I asked my son to show me how he wanted to do the division problems, because the way he was doing them was different from the way I had been taught and the way the books said to do it and because he was doing some of it mentally and I couldn't see what he was doing.
Example: 984 divided by 37. Instead of using estimation and multiplication to solve the problem he counts by 37's mentally until he finds how many times it will go into 98 and so on. No estimation involved and no having to multiply it out and change your answer if you didn't get it right the first time. He also does the subtraction mentally so there is no regrouping. He just writes the answer. He usually does get the answer right but if he doesn't, I can't quickly tell where he went wrong because I am not as good with mental math.
Maybe I should let him use a calculator to check his answer. He hates to be wrong.
My husband told me he has always done division this way (my son says it is obvious he inherited his dad's math genes) and can't see a problem with it. He told me when he was in school he was chosen by his school to compete in an interscholastic regional math competition when he was only in 8th grade and all the others were high school students. My husband never had handwriting problems--he just found it easier to do things his way.
When my son does problems that involve order of operations he is able to remember the PEMDAS rules and can even solve some of those problems mentally, but again if he doesn't write anything down and he gets something wrong, I can't tell what he did wrong.
I can see where a dysgraphic kid might benefit by using as much mental math as possible.
As far as writing backwards 5s occasionally, I think it is some kind of quirky left-right confusion thing that comes out when he is tired or distracted. I have noticed that he is still somewhat ambidextrous and will use both his right and left hands to eat.
