In the beginning of my teaching career, I was devoted to the idea that students needed to do nightly homework because math was a cumulative subject, and material kept building, and students needed to make sure they could do it on their own, and blah, blah, blah... But, I hated checking homework. I assigned only the odd problems, so students could check their own work and I could grade on completion. I still had students not even attempt the assignments, but more often than not, students just did the assignment for the grade. They never checked their answers. I had many students with high homework averages and extremely low quiz & test averages. The reverse was also true. I had students that mastered every test, but never completed a homework assignment. In the latter situation, I had students end up repeating the course because the grade was not high enough. Things needed to change!
My summer of 2017 was spent reading, researching, and stalking Twitter about other people's experiences. Processing my own personal "why homework?" question, I focused on that fact that homework, in my class, was purely extra practice. It was just a piece of the student's own personal math journey. I needed something that accurately reflected that learning. So, I completely revamped my grading policies. I decided to switch to Standards Based Grading AND eliminate the homework grade. Big steps!
I still believe that students need to practice, but more importantly, they need to learn when and how to practice. I no longer assign homework. I provide extra practice, daily. Additionally, I try to use sites like DeltaMath, where the students can have infinite amount of practice with immediate feedback. At the start of the school year, we have many class discussions on who the practice is for (their own personal use - not a teacher check), what should they be practicing (new AND previous material), when is good time to practice (daily when they can, definitely before quizzes and tests), why is there so much practice (so they can practice all the time, any time), and how they determine if they need the practice (low quiz grades or not solidifying understanding in class). Students should only practice enough to understand the material. It should not matter if they needed zero problems, 5 problems, or 20 problems to "get it." And they should not be rewarded nor penalized for needing or wanting that amount of practice.
In the years since I completely dropped the homework requirement, my overall class averages have not changed much. In fact, the class average has improved AND I have less repeaters each year.
I do have to constantly reiterate that just because I do not grade the practice does not mean they do not have to do it. It irks me when parents tell me that their child claims they have no homework, ever. At the beginning of the year, I make it clear to the students what happens when I hear this comment from parents. I proceed to show those parents exactly where to find the plethora of practice material AND explain how they can monitor the completion of the practice. Practice is not optional. The amount of practice needed, is optional.
UPDATE: At the end of the 3rd quarter of the 2019-2020, we moved to emergency remote learning due to the COVID-19 pandemic. My class average at the start of remote learning stayed the same as the end: 88.14%. I had no students repeat the course.