Gifted students differ from their classmates in three key areas that are especially important in mathematics. These are summarized below.

*How Gifted Learners Differ from Classmates:*

- Pace at which they learn
- Depth of their understanding
- Interests that they hold (Maker, 1982)

*Relationship to Mathematics Learning*

- The sequential nature of math content makes pacing an issue.
- Deeper levels of understanding and abstraction are possible for most mathematical topics, so differentiation becomes important.
- If the interest is snuffed out early, the talent may not be developed.

Mathematically gifted students differ from the general group of students studying math in the following abilities: spontaneous formation of problems, flexibility in handling data, mental agility of fluency of ideas, data organization ability, originality of interpretation, ability to transfer ideas, and ability to generalize (Greenes, 1981). No list of characteristics of the mathematically gifted includes "computational proficiency," and yet at levels prior to Algebra I, this is commonly used as the criterion that determines who gets to move on to more interesting material. Furthermore, there is a myth that gifted students don't need special attention since it is easy for them to learn what they need to know. On the contrary, their needs dictate curriculum that is deeper, broader, and faster than what is delivered to other students.

Mathematics can be the gatekeeper for many areas of advanced study. In particular, few gifted girls recognize that most college majors leading to high level careers and professions require four years of high school math and science (Kerr, 1997). Students may drop out of math courses or turn toward other fields of interest if they experience too much repetition, not enough depth, or boredom due to slow pacing.

An Agenda for Action: Recommendations for School Mathematics of the 1980s (NCTM, 1989, p. 18) says, "the student most neglected, in terms of realizing full potential, is the gifted student of mathematics. Outstanding mathematical ability is a precious societal resource, sorely needed to maintain leadership in a technological world." By 1995, when the NCTM created a Task Force on the Mathematically Promising, not much had changed (Sheffield et al., 1995).

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