There is a lot of debate out there on the grading of homework. You can easily find reasons to support all sides of the issue.
I'll begin by saying that I am not a fan of homework.
After researching and teaching my students about growth mindset, I am even less of a fan.
In my classroom, our focus is on the learning. Mistakes are welcome -- they are proof we are trying. Figuring out what we did to make those mistakes and taking steps to ensure it doesn't happen again is growth.
Growth mindset teaches us that our brains are always changing and growing. By trying new things, showing grit and perseverance, making mistakes and trying again, we are changing the physical structure of our brains for the better.
This does not work if I grade every assignment my students do.
They would be afraid to make mistakes.
They would hesitate to ask for help.
They would shy away from trying new things because they can't do it perfectly the first time.
So when I assign practice in math, my answer key is always open for students to check their answers. If we use a worksheet, I will often copy the answer key right on the back of the page. Sometimes, I just write the answers on the board. If my students got a problem wrong, they go back and fix it. If they can't figure out what they did, they ask for help.
It has also helped me correct misconceptions before a student has done 30 problems incorrectly and has the incorrect procedures cemented in their brain.
So what do I grade?
Which, ironically, makes students try harder on their practice work, thereby increasing their learning.