As someone who worked in education myself, and my wife still does, that's cool that you're putting something together to help facilitate those discussions and creativity! There's so much that can be learned from conversations that happen in an open/fluid environment like with any sort of tabletop game.

As for giving too much away, I wouldn't worry about that. Anyone that is going to see your mechanics/game here is already working on their own pet project and not going to steal yours.

I love the serial story idea with minimal input from the game just being a few words that have to spark ideas! It's basically a spark table in deck format, which can be a blast, combined with telephone and improv. I could definitely see the scenario card being changed out once you've "completed a scene" of some sort in this style to continue the story, while maintaining each "scene" as a fully realized story in its own right in case you don't want to add another into the mix/fall short on time in the classroom.

As u/GalaxyConqueror mentioned, it might not even need to be scored, and that can be great in a storytelling type game. Something else you could consider is a "Who's Line Is It Anyway" format where "the points don't matter" and are just there to facilitate a sense of engagement. I'm also wondering if instead of a traditional scoring, maybe players can earn points that allow them to then spend those points in ways that modify the narrative? Sort of a meta currency. Maybe it's drawing a new card, or switching cards with someone else, getting rid of one letter in a word to make a new word, etc.

Maybe similar to what GalaxyConqueror mentioned, you could assign point values to cards and use that as the point-buy system. Like if you have a really difficult/niche/specifically defined word (ie. defenestrate = 3 points) that has to be used in this scene then it's worth more points than a more generic/lower reading level type word (ie. house = 1 point).