The 'showing work' point is interesting. It's fine if they have all the answers correct, but if they don't, then how can you help them? Also, for homeschoolers, if there is any plan for the child to ever be mainstreamed ever again, most places require work to be shown (particularly as they get older, because of cheating). So it's such a good habit to show work, regardless of the system. Also, most teachers give partial credit for work. Again, showing work is important. The child can still write down a calculation he did in his head and say he did so, it just should be part of the process I think.
