Mathematics Education for Gifted and Talented Children
David L. Haury
Within the diverse student population in the United States are children who are fascinated with
numbers, quick to see patterns, adept at solving math problems, or who otherwise show a strong
aptitude for or interest in mathematics. These gifted and talented children (herein, gifted) present
a unique challenge as educators pursue the national goal to meet the needs of all children in
math: How can teachers nurture the ongoing academic development of gifted children within the
context of the mixed-ability math classroom?
This question causes great concern among many parents, teachers, and other members of the
education community, who believe that gifted children may not be challenged sufficiently in a
mixed-ability setting. Like other children, gifted children develop their math skills by struggling
with challenging mathematical ideas and procedures. Simply doing more problems than the other
children or covering more of the same material in less time will only increase the likelihood that
math class will become tedious or boring. If gifted children reach the limit of what they can do
with minimal effort, they may ultimately give up on themselves and quit the study of
mathematics (Lappan, 1999).
How To Recognize Giftedness in Mathematics
Not all high achievers in math are gifted. Some children may be high achievers simply because
they have good memories or have learned to apply rules and procedures to standard math
problems in predictable ways. Differentiating gifted children from other high achievers may
require some careful probing and observation. The characteristics and behaviors of gifted math
students--the top 2 to 3 percent of students--are as follows (Miller, 1990):
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An unusually keen awareness of and intense curiosity about numeric information. |
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An unusual quickness in learning, understanding, and applying mathematical ideas. |
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A high ability to think and work abstractly and the ability to see mathematical patterns
and relationships. |
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An unusual ability to think and work with mathematical problems in flexible, creative
ways rather than in a stereotypic fashion. |
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An unusual ability to transfer learning to new mathematical situations. |
Because math giftedness refers to an unusually high ability to understand mathematical ideas and
to reason mathematically, it is important not to confuse the ability to do arithmetic computations
or get good grades in math with being gifted.
Classrooms That Nurture Gifted Math Students
Like all students, gifted math students have a variety of interests, learning styles, and
preferences; there is no single instructional approach that is best suited for all of them. There
is, however, an array of program features that respond to the needs of this special population.
Some of the most essential elements are as follows (Miller, 1990).
First, gifted math students should have the opportunity to work with one another when possible.
"Pull-out" programs and separate classes for gifted children are increasingly uncommon, so the
desired grouping of gifted children may be restricted to clustering them within the mixed-ability
classroom. In the resulting differentiated classroom, the teacher recognizes the differing readiness
levels, interests, and learning profiles of the children and offers them, accordingly, a variety of
ways to (1) explore topics, (2) come to understand and "own" information and ideas, and (3)
demonstrate or exhibit what they have learned (Tomlinson, 1995).
Second, the program should stress mathematical reasoning, rather than computation, and develop
independent exploratory behavior. Gifted children in such a program are actively engaged in
learning, solving problems, discovering formulas, completing special projects, organizing data to
find relationships, and looking for patterns and underlying principles.
Third, less emphasis should be given to repetitious computations and cyclical reviews. Such
work should be minimal for gifted math students.
Fourth, the breadth of the math curriculum should be increased to provide an adequate
foundation for gifted children who may want to pursue math-related careers.
Finally, the math program should be structured for flexibility, enabling teachers to place gifted
children at an appropriate instructional level based on an assessment of knowledge and skill.
Flexible pacing can be achieved in a variety of ways. For example, continuous progress allows
gifted children to receive appropriate daily instruction and move ahead as they master content
and skill. Or gifted children may take a compacted course, in which they complete two or more
courses in an abbreviated time, or an advanced-level course, in which they learn course content
normally taught in a higher grade. Through concurrent or dual enrollment, gifted children at one
grade level take some courses at another grade level. Flexible pacing of gifted children can also
occur through grade skipping, credit by examination, or early entrance to elementary school,
middle school, high school, or college.
Recommendations for Teachers of Gifted Math Students
The following teacher activities can help gifted math students reach their potential (Sheffield,
1994):
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Use a variety of measures to identify gifted math students, tapping skills beyond
computation. These children need to have a wide range of exciting math classes, math clubs, and
contests in which they can demonstrate and hone their math abilities. |
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Use a wide variety of assessments beyond standardized achievement tests, which measure
low-level computation only. Teachers can expect gifted math students, unlike other high
achievers in math, to attain the highest levels of achievement on several types of assessments. |
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Provide all children with a wide variety of rich, inviting tasks that require spatial as well
as analytical skills. Gifted children should explore topics in more depth, draw more
generalizations, and create new problems and solutions related to the topic. |
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Encourage children to persist in solving math problems. Fewer problems need to be
tackled, but in far greater depth. Gifted children need the challenge of new and more complex
problems. They need to experience the joy of solving difficult problems, and they should have
the opportunity to share that joy with others. |
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Encourage children to construct their own mathematical understanding, and encourage
gifted children to reach the highest levels of construction. |
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Engage all children in the use of technology and manipulatives to aid in their construction
of mathematical concepts. Gifted children should use these materials to explore even further and
to create and display quality mathematics. |
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Show gifted children examples of advanced student work to challenge them to
ever-increasing levels of mathematical achievement. |
Finally, teachers should ask administrators for their support and assistance in obtaining the
materials, technology, and training necessary to educate gifted math students.
References
Lappan, G. March 1999. " Mathematics for All' Must Include High-Ability and Highly
Motivated Students." NCTM News Bulletin 35 (8): 3. (Available online at
http://www.nctm.org/news-bulletin/1999/03/1999-03.president.html)
Miller, R. C. 1990. Discovering Mathematical Talent. Reston, VA: ERIC Clearinghouse on
Disabilities and Gifted Education, and The Council for Exceptional Children. ERIC Document
Reproduction Service No. ED 321 487. (Available online at
http://www.cec.sped.org/digests/e482.htm)
Sheffield, J. N. 1994. The Development of Gifted and Talented Mathematics Students and the
National Council of Teachers of Mathematics Standards. (Available online at
http://www.gifted.uconn.edu/sheffiel.html)
Tomlinson, C. A. 1995. Differentiating Instruction for Advanced Learners in the Mixed-Ability
Middle School Classroom. Reston, VA: ERIC Clearinghouse on Disabilities and Gifted
Education, and The Council for Exceptional Children. ERIC Document Reproduction Service
No. ED 389 141. (Available online at http://www.cec.sped.org/digests/e536.htm)
| David L. Haury is Director of the ERIC Clearinghouse for Science, Mathematics, and
Environmental Education and Associate Professor of Mathematics, Science, and Technology
Education at The Ohio State University in Columbus, Ohio.
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 Encouraging Girls in Science and Math
 Table of Contents
 Science Education for Gifted and Talented Children
This page was updated on Fri Nov 2 19:14:43 GMT 2001
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