I was wondering what would have been the first film to depict stereotypical ideas of American High Schools. I can only think back as far as Grease (1978) or maybe Rebel Without a Cause (1955) but I'm not sure if that counts.
It's important to note the sociological underpinnings of the high school film.
From 1900 throughout the 1920s, most Americans lived in small rural communities. They usually only had one school, and by the time children were of high school age, they were usually working on the family farm or apprenticed to a vocation. Thus, there was no "stereotypical" high school, and very few movies were focused on the school aspects of children. Even in literature, stories about children in this time period usually focused on their adventures outside of the classroom.
The combined push of industrialization, the need to assimilate a major inflow of immigrants, and progressive educators like John Dewey and Maria Montessori helped created the American public school system we know today in the 1930s, and World War II cemented the high school's role in the life of the American teenager.
During this transitional period, movies about high school served as quasi-propaganda for this movement, and so you have movies like 1940's High School, which features Jane Withers as a rural rancher's daughter who gets bused into an urban (and strikingly beautiful) high school. You also have a series of famous "educational" shorts, primarily about PDA and dating, including Junior Prom from 1946 which has some of the stereotypes - primarily the hormonal ones - you've come to see, but it's very staid and dry. You also had a very witty radio series, Our Miss Brooks, which was turned into a successful long-running TV show, but it usually just used the children as fodder for jokes, and focused more on Miss Brooks' love life (or lack thereof.)
Finally Hollywood started taking a look inside these high schools (not coincidentally at a time when those very same teenagers were borrowing mom and dad's car, grabbing a date and heading to the movies) and found the themes that a high school fostered - students' newfound independence, causing alienation from their families before they could truly leave them; and industrialization, which had set them on a treadmill that many weren't prepared for - and the subsequent rebellion against that - were excellent fodder for movies.
The ur-Text often pointed to for the "high school film" is 1955's Blackboard Jungle which featured the music of rock n' roll pioneer Bill Haley and the Comets and has all the beats the modern high school film expects: a new teacher comes to a rough school, there's drama with relationships, school violence, fear of failure, and an unflinching bureaucracy, but with life-affirming results at the end.
Well, there was Edison's film in 1900 Lancaster, PA., High School ... I don't know if that is a "stereo typical" look at high school as it is just a documentary (and probably just Edison testing his movie camera), but that would be the first.
The first which was not a documentary or a short was probably A Girl of the Limberlost from 1924.
Here is a link to a search I did on IMDB. Search factors were just "high school" in plot.