I know it’s trendy for folks to proselytize “Ditching Homework” – it’s a catchy phrase, great memories of your own homework are likely hard to find and you won’t get invited to speak at conferences or sell books if you’re encouraging folks to do the something they’re already doing.
Now, I’m only speaking of high school — to elementary teachers, I would suggest you follow Hattie’s advice that 5 effective minutes is as good as 1-2 hours and to avoid “projects”(Link).  But people arbitrarily throw out statements that have little basis in research, or produce straw arguments to avoid the “homework as an effective learning device”.
So my suggestion is not that it will teach responsibility (one blogger insists there is no research indicating this, but of course, there is, but I don’t care either way — it’s not my goal) or will prepare them for post-secondary studies (who says they’re going to post-secondary?).
Instead, we give homework to provide meaningful spaced practice of skills the students have encountered and/or provide them with thoughts for our next class and/or to provide us with a temperature probe for when they arrive in class the next time.  It should be deliberately chosen (not “do all the odd exercises on this page”), it should be short (I ask my students to do 90 minutes a week), it should either reflect what they’ve done or push them to think about their next class and, most importantly, the teacher should do something with it.  I use OneNote with my students, so I can see all the student work before they come into class – so I can modify my instruction, discuss problems that were difficult and suggest alternative solution paths.
Teachers should do things with purpose.
 (It’s our first night of 3-hours of parent/teacher conferences so this is briefer and less-well-reference that I might prefer.)

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