Mathematically gifted students learn differently from other age group peers. They require curriculum to be differentiated to meet their specific needs (Johnson, 2006). When these gifted students are not presented with learning experiences that are appropriate for their abilities, they lose motivation and in time can lose interest in school. Brain research suggests that the brain will not maintain its level of development if students are not challenged (Stepanek, 1999). Challenge is a very important component of effective curriculum and instruction. Research of the gifted brain shows that stimulation of students' interests and abilities through an appropriate level of challenge is required for learning to take place. If mathematically gifted children are given content or tasks that are too easy, which is very common in a mixed-ability classroom, they may not become engaged in the activity and consequently will not be learning. "Brain research provides a physical explanation for students' failure to learn. When tasks are not sufficiently challenging, the brain does not release enough of the chemicals needed for learning: dopamine, noradrenalin, serotonin, and other neurochemicals" (Stepanek, 1999, p. 9).
The No Child Left Behind (NCLB) Legislation, a renewal of the Elementary and Secondary Act of 1965, was passed by the Bush administration in 2001. This legislation requires that all students be proficient in reading and math by 2014. High stakes standardized tests are used to measure student performance in any school receiving Title I funding. Schools failing to meet the state's Adequate Yearly Progress (AYP) are identified as "needing improvement" and are sanctioned with an array of consequences including a loss of funding. Mathematically gifted students tend to master the standards early and are ready to move onto more challenging work, interestingly, there are no penalties for schools failing to meet the needs of those students performing above or far exceeding the standard. As a result, funding and resources that had been allocated toward gifted programs are being reallocated toward reading initiatives to help struggling students gain proficiency (Golden, 2003). NCLB is sacrificing the education of the mathematically gifted students who have the potential of becoming the future biomedical, astro-physics, or aerospace researchers, engineers or other leaders in math and science (Goodkin, 2005).
Statement of the Problem
Miller defines mathematical talent as "an unusually high ability to understand mathematical ideas and to reason mathematically, rather than just a high ability to do arithmetic computations or get top grades in mathematics" (Miller, 1990, p. 1). When looking to identify mathematically gifted students, many teachers focus on those students who make the best grades and can compute math facts quickly and efficiently. These students may indeed be gifted, but there is more to mathematics than computations (Miller, 1990). Mathematically gifted students "take their understanding of the formulas and numbers and extend them to everyday situations. These students can see that math is more abstract than concrete and although these abstractions would confuse the normal student, they are able to generate solutions and obtain a fitting answer" (Giftedness: Overview, 2006, p. 1).
Mathematically gifted students learn differently and need a differentiated curriculum in order to succeed in a regular classroom. If mathematically gifted students are required to work on grade-level curriculum at the same pace as other grade level students, if they are not challenged and guided, they can become bored, frustrated and can eventually become underachievers (Characteristics of Highly Able Math Student, 2006). When a school adopts a curriculum, it typically comes with only one textbook for all students at each grade level. These books are aimed at average abilities within that grade level, and many times at the lowest reading level. …