Sometimes I get worried questions about giving choice about homework: "Isn't that giving students much too much freedom?", "Aren't you afriad that they will do nothing and learn nothing that way?" I reassure them that my experience is not so bad. Treating students as responsible and committed, is my experience, strengthens this responsibility and commitment.
I came across some research which support the idea that giving students choice in homework has important benefits. The research, done by Erika Patall and colleagues (2010), says that giving students a choice of homework -has important advantages: a) higher intrinsic motivation to do homework, b) feeling more competent regarding the homework, c) better performance, d) better homework completion.
Source: The effectiveness and relative importance of choice in the classroom