The term Vital Core merely refers to a return to the educational basics, or "core," which is vital to all future learning.
Most students are rushed through the fundamentals and never learn them well (just ask university professors, who must deal with this fact on a daily basis). Weakness in the core skill sets of reading, writing, vocabulary, and mathematics haunt most students for life.
However, with a complete mastery of the basics, students find education much more enjoyable and thus excel in lifelong learning...as well as move towards a perfect score on the SAT.