If I understand you correctly, you are asking whether Amy's experiences, as told by the author, are common for that time period. The answer to this would be yes. I used the examples from chapter seven to answer your question.
It was very common for non-public schools to be segregated - that is, for there to be schools for girls and schools for boys. Amy attended a school like this.
It was also common for classrooms to be very large (Amy's had 50 girls) and for the schoolmaster to be very well trained in his/her subjects (Latin, Greek, grammar, Algebra, etc.) but not well trained as a teacher. In addition, it was common for the teacher to intensely dislike teaching. Mr. Davis was one of those teachers - he was trained in his subjects very well, and thus considered highly qualified for teaching, but disliked children and teaching in general.
It was also common for teachers to have pretty much complete say over what students did in school, brought to school, said in school, etc. Thus, Mr. Davis could rule that limes were not to be brought. Additionally, teachers were free to punish students in almost any manner they saw fit, as long as students were not injured. Thus, corporal punishment was common, as was "shaming" such as Amy endured. Having students stand in the corner, or the front of the room, was considered a good way to make an example of an errant student. Punishment, including corporal punishment, was generally carried out at the front of the room where everyone could see it, and thus be deterred from committing the same sin as the child being punished.
The book presents a pretty accurate picture of what some schools were like during this time period. Of course, there were other schools that were different - not all teachers were grumpy and sour. However, this school wasn't all that unusual and Amy's experiences were probably fairly common for most well-off children.