„What could be the reason that a child can obviously not see the writing in a book or on the blackboard properly and nothing is found in a medical examination?“

The answer is: the child probably suffers from weak dynamic vision. The child is not able to follow a moving object with the eyes without looking somewhere else in between. A very simple device to test the ability of dynamic vision is this object for fixation. By moving this object in front of the child (e.g.in the form of a lying eight) you can easily find out if the child’s eyes can fix a moving spot (the silver ballon top) continuously.