Firstly, I do want to stress that I have little respect for a teacher like that - nitpicking for the sake of it has always irked me having been on the receiving end of it from borderline cretinous teachers as a kid myself. With that said, a sharp pencil or very fine tipped pen is pretty useful especially for drawing nice graphs, plans and geometry exercises.
Have you suggested to his teacher that she let him do his work with a pen, instead? (Thinking of people who do crossword puzzles in pen....)
My DD uses a 0.5mm mechanical pencil because it is always 'sharp'. We use HB lead. They can be purchased in packs of two and probably in bulk fairly cheaply.
I use one myself and love, love, love it - I even feel Mathy once I am holding one LOL
Best thing since sliced bread IMO
