Math Homework and Mistakes

This year Kaiya has math homework, which is to be checked by parents before it goes back to school. When I find a mistake, I tell her and she works to fix it. She then comes back for me to re-check it and/or get my help.
In life we often make mistakes. Our mistakes often can not be completely erased. It's like doing homework in pen or using an eraser that never completely removes all the pencil marks. Traces of our mistakes can remain. Not a comforting thought!
Another uncomfortable thought: being corrected. How is our response to correction? We may get defensive when someone corrects us. We may let our feelings overwhelm us. We may lose sight of all the things we have right and let only our mistakes define us. For example, we might falsely think, "If this one thing is wrong, then all of me is wrong." All of these responses prevent us from fixing the mistake and moving on.
I want to be more like my daughter. When she has a mistake on her math homework, she works to fix it. She doesn't get bogged down by negative thoughts. Instead, she fixes the problem and seeks help if she can't do it on her own.