Creative Dramatics (or narrator's script):
The teacher/narrator reads a "creative dramatics script" or just guides the children through the story using suggestions.
This technique is based on my work as a childrens' librarian, where books are re-enacted using creative dramatics.
The scripts I include in my lesson plans are to help the teacher (who may not be comfortable with drama) lead the children as they recreate the story in their own words. The children do not have scripted lines to read, so they can focus on remembering the story they have internalized rather than on reading words off of a page. So I guess you could call what I write a narrator's script (with notes on things to say to the children to help them feel out the parts of the story and portray them in an informal way).
I usually take the scripts straight from the Bible, with clarifications (mostly to add historical background or reminders of related stories or action that may have preceded the story being studied) and deletions (I leave the dialog out so the children can create and amplify and imagine what else may have been said).
I sometimes use this technique with puppets instead of human actors (the children are sometimes more free and creative when they are not personally "on stage."