Good points.  When I was in school we were forced to do math by hand.  I was helping my nephew with his math the other day and he only had 2 steps written down.  I noticed the answer was wrong so I asked him to walk through the steps and show me what he did.  He paused and told me he put the equation in the calculator.  I knew the problem immediately was an issue with order of operation, but I explained to him you cant just blindly plug it in the calculator and expect it to be right.  I still have him walk through it and show me he knew how to do it.