The book "Upside Down Brilliance: The Visual Spatial Learner" gives interesting insights into kids who can solve complicated math problems but can't explain their work or show their steps. My 6 year old appears to be that way, although has an obvious fantasic visual memory and has about a 25-30 point gap between his verbal and performance IQs (performance being very high). I gave him some double/triple digit addition/subtraction problems with regrouping (he had never seen that before) and he figured out the answers very quickly, but his explanation as to how he solved them did not make any sense and was not the way I was trying to show him (i.e. you borrow a ten). I had to re-teach him but he still does not want to show his work regrouping, he just does everything in his head. His teacher is going to love that.
In terms of handwriting, my DS struggles a lot and part of the problem in math and showing work is that it just takes too much effort to write. His writing looks age appropriate for the most part, but he scores extremely low on tests of fine motor coordination, meaning he has to put a lot of thought/effort into writing (much more than other kids). DS was diagnosed with developmental coordination disorder. If you continue to have concerns, perhaps get an occupational therapy assessment and ask specifically that they test both for visual-motor integration and coordination. My DS is above average for visual-motor integration (so that has masked some of his problems) but on tests of just motor coordination (like the grooved pegboard) he is very poor.
