Mathematically talented students often show an early interest in and facility with numbers. For example, they may learn to tell time at age two and begin adding and subtracting long before they enter kindergarten. Anecdotes shared by parents about their precocious youngsters are helpful in identifying these students initially, but the objective information determined from an appropriate assessment is essential in determining the extent of their abilities and providing them with a challenging level of mathematics.

Although IQ testing is useful, it doesn’t provide enough specific information to pinpoint students’ abilities in math. Grade-level tests are not advanced enough and don’t accurately gauge these abilities. Students need to take an above-level test, such as university talent searches offer, to measure their mathematical reasoning. The tests are called “above-level” because they have been developed for older students. They determine what mathematical concepts students do and do not know, and this information is useful for good curriculum planning.

##### Options for Math-Talented Students

Based on the results of the testing, a student’s abilities can be matched to the curriculum level. A variety of programs may be implemented for math-talented students:

- Enrichment within the regular classroom. The teacher presents challenging and interesting content that may or may not be related to the topics covered in the regular class.
- Curriculum compacting within the regular classroom. Students who demonstrate mastery on pretests are permitted to work on more complex topics assigned by the teacher.
- Independent study projects. Talented students who complete their work early or who have mastered the content presented in class can work on a math-related project on their own.
- Pull-out enrichment programs. Students are taken out of the regular classroom to attend a special class. The teacher provides challenging math work but does not accelerate the student in mathematics.
- Acceleration. Students may advance one or more grade levels in math.
- Individualized instruction. Working one-on-one or in a small group with a teacher, a student moves systematically through a predetermined curriculum.
- Ability grouping. Talented students meet together to study mathematics. This may or may not result in acceleration.
- Distance-learning programs. Students can enroll in computer-based or correspondence distance-learning programs. This work can occur either in or outside school.

##### The Diagnostic Testing —> Prescriptive Instruction Model

Developed by the late Julian C. Stanley at Johns Hopkins University, this model was designed to match the level and pace of mathematics instruction to students’ abilities and achievements. In this individualized program, students go through several steps:

- They take an above-level aptitude test to assess their mathematical abilities.
- They take a diagnostic pretest that measures their specific achievements in mathematics.
- The test proctor readministers items that the student missed, skipped, or did not have time to answer. The student’s

mentor then analyzes the information from this step to clarify what the student does and does not understand. - The mentor works with the student on the topics that he or she has not yet mastered. This prescriptive instruction is the heart of the model.
- The student takes a posttest to demonstrate mastery.

This model has been carefully researched and shown to be extremely useful for teaching math-talented students. Since the student is required to demonstrate mastery of each topic before moving ahead, unsuspected gaps in knowledge are not a concern. Students appreciate that the model is tailored to their individual needs and allows them to move at a pace that is appropriate for their own development and maturity.

##### Acceleration

Sixty years of research clearly demonstrates that acceleration is an effective option for talented students. Not only are accelerated students more challenged academically, but they are more satisfied socially, because they are placed with their intellectual peers.

When students skip a grade or move ahead only in math, challenging them in mathematics every year from then on calls for long-term planning. To prevent students from exhausting their high-level math options before completing high school, they might be transported to a different building for math class, work with tutors individually, participate in a distance-learning program, or take a college math class while still in high school.

Issues of credit and placement are important. The student should be given the appropriate credit or placement for work completed at a satisfactory level. So, for example, a sixth-grader who takes a high school math course should receive high school credit or appropriate math sequence placement for the work completed.

##### Outside-of-School Resources

Math clubs and competitions allow students to interact with other mathematically inclined children. Competitions include the Mathematical Olympiads for Elementary and Middle Schools, MATHCOUNTS, the American Mathematics Competitions, and the American Regions Mathematics League. University-based campus or distance learning programs such as those offered by Duke, Johns Hopkins, Northwestern, and Carnegie Mellon Universities, the University of Denver, and other institutions unite exceptionally talented students with teachers who can offer them exciting, stimulating mathematics.

In addition, many familiar games have strong mathematical components. These include Battleship, checkers, chess, Connect-Four, dominoes, MasterMind, Othello, and Pente. These are all great games for teaching logical thinking and practicing mathematical reasoning.

##### Parents as Advocates for Their Math-Talented Children

Many schools do not have specific programs in place for mathematically talented students. It is often up to the parents to call attention to their children’s needs and to encourage school personnel to make educational accommodations for them. What can you do to be an advocate?

- Become informed: learn what has worked and what has not worked for other families, find out what the research says, and so forth.
- Obtain an assessment of your child’s abilities and achievements. The objective information from the testing, combined with representative work samples and classroom performance information, provides the data that school personnel need to make decisions about appropriate programming for your child.

Making changes for your child, such as moving him or her into a different classroom or getting different enrichment materials, is relatively easy. Changing a whole educational program in a school district is much more difficult and time-consuming. However, the efforts that result in short-term changes for your child may result in long-term benefits for other mathematically talented students.

—*Ann Lupkowski-Shoplik, PhD*

*Ann Lupkowski-Shoplik is director of the Carnegie Mellon Institute for Talented Elementary and Secondary Students (C-MITES) at Carnegie Mellon University.*

###### Competitions

**Mathematical Olympiads for Elementary and Middle Schools****MATHCOUNTS****American Regions Mathematics League**

###### Web Sites

**Math Forum : try the Ask Dr. Math section and the Problem of the Week****Hoagies’ Gifted Education Page math section**

###### Readings

*Developing Mathematical Talent: A Guide for Challenging and Educating Gifted Students*, by Susan G. Assouline and Ann Lupkowski-Shoplik, Prufrock, 2003*Challenge Math: For the Elementary and Middle School Child*, by Edward Zaccaro, Hickory Grove, 2000*Creative Problem Solving in School Mathematics*, by George Lenchner, out of print, available from**www.moems.org**

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