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The Development of Gifted and Talented Mathematics Students and the National Council of Teachers of Mathematics Standards

Linda Jensen Sheffield

Our top students in mathematics are crucial to the well-being of our country. The only way we can meet our national goal of being first in the world in mathematics and science is to raise the mathematical competence of all our students, including the gifted and talented ones.

Currently, the top mathematics students in the United States have fallen behind those in the rest of the world. These students must be nurtured and encouraged to develop their talents. The National Council of Teachers of Mathematics (NCTM) has stated in their position paper on Provisions for Mathematically Talented and Gifted Students that "while all students need curricula that develop the students' problem solving, reasoning, and communication abilities, the mathematically talented and gifted need in-depth and expanded curricula that emphasize higher order thinking skills, nontraditional topics, and the application of skills and concepts in a variety of contexts" (NCTM, 1993). In 1989, NCTM developed the Curriculum and Evaluation Standards for School Mathematics as guidelines for improving the mathematical competence of all our students. This was followed in 1991 by the Professional Standards for Teaching Mathematics, a set of guidelines designed to help teachers create an environment in which all students can develop mathematical power. In 1993, a working draft of a third document, Assessment Standards for School Mathematics, was developed to expand and complement the Evaluation Standards that were included in the 1989 document. The implications for the development of mathematical talent using all three sets of these Standards are included in this paper.

Mathematical talent must be identified through a range of measures that go beyond traditional standardized tests. Measures should include observations, student interviews, open-ended questions, portfolios, and teacher-, parent-, peer- and self-nomination. Recognition should be made of the fact that mathematical talents can be developed; they are not just something with which some students were born. Interesting tasks must be presented that engage students and encourage them to develop their mathematical talents.

Qualified mathematics teachers, improved opportunities for mathematics learning, and a much more challenging, nonrepetitive, integrated curriculum are needed to help students develop mathematical talents. Students must be challenged to create questions, to explore, and to develop mathematics that is new to them. They need outlets where they can share their discoveries with others.

Program options for the development of gifted and talented students might encompass a variety of methods including differentiated assignments, a core curriculum, pull-out programs, in-class programs, magnet schools, and extracurricular activities such as after-school or Saturday programs, mentorship programs, summer programs, and competitions.

We must act immediately on a national level to upgrade the level of mathematics being offered to all our top students from kindergarten through graduate school. Perhaps, even more importantly, we must improve the ways in which our students learn mathematics. Teachers must become facilitators of learning to encourage all students to construct new, complex mathematical concepts. Students must be challenged to reach for ever-increasing levels of mathematical understanding. We must strive to help many more students including females, minorities, and students from rural and inner-city schools reach those top levels of mathematical ability. The potential exists in every school in our country for far more expertise in mathematics, and we must help students unlock their talents in this area.

Reference:
Jensen Sheffield, L. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics standards (RBDM 9404). Storrs, CT: The National Research Center on Gifted and Talented, University of Connecticut.


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The Development of Gifted and Talented Mathematics Students and the National Council of Teachers of Mathematics Standards
Linda Jensen Sheffield

Recommendations

  1. Teachers should use a variety of measures to identify mathematically talented students, tapping skills beyond computation. These students need to have a wide range of exciting math classes, math clubs, and contests where they can demonstrate and hone their mathematical abilities.
  2. Teachers should provide all students with a wide variety of rich, inviting tasks that require spatial as well as analytical skills. Talented students should explore topics in more depth, draw more generalizations, and create new problems and solutions related to the topic.
  3. Teachers should encourage students to persist in solving mathematical problems. Fewer problems need to be tackled, but in far greater depth. Talented students need the challenge of new and more complex problems. They need to experience the joy of solving difficult problems and be able to share that joy with others.
  4. Teachers should encourage students to construct their own mathematical understanding, and talented students should be encouraged to reach the highest levels of construction.
  5. Teachers should engage all students in the use of technology and manipulatives to aid in their construction of mathematical concepts. Talented students should use these materials to explore even further and to create and display quality mathematics.
  6. Teachers need to show students examples of superior student work in order to challenge them to ever-increasing levels of mathematical achievement.
  7. Teachers need adequate resources and support to obtain the materials, technology, and training they need to assist in the development of mathematically talented students.
  8. Teachers, students, parents, and others in our society must be encouraged to believe that all students can learn mathematics and our talented students are capable of greater mathematical power than we have ever asked of them.
  9. Teachers should use a wide variety of assessment measures beyond standardized achievement tests which limit mathematics to low level computation. Teachers must expect the highest levels of achievement on several types of assessment from mathematically talented students.