In many areas when a formal education system was established they were in an agricultural economy so the school year was established so that the children could be free during the time of year that they were most needed to help on the farm.
However when the economy shifted to an industrial one and this need was no long required the school year more often than not was not changed. Resulting in a tradition of a long vacation for students.
This vacation was not was not mirrored in the adult workforce so that when economies further shifted requiring most families to have both parents in the workforce this left issues of child supervision without a corresponding will to revise the school year. So many non-academic programs were establish, some of these sponsored by the schools they go by many names one of which is they occasionally also get called summer school by this is not the primary usage.
Many western school systems are reluctant make a student repeat a school year if they fail to meet the standards of their level. This is partiality due to physical and social development reasons for wanting to keep a student with other students of their own age. But also it often only in some areas of learning that are not up to standard which repeating the entire year would mostly bore the child causing related issues. So summer remedial programs were established as last chance to avoid holding the child back to repeat the year.
In eastern school systems summer school are just a likely to be academic as their western counter parts however the focused isn't on remedial students but on advancement to increase their ability on placement tests which determinate which school they can attend at the next level, for in may cases it not how well you did in school but which ranking of schools you attended that will secure job offers. This results in the intermediate and secondary school years earning a nickname of cram hell.
In Tertiary school summer classes are normally called the Summer Semester. This semester tends offer less classes. While they do offer key courses for those that need repeat a class of the western style, This semester tends to also cater for advancement reason as well, offering courses that tend to be over subscribed during the other semesters. It also caters to those that wish to take a lighter work load during the other semesters and still finish in the traditional time frame. Some might even offer an increase of non-essential electives as a busman's holiday for students.
Summer school and spanking
Partially due to denial of vacation time many people view attendance remedial summer school as a punitive response to bad report card; particularly those that never needed it.
Spanking fiction can use summer school as a school spanking story setting casting the student body general group delinquents or lazy students needing a firm hand with liberal use of corporal punishment due the presumption that the students wouldn't be here if it they didn't deserve it. Conversely it can be use in the reverse by having a character who have actual learning problems being assigned to a class with this environment.
This have many common elements with Reform school style boarding school settings except with the minor still living at home during this period allowing the mix of domestic pairings as along side the other academic pairings.
This setting works well with concept of beginning each day with a motivational spanking to counter act the presumed laziness that put the minor in this setting. It works both with this be a parental option, or even a classroom scene along side roll call, and in harsher works even both.