Despite anyone's protestations, gifted mathematics students are generally ignored in classrooms, as the teacher claims the need to focus (attention, discussions, curriculum, and assessments) on the other students. The common mantra is: "Oh, the gifted math students in my class are smart, and they will do fine on their own...with or without my attention."
It is time that gifted students received special attention, which includes a higher level of questioning, posing deeper challenges, using appropriate curricular materials (possibly with a higher reading level), and even giving them some of our time as teachers.
But, when you consult the literature, a constant problem arises: What exactly is the definition of a "gifted mathematics student"? We all know them as a type, but often the most gifted elude our view and concern (i.e. they range from being quiet to being loud, from paying attention to being in dreamworlds, from passively trying to fight the system).
A "theoretical" approach is to define gifted mathematics students as being those in the upper 3-5% compared to their peers in areas such as general intellectual ability, specific competence in mathematics, acute visual abilities, and creativity as a problem-solver.
Unfortunately, it is difficult to turn these theoretical criteria into a real-world identification process. Such is beyond an exam, past performance, or even teacher identification.
In my own experiences as a math educator, I am frustrated with the system often implemented. That is, if a student can perform algorithms in the elementary grades and responds to teacher requests appropriately, he or she becomes a candidate for a gifted and talented program. Neither of these items is connected to the previous theoretical criteria used as a definition of giftedness.
Yet, it seems to make every one happy...the teacher, the administrator, the parents, and perhaps even the student so identified. But, such a process usually misses the truly gifted student in mathematics, who perhaps neglected the tedious algorithms in order to play with numerical patterns on a calculator.
Unfortunatley, I have no real answers, despite spending more than 40-years confronting the problem. And, I will continue to bang this "drum" loudly...and am open to publishing your creative solutions.