I need to write a teaser about the short story "The School by Donald Barthelme" with NO spoilers in order to capture peoples attention for them to want to read this story.

I can see why this might be a confounding assignment! This is a tricky (and rather odd) task as Barthelme's story seems, to me, to be rather unteasable. It's more in the vein of a shaggy dog story (a long, elaborate joke with an unsatisfying punchline). It lacks plot, stable characters, and a literary universe that we can identify or relate to. In fact, "The School" exemplifies a movement in American fiction writing called "postmodernism," which aimed to actively do away with recognizable narrative conventions. Postmodern writers used heightened language or surreal plot devices to illustrate to the reader the deceptions and tricks that fiction writers use to make their writing seem real. Postmodern writing is often self-conscious—that is, it constantly reminds the reader that what he/she is reading is a fiction. In "The School," the increasingly violent and bizarre events of the plot and the sudden switches in narrative voice both serve to jar the reader loose from a certain readerly complacency and to remind them that what they're doing is reading a story.
I won't write the teaser itself for you, but I'll give you the skeleton of a teaser to make your job a little bit easier. Hopefully, the following will spark your imagination and ease the assignment along for you.
One of the most common ways to start a teaser is with an ambiguous but startling question that relates, loosely, to the themes of the story, kind of like the first sentence on a book jacket: "Have you ever wanted to cheat death?" or, even better, "What if you wanted to live forever?" (These are cheesy and poorly written examples, but I hope you get the gist).
Spend the next few sentences describing the situation (not the plot) of the story. This way, you can avoid spoilers. "The School" starts with a rather ordinary set up: a failed classroom gardening project. It mostly derives its humor and its surreality from the way that this mundane situation escalates. By the end of the story, there are people (including children!) dying left and right. This is definitely dark, but it's also extremely funny, especially since the narrative voice stays so deadpan throughout.
Spend the next few sentences giving your opinion on why somebody would want to read "The School." What do you, in particular, find intriguing about it? The language? The humor? The weirdness? Its historical significance as a piece of postmodern writing? Optimally, your endorsement of the story will relate to the question that you used to open the teaser in the first place. This will give the piece a nice sense of circularity.
I hope this was helpful. Good luck!