My son with motor dyspraxia/dysgraphia would have been much like the boy with the broken pencil. He would have difficulty with writing quickly and he would make careless mistakes just trying to keep up with the writing, so we have to homeschool. I recently met two other homeschooling moms, former teachers, and one is a former teacher of gifted students. They tell me I am doing the right thing by homeschooling.
My son does well on online math drills that he uses to increase his speed. He often figures out the answers to math questions mentally while I need a pencil and paper or a calculator. Just because I can write faster than he can does not make me smarter. I don't know why some teachers have a hard time understanding this.