Purticordes was Saint Fidgeta's teacher at pagan grammar school; known as a "notorious skeptic" (Saint Fidgeta and Other Parodies; 11-12). Saint Fidgeta "crossed the pagan teacher constantly" such that the "distraught pedagogue" later slapped Fidgeta to death (12).
Religious skeptics question religious authority and are not necessarily anti-religious but are skeptical of a specific or all religious beliefs and/or practices.
Whether or not Bellairs meant it or not, that the Christian Fidgeta “crossed” her pagan teacher is a clever pun. Her praying, stringing rosary beads, plaiting whips, all but refusing to worship idols, and secretly carrying holy water are the sort of things that would not normally be found as part of the curriculum at a pagan school.
A pedagogue is a teacher or instructor of children; a pedant.