While doing homework, tweens and teens love to listen to music — not to mention watch TV or instant-message on the computer! So parents often ask me whether this interferes with learning.
I must say that in my classroom and home, I want children to be engaged and focused, doing one thing at a time — which means quiet during homework. However, I can't say that I've not relented on occasion and allowed some background music and (even more rarely) some TV viewing while homework was also under way.
Multitasking may interfere with full comprehension. I suggest that your child do one thing at a time and that she give her homework her full attention. However, no one knows your child like you do. You may decide, based on how well she is doing in school, that some soft music is okay. You may want to have her do her most difficult assignments in the most quiet setting. Studying for a test, for example, is a good candidate for no-media-allowed working conditions. They also most closely replicate the environment in which she'll take the test.
In the spirit of even fuller disclosure, I admit that I multitask on occasion myself. However, right now I'm solely focused on writing this advice. When something is important, it deserves unimpeded attention.