I personally have not used The Bear Went Over the Mountain with my students, but many of my early childhood education colleagues do. I can hear the kids singing this song in their classrooms, so I decided that I would crack it open to see its potential benefits for the music classroom.
Suggested Grade Levels: Prekindergarten, Kindergarten, 1st grade, 4th grade
Analysis:

History:
Through my research I have found two potential histories for this song. The first train of thought is that the song originated in the mountainous region of the mid-Atlantic United States. Bears are common in this area, so it would make sense to have a song that discusses their movements within their habitat.
The second proposed history is that the song originated from Germany. In Germany, they have a tradition of observing animal behavior to determine when winter will be over, similar to the American tradition of Groundhog Day. In some areas of Germany, people look to badgers, foxes, and even bears for weather advice. There is speculation that The Bear Went Over the Mountain is a song that details the experience of a bear coming out to see if the weather is pleasant enough to end its hibernation or if it must continue its deep slumber.
Game:
Children will sit on the floor and bring their knees up, creating a triangle shape with their legs. Have the children walk their fingers up their legs (or the “mountain”) while singing the first verse. On the second verse, have them walk their fingers down the “mountain.” Repeat using different prepositions as desired.
Classroom Applications:
–Opens discussion for geography/nature
–Discuss prepositions as they relate to the bear’s space
–Experiencing/performing an anacrusis
–Fermata
–Experiencing 6/8
–Singing “fa”
–Good piece for recorder performances; practicing and playing F#
Resources:
—The bear went over the mountain. (2017, October 18). Nursery Rhymes for Babies. http://nurseryrhymesforbabies.com/the-bear-went-over-the-mountain/
–Holy Names University. (n.d.). Bear went over the mountain, the. Kodály Center: The American Folk Song Collection. https://kodaly.hnu.edu/song.cfm?id=455
–Intellidance Method. (2015, December 1). The bear went over the mountain: Action song for kids [Video]. YouTube. https://www.youtube.com/watch?v=l4ADvumhIjg
–Thompson, B. (n.d.). The bear went over the mountain. Beth’s Notes. https://www.bethsnotesplus.com/2013/08/the-bear-went-over-mountain.html
–Yannucci, L. (n.d.). The bear went over the mountain children’s song. Mama Lisa’s World. https://www.mamalisa.com/?t=es&p=1757