“Overall and in line with self-determination theory, results suggested that providing students with choices among homework tasks effectively enhanced motivational and performance outcomes and that choice is an important component to creating a classroom environment supportive of autonomy and intrinsic motivation...Consistent with self-determination theory, we found that students reported feeling more interested in and enjoying homework more as well as more competent regarding their homework and that they scored higher on the unit test when they received a choice between two homework assignments covering the same content and of intermediate difficulty, compared with when they were not given a choice. Students also tended to complete more of their homework when provided with choices.” (p.910)
Patall, E. A., Cooper, H., & Wynn, S. R. (2010). The effectiveness and relative importance of choice in the classroom. Journal of Educational Psychology, 102(4), 896–915.