So I am still thinking about homework, how to do it (or should I), how much value does it have, what is the best thing for my students?

Where I started teaching just 8 years ago I ran a traditional class -
or at least the class I was use to in High School (even though I was more than 15
years removed from it). I did like many first time teachers - I
taught like I was taught (quite a bit).

Class
started with checking homework, I usually collected it too. But we
spend time grading it, answering questions and then answering more
questions. Then correcting what students did incorrectly the evening
before, or copied in the hall. And the whole time - 6 students really
focused while 20 were zombies - eyes open and nothing going on. Then I would be pressed to teach the lesson.

I
quickly moved to just collecting and handling questions by doing a
different problem with similar content so everyone could work it. That
quickly help, at least everyone was involved. But I still had a ton of
questions from homework and misconceptions to "clean up" from students
trying to do their work and doing it incorrectly. And why wouldn't I have
to fix misconceptions? I was assigning something new, something that
we had just been introduced too.

Then I started not
assigning new concepts immediately, we would do new in class together for a number of days, and then my question
time quickly decreased I would lead the problem as I walked the isles.

And now over the span of years I have migrated where I supply solutions
and just have students turn in their work occasionally. That way a student who is
struggling can have an extra day, find time for help in the class or study hall. It opens up a ton of my time to help students during the hour.

And there you see the progression, I no longer consider homework really important. Otherwise I would be "on my students" to be done every day. But homework is for the student, it is what he/she needs, thus I give some flexibility.

The students know they are responsible for the material in the text (I sure say it often enough) and their grade is based on their knowledge of that material. I often joke that students "can learn through homework or through test and quizzes, I really don't care which way." Note, in my class, grades are based upon summative recursive assessments on mastered material. And since the quizzes are recursive, always focusing on mastered material students are continually "practicing" twice per week.

Now is good time to mention that my goal is not their grades but the knowledge they leave my school with, are they college and career ready. (They can be a pain with some students or parents sometimes - but when is last time a person was asked about their Algebra 2 grade when applying for a job?)

I don't care how they learn it, students that play school do the work and earn a better grade typically. But the student who really won't play school still typically gets the skills! And a D in my class means they are ready for the next course. (I find the D thing to be an epidemic - if a student gets a D and cannot do the work - how are they ready for college/career -- no wonder we have 30-40% of college students doing remedial math!)

And over the span of time the end results have gotten constantly better. I have had better results on the ACT test, better results on the class assessments, better results from students who report back to me about how they are doing in their jobs or in their college math courses. And that is because I feel I have increased the time a student does math! I went from most students being zombies, who spent 20-30 minutes per day on math with homework, to an entire class doing math for 45 minutes, 5 days per week minimum. Now the 6 students with questions just wander in before school or during homeroom for help. My room is now a whirling dervish of math activity! The homework is beyond that, and so if a student copies it (and that never happens) he or she is still doing 45 minutes of work per day.

Now I am pushing for less paper & pencil and more instant feedback practice - websites (Khan, IXL, textbook), spreadsheets, etc. The hard part is changing me, I still find myself more comfortable collecting homework, than checking website reports -- and weird as that sounds it takes a lot more time to change me than to stay the same.

I know practice is important and I will keep working for a balance between paper/pencil (a skill that must be maintained) and some sort of on-line portion (which I think gives students better feedback and increases the return on their practice time).

Most importantly - we will keep on trying to be better each day.