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A Position of the National Council of Teachers of Mathematics

**Question**

How can teachers and schools identify and support students with exceptional mathematical promise to nurture and sustain their mathematical development and interest in mathematics?

**NCTM Position**

Students with exceptional mathematical promise must be engaged in enriching learning opportunities during and outside the school day to allow them to pursue their interests, develop their talent, and maintain their passion for mathematics. Such opportunities must be open to a wide range of
students who express a higher degree of interest in mathematics, not just to those who are identified through traditional assessment instruments.

We use the term “students with exceptional mathematical promise” to include those who are talented or express higher levels of interest in mathematics as well as students who are identified as “gifted” in mathematics through a battery of standardized assessments. We have
deliberately chosen this term over the terms “gifted” and “talented” because historically “gifted” and “talented” students have been identified through a single assessment that often is not mathematics-specific. In this position statement we seek to broaden the range of students identified as “students with
exceptional mathematical promise” while acknowledging that each and every student has mathematical promise.

Students with exceptional mathematical promise must be provided with differentiated instruction in an engaging mathematics learning environment that ignites and enhances their mathematical passions and challenges them to make continuing progress throughout their K–16 schooling and
beyond. They must have a variety of opportunities inside and outside of school to develop and expand their mathematical talents, creativity, and passions. These experiences may include formal courses; extracurricular experiences such as math clubs, circles, and competitions; and mentoring by and of those with
similar interests and talents. These experiences must allow opportunities for individual mathematical development as well as collective, social mathematical engagement. When considering opportunities for acceleration in mathematics, care must be taken to ensure that opportunities are available to each and every
prepared student and that no critical concepts are rushed or skipped, that students have multiple opportunities to investigate topics of interest in depth, and that students continue to take mathematics courses while still in high school and beyond.

Although some students may show rapid or early mastery of mathematical skills, such as computation, teachers have a responsibility to identify and nurture students whose exceptional mathematical promise is manifested in other ways. Students with exceptional mathematical promise
include those who demonstrate patterns of focused interest; are eager to try more difficult problems or extensions or to solve problems in different, creative ways; are particularly good at explaining complex concepts to others or demonstrate in other ways that they understand mathematical material deeply;
and/or are strongly interested in the material. Exceptional mathematical promise is not a fixed trait; rather it is fluid, dynamic, and can grow and be developed; it also varies by mathematical topic. Exceptional mathematical promise is evenly distributed
across geographic, demographic, and economic boundaries. Growing and leveraging such mathematical promise is essential for our field and society to thrive.

Finally, for students with exceptional mathematical promise to have learning environments and opportunities as described here, the preparation and ongoing professional development of teachers of mathematics must address the specific learning needs of these
students. Methods of recognizing, nurturing, and challenging students with exceptional mathematical promise must be included in courses and professional development for all preservice and in-service teachers. All teachers must have access to print, electronic, and human resources to support them in meeting the
needs of students with exceptional mathematical promise during and outside the school day.

**Resources **

Clynes, T. (2015). How to raise a genius: Lessons from a 45-year study of supersmart children. *Nature, 537*, 152–155.

Johnsen, S. K., & Sheffield, L. J. (eds.) (2012). Using the Common Core State Standards for Mathematics with gifted and advanced learners. Reston, VA: NCTM

Lubinski, D., & Benbow, C. P. (2006). Study of Mathematically Precocious Youth after 35 years: Uncovering antecedents for the development of math-science expertise. *Perspectives on Psychological
Science, 1, *316–345.

Park, G., Lubinski, D., & Benbow, C. P. (2013). When less is more: Effects of grade skipping on adult STEM productivity among mathematically precocious adolescents. *Journal of
Educational Psychology*, *105,*176–198.

Saul, M., Assouline, S., & Sheffield, L., eds. (2010). *The peak in the middle: Developing mathematically gifted
students in the middle grades*. Reston, VA: NCTM.

Sheffield, L. J., ed. (1999). *Developing mathematically promising
students.* Reston, VA: NCTM.

Steenbergen-Hu, S., & Moon, S. M. (2011). The effects of acceleration on high-ability learners: A meta-analysis. *Gifted Child Quarterly*, *55,* 39–53.

VanTassel-Baska, J., & Brown, E. F. (2015). An analysis of gifted education curriculum models. In F. Karnes & S. Bean (Eds.), *Methods and materials for teaching the gifted *(pp. 107–138). Waco, TX: Prufrock Press.

October 2016