In this paper, we propose a taxonomy of handwriting errors exhibited by children as a way to build adequate strategies for integration with a co-writing peer. The exploration includes the collection of letters written by children in an initial study, which were then revised in a second study. The second study also analyses the "peer-learning" (PL) and "peer-tutoring" (PT) learning methods in an educational scenario, where a pair of children perform a collaborative writing activity in the presence of a robot facilitator. The data obtained in the first two studies allowed us to create a "taxonomy of handwriting errors". A set of writing errors were selected and implemented in an educational activity for validation. This activity constituted a third study, wherein we systematically induced the errors into a Nao robot's handwriting using the {PT} method - A teacher-child corrects the handwriting errors of the learner-robot. The preliminary results suggest that the children in general showed awareness to the writing errors and were able to perceive the writing abilities of the robot.