Another question based in a false premise! The question assumes that "schools," i.e., specialized facilities within the community that offered free or low-cost education for children and young people, were common in sixteenth-century England. They were not (despite claims to the contrary by some websites). There was no national or even local regional educational system in existence in England in the 1500s. In actual fact, the children of the wealthy were educated at home by private tutors hired for the purpose. At the other end of the spectrum, children from poor families were not usually educated at all and remained illiterate as adults. On rare occasions, a child from a poor family might receive a limited education through some charitable endeavour, such as a local church or perhaps a very small (handful of students) grammar school privately established by a local benefactor. But the vast majority of children were not formally educated at all and did not attend "school" in the modern sense. It is important to note that in 1500, fewer than 5 out of every 100 people could read, and only 1 or 2 out of 100 could write. By 1600, the proportion of non-wealthy people who could read and write remained less than 10 in 100. The poorer classes remained almost entirely illiterate because children were put to work at a young age. Education throughout the sixteenth was available only to those who could afford to pay for it ... the landlord, merchant, and professional classes (large landowners, successful merchants, lawyers, etc.). It is difficult to address the question of bullying in the schools if there were exceedingly few schools. Undoubtedly there was some level of bullying in the very few schools that did exist, but response to that bullying would have been entirely dependent on the individual and variable disposition of the teacher or teachers in charge of that school. But in any event, "bullying" is largely a modern concern. People of the sixteenth century were far less attuned to such social issues. See, for example, my response to the previous question about domestic violence and abuse.
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