I usually went for anything "dancey" like little figurines, and unusual picture or poster, costume jewerly (the inexpesive stuff) a card with something homemade from your daughter is also really nice. Don't go overboard and I usually never spent more than $15-20. Gifts aren't required, but they are appreciated by the teachers espically if you go to a good studio that you plan on staying with for a while.
FYI don't stop going if your daughter doesn't "do" any dancing at the recitals for the first year or two. It takes a while for some kids to warm up to performing. My youngest actually stoped and yawned in the middle of her little christmas show the first year...it was soo funny!! But let me tell you that changes in a hurry if you stick with it. Also dance give kids an appreciation for movement, music and their bodies. It also teaches them focus...almost every girl that graduates out of the studio we used to attend is in the top 10 of their high school class!! Have fun!!