Educational music, including, but not limited to children's music, has been shown in research to promote learning.
The subject of "Brain-Based Learning" addresses the following components of the learning process:
* Keeping interest high
* Providing "state changes" in which learners can vary their activity and their incoming stimulation.
* Using a wide variety of learning styles, as outlined by Howard Gardner, such as kinesthetic, auditory, emotional, etc.
Additionally, music study in general has been shown to improve academic performance of students. Prominent examples include songs from Sesame Street, Schoolhouse Rock, and Tom Lehrer's songs for the PBS show The Electric Company.

References

1. http://www.smartsongs.org
2. http://www.songsforteaching.com/references.htm
3. http://www.menc.org/publication/articles/academic/pawtuck.htm
4. http://www.twinsisters.com/news-detail.php?newsid=2
5. http://www.googolpower.com/content/articles/educational-music-googols-to-learn-with-music