One of the things I attempted to do during the last school year was to assign homework but not include it in my students' grade. The thought at the time was that those students that chose to do the homework would be serious about it and gain full benefit from the practice that the assignment was intended to give.
In theory, the plan sounded good but also failed its intent miserably; so much so that I decided to abandon it before the year was over and re-institute the old grading paradigm where the completion of homework counted towards a portion, (15% or so), of a term grade.
I grossly underestimated the maturity level of middle school students. Once my students figured out, during the middle of the first term, that homework was not being counted towards their grade, homework participation rates dropped immediately and precipitously. I had anticipated this. What I did not anticipate - Despite obvious negative impacts on many student's quiz grades and learning for the second half of the first term and the second term; a paltry few of those students were mature enough to make the connection between the necessary practice that the homework provided them and how well they learned the material and performed on assessments. Most never started doing the homework again.
Thus, the homework "cure" that I had instituted became worse than the disease. I still feel that my original goal had merit and was worth a try. It is also something I am unlikely to implement again any time soon.