HOLDENVILLE – In a cramped space behind the stage of Reed Elementary in Holdenville, school secretary Diane McCoy and four students discuss the whys of the letter Y. Her many tasks in the office are on hold while she attends to more important business: boosting kids’ reading skills in a targeted intervention program that has helped propel the school’s report card from a D to an A+.

The scene is much the same across the school for a half-hour block four mornings a week. Students leave their classrooms to join small groups strategically placed in every pocket of the school. Nearly every adult on...