It isn’t really surprising that school officials may not understand giftedness since even experts in the gifted field can’t agree on a single definition of gifted. The term has an interesting history and has led to the many definitions of gifted that exist today. Some definitions of gifted include motivation and achievement, while others don’t. Some schools may also be working under the constraints of their state’s definition of gifted. Such definitions often define gifted children as those who are working above the level of the majority of their classmates. Giftedness, in other words, is relative. A child may be identified as gifted in one school system, but not in another. It depends on the abilities of the majority of students in the school.
Regardless of the definition of gifted schools use, they have very real practical considerations. For example, if they have funds for only one teacher for gifted children, they can identify only so many students, usually twenty or twenty-five, or the class will be too large. On the other hand, a class of only ten or eleven students would not justify the salary of a teacher. That means that the school determines the size of the class and then sets the cutoff score that makes it most possible to get that number of students. They will use other criteria to keep to the number they had set. If they have more or less than the set number, they will most likely use criteria like motivation and teacher recommendation to decide who gets into their program. When there are too many students, the unmotivated ones will not be chosen, but if the number is too low, those students will be admitted.
What this means, then, is that there is no right score for a school to use as a cut-off score into a gifted program. It depends on the school's definition of "gifted," the abilities of the majority of students in the school, and the school's budget and resources.