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The OP was stating that the homework given by the school was not at the child's level, and the extra work given at home was more challenging. If I was going to tell my DS's teacher that he was not going to do the easy homework because I am giving him more challenging work, then I might as well homeschool. I don't see how telling a child not to do the "easy" homework is teaching them responsibility. If the child needs harder work, then it's up to the parent to go to the teacher and/or the school to work out a better situation. While I agree that parents are responsible for their children's learning outside of school, I don't agree with my child not doing school assignments because of the level of difficulty.
But if the teacher doesn't have the tools or background or time to perfectly tailor a curriculum to the child's ability, isn't afterschooling the perfect way to do it? I have no desire to homeschool, but I have to afterschool in one subject. That doesn't mean my DD gets no benefit from the social aspects of school, learning to read and write there, doing music, art and PE, science, show and tell. So what is the problem with arranging with the teacher that the studying at home time will be spent doing the work that she's unable to provide between 9 and 3?

I've seen lots of arguments for homework:
- good study habits (so it doesn't matter what they're doing)
- drill and memorisation (only counts if you're actually drilling/memorising new facts)
- extra practise time (only counts if you need the extra practise)

A child's going to get more of those benefits if they're doing appropriate work.