C-MITES offers weekend workshops and summer programs
for gifted and academically talented students.
Be sure to check out the C-MITES Home Page at www.cmites.org.

Guiding Mathematically Talented Elementary Students

Dr. Ann Lupkowski Shoplik
Director, C-MITES
(An earlier version of this article was published in the
Ohio Association for Gifted Children newsletter, OAGCReview.
Reprinted with permission.)

Perhaps you have suspected that your child was gifted in math ever since he could tell time at age 2 1/2 or since she seemed to understand the concept of multiplication at age 3. You thought everything would be fine once your children entered school, but they are now in third grade, and they are still doing two-digit addition with the rest of the class. What’s a parent to do?

Some Not-So-Good News

  1. Placing your child in the school’s gifted program might not meet all of his math needs. Too often, gifted programs are “tacked on” to school curricula. What students do in a gifted program might not be related to anything they do in the regular classroom. For example, a group of gifted students spent the entire school year researching candidates for the official state fish, presenting their ideas to the legislature, and having the satisfaction of knowing that they were instrumental in identifying the official fish for their state. While this was an enjoyable activity, and one in which the students learned a lot, it did not have any impact on whether they were studying two-digit addition or trigonometry in math class.
  2. While gifted programs in some schools may be more closely related to the traditional curriculum, in my experience, many gifted programs are language-arts based. Too many teachers, especially elementary teachers, just don’t seem comfortable developing comprehensive programs in mathematics for gifted students.

  3. School officials, although they have good intentions, may have limited experience or knowledge about mathematically talented youth. For example, in Pennsylvania, teachers of the gifted aren’t even required to complete one college course in gifted education before being hired. They may not be aware of the large number of options and opportunities for mathematically talented youth, let alone what research has taught us about the best methods of education for these students.
  4. Due to their lack of knowledge about mathematically gifted students, school personnel may “ hold back” a talented student because, “He makes computational errors and gifted students should be able to get computations right.” Research with thousands of mathematically talented students has shown that they perform significantly better on conceptual tasks. This means that they can understand high-level concepts (like algebra) while still making mistakes in two-digit addition. This may happen because these bright youngsters have been so routinely bored by the math they are required to do in school that they make careless errors. They have developed bad habits such as not writing down their thinking, not checking their work, and working too quickly because they are so under-challenged.

Some Advice

  1. Get objective information. If you suspect your child is talented in mathematics, have him or her tested. An IQ test won’t tell the whole story, however. What is needed is a measure of the student’s specific achievements in mathematics. I recommend above-level testing such as the EXPLORE test (for 3rd - 6th graders each January) offered by Carnegie Mellon Institute for Talented Elementary Students, the Belin-Blank Center at the University of Iowa, the Center for Talented Development at Northwestern University, and by the Talent Identification Program at Duke University. This above-level test (designed for 8th graders) has been used since 1993, and we have found it an effective tool for identifying math-talented youth. (The EXPLORE test also measures abilities in Science Reasoning, English, and Reading). Use the EXPLORE test as a means of identifying exceptional mathematical talent, and combine it with curriculum-based assessment to see exactly which topics a student does or does not know. For example, a 4th grader taking the EXPLORE and scoring 15 on mathematics (better that 55% of 8th graders) should also take the 4th and 5th grade math final exams from his or her school curriculum, and possibly the 6th grade final. If final exams are not available, chapter tests may be useful. Items the student gets wrong on those exams provide a basis for instruction - the underlying concepts are those that the student has not yet mastered.
  2. Participate in outside-of-school opportunities. Programs offered by the universities listed above and others give talented students a chance to be challenged academically, while being in a social situation with like-minded students. The students appreciate the fact that the teachers hired by these special programs “really like math” and inspire them to try more challenging material.
  3. Weigh the advantages of pursuing changes in the programs your school offers versus the advantages of pursuing changes in your child’s individual educational program. For example, the parent who demands that the school immediately hire a teacher and devise a comprehensive program for its mathematically talented students probably won’t get very far. Instead, the parent can focus on the individual child and how his or her needs can be met by making modifications in the school day, adjusting the requirements for a particular course, etc. Sharon, a mathematically talented fifth grader, gets the challenging mathematics she needs through a twice-weekly meeting with a high school mathematics teacher. During her regular math class, Sharon works on homework assigned by her “mentor,” participates in whole class activities such as math games, or works on the computer. Although it would have been ideal for Sharon to study math with several other talented students, scheduling constraints made it impossible.

What Options Do Math-Talented Students Have?

Rather than recommending just one type of program for all mathematically talented students, I recommend selecting from a continuum of options. Match the right option to the varying abilities of the students.

  1. Enrichment in the regular classroom may include enrichment topics provided by textbook publishers, independent study projects, or working on the same material as the other students only in greater depth. Cuisenaire/Dale Seymour Publications 800-872-1100) offers many excellent materials useful for this purpose. I recommend this type of challenge for students scoring in the top 5% (local norms) on a grade level standardized achievement test such as the Iowa Tests of Basic Skills or Stanford Achievement Test.
  2. Working on mathematics assignments in small groups with other advanced students is also known as “homogeneous grouping.” This occurs when students are ability-grouped within a class or when an entire class is comprised of able students. Teachers match the pace of the curriculum to the pace of each small group.
  3. Move up a grade just for math. The advantage of this approach is that a student can remain with age-peers for part of the school day, while participating in a more challenging math course. Disadvantages include potential scheduling and transportation conflicts. In addition, even though the class is more advanced, the pace may still be too slow for exceptionally talented students.
  4. Participate in a mentor-paced program instead of regular class. In this individualized approach, students are tested to determine what they know and what they don’t know. Then, the mentor works with the student once or twice a week on topics he or she does not yet understand. The student is given assignments to work on between meetings, and the students may call the mentor between meetings to ask questions about the homework. For more information about this option, see Lupkowski, Assouline, and Vestal (1992) or Lupkowski and Assouline (1992).

Notes on Acceleration

Rather than skipping a grade or two in mathematics and hoping a student doesn’t have any significant “gaps” in his mathematical background, I like to recommend a systematic, deliberate approach for acceleration. Curriculum-based assessment is an essential step to determine what the student does and doesn’t know. Misunderstandings should be cleared up in a relatively short period of time, and the student won’t be left with the gaps in his background that school personnel fear. For example, Jason had taken the EXPLORE the previous January as a fourth grader and earned a score of 15 (out of a possible 25) on the mathematics section. In October if his fifth grade year, he took the fifth grade comprehensive exam and missed only one item on fractions due to a computational error. Then, he took the sixth grade exam, and correctly answered 90% of the items. His mentor, a high school math teacher, worked with him for a week on the concepts he didn’t understand from the sixth grade mathematics curriculum. That way, he avoided possible “gaps” in his background. Next Jason took the 7th grade pre-algebra comprehensive exam and correctly answered only 70% of the items, indicating he had not mastered the material. Again, his mentor worked with him on the concepts he did not understand. By the end of the school year, Jason had completed the pre-algebra curriculum, and he was scheduled to study algebra with 8th graders the next fall (when he was in 6th grade).

What about Jason’s social development? This appears to be the main concern of school personnel and some parents when it comes to acceleration. Research has shown repeatedly (e.g. Southern & Jones, 1991) that gifted students do not suffer socially if they are placed ahead of their age peers in mathematics. Again, we are looking for the optional match between the students’ abilities and the level of mathematics they are studying. If they are placed with older students to study math, there are still ample opportunities in the school day for interactions with age peers (other courses, lunch, study halls, recess, physical education, Scouts, band, etc.).

A Final Note

Parents, try to learn as much as you can about mathematically talented youth and about gifted students. You are your child’s best advocate, since you know your child well. Take advantage of the many resources available to you, including those of your local or state gifted association, and the National Association for Gifted Children.


Lupkowski, A. E., Assouline, S. G., & Vestal, J. (1992). Mentors in Math. Gifted Child Today, 15(3), 26 - 31.

Lupkowski, A. E., Assouline, S. G. (1992). Jane and Johnny Love Math: Recognizing and encouraging mathematically talented elementary students. Unionville, NY: Trillium.

Southern, W. & Jones, E. (1991). The academic acceleration of gifted children. New York: Teachers College Press.

Selected Resources

Center for Talent Development, Northwestern University (847-491-3782; http://www.ctd.northwestern.edu/)

Carnegie Mellon Institute for Talented Elementary Students (C-MITES) 412-268-1629. (http://www.cmites.org).

National Association for Gifted Children: telephone: 202-785-4268 http://www.nagc.org/

Web sites: One of the best web sites I have found is The Hoagies Gifted Education Page (http://www.hoagiesgifted.com). It has quite a comprehensive list of information.

Cuisenaire/Dale Seymour Publications (1-800-872-1100) publishes many books and materials we use in classes for mathematically talented students.

Software: Logical Journey of the Zoombinis (published by Broderbund, 415-382-4419)


Lechner, G. (1983). Creative problem solving in school mathematics. Boston: Houghton Mifflin.

Philips, E., Lappan, G., Winter, M. J., & Fitzgerald, W. (1986). Middle grades mathematics project: Probability. Menlo Park, CA: Addison-Wesley. (Note: check out other books in this series, too.)

About the Author

Dr. Ann Lupkowski-Shoplik is the Director of Carnegie Mellon Institute for Talented Elementary Students (C-MITES), which she founded in 1992. She conducts the annual Elementary Student Talent Search for 3rd - 6th graders and offers summer and weekend programs in math, science, and humanities for K-7th grade. She can be reached at C-MITES, Carnegie Mellon University, 5136 Margaret Morrison St. MMP30, Pittsburgh, PA 15213.

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